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LIBRARY 

OF  THE 

University  of  California. 


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Class 


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INTO.  9. 


HYDROGRAPHIC    OFFICE. 


THE 


AMEKICAS  PRACTICAL  lAVIGATOR 

BEING    AN 

epitom:e 

OF 

NAVIGATION  AND  NAUTICAL  ASTRONOMY. 

BY 

NATHANIEL  BOWDITCH,  LL.  D., 

Fellow  of  the  Royal  Societies  of  London,  Edinburgh,  and  Dublin;  of  the  Astronomical  Society  in  London;   of  the 

American  Philosophical  Society,  held  at  Philadelphia  ;   of  the  American  Academy  of  Arts  and  Sciences  ; 

of  the  Connecticut  Academy  of  Arts  and  Sciences ;  of  the  Literary  and  Philosophical  Society 

of  New  York  ;  Corresponding  Member  of  the  Royal  Societies  of  Berlin,  Palermo,  &c. 


Revised  in  1880,  under  the  direction  of  the  Bureau  of  Navigation, 
Navy  Department, 

BY 

Commander  P.  H.  COOPER,  U.  s.  Navy. 


Revised  in  1903,  under  the  direction  of  the  Bureau  of  Equipment, 
Navy  Department, 

BY 

Lieutenant  G.  W.  LOGAN,  U.  S.  Navy. 


WASHINGTON: 

GOVERNMENT    PRINTING    OFFICE. 
1903. 

OF  THE 

UNIVERSITY 


n^ 


A 


^^ 


^^ 


ORDERS  RELATING  TO  REVISION. 


Bureau  of  Navigation, 
Navy  Departtnent^  January  1\  1881. 
In  accordance  with  the  purpose  contemplated  in  the  purchase  of  the  copyright  of 
the  New  American  Practical  Navigator,  a  thorough  and  complete  revision  has  been 
made  by  Commander  P.  H.  Cooper,  U.  S.  Navy,  acting  under  the  direction  of  the 
Bureau.  The  revision  consists  principally  in  the  substitution  of  the  more  concise  and 
convenient  methods  of  the  present  day  for  the  obsolete  methods  of  the  past,  and  a 
complete  rearrangement  under  proper  chapters  and  paragraphs  for  ready  reference, 
keeping  in  view,  however,  the  character  of  the  work  as  a  Practical  Navigator. 

The  revision  having  been  completed,  it  was  submitted  to  Capt.  Ralph  Chandler, 
U.  S.  Navy,  for  a  final  review,  and  having  received  a  satisfactory  report  from  that 
officer  it  has  been  accepted  by  the  Bureau  and  will  hereafter  be  substituted  for  the 
former  editions  of  the  work. 

WiLLiA^r  D.  Whiting, 

Chief  of  Bureau. 


Bureau  of  Equipment, 
Navy  Department,  March  18,  1903. 
A  revision  of  Bowditch's  American  Practical  Navigator  having  become  neces- 
sar}'-,  the  work  has  been  completed  by  Lieut.  G.  VV.  Logan,  U.  S.  Navy,  under  the 
supervision  of  the  Hydrographer  to  the  Bureau  of  Equipment.  The  revision  was 
approved  by  a  Board  consisting  of  Capt.  Colby  M.  Chester,  U.  S.  Navy,  Commander 
C.  J.  Badger,  U.  S.  Navy,  and  Lieut.  Commander  C.  C.  Rogers,  U.  S.  Navy.  It 
is  directed  that  this  revised  edition  be  substituted  for  all  former  editions. 

R.  B.  Bradford, 

Chief  (f  Bureau. 


p»ref^ch:. 


The  copyright  of  the  New  American  Practical  Navigator,  by  the  late  Dr. 
Bowditch,  became  the  property  of  the  United  States  Government  under  the  provision 
of  an  act  of  Congress  to  establish  a  Hydrographic  Office  in  the  Navy  Department, 
approved  June  21,  1866. 

Under  the  direction  of  the  Bureau  of  Navigation,  at  that  time  charged  with  such 
publications,  the  work  was  revised  in  1880  by  Commander  P.  H.  Cooper,  U.  S.  Navy, 
certain  chapters  being  contributed  by  Lieuts.  Richard  Wainwright  and  Charles  H. 
Judd,  U.  S.  Navy,  and  the  whole  being  reviewed  by  Capt.  Ralph  Chandler,  U.  S. 
Navy.  The  object  of  this  revision  was  to  improve  the  general  arrangement,  and  to 
introduce  the  more  convenient  and  precise  methods  of  navigation  that  had  come  into 
practice  since  the  book  was  originally  written. 

The  progress  that  has  been  made  in  the  science  of  navigation  since  1880  has 
rendered  necessary  a  second  extensive  revision,  to  take  cognizance  of  the  changes  of 
methods  and  instruments  that  have  accompanied  the  general  introduction  of  high-speed 
vessels  built  of  iron  and  steel.  This  work  has  been  carried  out,  under  the  direction 
of  the  Bureau  of  Equipment,  by  Lieut.  G.  W.  Logan,  U.  S.  Navy,  who  was  aided  in 
the  collection  of  data  and  preparation  for  publication  b}^  Lieut.  T.  A.  Kearney,  U.  S. 
Navy;  the  chapters  on  AVinds  and  Cyclonic  Storms  were  contributed  by  Mr.  James 
Page,  nautical  expert,  Hydrographic  Office. 

There  has  been  an  extensive  rewriting  of  the  text,  with  the  object  of  amplifying 
those  matters  that  are  of  the  greatest  importance  in  the  modern  practice  of  navigation, 
and  of  omitting  or  condensing  those  of  lesser  importance;  and  the  revision  of  the 
tables  has  proceeded  along  similar  lines.  This  has  involved,  among  other  things,  a 
much  wider  treatment  of  the  subject  of  the  compass;  an  extension  of  the  traverse 
table  for  degrees  to  distances  up  to  600  miles:  an  improved  table  for  reducing  circum- 
meridian  altitudes;  the  combination  of  the  tables  of  maritime  positions  and  tidal  data; 
the  omission  of  certain  special  methods  for  finding  position  by  two  observations;  the 
addition  of  a  series  of  annotated  forms  for  the  working  of  all  sights,  and  the  intro- 
duction of  a  number  of  new  tables  of  use  to  the  navigator. 

The  explanation  of  the  method  of  lunar  distances,  with  its  accompanying  tables, 
has  been  retained,  in  order  to  be  available  for  use  when  required;  but  since  this  obser- 
vation is  so  rarely  employed  in  modern  navigation,  everything  pertaining  thereto  has 
been  incorporated  ih  an  appendix,  that  it  may  be  distinct  from  matter  of  every-day 
use  to  the  navigator. 

For  convenience  in  use  the  work  has  been  divided  into  two  parts,  of  which  the  first 
comprises  the  text  and  its  appendices,  and  the  second  the  tables. 

W.  H.  H.   SOUTHERLAND, 

-     Commander^  U.  S.  Navy^  Hydrographer. 
Hydrographic  Office, 

Bureau  of  Equipment,  Navy  Department, 
Washington^  D.  C,  March  19^  1903. 

3 


1 1 1 140 


Digitized  by  the  Internet  Archive 

in  2008  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/americanpracticaOObowdrich 


P  J^Pt  T    I. 


TEXT  AND  APPENDICES, 


OOISTTEISTTS    O  F    I>  A.  R  T    I. 


Page. 

Orders  relatipg  to  revision 2 

Preface 3 

Abbreviations '  9 

Chapter    I.  Definitions  relating  to  Navigation 11 

II.  Instruments  and  Accessories  in  Navigation 13 

III.  The  Compass  Error 29 

IV.  Piloting 42 

V.  The  Sailings 50 

VI.  Dead  Reckoning 60 

VII.  Definitions  relating  to  Nautical  Astronomy 63 

VIII.  Instruments  employed  in  Nautical  Astronomy 66 

IX.  Time  and  the  Nautical  Almanac 74 

X.  Correction  of  Observed  Altitudes 82 

XI.  The  Chronometer  Error 87 

XII.  Latitude 94 

XIII.  Longitude 103 

XIV.  Azimuth 109 

XV.  The  Sumner  Line 114 

XVI.  The  Practice  of  Navigation  at  Sea 1 24 

XVII.  Marine  Surveying 131 

XVIIL  Winds .' 142 

XIX.  Cyclonic  Storms 147 

XX.  Tides 153 

XXI.  Ocean  Currents 158 

Appendix  I.  Extracts  from  the  American  Ephemerls  and  Nautical  Almanac  for  the  year  1879, 

which  have  reference  to  examples  for  that  year  given  in  this  Avork 163 

II.  A  collection  of  Forms  for  working  Dead   Reckoning  and   various   Astronomical 

Sights,  with  notes  explaining  their  application  under  all  circumstances 171 

III.  Explanation   of  certain  Rules  and  Principles  of  Mathematics  of  use  in  the  Solu- 

tion of  Problems  in  Navigation 178 

IV.  Maritime  Positions  and  Tidal  Data 190 

V.  Lunar  Distances 288 

Index 333 

7 


ABBREVIATIONS  USED  IN  THIS  WORK. 


Alt.  {orh) Altitude. 

A.  M Ante  meridian. 

Amp Amplitude. 

App . Apparent. 

App.  t Apparent  time. 

Ast Astronomical. 

Ast.  t Astronomical  time. 

Aug Augmentation. 

Az.  (or  Z) Azimuth. 

C Course. 

C.  C Chronometer  correction. 

C  — W Chronometer  minus  watch. 

Chro.  t Chronometer  time. 

Co.  L Co.  latitude. 

Col Column. 

Corr Correction. 

Cos Cosine. 

Cosec Cosecant. 

Cot Cotangent. 

d  (or  Dec. ) Declination. 

D  ( or  DLo ) Difference  longitude. 

Dep Departure. 

Dev Deviation. 

Diff Difference. 

Dist Distance. 

DL Difference  latitude. 

D.  R Dead  reckoning. 

E.,  Ely East,  easterly. 

Elap.  t Elapsed  time. 

Eq.  eq.  alt Equation  equal  altitude" 

Eq.  t Equation  of  time. 

G.  (or  Gr. ) Greenwich. 

G.  A.  T Greenwich  apparent     .ne. 

G.  M.  T Greenwich  mean  time. 

G.  S.  T : Greenwich  sidereal  time. 

h Altitude. 

H Meridian  altitude. 

H.  A.  (or  /) Hour  angle. 

H.  D Hourly  difference. 

H.  P.  (or  Hor.  par. ) . . .  Horizontal  parallax. 

Hr-s Hour-8. 

H.  W High  water. 

I.  C Index  correction. 

L.  (or  Lat. ) Latitude. 

L.  A.  T Local  apparent  time. 


L.  M.  T Local  mean  time. 

L.  S.  T Local  sidereal  time. 

Lo.  (or  Long) Longitude. 

Log Logarithm. 

Lun.  Int Lunitidal  interval. 

L.  W Low  water. 

m Meridional  difference. 

Merid Meridian  or  noon. 

Mag Magnetic. 

M.  D Minute's  difference. 

Mid Middle. 

Mid.  L Middle  latitude. 

M.  T Mean  time. 

N. ,  Nly North,  northerly. 

N.  A.  (or  Naut.  Aim. ). Nautical  Almanac. 

Np Neap. 

Obs Observation. 

p  (or  P.  D. ) Polar  distance. 

p.  c Per  compass. 

P.  D.  (or  «) Polar  distance. 

P.  L.  (or  Prop.  Log.)  .Proportional  logarithm. 

P.  M Post  meridian. 

p.  &  r Parallax  and  refraction. 

Par Parallax. 

R.  A Right  ascension. 

R.  A.  M.  S Right  ascension  mean  sun. 

Red Reduction. 

Ref Refraction. 

S. ,  Sly South,  southerly. 

S.  D Semi-diameter. 

Sec Secant. 

Sid Sidereal. 

Sin Sine. 

Spg Spring. 

t Hour  angle. 

T Time. 

Tab Table. 

Tan Tangent. 

Tr.  (or  Trans. ) Transit. 

Var V'^ariation. 

Vert Vertex  or  vertical. 

W.,  Wlv West,  westerly. 

W.  T  . .' AVatch  time 

2 Zenith  distance. 

Z Azimuth. 


0 

The  Sun. 

°    Degrees. 

c 

The  Moon. 

'     Minutes  of  Arc. 

* 

A  Star  or  Planet. 

^^    Seconds  of  Arc. 

(^C 

Alt.  upper  limb. 

"     Hours. 

(•)C 

Alt.  lower  limb. 

""    Minutes  of  Time 

(l)0 

Azimuthal  angle. 

•^     Seconds  of  Time. 

GREEK   LETTERS. 

A  a. 

.Alpha. 

N  v.... 

.Nu. 

B(i. 

.Beta. 

SI  .... 

.Xi. 

ry. 

.Gamma. 

Oo  .... 

.Omicron. 

J  6. 

.Delta. 

n  n.... 

.Pi. 

E  s  . 

.Epsilon. 

Pp. ... 

.Rho. 

ZC. 

.Zeta. 

26{i). 

.  Sigma. 

Hr^. 

.Eta. 

Tr  .... 

.Tau. 

t)0  . 

.Theta. 

Tv.... 

.Upsilon. 

1  I  .. 

.Iota. 

$  0 

.Phi. 

Kk. 

.  Kappa. 

^;«:..-- 

.Chi. 

AX. 

.Lambda. 

Wrl).... 

.Psi. 

Mjii. 

.Mu. 

£1  00  ... 

.Omega. 

DEFINITIONS    RELATING    TO    NAVIGATION. 


11 


BR      ., 
or  THE 

UNIVERSITY 


CHAPTER  I. 
DEFINITIONS  KELATINQ  TO  NAVIGATION. 


1.  That  science,  generally  termed  Navigatiou,  which  affords  the  knowledge  necessary  to  conduct 
a  ship  from  point  to  point  upon  the  earth,  enabling  the  mariner  to  determine,  with  a  sufficient  degree 
of  accuracy,  the  position  of  his  vessel  at  any  time,  is  properly  divided  into  two  branches:  Navigation 
and  Nautical  Astronomy. 

2.  Navigation,  in  its  limited  sense,  is  that  branch  which  treats  of  the  determination  of  the  position 
of  the  ship  by  reference  to  the  earth,  or  to  objects  thereon.  It  comprises  {a)  Piloting,  in  which  the 
position  is  ascertained  from  visible  objects  upon  the  earth,  or  from  soundings  of  the  depth  of  the  sea, 
and  {h)  Dead  Reckoning,  in  which  the  position  at  any  moment  is  deduced  from  the  direction  and 
amount  of  a  vessel's  progress  from  a  known  point  of  departure. 

3.  Nautical  Astronoim/  is  that  branch  of  the  science  which  treats  of  the  determination  of  the 
vessel's  place  by  the  aid  of  celestial  objects — the  sun,  moon,  planets,  or  stars. 

4.  Navigation  and  Nautical  Astronomy  have  been  respectively  termed  Geo-Naviga^don  and  Celo- 
Navigation,  to  indicate  the  processes  upon  which  they  depend. 

5.  As  the  method  of  piloting  can  not  be  employed  excepting  near  land  or  in  moderate  depths  of 
water,  the  navigator  at  sea  must  fix  his  position  either  by  dead  reckoning  or  by  observation  {of  celestial 
objects) ;  the  latter  method  is  more  exact,  but  as  it  is  not  always  available,  the  former  must  often  be 
depended  upon. 

6.  The  Earth. — The  Earth  is  an  oblate  spheroid,  being  a  nearly  spherical  body  slightly  flattened 
at  the  poles;  its  longer  or  equatorial  axis  measures  about  7,927  statute  miles,  and  its  shorter  axis, 
around  which  it  rotates,  about  7,900  statute  miles. 

The  Earth  (assumed  for  purposes  of  illustration  to  be  a 
sphere)  is  represented  in  figure  1. 

The  ^Lris  of  Rotation,  usually  spoken  of  simply  as  the 
Axis,  is  PP''. 

The  Poles  are  the  points,  P  and  P',  in  which  the  axis 
intersects  the  surface,  and  are  designated,  respectively,  as 
the  North  Pole  and  the  South  Pole. 

The  Equator  is  the  great  circle  EQMW,  formed  by  the 
intersection  with  the  earth's  surface  of  a  plane  perpendicular 
to  the  axis;  the  equator  is  equidistant  from  the  poles,  every 
point  upon  it  being  90°  from  each  pole. 

Meridians  are  the  great  c-ircles  PQP^  PMP^  PM'P^ 
formed  by  the  intersection  with  the  earth's  surface  <4i  planes 
secondary  to  the  equator  (that  is,  passing  through  its  poles 
and  therefore  perpendicular  to  its  plane) . 

Parallels  of  Latitude  are  small  circles  NT/*,  N^?/T',  formed 
by  the  intersection  with  the  earth's  surface  of  planes  passed 
parallel  to  the  eciuator. 

The  Latitude  of  a  place  on  the  surface  of  the  earth  is  the 
arc  of  the  meridian  intercepted  between  the  equator  and  •p' 

that  place.     Latitude  is  reckoned  JWr//*  and  »S'Ji<</i,  from  the  Fig.  1. 

equator  as  an  origin,  through  90°  to  the  poles;  thus,  the 

latitude  of  the  point  T  is  MT,  north,  and  of  the  point  T^  M^T',  north.  The  Difference  of  Latitude 
between  any  two  places  is  the  arc  of  a  meridian  intercepted  between  their  parallels  of  latitude,  and  is 
called  North  or  South,  according  to  direction;  thus,  the  difference  of  latitude  between  T  and  T'  is  Tn^  or 
T^»,  north  from  T  or  south  from  T'. 

The  Longitude  of  a  place  on  the  surface  of  the  earth  is  the  arc  of  the  equator  intercepted  between 
its  meridian  and  that  of  some  place  from  which  the  longitude  is  reckoned.  Longitude  is  measured  East 
or  West  through  180°  from  the  meridian  of  a  designated  place,  such  meridian  being  termed  the  Printe 
Meridian;  the  prime  meridian  used  by  most  nations,  including  the  United  States,  is  that  of  Greenwich, 
England.  If,  in  the  figure,  the  prime  meridian  be  PGQP^,  then  the  longitude  of  the  point  T  is  QM,  east, 
and  of  T^,  QM^,  east.  The  Difference  of  Longitude  between  any  two  places  is  the  arc  of  the  equator  inter- 
cepted between  their  meridians,  and  is  called  East  or  West,  accordmg  to  direction;  thus,  the  difference 
of  longitude  between  T  and  T''  is  MAP,  east  from  M  or  west  from  AP.  The  Departure  is  the  linear  distance, 
measured  on  a  parallel  of  latitude,  between  two  meridians;  unlike  the  various  quantities  previously 
defined,  departure  is  reckoned  in  miles;  the  departure  between  two  meridians  varies  with  the  parallel  of 
latitude  upon  which  it  is  measured;  thus,  the  departure  between  the  meridians  of  T  and  T^  is  the  number 
of  miles  corresponding  to  the  distance  Tji  in  the  latitude  of  T,  or  to  n'T'  in  the  latitude  of  T'. 


uy\ 

^yy         Ny 

1  T 

«                     1      M 

M'     r 

12  DEBINITIONS    RELATING    TO    NAVIGATION. 

The  curved  line  which  joins  any  two  places  on  the  earth's  surface,  cutting  all  the  meridians  at  the 
same  angle,  is  called  the  Rhumb  Line,  Loxodromic  Chinr,,  or  Equiangular  Spiral.  In  the  figure,  this  line 
is  represented  by  TrT''.  The  constant  angle  which  this  line  makes  with  the  meridians  is  called  the 
Course;  and  the  length  of  the  line  between  any  two  places  is  called  the  Distance  between  those  places. 

The  unit  of  linear  measure  employed  by  navigators  is  the  Nautical  or  Sea  Mile,  or  Knot.  It  is 
equal  to  one  minute  of  platitude — that  is,  to  the  length  of  that  portion  of  a  meridian  which  subtends  at 
the  earth's  center  the  angular  measure  of  one  minute;  since,  however,  on  account  of  the  fact  that  the 
earth  is  not  a  perfect  sphere,  this  distance  is  not  exactly  the  same  in  all  latitudes,  a  mean  value  is  adopted  for 
the  length  of  the  knot,  and  it  is  regarded  as  equal  to  6,080.27  feet.  For  the  purposes  of  navigation,  the 
variation  from  this  value  in  different  latitudes  is  so  small  that  it  may  be  neglected,  and  the  knot  may 
be  assumed  equal  to  a  minute  of  latitude  in  all  parts  of  the  earth;  hence,  when  a  vessel  changes  her 
position  to  the  north  or  south  by  one  nautical  mile,  it  may  always  be  considered  that  the  latitude  has 
changed  1''.  Owing  to  the  fact  that  the  meridians  all  convei^e  toward  the  poles,  the  difference  of  longi- 
tude produced  by  a  change  of  position  of  one  mile  to  the  east  or  west  will  vary  with  the  latitude;  thus 
a  departure  of  one  mile  will  equal  a  difference  of  longitude  of  1^.0  at  the  equator,  of  V.l  in  the  latitude 
of  30°,  and  of  2^0  in  the  latitude  of  60°. 

The  Great  Circle  Track  or  Course  between  any  two  places  is  the  route  between  those  places  along  the 
circumference  of  the  great  circle  which  joins  them.  In  the  figure,  this  line  is  represented  by  TgT^. 
From  the  properties  of  a  great  circle  (which  is  a  circle  upon  the  earth's  surface  formed  by  the  inter- 
section of  a  plane  passed  through  its  center)  the  distance  between  two  points  measured  on  a  great  circle 
track  is  shorter  than  the  distance  upon  any  other  line  which  joins  them.  Except  when  the  two  points 
are  on  the  same  meridian  or  when  both  lie  upon  the  equator,  the  great  circle  track  will  always  differ 
from  the  rhumb  line,  and  the  great  circle  track  will  intersect  each  intervening  meridian  at  a  different 
angle. 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION.  13 


CHAPTER  II. 

INSTRUMENTS  AND  ACCESSORIES  IN  NAVIGATION. 


DIVIDERS  OR  COMPASSES. 

7.  This  instrument  consists  of  two  legs  movable  about  a  joint,  so  that  the  points  at  the  extremities 
of  the  legs  may  be  set  at  any  required  distance  from  each  other.  It  is  used  to  take  and  transfer  dis- 
tances and  to  describe  arcs'and  circles.  When  used  for  the  former  purpose  it  is  termed  didders,  and 
the  extremities  of  both  legs  are  metal  points;  when  used  for  describing  arcs  or  circles,  it  is  called  a  com- 
pass, and  one  of  the  metal  points  is  replaced  by  a  pencil  or  pen. 

PARALLEL  RXTLERS. 

§.  Parallel  rulers  are  used  for  drawing  lines  parallel  t(j  each  other  in  any  direction,  and  are  particu- 
larly useful  in  transferring  the  rhuml)-]ine  on  the  chart  to  the  nearest  compass-rose  to  ascertain  the 
course,  or  to  lay  off  bearings  and  courses. 

PROTRACTOR. 

9.  This  is  an  instrument  used  for  the  measurement  of  angles  upon  paper;  there  is  a  wide  variation  in 
the  material,  size,  and  shape  in  which  it  mav  be  made.  (For  a  description  of  the  Three  Armed  Protractor, 
see  art.  432,  Chap.  XVII. ) 

THE  CHIP  LOG. 

10.  This  instrument,  for  measuring  the  rate  of  sailing,  consists  of  three  parts;  viz,  the  log-chip, 
the  log-line,  and  the  log-glass.  A  light  substance  thrown  from  the  ship  ceases  to  partake  of  the  motion 
of  the  vessel  as  soon  as  it  strikes  the  water,  and  will  be  left  behind  on  the  surface;  after  a  certain  inter- 
val, if  the  distance  of  the  ship  from  this  stationary  object  be  measured,  the  approximate  rate  of  sailing 
will  be  given.  The  log-chip  is  the  float,  the  log-line  is  the  measure  of  the  distance,  and  the  log-glass 
defines  the  interval  of  time. 

The  log-chip  is  a  thin  wooden  quadrant  of  about  5  inches  radius,  loaded  with  lead  on  the  circular 
edge  sufficiently  to  make  it  swim  upright  in  the  water.  There  is  a  hole  in  each  comer  of  the  log- 
chip,  and  the  log-line  is  knotted  in  the  one  at  the  apex;  at  about  8  inches  from  the  end  there  is  seized 
a  wooden  socket;  a  piece  of  line  of  proper  length,  being  knotted  in  the  other  holes,  has  seized  into  its 
bight  a  wooden  peg  to  fit  snugly  into  the  socket  before  the  log-chip  is  thrown;  as  soon  as  the  line  is 
checked  this  peg  pulls  out,  thus  allowing  the  log-chip  to  be  hauled  in  with  the  least  resistance. 

The  log-line  is  about  150  fathoms  in  length,  one  end  made  fast  to  the  log-chip,  the  other  to  a 
reel  upon  which  it  is  wound.  At  a  distance  oi  from  15  to  20  fathoms  from  the  log-chip  a  permanent 
mark  of  red  bunting  about  6  inches  long  is  placed  to  allow  sufficient  stray  line  for  the  log-chip  to  clear 
the  vessel's  eddy  or  Make.  The  rest  of  the  line  is  divided  into  lengths  of  47  feet  3  inches  called  knots, 
by  pieces  of  fish-line  thrust  through  the  strands,  with  one,  two,  three,  etc.,  knots,  according  to  the 
number  from  stray -line  mark;  each  knot  is  further  subdivided  into  five  equal  lengths  of  two-tenths  of  a 
knot  each,  marked  by  pieces  of  white  rag. 

The  length  of  a  knot  depends  upon  the  number  of  seconds  which  the  log-glass  measures;  the  length 
of  each  knot  must  bear  the  same  ratio  to  the  nautical  mile  (^V  of  a  degree  of  a  great  circle  of  the  earth 
or  6,080  feet)  that  the  time  of  the  glass  does  to  an  hour. 

In  the  United  States  Navy  all  log-lines  are  marked  for  log  glasses  of  28  seconds,  for  which  the 
proportion  is: 

3600  :  6080  =  28'  :  x, 
X  being  the  length  of  the  knot. 

Ughcg 

a:  =  47".29,  or47"3i". 

The  speed  of  the  ship  is  estimated  in  knots  and  tenths  of  a  knot. 

The  log-glass  is  a  sand  glass  of  the  same  shape  and  construction  as  the  old  hour-glass.  Two  glasses 
are  used,  one  of  28  seconds  and  one  of  14  seconds;  the  latter  is  employed  when  the  ship  is  going  at  a 
high  rate  of  speed,  the  number  of  knots  indicated  on  a  line  marked  for  a  28-second  glass  being  doubled 
to  obtain  the  true  rate  of  speed. 

11.  The  log  in  all  its  parts  should  be  frequently  examined  and  adjusted;  the  peg  must  be  found  to 
fit  sufficiently  tight  to  keep  the  log-chip  upright;  the  log-line  shrinks  and  stretches  and  should  often  be 
verified ;  the  log-glass  should  be  compared  with  a  watch.  One  end  of  the  glass  is  stopped  with  a  cork, 
by  removing  which  the  sand  may  be  dried  or  its  quantity  corrected. 

12.  A  ground  log  consists  of  an  ordinary  log-line,  with  a  lead  attached  instead  of  a  chip;  in  shoal 
water,  where  there  are  no  well-defined  objects  available  for  fixing  the  position  of  the  vessel  and  the 
course  and  speed  are  influenced  by  a  tidal  or  other  current,  this  log  is  sometimes  used,  its  advantage 
being  that  the  lead  marks  a  stationary  point  to  which  motion  may  be  referred,  whereas  the  chip  would 
drift  with  the  stream.  The  speed,  which  is  marked  in  the  usual  manner,  is  the  speed  over  the 
:?round,  and  the  trend  of  the  line  gives  the  course  actually  made  good  by  the  vessel. 


14  INSTRUMENTS    AND    ACCJISSORIES    IN    NAVIGATION. 

THE  PATENT   LOG. 

1 3.  This  is  a  mechanical  contrivance  for  registering  the  distance  actually  run  by  a  vessel  through  the 
water.  There  are  various  types  of  patent  logs,  but  for  the  most  part  they  act  upon  the  same  principle, 
consisting  of  a  registering  device,  a  fly  or  rotator,  and  a  log  or  tow  line;  the  rotator  is  a  small  spindle 
with  a  number  of  wings  extending  radially  in  such  manner  as  to  form  a  spiral,  and,  when  drawn 
through  the  water  in4;he  direction  of  its  axis,  rotates  about  that  axis  after  the  manner  of  a  screw  pro- 
peller; the  rotator  is  towed  from  the  vessel  by  means  of  a  log  or  tow  line  from  20  to  50  fathoms  in  I'^ngth, 
made  fast  at  its  apex,  the  line  being  of  special  make  so  that  the  turns  of  the  rotator  are  transmitted 
through  it  to  the  worm  shaft  of  the  register,  to  which  the  inboard  end  of  the  line  is  attached;  the  regis- 
tering device  is  so  constructed  as  to  show  upon  a  dial  face  the  distance  run,  according  to  the  number  of 
turns  of  its  worm  shaft  due  to  the  motion  of  the  rotator;  the  register  is  carried  at  some  convenient  point 
on  the  vessel's  quarter;  it  is  frequently  found  expedient  to  rig  it  out  upon  a  small  boom,  so  that  the 
rotator  will  be  towed  clear  of  the  wake. 

14.  Though  not  a  perfect  instrument,  the  patent  log  affords  the  most  accurate  means  available  for 
determining  the  vessel's  speed  through  the  water.  It  will  usually  )je  found  that  the  indications  of  the 
log  are  in  error  by  a  constant  percentage,  and  the  amount  of  this  error  should  be  determined  l)y  careful 
experiment  and  apjilied  to  all  readings. 

Various  causes  may  operate  to  produce  inaccuracy  of  working  in  the  patent  log,  such  as  the  bending 
of  the  wings  of  the  rotator  by  accidental  blows,  fouling  of  the  rotator  by  sea  weed  or  refuse  from  the 
ship,  or  mechanical  wear  of  parts  of  the  register.  The  length  of  the  tow-line  has  much  to  do  with  the 
wqrking  of  the  log,  and  by  varying  the  length  the  indications  of  the  instrument  may  sometimes  be 
adjusted  when  the  percentage  of  error  is  small;  it  is  particularly  important  that  the  line  shall  not  be  too 
short.  The  readings  of  the  jjatent  log  can  not  be  depended  upon  for  accuracy  at  low  speeds,  when  the 
rotator  does  not  tow  horizontally,  nor  in  a  head  or  a  following  sea,  when  the  effect  depends  upon  the 
wave  motion  as  well  as  upon  the  speed  of  the  vessel. 

1 5.  Electrical  registers  for  patent  logs  are  in  use,  the  distance  recorded  by  the  mechanical  register 
being  communicated  electrically  to  some  point  of  the  vessel  which  is  most  convenient  for  the  purposes  of 
those  charged  with  the  navigation. 

16.  A  number  of  instruments  based  upon  different  physical  principles  have  been  devised  for 
recording  the  speed  of  a  vessel  through  the  water  and  have  been  used  with  varying  degrees  of  success. 

1 7.  The  revolutions  of  the  screw  i)ropeller  afford  in  a  steamer  a  valuable  check  upon  the  patent 
log  and  a  means  of  replacing  it  if  necessary.  To  be  of  service  the  number  of  revolutions  i)er  knot  must 
be  carefully  determined  for  the  vessel  by  experiment  under  varying  conditions  of  speed,  draft,  and  foul- 
ness of  bottom. 

THE  LEAD. 

18.  This  device,  for  ascertaining  the  depth  of  water,  consists  essentially  of  a  suitaljly  marked  line, 
having  a  lead  attached  to  one  of  its  ends.  It  is  an  invaluaVjle  aid  to  the  navigator  in  shallow  water, 
particularly  in  thick  or  foggy  weather,  and  is  often  of  service  when  the  vessel  is  out  of  sight  of  land. 

Two  leads  are  use<l  for  soundings — the  htmd-ledd,  weighing  from  7  to  14  jjounds,  with  a  line  marked 
to  about  25  fathoms,  and  the  deep-sea  lead,  weighing  from  30  to  100  pounds,  the  line  being  100  fathoms  or 
upward  in  length. 

Lines  are  generally  marked  as  follows: 

2  fathoms  from  the  lead,  with  2  strips  of  leather. 

3  fathoms  from  the  lead,  with  3  strips  of  leather. 
5  fathoms  from  the  lead,  with  a  white  rag. 
7  fathoms  from  the  lead,  with  a  red  rag. 
10  fathoms  from  the  lead,  with  leather  having  a 

hole  in  it. 
13  fathoms  from  the  lead,  same  as  at  3  fathoms.        !  And  so  on. 

15  fathoms  from  the  lead,  same  as  at  5  fathoms.        | 

Fathoms  which  correspond  with  the  depths  marked  are  called  )nark-<;  the  intermediate  fathoms  are 
called  deeps;  the  only  fractions  of  a  fathom  used  are  a  half  and  a  quarter. 

A  practice  sometimes  followed  is  to  mark  the  hand-lead  line  in  feet  around  the  critical  depths  of 
the  vessel  by  which  it  is  to  be  used. 

Lead  lines  should  be  measured  frequently  while  wet  and  the  correctness  of  the  marking  verified. 
The  distance  from  the  leadsman's  hand  to  the  water's  edge  should  be  ascertained  in  order  that  proper 
allowance  may  be  made  therefor  in  taking  soundings  at  night. 

19.  The  deep-sea  lead  may  be  armed  by  tilling  with  tallow  a  hole  lioUowed  out  in  its  lower  end, 
by  which  means  a  sample  of  the  bottom  is  brought  up. 

THE  SOUNDING  MACHINE. 

20.  This  machine  possesses  advantages  over  the  deep-sea  lead,  for  which  it  is  a  substitute,  in  that 
soundings  may  be  obtained  at  great  depths  and  with  rapidity  and  accuracy  without  stopping  the  ship. 
It  consists  essentially  of  a  stand  holding  a  reel  upon  which  is  wound  the  sounding  wire,  and  which  is 
controlled  by  a  suitable  Ijrake.  Crank  handles  are  provided  for  reeling  in  the  wire  after  the  sounding 
has  been  taken.  Attached  to  the  outer  end  of  the  wire  is  the  lead,  which  has  a  cavity  at  its  lower  end 
for  the  rece[>tion  of  the  tallow  for  arming.  Above  the  lead  is  a  cylindrical  case  containing  the  depth- 
registering  mechanism;  various  devices  are  in  use  for  this  purpose,  all  depending,  however,  upon  the 
increasing  pressure  of  the  water  with  increasing  depths. 

21.  In  the  Lord  Keliin  machine  z.  slender  glass  tube  is  used,  sealed  at  one  end  and  open  at  the 
other,  and  coated  inside  with  a  chemical  substance  which  changes  color  upon  contact  with  sea  water; 
this  tube  is  placed,  closed  end  up,  in  the  metal  cylinder;  as  it  sinks  the  water  rises  in  the  tube,  the 
contained  air  being  compressed  with  a  force  dependent  upon  the  depth.  The  limit  of  discoloration  is 
marked  by  a  clearly  defined  line,  and  the  dei)th  of  the  sounding  corresponding  to  this  line  is  read  off 
from  a  scale.  Tubes  that  have  been  used  in  comparatively  shallow  water  may  be  used  again  where  the 
water  is  known  to  be  deeper. 


17  fathoms  from  the  lead,  same  as  at  7  fathoms. 

20  fathoms  from  the  lead,  with  2  knots. 

25  fathoms  from  the  lead,  wi:h  1  knot. 

30  fathoms  from  the  lead,  with  3  knots. 

35  fathoms  from  the  lead,  with  1  knot. 

40  fathoms  from  the  lead,  with  4  knots. 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


15 


22.  A  tube  whose  inner  surface  is  ground  has  been  substituted  for  the  chemical-coated  tube,  ground 
glass,  when  wet,  showing  clear.  The  advantage  of  these  tubes  is  that  they  may  be  used  an  indefinite 
number  of  times  if  thoroughly  dried.  To  facilitate  drying,  a  rubber  cap  is  fitted  to  the  upper  end,  which, 
when  removed,  admits  of  a  circulation  of  the  air  through  the  tube. 

23.  As  a  substitute  for  the  glass  tubes  a  mechanical  depth  recorder  contained  in  a  suitable  case  has 
been  used.  In  this  device  the  pressure  of  the  water  acts  upon  a  piston  against  the  tension  of  a  spring.  A 
scale  with  an  index  pointer  records  the  depth  reached.  The  index  pointer  must  be  set  at  zero  before 
each  sounding. 

24.  Since  the  action  of  the  sounding  machine,  when  glass  tubes  are  used,  depends  upon  the  com- 
pression of  the  air,  the  barometric  pressure  of  the  atmosphere  must  be  taken  into  account  w^hen  accurate 
results  are  required.  The  correction  consists  in  increasing  the  indicated  depth  bj'  a  fractional  amount 
according  to  the  following  table: 


Bar.  reading. 

Increase. 

// 

29.  75 

m.  00 

.so.  50 

30.  75 

j 

1  One-fortieth. 
:  One-thirtieth. 
;  One-tv.'entieth. 
One-fifteenth. 

THE  MARINER'S  COMPASS. 

25.  The  Mariner^ s  Compass  i.s  an  instrument  consisting  either  ot  a  single  magnet,  or,  more  usually, 
of  a  series  of  magnets,  which,  being  attached  to  a  graduated  circle  i)iv<»ted  at  the  center  and  allowed  to 


Fig.  2. 

swing  freely  in  a  horizontal  plane,  has  a  tendency  to  lie  with  its  magnetic  axis  in  the  plane  of  the  earth's 
magnetic  meridian,  thus  affording  a  means  of  determining  the  azimuth,  or  horizontal  angular  distance 
from  that  meridian,  of  the  ship's  c-ourse  and  of  all  visible  objects,  terrestrial  or  celestial. 


/ 


16 


INSTRUMENTS    AND   ACCESSORIES    IN    NAVIGATION. 


26.  The  circular  card  of  the  compass  (fig.  2)  is  divided  on  its  periphery  into  360°,  numbered  from  0° 
at  North  and  South  to  90°  at  East  and  West;  also  into  thirty-two  divisions  of  1^°  each,  called  jmnts,  the 
latter  being  further  divided  into  half-points  and  quarter-points ;  still  finer  suMivisions,  eighth-]>oints,  are 
sometimes  used,  though  not  indicated  on  the  card.  A  system  of  numbering  the  degrees  from  0°  to  360°, 
always  increasing  toward  the  right,  is  shown  in  the  figure.  This  system  is  in  use  by  the  mariners  of 
some'  nations,  and  itsgeneral  adoption  would  carry  with  it  certain  undoubted  advantages. 

27.  Boxing  the  (Mmpass  is  the  process  of  naniing  the  points  in  their  order,  and  is  one  of  the  first 
things  to  be  learned  by  the  young  mariner.  The  four  principal  points  are  called  cardinal  points  and  are 
named  North,  South,  East,  and  West;  each  differs  in  direction  from  the  adjacent  one  by  90°,  or  8  points. 
Midway  between  the  cardinal  points,  at  an  angular  distance  of  45°,  or  4  points,  are  the  inter-cardinal 
points,  named  according  to  their  posititm  Northeast,  Southeast,  etc.  Midway  between  each  cardinal 
and  inter-cardinal  point,  at  an  angular  distance  of  22J°,  or  2  points,  is  a  point  whose  name  is  made  up 
of  a  combination  of  that  of  the  cardinal  with  that  of  the  inter-cardinal  point:  North-Northeast,  East- 
Northeast,  East-Southeast,  etc.  At  an  angular  distance  of  1  point,  or  lli°,  from  each  cardinaland  inter- 
cardinal  point  (and  therefore  midway  between  it  and  the  22J°-division  last  described),  is  a  point 
which  bears  the  name  of  that  cardinal  or  inter-cardinal  point  joined  by  the  word  by  to  that  of  the  cardi- 
nal point  in  the  dire<'tion  of  which  it  lies:  North  by  East,  Northeast  by  North,  Northeast  by  East,  etc. 

In  boxing  by  fractional  points,  it  is  evident  that  each  division  may  be  referred  to  either  of  the 
whole  points  to  which  it  is  adjacent;  for  instance,  NE.  by  N.  j  N.  and  NNE.  J  E.  would  describe  the 
same  division.  It  is  the  custom  in  the  United  States  Navy  to  box  from  North  and  South  toward  East  and 
West,  excepting  that  divisions  adjacent  to  a  cardinal  or  inter-cardinal  point  are  always  referred  to  that 
point;  as  N.  i  E.,  N.  by  E.  ^  E.,  NNE.  J  E.,  NE.  j  N.,  etc.  Some  mariners,  however,  make  it  a  prac- 
tice to  box  from  each  cardinal  and  inter-cardinal  point  tmiard  a  22i°-point  (NNE.,  ENE.,  etc.);  as 
N.  i  E.,  N.  by  E.  J  E.,  NE.  by  N.  J  N.,  NE.  \  N.,  etc. 

The  names  of  the  whole  points,  together  with  fractional  points  (according  to  the  nomenclature  of 
the  United  States  Navy),  are  given  in  the  following  table,  which  shows  also  the  degrees,  minutes,  and 
seconds  from  North  or  South  to  which  each  division  corresponds: 

-       '•>  ^ 


N.  to  E. 


N.  to  W. 


S.  to  E. 


Pts. 


Angular 
measure. 


North: 

N.  iE 

N.  JE 

N.  |E 

N.byE 

N.  by  E.  i  E.. 

N.  by  E.  ^E.. 

N.  by  E.  |E.. 
NNE 

NNE.  \E 

NNE.  iE 

NNE.  f  E 

NE.  byN 

NE.  J  N 

NE.  i  N 

NE.  i  N 

NE 

NE.  iE 

NE.  i  E 

NH  |E 

NE.  byE 

NE.  by  E.  i  E. 

NE.  by  E.  i  E. 

NE.  by  E.  I  E. 
ENE 

ENE.  iE 

ENE.  iE 

ENE.  f  E 

E.  byN 

E.  IN 

E.  IN 

v..  iN 

East 


North: 

N.  i  W 

N.  J  W 

N.  f  W 

N.byW 

N.  by  W.  iW.. 

N.  by  W.J  W.. 

N.  by  W.  f  W.. 
NNW 

NNW.  }  W.... 

NNW.  iW.... 

NNW.  f  W  . . . . 
NW.  byN 

NW.  |N 

NW.  IN 

NW.  iN 

NW 

NW.  i  W 

NW.  J  W 

NW.  I  W 

NW.  by  W 

NW.byW.iW. 

NW.byW.JW. 

NW.byW.  JW. 
WNW 

WNW.  J  W.... 

WNW.  J  W.... 

WNW.  f  W.... 
W.byN 

W.  I  N 

W.  JN 

W.  }  N 

West 


South: 

S.  \E 

S.  JE 

S.  |E 

S.  byE 

S.  by  E.  i  E . 

S.  by  E.  J  E  . 

S.  by  E.  I  E . 
SSE 

SSE.  iE 

SSE.  JE 

SSE.  f  E.... 
SE.  by  S 

SE.  |S 

SE.  ^S 

SE.  i-S 

SE 

SE.iE 

SE.  JE 

SUf  E 

SE.  byE 

SE.  by  E.  i  E 

SE.  by  E.  i  E 

SE.  by  E.  f  E 
ESE 

ESE.  iE.... 

ESE.  J  E . . . . 

ESE.  f  E . . . . 
E.byS 

E.  f  S 

E.  JS 

E.  }S 

East 


South : 

S.  J  W 

S.  iW 

S.  |W 

S.  by  W 

S.  by  W.  i  W.. 

S.  by  W.J  W.. 

S.  by  W.  I  W.. 
ssw 

ssw.  i  w 

ssw.  J  w 

ssw.  I  w 

SW.  byS 

SW.  f  s 

SW.  JS 

SW.  JS 

SW 

SW.  i  w 

SW.  J  w 

SW.  f  w 

SW.  by  W 

SW.  by  W.  i  W 

SW.  by  W.  J  W 

SW.  by  W.  I  W 
WSW 

wsw.  nv.... 

WSW.  J  W.... 

WSW.  iw.... 

W.  byS 

W.  f  s 

W.  JS 

AV.  iS 

West 


1 
U 

1| 

2 

2\ 

2i 

2J 

3 

3i 

3J 

3i 

4 

^ 

4i 

5 

b\ 

5J 

5J 

6 

6i 

6i 

61 

7 

n 

n 

71 


2 
5 
8 
11 
14 
16 
19 
22 
25 
28 
30 
33 
36 
39 
42 
45 
47 
50 
53 
56 
59 
61 
64 
67 
70 
73 
75 
78 
81 
84 
87 
90 


48  45 
37  30 
26  15 
15  00 
03  45 
52  30 
41  15 
30  00 
18  45 
07  30 
56  15 
45  00 
33  45 
22  30 
11  15 
00  00 
48  45 
37  30 
26  15 
15  00 
03  45 
52  30 
41  15 
30  00 
18  45 
07  30 
56  15 
45  00 
33  45 
22  30 
n  15 
00  00 


2§.  The  compass  card  is  mounted  in  a  bowl  which  is  carri^  in  gimbals,  thus  enabling  the  card  to 
retain  a  horizontal  position  while  the  ship  is  pitching  and  rolling.  A  vertical  black  line  called  the  bib- 
ber's line  is  marked  on  the  inner  surface  of  the  bowl,  and  the  compass  is  so  mounted  that  a  line  joining 
its  pivot  with  the  lubber's  line  is  parallel  to  the  keel  line  of  the  vessel;  thus  the  lubber's  line  always 
indicates  the  compass  direction  of  the  ship's  head. 

29.  According  to  the  purpose  which  it  is  designed  to  fulfill,  a  compass  is  designated  as  a  Standard, 
Peering,  Check,  or  Boat  Compass. 


INSTEUMENTS    AND    ACCESSORIES    IN    NAVIGATION.  17 

30.  There  are  two  types  of  compass  in  use,  the  v:et  or  liquid  and  the  dry;  in  the  former  the  bowl  i;j 
filled  with  liquid,  the  card  being  thus  partially  buoyed,  with  consequent  increased  ease  of  working  on 
the  pivot,  and  the  liquid  further  serving  to  decrease  the  vibrations  of  the  card  when  deflected  by  reason 
of  the  motion  of  the  vessel  or  other  cause.  On  account  of  its  advantages  the  liquid  compass  is  used  in 
the  United  States  Xavy. 

31.  The  Navy  Service  7^-ixch  Liquid  Compass. — This  consists  of  a  skeleton  card  7 J  inches  in 
diameter,  made  of  tinned  brass,  resting  on  a  pivot  in  liquid,  with  provisions  for  two  pairs  of  magnets 
symmetrically  placed. 

The  magnet  system  of  the  card  consists  of  four  cylindrical  bundles  of  steel  wires;  these  wires  are 
laid  side  by  side  aiid  magnetized  as  a  bundle  between  the  poles  of  a  powerful  electromagnet.  They  are 
afterwards  placed  in  a  cylindrical  case,  sealed,  and  secured  to  the  card.  Steel  wires  made  up  into  a 
bundle  were  adopted  Ijeckuse  they  are  more  homogeneous,  can  be  more  perfectly  tempered,  and  for  the 
same  weiglit  give  greater  magnetic  power  than  a  solid  steel  bar. 

Two  of  the  magnets  are  placed  parallel  to  the  north  and  south  diameter  of  the  card,  and  on  the 
chords  of  15°  (nearly)  of  a  circle  passing  through  their  extremities.  These  magnets  penetrate  the  air 
vessel,  to  which  they  are  soldered,  and  are  further  secured  to  the  bottom  of  the  ring  of  the  card.  The 
other  two  magnets  of  the  system  are  placed  parallel  to  the  longer  magnets  on  the  chords  of  45°  (nearly) 
of  a  circle  passing  through  their  extremities,  and  are  secured  to  the  bottom  of  the  ring  ofthe  card. 

The  card  is  of  a  curved  annular  type,  the  outer  ring  being  convex  on  the  upper  and  inner  side,  and 
is  graduated  to  read  to  one-fourth  point,  a  card  circle  being  adjusted  to  its  outer  edge  and  divided  to 
half-degrees,  with  legible  figures  at  each  3°,  for  use  in  reading  bearings  by  an  azimuth  circle  or  in  laying 
the  course  to  degrees. 

The  card  is  provided  with  a  concentric  spheroidal  air  vessel,  to  buoy  its  own  weight  and  that  of  the 
magnets,  allowing  a  pressure  of  between  60  and  90  grains  on  the  pivot  at  60°  F. ;  the  weight  of  the  card 
in  air  is  3,060  grains.  The  air  vessel  has  within  it  a  hollow  cone,  open  at  its  lower  end,  and  provided 
with  the  pivot  bearing,  or  cap,  containing  a  sapphire,  which  rests  upon  the  pivot  and  thus  supports  the 
card;  the  cap  is  provided  with  adjusting  screws  for  accurately  centering  the  i-ard.  The  pivot  is  fastened 
to  the  center  of  the  bottom  of  the  bowl  by  a  flanged  plate  and  screws.  Through  this  plate  aiid  the 
bottom  of  the  bowl  are  two  small  holes  which  communicate  Avith  the  expansion  chamber  and  admit  of 
a  circulation  of  the  liquid  between  it  and  the  bowl.     The  pivot  is  of  gun  metal  with  an  iridium  cap. 

The  card  is  mounted  in  a  bowl  of  cast  bronze,  the  glass  cover  of  which  is  closely  packed  with  rubber, 
preventing  the  evaporation  or  leakage  of  the  liquid,  which  entirely  tills  the  bowl.  This  liquid  is  com- 
posed of  45  per  cent  pure  alcohol  and  55  per  cent  distilled  water,  and  remains  liquid  below  —10°  F.  _ 

The  luljber's  line  is  a  fine  line  drawn  on  an  enameled  plate  on  the  inside  of  the  bowl,  the  inner 
surface  of  the  latter  l)eing  covered  with  an  insolul)le  white  paint. 

Beneath  the  bowl  is  a  metallic  self-adjusting  expansion  chamber  of  elastic  metal,  by  means  of  which 
the  bowl  is  kept  constantly  full  Avithout  the  show  of  bubbles  or  the  development  of  undue  pressure 
caused  by  the  change  in  volume  of  the  liquid  due  to  changes  of  temperature. 

The  Vim  of  the  compass  bowl  is  made  rigid  and  its  outer  edge  turned  strictly  to  gauge  to  receive  the 
azimuth  circle. 

32.  The  Dry  Compass. — The  Lord  Kelrin  Compass,  which  may  be  regarded  as  the  standard  for 
the  nonliquid  type,  consists  of  a  strong  paper  card  with  the  central  parts  cut  away  and  its  outer  edge 
stiffened  1)y  a  thin  aluminum  ring.  The  pivot  is  fitted  with  an  iridium  point,  upon  which. rests  a  small 
light  aluminum  boss  fitted  with  a  sapphire  Ijearing.  Radiating  from  this  boss  are  32  silk  threads  whose 
outer  ends  are  made  fast  to  the  inner  edge  of  the  compass  card;  these  threads  sustain  the  weight  of  the 
suspended  card,  and,  as  they  possess  some  elasticity,  tend  to  decrease  the  shocks  due  to  motion. 

Eight  small  steel  wire  needles,  3^  to  2  inches  long,  are  secured  normally  to  two  parallel  silk  threads, 
and  are  slung  from  the  aluminum  rim  of  the  card  by  other  silk  threads  which  pass  through  eyes  in  the 
ends  of  the  outer  pair  of  needles.  The  needles  are  below  the  radial  threads,  thus  keeping  the  center  of 
gravity  low. 

33.  The  Azimuth  Circle. — This  is  a  necessary  fitting  for  all  compasses  employed  for  taking 
bearings — that  is,  noting  the  directions — of  either  celestial  or  terrestrial  objects.  The  instrument  varies 
widely  in  its  different  forms;  the  essential  features  which  all  share  consist  in  (a)  a  pair  of  sight  vanes, 
or  equivalent  device,  at  the  extremities  of  the  diameter  of  a  circle  that  revolves  concentrically  with  the 
compass  bowl,  the  line  of  sight  thus  always  passing  through  the  vertical  axis  of  the  compass;  and  (h) 
a  system,  usually  of  mirrors  and  prisms,  by  which  the  point  of  the  compass  card  cut  by  the  vertical 
plane  through  the  line  of  sight — in  other  words,  the  compass  direction — is  brought  into  the  field  of  view 
of  the  person  making  the  observation.  In  some  circles,  for  observing  azimuths  of  the  sun  advantage  is 
taken  of  the  brightness  of  that  body  to  reflect  a  pencil  of  light  upon  the  card  in  such  a  manner  as  to 
indicate  the  bearing;  such  an  azimuth  circle  is  used  in  the  United  States  Navy. 

34.  Binnacles. — Compasses  are  mounted  for  use  in  stands  known  as  Binnacles,  of  which  there  are 
two  principal  types — the  Compensating  and  the  Non-Compensating  Binnacle,  so  designated  according  as 
they  are  or  are  not  equipped  with  appliances  by  which  the  deviation  of  the  compass,  or  error  in  its 
indications  due  to  disturbing  magnetic  features  within  the  ship,  may  be  compensated. 

4  Binnacles  may  be  of  wood  or  of  some  nonmagnetic  metal;  all  contain  a  compass  chamber  within 
.  which  the  compass  is  suspended  in  its  gimbal  ring,  the  knife  edges  upon  which  it  is  suspended  resting 
in  V-shaped  bearings;  an  appropriate  method  is  supplied  for  centering  the  compass.  A  hood  is  proAided 
for  the  protection  of  the  compass  and  for  lighting  it  at  night.  Binnacles  must  be  rigidly  secured  to  the 
deck  of  the  vessel  in  such  position  that  the  lubber's  line  of  the  compass  gives  true  indications  of  the 
direction  of  the  ship's  head. 

The  position  of  the  various  binnacles  on  shipboard  and  the  height  at  which  they  carry  the  compas-^ 
must  be  chosen  with  regard  to  the  purpose  which  the  compass  is  to  serve,  having  in  mind  the  magnetic 
conditions  of  the  ship. 

Compensating  binnacles  contain  the  appliances  for  carrying  the  various  correctors  used  in  the  com- 
pensation of  the  deviation  of  the  compass.     These  consist  of  (a)  a  system  of  permanent  magnets  for 

22489—03 2 


18  INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 

semicircular  deviation,  placed  in  a  magnet  chamber  lying  immediately  beneath  the  compass  chamber, 
so  arranged  as  to  permit  variation  in  the  height  and  direction  of  the  magnets  employed;  (b)  a  pair  of 
arms  projecting  horizontally  from  the  compass  chamber  and  supporting  masses  of  soft  iron  for  quad- 
rantal  deviation;  (c)  a  central  tube  in  the  vertical  axis  of  the  binnacle  for  a  permanent  magnet  used  to 
correct  the  heeling  error,  and  (d)  an  attachment,  sometimes  fitted,  for  securinjj  a  vertical  soft  iron  rod, 
or  "Flinders  bar,"  u^d  in  certain  cases  for  correction  of  a  part  of  the  semicircular  deviation.  An 
explanation  of  the  various  terms  here  used,  together  with  the  method  of  compensating  the  compass, 
will  be  given  in  Chapter  III. 

THE  PELORXJS. 

35.  This  instrument  consists  of  a  circular  plate,  mounted  horizontally  in  gimbals  upon  a  vertical 
standard,  at  some  point  on  board  ship  affording  a  clear  view  for  taking  bearings;  radial  scores  upon  a 
raised  flange  on  the  periphery  of  this  plate  indicate  true  directions  from  its  center  parallel  with  the  keel 
line  of  the  vessel  and  perpendicular  thereto — in  other  words,  lines  of  bearing  directly  ahead,  astern,  and 
abeam.  Eevolving  about  a  common  center,  which  is  also  the  center  of  the  plate,  are  (a)  a  dumb  com- 
pass card,  usually  engraved  on  metal,  whose  face  is  level  with  the  raised  periphery  of  the  plate  on  which 
are  marked  the  scores,  and  (6)  a  pivoted  horizontal  bar  carrying  at  its  extremities  a  pair  of  sight  vanes 
so  arranged  that  the  line  of  sight  always  passes  through  the  vertical  axis  of  the  instrument,  and  having 
an  index  showing  the  point  at  which  the  line  of  sight  cuts  the  dumb  compass.  The  dumb  compass  and 
the  sight-vane  bar  can  each  be  rigidly  clamped. 

The  instrument  is  used  for  taking  bearings,  and  may  be  more  convenient  than  the  compass  for  that 
purpose  because  of  the  better  view  that  it  affords,  as  well  as  because  it  may  be  made  to  eliminate  the 
compass  error  from  observed  bearings.  Suppose  that  the  dumb  compass  be  revolved  until  the  degree  or 
division  which  is  coincident  with  the  right-ahead  score  of  the  plate  is  the  same  as  that  which  is  abreast 
the  lubber's  line  of  the  ship's  compass.  Then  all  directions  indicated  by  the  dumb  compass  will  be 
parallel  to  the  corresponding  directions  of  the  live  one,  and  all  bearings  taken  by  the  pelorus  will  be. 
identical  with  those  taken  by  the  compass  (leaving  out  of  the  question  the  diffence  due  to  the  distance 
that  separates  them).  Suppose,  now,  that  it  is  known  that  the  ship's  compass  has  a  certain  error  and 
that  the  correct  direction  that  we  seek  ( which  is  the  one  indicated  on  the  charts )  is  a  certain  angular 
distance  to  the  right  or  left  of  that  which  the  compass  shows;  if,  in  such  a  case,  instead  of  setting  the 
pelorus  for  the  direction  indicated  by  compass,  we  set  it  for  the  correct  direction  in  which  we  know  the 
ship  to  be  heading,  all  bearings  observed  by  the  pelorus  will  be  correct  bearings  as  given  by  the  chart 
and  may  be  plotted  directly  thereon  without  the  necessity  for  the  intermediate  i)rocess  of  correction  to 
which  the  bearings  shown  by  compass  are  subject.  It  will  at  once  be  evident  that  the  indications  of  the 
pelorus  will  be  accurate  only  when  bearings  are  taken  at  an  instant  when  the  ship  is  heading  exactly  in 
the  direction  for  which  it  is  set,  and  care  must  be  taken  accordingly  in  its  use. 

The  most  modern  types  of  pelorus  are  fitted  for  illuminating  the  dumb  compass,  thus  greatly  facili- 
tating night  work. 

THE  CHART. 

36.  A  nautical  chart  is  a  miniature  representation  upon  a  plane  surface,  in  accordance  with  a  defi- 
nite system  of  projection  or  development,  of  a  portion  of  the  navigable  waters  of  the  world.  It  generally 
incluaes  the  outline  of  the  adjacent  land,  together  with  the  surface  forms  and  artificial  features  that  are 
useful  as  aids  to  navigation,  and  sets  forth  the  depths  of  water,  especially  in  the  near  approaches  to  the 
land,  by  soundings  that  are  fixed  in  position  by  accurate  determinations.  Except  in  charts  of  harbors 
or  other  localities  so  limited  that  the  curvature  of  the  earth  is  inappreciable  on  the  scale  of  construction, 
a  nautical  chart  is  always  framed  over  with  a  network  of  parallels  of  latitude  and  meridians  of  longitude 
in  relation  to  which  the  features  to  be  depicted  on  the  chart  are  located  and  drawn;  and  the  mathematical 
relation  between  the  meridians  and  parallels  of  the  chart  and  those  of  the  terrestrial  sphere  determines 
the  method  of  measurement  that  is  to  be  employed  on  the  chart  and  the  special  uses  to  which  it  is 
adapted 

37.  There  are  three  principal  systems  of  projection  in  use:  (a)  the  Mercator,  (h)  the  polyccmic,  and 
(c)  the  gnomonic;  of  these,  the  Mercator  is  by  far  the  most  generally  used  for  purposes  of  navigation 
proper,  while  the  polyconic  and  the  gnomonic  charts  are  employed  for  nautical  purposes  in  a  more 
restricted  manner,  as  for  plotting  surveys  or  for  facilitating  great  circle  sailing. 

3§.  The  Mercator  Pro.iection. — The  Mercator  Projection,  so  called,  may  be  said  to  result  from 
the  development,  upon  a  plane  surface,  of  a  cylinder  which  is  tangent  to  the  earth  at  the  equator,  the 
various  points  of  the  earth's  surface  having  l:>een  projected  upon  the  cylinder  in  such  manner  as  they 
would  appear  to  an  observer  at  the  earth's  center;  this  method  of  projection  and  development  results 
in  a  characteristic  feature — namely,  that  the  loxodrornic  curve  or  rhumb  line  (art.  6,  Chap.  I)  apjiears  as 
a  right  line  preserving  the  same  angle  of  bearing  with  respect  to  the  intersected  meridians  as  does  the 
ship's  track. 

In  order  to  realize  this  condition,  the  line  of  tangency,  which  coincides  with  the  earth's  equator, 
being  the  circumference  of  a  right  section  of  the  cylinder,  will  appear  as  a  right  line  on  the  develop- 
ment; while  the  series  of  elements  of  the  cylinder  corresponding  to  the  projected  terrestrial  meridians 
will  appear  as  equidistant  right  lines,  parallel  to  each  other  and  perpendicular  to  the  equator  of  the 
chart,  maintaining  the  same  relative  positions  and  the  same  distance  apart  on  that  equator  as  the 
meridians  have  on  the  terrestrial  spheroid.  The  series  of  terrestrial  parallels  will  also  appear  as  a 
system  of  right  lines  parallel  to  each  other  and  to  the  equator,  and  will  so  intersect  the  meridians  as  to 
form  a  system  of  rectangles  whose  altitudes,  for  successive  intervals  of  latitude,  must  be  variable, 
increasing  from  the  equator  in  such  manner  that  the  angles  made  by  the  rhumb  line  with  the  meridian 
on  the  chart  may  maintain  the  required  equality  with  the  (iorresponding  angles  on  the  spheroid. 

39.  Meridional  Parts. — At  the  equator  a  degree  of  longitude  is  equal  to  a  degree  of  latitude,  but 
in  receding  from  the  equator  and  approaching  the  pole,  while  the  degrees  of  latitude  remain  always  of 
the  same  length  (save  for  a  slight  change  due  to  the  fact  that  the  earth  is  not  a  perfect  sphere),  the 
degrees  of  longitude  become  less  and  less. 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION.  19 

Since,  in  the  Mereator  projection,  the  degrees  of  longitude  are  made  to  appear  everywhere  of  the 
same  length,  it  becomes  necessary,  in  order  to  preserve  the  proportion  that  exists  at  different  parts  of 
the  earth's  surface  between  degrees  of  latitude  and  degrees  of  longitude,  that  the  former  be  increased 
from  their  natural  lengths,  and  such  increase  must  become  greater  and  greater  the  higher  the  latitude. 

The  length  of  the  meridian,  as  thus  increased,  between  the  equator  and  any  given  latitude, 
expressed  in  minutes  at  the  equator  as  a  unit,  constitutes  the  number  of  Meridional  Parts  corresponding 
to  that  latitude.  The  Table  of  Meridional  Parts  or  Increased  Latitudes  (Table  3) ,  computed  for  every 
minute  of  latitude  between  0°  and  80°,  affords  facilities  for  constructing  charts  on  the  Mereator  pro- 
jection and  for  solving  problems  in  Mereator  sailing. 

40.  To  Construct  a  Mercator  Chart. — If  the  chart  for  which  a  projection  is  to  be  made  includes 
the  equator,  the  values  to  be  measured  off  are  given  directly  by  Table  3.  If  the  equator  does  not  come 
upon  the  chart,  then  the  parallels  of  latitude  to  be  laid  down  should  be  referred  to  a  principal  parallel, 
preferably  the  lowest  parallel  to  be  drawn  on  the  chart.  The  distance  of  any  other  parallel  of  latitude 
from  the  "principal  parallel  is  then  the  difference  of  the  values  for  the  two  taken  from  Table  3. 

The  values  so  found  may  either  be  measured  off,  without  previous  numerical  conversion,  by  means 
of  a  diagonal  scale  constructed  on  the  chart,  or  they  may  be  laid  down  on  the  chart  by  means  of  any 
properly  divided  scale  of  yards,  meters,  feet,  or  miles^  after  having  been  reduced  to  the  scale  of  proportions 
adopted  for  the  chart. 

If,  for  example,  it  be  required  to  construct  a  chart  on  a  scale  of  one-quarter  of  an  inch  to  five  minutes 
of  arc  on  the  equator,  a  diagonal  scale  may  first  be  constructed,  on  which  ten  meridional  parts,  or  ten 
minutes  of  arc  on  the  equator,  have  a  length  of  half  an  inch. 

It  may  often  be  desirable  to  adapt  the  scale  to  a  certain  allotment  of  paper.  In  this  case,  the  lowest 
and  the  highest  parallels  of  latitude  may  first  be  drawn  on  the  sheet  on  which  the  transfer  is  to  be  made. 
The  distance  between  these  parallels  may  then  be  measured,  and  the  number  of  meridional  parts 
between  them  ascertained.  Dividing  the  distance  by  this  number  will  then  give  the  length  of  one 
meridional  part,  or  the  quantity  by  which  all  the  meridional  parts  taken  from  Table  3  must  be  multi- 
plied. This  quantity  will  represent  the  scale  of  the  chart.  If  it  occurs  that  the  limits  of  longitude  are 
a  governing  consideration,  the  case  may  be  similarly  treated. 

E.K ample:  Let  a  projection  be  required  for  a  chart  of  14°  extent  in  longitude  between  the  parallels 
of  latitude  20°  30^  and  30°  25'',  and  let  the  space  allowable  on  the  paper  between  these  parallels  measure 
10  inches. 

Entering  the  column  in  Table  3  headed  20°,  and  running  down  to  the  line  marked  30'  in  the  side 
column,  will  be  found  1248  9;  then,  entering  the  column  30°,  and  running  down  to  the  line  of  25',  will 
be  found  1905.5.  The  difference,  or  1905.5  —  1248.9  =  656.6,  is  the  value  of  the  meridional  arc  between 
these  latitudes,  forjvhich  1' of  arc  of  the_equator  is  taken  as  the  unit.     On  the  intended  projection, 

therefore,  V  of  arc  of  longitude  will  measure  J—-'.  =  0.0152  inch,  which  will  be  the  scale  of  the  chart. 

606.6 
For  the  sake  of  brevity  call  it  0.015.     By  this  quantity  all  the  values  derived  from  Table  3  will  have  to 
be  multiplied  before  laying  them  down  on  the  projection,  if  they  are  to  be  measured  on  a  diagonal  scale 
of  one  inch. 

Draw  in  the  center  of  the  sheet  a  straight  line,  and  assume  it  to  be  the  middle  meridian  of  the  chart. 
Construct  very  carefully  on  this  line  a  perpendicular  near  the  lower  border  of  the  sheet,  and  assume  this 
perpendicular  to  be  the' parallel  of  latitude  20°  30';  this  will  be  the  southern  inner  neat  line  of  the  chart. 
From  the  intersection  of  the  lines  lay  off  on  the  parallel,  on  each  side  of  the  middle  meridian,  seven 
degrees  of  longitude,  or  distances  each  equal  to  0.015  X  60  X  7  =  6.3  inches;  and  through  the  points  thus 
obtained  draw  parallel  lines  to  the  middle  meridian,  and  these  will  be  the  eastern  and  western  neat  lines 
of  the  chart. 

In  order  to  construct  the  parallel  of  latitude  for  21°  00',  find,  in  Table  3,  the  meridional  parts  for 
21°  00',  which  are  1280.8.  Subtracting  from  this  number  the  number  for  20°  30',  and  multiplying  the 
difference  by  0.015,  we  obtain  0.478  inch,  which  is  the  di.stance  on  the  chart  V)etween  20°  30'  and 
21°  00'.  On  the  meridians  lay  off  distances  equal  to  0.478  inch,  and  through  the  three  points  thus 
obtained  draw  a  straight  line,  which  will  be  the  parallel  of  21°  00'. 

Proceed  in  the  same  manner  to  lay  down  all  the  parallels  answering  to  full  degrees  of  latitude;  the 
distances  will  be  respectively : 

0"'.015X (1344.9—1248.9)  =  1.440  inches, 
0'".015X (1409.5-1248.9)  =2.409  inches, 
0'°.015X  (1474.5-1248.9)  =3.384  inches,  etc. 

Thus  will  be  shown  the  parallels  of  latitude  22°  00',  23°  00',  24°  00',  etc.     Finally,  lay  down  in  the  same 
way  the  parallel  of  latitude  30°  25',  which  will  be  the  northern  inner  neat  line  of  the  chart. 

'  A  degree  of  longitude  will  measure  on  this  chart  0'".015x60=0'".9.  Lay  off,  therefore,  on  the  low- 
est parallel  of  latitude  drawn  on  the  chart,  on  a  middle  one,  and  on  the  highest  parallel,  measuring 
from  the  middle  meridian  toward  each  side,  the  distances  of  0"'.9,  1"'.8,  2"'. 7,  3'". 6,  etc.,  in  order  to 
determine  the  points  where  meridians  answering  to  full  degrees  cross  the  parallels  drawn  on  the  chart. 
Through  the  points  thus  found  draw  the  meridians.  Draw  then  the  outer  neat  lines  of  the  chart  at  a 
convenient  distance  outside  of  the  inner  neat  lines,  and  extend  to  them  the  meridians  and  parallels. 
Between  the  inner  and  outer  neat  lines  of  the  chart  subdivide  the  degrees  of  latitude  and  longitude  as 
minutely  as  the  scale  of  the  chart  will  permit,  the  subdivisions  of  the  degrees  of  longitude  being  found 
by  dividing  the  degrees  into  equal  parts,  and  the  subdivisions  of  the  degrees  of  latitude  being  accu- 
rately found  in  the  same  manner  as  the  full  degrees  of  latitude  previously  described,  though  it  will 
generally  be  found  sufficiently  exact  to  make  even  subdivisions  of  the  degrees,  as  in  the  case  of  the 
longitude. 

The  subdivisions  between  the  two  eastern  as  well  as  those  between  the  two  western  neat  lines  will 
serve  for  measuring  or  estimating  terrestrial  distances.  Distances  between  points  bearing  North  and 
South  of  each  other  may  be  ascertained  by  referring  them  to  the  subdivisions  between  the  same  paral- 
lels.    Distances  represented  by  lines  at  an  angle  to  the  meridians  (loxodromic  lines)  may  be  measured 


X 


20 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


by  taking  between  the  dividers  a  small  number  of  the  subdivisions  near  the  middle  latitude  of  the 
line  to  be  measured,  and  stepping  them  off  on  that  line.  If,  for  instance,  the  terrestrial  length  of  a  line 
running  at  an  angle  to  the  meridians  between  the  parallels  of  latitude  of  24°  00^  and  29°  OC  be  required, 
the  distance  shown  on  the  neat  space  between  26°  15'  and  26°  45^  (  =  30  nautical  miles)  may  be  taken 
between  the  dividers  and  stepped  off  on  that  line. 

41.  Coast  lines  an*  other  positions  are  plotted  on  the  chart  by  their  latitude  and  longitude.  A 
chart  may  be  transferred  from  any  other  projection  to  that  of  Mercator  by  drawing  a  system  of  corre- 
sponding parallels  of  latitude  and"  meridians  over  both  charts  so  close  to  each  other  as  to  form  minute 
squares,  and  then  the  lines  and  characters  contained  in  each  square  of  the  map  to  be  transferred  may 
be  copied  by  the  eye  in  the  corresponding  squares  of  the  Mercator  projection. 

Since  the  unit  of  measure,  the  mile  or  minute  of  latitude,  has  a  different  value  in  every  latitude,  there 
is  an  appearance  of  distortion  in  a  Mercator  chart  that  covers  any  large  extent  of  surface;  for  instance, 
an  island  near  the  j^ole  will  be  represented  as  being  much  larger  than  one  of  the  same  size  near  th6 
equator,  due  to  the  different  scale  used  to  preserve  the  character  of  the  ])rojection. 

42.  The  Polyco.nic  Projection. — This  projection  is  based  upon  the  development  of  the  earth's 
surface  on  a  series  of  cones,  a  different  one  fi>r  each  parallel  of  latitude,  each  one  having  the  parallel  as 
its  base,  and  its  vertex  in  the  pointwhere  a  tangent  to  the  earth  at  that  latitude  intersects  the  earth's  axis. 
The  degrees  of  latitude  and  longitude  on  this  chart  are  projected  in  their  true  length,  and  the  general 
distortion  of  the  figure  is  less  than  in  any  other  method  of  projection,  the  relative  magnitudes  being 
closely  preserved. 

A  straight  line  on  the  polyconic  chart  represents  a  great  circle,  making  a  slightly  different  angle 
with  each  successive  meridian  as  the  meridians  converge  toward  the  pole  and  are  theoretically  curved 
lines;  but  it  is  only  on  charts  of  large  extent  that  this  curvature  is  apparent;  the  parallels  are  also 
curved,  this  fact  being  apparent  to  the  eye  upon  all  excepting  the  largest  scale  charts. 

This  method  of  projection  is  especially  adapted  to  the  plotting  of  surveys;  it  is  also  employed  for 
nearly  all  of  the  charts  of  the  United  States  Coast  and  Geodetic  Survey. 

43.  Gnomonic  Peojectiox. — This  is  based  upon  a  system  in  which  the  plane  of  projection  is  tangent 
to  the  earth  at  some  given  point;  the  eye  of  the  spectator  is  situated  at  the  center  of  the  sphere,  where, 
being  at  once  in  the  plane  of  every  great  circle,  it  will  see  all  such  circles  projected  as  straight  lines 
where  the  visual  rays  passing  through  them  intersect  the  plane  of  projection.  In  a  gnomonic  chart,  a 
straight  line  between  any  two  points  is  projected  as  an  arc  of  a  great  circle,  and  is  therefore  the  shortest 
line  l)etween  those  points. 

Excepting  in  the  Polar  regions,  for  which  latitudes  the  Mercator  projection  can  not  be  constructed, 
the  gnomonic  charts  are  not  used  for  general  navigating  purposes.  Their  greatest  application  is  to  afford 
a  ready  means  of  finding  the  course  and  distance  at  any  time  in  great  circle  sailing,  the  method  of  doing 
which  will  be  explained  in  (^hapter  \". 

44.  Meridiaxs  Employed  in  Chart  Construction. — The  United  States,  England,  Germany,  Italy, 
Russia,  Norway,  Sw^eden,  Denmark,  Holland,  Austria,  Portugal,  and  Japan  adopt  as  a  prime  meridian 
the  meridian  of  Greemvich. 

France  adopts  the  meridian  of  Paris  in  Long.  2°  20''  14'". 5  E.  of  Greenwich. 

Spain  adopts  the  meridian  of  Sun  Fernando,  Cadiz,  in  Long.  6°  12''  20"  W.  of  Greenwich. 

The  Pulkowa  Observatory  of  St.  Petersburg  (sometimes  referred  to  in  Russian  charts)  is  in  Long. 
30°  19'  39''.6  E.  of  Greenwich. 

The  Royal  Observatory  of  Naples  (sometimes  referred  to  in  Italian  charts)  is  in  Long.  14°  14'  06"  V.. 
of  Greenwich. 

The  meridian  of  Genoa  is  8°  55'  21"  E. ;  of  Lisbon,  9°  08'  36"  W. ;  of  Rio  de  Janeiro,  43°  10'  21".2 
W.;  of  Amsterdam,  4°  53'  03". 8  E.;  of  Washington,  77°  03'  56". 7  AV. 

45.  Quality  of  Bottom. — The  following  table  shows  the  qualities  of  the  bottom,  as  expressed  on 
charts  of  various  nations: 


United  States. 


English. 


French. 


Italian. 


Spanish. 


German. 


Clay 

Coral 

Gravel  . . . 

Mud 

Rocky 

C. 

Co. 

G. 

M. 

Sh. 

Sf. 

Clay 

Coral 

Gravel . . . 

Mud 

Rock 

Sand 

Shells  ... 

Stones 

Weed.... 

Fine 

Coarse . . . 

Stiff 

Soft 

Black  ... 

Red 

Yellow  . . 

cl. 

....cri. 

g- 

m. 

....rk. 
s. 

....sh. 

St. 

...wd. 

f. 

c. 

....Stf. 

....sft. 
...blk. 
....rd. 

V 

Argile 

Corail 

Gravier  .. 

Vase 

Roche 

Sable 

Coquille  . 
Pierre.... 

Herb 

Fin 

Gros 

Dure 

Molle.... 

Noire 

Rouge  ... 
Jaune 

....A. 

...Cor. 
....Gr. 

....V. 

....R. 

S. 

..Coq. 

V.  .Vh." 

...fin. 

m. 

n. 

r. 

J- 

Argila 

CoRlllo 

Rena  orGhiaja 

Fango 

Roccia ; . . 

Arcillo  or  Barro 

Coral 

Cascfljo  

Fango  or  Luno . 
I^iedra  or  Roca . 

Arena 

Conchuela 

IMedra 

Alga 

Fina 

Gruesa 

Tenaz 

Muelle 

Negro 

RoJo 

Amarillo 

.cl. 

Co. 

-F. 
..P. 

.A. 
.ca. 
..P. 

.A. 

..f. 

!  Lehm 

Korallen... 
1  Grob  sand  . . 
'  Schlemm  .. 

Fels 

Sand 

Muschel . . . 

Stein. 

Gras 

L. 

K. 

....g.  s. 
....Sch. 
F. 

Sand 

Shells.... 
Stone . 

Sabia  or  Arena 

Conc'higlia 

S. 

M. 

Weed 

Wd. 

Alga 

Fino 

G  rosso 

Tenace 

G. 

Fine 

fne. 

—  crs. 

stf. 

sft. 

bk. 

rd. 

yi. 

gy. 

f. 

Coarse . . . 
Stiff 

1  Grob 

Zahe 

;  Welch 

Schwarz... 

Roth. 

Gelb. 

Soft 

Molle 

W. 

Black  

..schw. 

Red 

Rosse 

Yellow... 

Giallo 

Gray 

INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


21 


46.  Measures  of  Depth. — The  following  table  shows  the  measures  of  depth  employed  in  the  charts 
of  certain  foreign  nations,  with  their  equivalents  in  English  measures: 


1  English  feet.  I     EngH^h 


Austrian fathom  (klafter) . . 

Danish  and  Norwegian fathom  (farn) . . 

Dutch fathom  ( vaden ) . . 

p        ,  /fathom  ( brasse) . . 

^  ^^"^^ \meter  ( metre )  . . . 

Portuguese  . .'. fathom  ( braga) . . 

Prussian fathom  (faden) . . 

Russian fathom  (sajen) . . 

Spanish fathom  (braza ) . . 

Swedish fathom  (famn) . . 


6.222 
6.175 
5.575 
5.329 
3.281 
6.004 
5.906 
6.000 
5.492 
5.843 


fathoms. 


1.030 
1.029 
0.929 
0.888 
0.547 
1.000 
0.984 
1.000 
0.915 
0.974 


The  Dutch  elle,  the  Spanish,  Portuguese,  and  Italian  metro,  and  the  French  vu'tre  are  identical. 

A  pied  usael=l3A2A  inches,  or  1.094  feet.  A  mPtre  is  3  pieds;  a  pied  da  ro/=12.7896  inches;  brasse 
is  used  upon  old  French  charts  instead  of  vii'tre.  I'^pon  some  Italian  charts  soundings  are  in  French 
pieds. 

THE   BAROMETER. 

47.  The  barometer  is  an  instrument  for  measuring  the  pressure  of  the  atmosphere,  and  is  of  great 
service  to  the  mariner  in  affording  a  knowledge  of  existing  meteorological  con- 
ditions and  of  the  probable  changes  therein.     There  are  two  cla.sses  of  barome- 
ter— mercurial  and  aneroid. 

4§.  The  Mercurial  Barometer. — This  instrument,  invented  by  Torricelli 
in  1643,  indicates  the  pressure  of  the  atmosphere  by  the  height  of  a  column 
of  mercury. 

If  a  glass  tube  of  uniform  internal  diameter  somewhat  more  than  30  inches 
in  length  and  closed  at  one  end  be  completely  filled  with  pure  mercury,  and 
then  placed,  open  end  down,  in  a  cup  of  mercury  (the  open  end  having  been 
temporarily  sealed  to  retain  the  liquid  during  the  process  of  inverting),  it  will 
be  found  that  the  mercurv  in  the  tube  will  fall  until  the  top  of  the  colunm  is 
about  30  inches  above  the  level  of  that  which  is  in  the  cup,  leaving  in  the  upper 
part  of  the  tube  a  perfect  vacuum.  Since  the  weight  of  the  colunm  of  mercury 
thus  left  standing  in  the  tube  is  equal  to  the  pressure  by  which  it  is  held  in 
position — namely,  that  of  the  atmospheric  air — it  follows  that  the  height  of  the 
column  is  subject  to  variation  upon  variation  of  that  pressure;  hence  the  mer- 
cury falls  as  the  pressure  of  the  atmosphere  decreases  and  rises  as  that  pres- 
sure increases.  The  mean  pressure  of  the  atmosphere  is  equal  to  nearly  15 
pounds  to  the  square  inch ;  the  mean  height  of  the  barometer  is  about  30  inches. 

49.  In  the  practical  construction  of  the  barometer  the  glass  tube  which 
contains  the  mercury  is  encased  in  a  brass  tube,  the  latter  terminating  at  the 
top  in  a  ring  to  be  used  for  suspension,  and  at  the  bottom  in  a  flange,  to  which 
the  several  i)arts  forming  the  cistern  are  attached.  The  upper  part  of  the  brass 
tube  is  partially  cut  away  to  expose  the  mercurial  column  for  observation ; 
abreast  this  opening  is  fitted  a  scale  for  measuring  the  height,  and  along  the 
scale  travels  a  vernier  for  exact  reading;  the  motion  of  the  vernier  is  controlled 
by  a  rack  and  pinion,  the  latter  having  a  milled  head  accessible  to  the  observer, 
by  which  the  adjustment  is  made.  In  the  mitldle  of  the  brass  tube  is  fixed  a 
thermometer,  the  bulb  of  which  is  covered  from  the  outside  but  open  toward 
the  mercury,  and  which,  being  nearly  in  contact  with  the  glass  tube,  indicates 
the  temperature  of  the  mercury  and  not  that  of  the  external  air;  the  central 
position  of  the  column  is  selected  in  order  that  the  mean  temperature  may  be 
obtained — a  matter  of  importance,  as  the  temperature  of  the  mercurial  colunm 
must  ])e  taken  into  account  in  ever}'  accurate  application  of  its  reading. 

50.  In  the  arrangement  of  further  details  mercurial  barometers  are  di- 
vided into  two  classes,  according  as  they  are  to  be  used  a«  Standards  (lig.  4) 
on  shore,  or  as  Sea  Bcironicter-'i  (fig.  3)  on  shipboard. 

In  the  Standard  Barometer  the  scale  and  vernier  are  so  graduated  as  to 
enable  an  observer  to  read  the  height  of  the  mercurial  column  to  the  nearest 
0.002  inch,  while  in  the  Sea  Barometer  the  reading  can  not  be  made  closer 
than  0.01  inch. 

tThe  instruments  also  differ  in  the  method  of  obtaining  the  true  height  of 
the  mercurial  column  at  varying  levels  of  the  liquid  in  the  cistern.  It  is  evi- 
dent that  as  the  mercury  in  "the  tube  rises,  upon  increase  of  atmospheric  pres- 
sure, the  mercury  in  the  cistern  must  fall;  and,  conversely,  when  the  mercurial 
column  falls  the  amount  of  fluid  in  the  cistern  will  thereby  be  increased  and  a 
Fig  3  ^^^®  ^^  level  will  occur.     As  the  height  of  the  mercurial  colunm  is  required  Yig.  4. 

above  the  existing  level  -in  the  cistern,  some  means  must  be  adopted  to  obtain 
the  true  height  under  varying  conditions.     In  the  Standard  Barometer  the  mercury  of  the  cistern  is 
contained  in  a  leather  bag,  against  the  bottom  of  which  presses  the  point  of  a  vertical  screw,  the  milled 


22 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


head  of  the  screw  projecting  from  the  bottom  of  the  instrument  and  thus  placing  it  under  control  of  the 
observer.  By  this  means  the  surface  of  the  mercury  in  the  cistern  (which  is  visible  through  a  glass 
casing)  may  be  raised  or  lowered  until  it  exactly  coincides  with  that  level  which  is  chosen  as  the  zero 
of  the  scale,  and  which  is  indicated  by  an  ivory  pointer  in  plain  view. 

In  the  Sea  Barometer  there  is  no  provision  for  adjusting  the  level  of  the  cistern  to  a  fixed  point, 
but  compensation  for  tke  Aariable  level  is  made  in  the  scale  graduations;  a  division  representing  an 
inch  on  the  scale  is  a  certain  fraction  short  of  the  true  inch,  proper  allowance  being  thus  made  for  the 
rise  in  level  which  occurs  with  a  fall  of  the  column,  and  for  the  reverse  condition. 

Further  modification  is  made  in  the  Sea  Barometer  to  adapt  it  to  the  special  use  for  which  intended. 
The  tube  toward  its  lower  end  is  much  contracted  to  prevent  the  oscillation  of  the  mercurial  column 
known  as  "pumping,"  which  arises  from  the  motion  of  the  ship;  and  just  below  this  point  is  a  trap  to 
arrest  any  small  bubbles  of  air  from  finding  their  way  upward.  The  instrument  aboard  ship  is  sus- 
pended ill  a  revolving  center-ring,  in  giml)als,  supported  on  a  horizontal  brass  arm  which  is  screwed 
to  the  bulkhead;  a  vertical  position  is  thus  maintained  by  the  tube  at  all  times. 

51.  The  ?'frn(Vr  is  an  attachment  for  facilitating  the  exact  reading  of  the  scale  of  the  barometer, 
and  is  also  applied  to  many  other  instruments  of  precision,  as,  for  example,  the  sextant  and  theodolite. 
It  consists  of  a  metal  scale  similar  in  general  construction  to  that  of  the  instrument  to  which  it  is  fitted, 
and  arranged  to  move  alongside  of  and  in  contact  with  the  main  scale. 

The  general  principle  of  the  vernier  requires  that  its  scale  shall  have  a  total  length  exactly  equal 
to  some  whole  number  of  divisions  of  the  scale  of  the  instrument  and  that  this  length  shall  be  subdivided 
into  a  number  of  parts  equal  to  1  more  or  1  less  than  the  number  of  divisions  of  the  instrument  scale 
which  are  covered;  thus,  if  a  space  of  9  divisions  of  the  main  scale  be  designated  as  the  length  of  the 
vernier,  the  vernier  scale  would  be  divided  into  either  8  or  10  parts. 

Suppose  that  a  barometer  scale  be  divided  into  tenths  of  an  inch  and  that  a  length  of  9 
divisions  of  such  a  scale  be  divided  into  10  parts  for  a  vernier  (fig.  5) ;  and  suppose  that  the 
31  divisions  of  the  vernier  be  numbered  consecutively  from  zero  at  the  origin  to  10  at  the  upper 
extremity.  If,  now,  by  means  of  the  movable  rack  and  pinion,  the  bottom  or  zero  division 
of  the  vernier  be  brought  level  with  the  top  of  the  mercurial  column,  and  that  division  falls 
into  exact  coincidence  with  a  division  of  the  main  scale,  then  the  height  of  the  column  will 
correspond  with  the  scale  reading  indicated.  In  such  a  case  the  top  of  the  vernier  will  also 
exactly  coincide  with  a  scale  division,  but  none  of  the  intermediate  divisions  will  be  evenly 
abreast  of  such  a  division;  the  division  marked  "1"  will  fall  short  of  a  scale  division  by  one- 
tenth  of  1  divison  of  the  scale,  or  by  0.01  inch;  that  marked  "2"  by  two-tenths  of  a  division, 
or  0.02  inch,  and  so  on.  If  the  vernier,  instead  of  having  the  zero  coincide  with  a  scale 
30  division,  has  the  division  "  1 "  in  such  coincidence,  it  follows  that  the  mercurial  column  stands 
at  0.01  inch  above  that  scale  division  which  is  next  below  the  zero;  for  the  division  "2,"  at 
0.02  inch;  and  similarly  for  the  others.  In  the  case  portrayed  in  figure  5,  the  reading  of  the 
column  is  29.81  inches,  the  scale  division  next  below  the  zero  being  29.80  inches,  while  the 
fact  that  the  first  division  is  abreast  a  mark  of  the  scale  shows  that  0.01  inch  must  be  added 
to  this  to  obtain  the  exact  reading. 

Had  an  example  been  chosen  in  which  8  vernier  divisions  covered  9  scale  divisions — that 
is,  where  the  number  of  vernier  divisions  was  1  less  than  the  number  of  scale  divisions 
covered — the  principle  would  still  have  applied.  But,  instead  of  the  length  of  1  division  of 
the  vernier  falling  short  of  a  division  of  the  scale  by  one-tenth  the  length  of  the  latter,  it  would 
have  fallen  beyond  by  one-eighth.  To  read  in  such  a  case  it  would  therefore  be  necessary  to 
number  the  vernier  divisions  from  up  downward  and  to  regard  the  subdivisions  as  ^^  instead 
of  0.01  inch. 

It  is  a  general  rule  that  the  smallest  measure  to  which  a  vernier  reads  is  equal  to  the 
length  of  1  division  of  the  scale  divided  by  the  number  of  divisions  of  the  vernier;  hence,  by  varying 
either  the  scale  or  the  vernier,  we  may  arrive  at  any  subdivision  that  may  be  desired. 

52.  The  Sea  Barometer  is  arranged  as  described  for  the  instrument  assumed  in  the  illustration;  the 
scale  divisions  are  tenths  of  an  inch,  and  the  vernier  has  10  divisions,  whence  it  reads  to  0.01  inch.  It  is 
not  necessary  to  seek  a  closer  reading,  as  complete  accunu->'  is  not  attainable  in  observing  the  height  of  a 
barometer  on  a  vessel  at  sea,  nor  is  it  essential.  The  Standard  Barometer  on  shore,  however,  is  capa- 
ble of  very  exact  reading;  hence  each  scale  division  is  made  equal  to  half  a  tenth,  or  0.05  inch,  while 
a  vernier  covering  24  such  divisions  is  divided  into  25  parts;  hence  the  column  may  be  read  to  0.002  inch. 

53.  To  adjust  the  vernier  for  reading  the  height  of  the  mercurial  column  the  eye  should  be  brought 
exactly  on  a  level  with  the  top  of  the  column;  that  is,  the  line  of  sight  should  be  at  right  angles  to  the 
scale.  When  properly  set,  the  front  and  rear  edges  of  the  vernier  and  the  uppermost  point  of  the  mer- 
cury should  all  be  in  the  line  of  sight.  A  piece  of  white  paper,  held  at  the  back  of  the  tube  so  as  to 
reflect  the  light,  assists  in  accurately  setting  the  Aeniier  by  day,  while  a  small  bull's-eye  lamp  held 
behind  the  instrument  enables  the  observer  to  get  a  correct  reading  at  night.  When  observing  the 
barometer  it  should  hang  freely,  not  being  inclined  by  holding  or  even  by  touch,  because  any  inclina- 
tion will  cause  the  column  to  rise  in  the  tube. 

54.  Other  things  being  equal,  the  mercury  will  stand  higher  in  the  tube  when  it  is  warm  than 
when  it  is  cold,  owing  to  expansion.  For  the  purjxjses  of  comparison,  all  barometric  observations  are 
reduced  to  a  standard  which  assumes  32°  F.  as  the  temperature  of  the  mercurial  column,  and  62°  F.  as 
that  of  the  metal  scale;  it  is  therefore  important  to  make  this  reduction,  as  well  as  that  for  instrumental 
error  (art.  56),  in  order  to  be  enabled  to  compare  the  true  barometric  pressure  with  the  normal  that 
may  be  expected  for  any  locality.     The  following  table  gives  the  value  of  this  correction  for  each  2°  F., 


Fig.  5. 


INSTKUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


23 


the  plus  sign  showing  that  tiie  correction  is  to  be  added  to  the  reading  of  the  ship's  barometer  and  the 
minus  sign  that  it  is  to  be  subtracted: 


Tempera- 
ture. 

Correction. 

Tempera- 
ture. 

Correction. 

Tempera- 
ture. 

Correction. 

Tempera- 
ture. 

Correction. 

o 

Inch. 

o 

Inch. 

o 

Inch. 

o 

Inch. 

20 

+0.02 

40 

-0.03 

60 

-0.09 

80 

-0.14 

22 

+0.02 

42 

-0.04 

62 

-0.09 

82 

-0.14 

24 

+0.01 

44 

-0.04 

64 

,-0.09 

84 

-0.15 

26 

+0.01 

46 

-0.  05 

66 

-0.10 

86 

-0.15 

28 

0.00 

48 

-0.05 

68 

-0.10 

88 

-0.16 

30 

0.00 

50 

-0.06 

70 

-0.11 

90 

-0.16 

32 

-0.  01 

52 

-0.06 

72 

-0.12 

92 

-0.17 

34 

-  0.  02 

54 

-0.07 

74 

-0.12 

94 

-0.17 

36 

-0.02 

56 

-0.07 

76 

-0.13 

1         96 

-0.18 

38. 

-0.03 

58 

-0.08 

78 

-0. 13 

98 

-0.18 

As  an  example,  let  the  ol^served  reading  of  the  mercurial  Vjarometer  be  29.95  inches,  and  the  tem- 
perature as  given  by  the  attached  thermometer  74°;  then  we  have: 

Observed  height  of  the  mercury 29.  95 

Correction  for  temperature  (74° ) —0. 12 

Height  of  the  mercury  at  standard  temperature 29.  83 

55.  The  Aneroid  Barometer. — This  is  an  instrument  in.  which  the  pressure  of  the  air  is  measured 
by  means  of  the  elasticity  of  a  plate  of  metal.  It  consists  of  a  cylindrical  brass  box,  the  metal  in  the 
sides  being  very  thin;  the  contained  air  having  been  partially,  tnough  not  completely,  exhausted,  the 
box  is  hermetically  sealed .  When  the  pressure  of  the  atmosphere  increases  the  inclosed  air  is  compressed, 
the  capacity  of  the  box  is  diminished,  and  the  two  flat  ends  approach  each  other;  when  the  pressure  of 
the  atmosphere  decreases,  the  ends  recede  from  one  another  in  consequence  of  the  expansion  of  the 
inclosed  air.  By  means  of  a  combination  of  levers,  this  motion  of  the  ends  of  the  box  is  communicated 
to  an  index  pointer  which  travels  over  a  graduated  dial  plate,  the  mechanical  arrangement  being  such 
that  the  motion  of  the  ends  of  the  box  is  magnified  many  times,  a  very  minute  movement  of  the  box 
making  a  considerable  difference  in  the  indication  of  the  pointer.  The  graduations  of  the  aneroid  scale 
are  obtained  by  comparison  with  the  correct  readings  of  a  standard  mercurial  barometer  under  normal 
and  reduced  atmospheric  pressure. 

The  thermometer  attached  to  the  aneroid  barometer  is  merely  for  convenience  in  indicating  the 
temperature  of  the  air,  but  as  regards  the  instrument  itself,  no  correction  for  temperature  can  be  applied 
with  certainty.  Aneroids,  as  now  manufactured,  are  almost  perfectly  compensated  for  temperature  by 
the  use  of  different  metals  having  unequal  coefficients  of  expansion;  they  ought,  therefore,  to  show  the 
same  pressure  at  all  temperatures. 

The  aneroid  barometer,  from  its  small  size  and  the  ease  with  which  it  may  be  transported,  can  often 
be  usefully  employed  under  circumstances  where  a  mercurial  barometer  would  not  be  available.  It  also 
has  an  advantage  over  the  mercurial  instrument  in  its  greater  sensitiveness,  and  the  fact  that  it  gives 
earlier  indications  of  change  of  pressure.  It  can,  however,  be  relied  upon  only  when  frequently  com- 
pared with  a  standard  mercurial  barometer;  moreover,  considerable  care  is  required  in  its  handling; 
while  slight  shocks  will  not  ordinarily  affect  it,  a  severe  jar  or  knock  may  change  its  indications  by  a 
large  amount. 

When  in  use  the  aneroid  barometer  may  be  suspended  vertically  or  placed  flat,  but  changing  from 
one  position  to  another  ordinarily  makes  a  sensible  change  in  the  readings;  the  instrument  should 
always,  therefore,  be  kept  in  the  same  position,  and  the  errors  determined  by  comparisons  made  while 
occupying  its  customary  place. 

56.  Comparison  of  Barometers. — To  determine  the  reliability  of  the  ship's  barometer,  whether 
mercurial  or  aneroid,  comparisons  should  from  time  to  time  be  made  with  a  standard  barometer. 
Nearly  all  instruments  read  either  too  high  or  too  low  by  a  small  amount.  These  errors  arise,  in  a 
mercurial  barometer,  from  the  improper  placing  of  the  scale,  lack  of  uniformity  of  caliber  of  the  glass 
tube,  or  similar  causes;  in  an  aneroid,  which  is  less  accurate  and  in  which  there  is  even  more  necessity 
for  frequent  comparisons,  errors  may  be  due  to  derangement  of  any  of  the  various  mechanical  features 
upon  which  its  working  depends.  The  errors  of  the  barometer  should  be  determined  for  various 
heights,  as  they  are  seldom  the  same  at  all  parts  of  the  scale. 

In  the  principal  ports  of  the  world  standard  barometers  are  observed  at  specified  times  each  day, 
and  the  readings,  reduced  to  zero  and  to  sea  level,  are  published.  It  is  therefore  only  necessary  to  read 
the  barometer  on  shipboard  at  those  times,  and,  if  a  mercurial  instrument  is  used,  to  note  the  attached 
thermometer  and  apply  the  correction  for  temperature  (art.  54).  It  is  evident  that  a  comparison  of  the 
heights  by  reduced  standard  and  by  the  ship's  barometer  will  give  the  correction  to  be  applied  to  the 
latter,  including  the  instrumental  error,  the  reduction  to  sea  level,  and  the  personal  error  of  the 
observer.  In  the  United  States,  standard  barometer  readings  are  made  by  the  Weather  Bureau  and 
Branch  Hydrographic  offices. 

Aneroid  barometers  may  be  adjusted  for  instrumental  error  by  moving  the  index  hand,  but  this  is 
usually  done  only  in  the  case  of  errors  of  considerable  magnitude. 

57.  Determination  of  Heights  by  Barometer. — The  barometer  may  be  used  to  determine  the 
difference  in  heights  between  any  two  stations  by  means  of  the  difference  in  atmospheric  pressure 


24 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


between  them.     An  approximate  rule  is  to  allow  0.0011  inch  for  each  difference  in  level  of  one  foot,  or, 
more  roughly,  0.01  inch  for  every  9  feet. 

A  very  exact  method  is  afforded  by  Babinet's  formula.  If  B^  and  B  represent  the  barometric  pres- 
sure (corrected  for  all  sources  of  instrumental  error)  at  the  lower  and  at  the  upper  stations  respectively, 
and  to  and  t  the  corresponding  temperatures  of  the  air;  then, 


Diff.  in  height=Cx 


B„-B 


My 


B„-B' 

if  the  temperatures  be  taken  by  a  Farhenheit  thermometer, 

C  ( in  feet)  =  52,494  (^i+  h+^- 
if  a  centigrade  thermometer  is  used,  ^ 

C  (in  meters)-  10,000(^1-^  V^^. 

THE  THERMOMETER.  * 

58.  The  Thermometer  is  an  instrument  for  indicating  temperature.  In  its  construction  advantage 
is  taken  of  the  fact  that  bodies  are  expanded  by  heat  and  contracted  by  cold.  In  its  most  usual  form 
the  thermometer  consists  of  a  bulb  filled  with  mercury,  connected  with  a  tube  of  very  fine  cross-sectional 
area,  the  liquid  column  rising  or  falling  in  the  tube  according  to  the  volume  of  the  mercury  due  to  the 
actual  degree  of  heat,  and  the  height  of  the  mercury  indicating  upon  a  scale  the  temperature;  the  mer- 
cury contained  in  the  tube  moves  in  a  vacuum  produced  by  the  expulsion  of  the  air  through  boiling  the 
mercury  and  then  closing  the  top  of  the  tube  by  means  of  the  blowpipe. 

There  are  three  classes  of  thermometer,  distinguished  according  to  the  method  of  graduating  the 
scale  as  follows:  the  Fahrenheit,  in  which  the  freezing  point  of  water  is  placed  at  32°  and  its  boiling 
point  (under  normal  atmospheric  pressure)  at  212°;  the  Centifjraxh',  in  which  the  freezing  point  is  at  0° 
and  the  boiling  point  at  100°;  and  the  R'aumur,  in  which  these  points  are  at  0°  and  80°,  respectively. 
The  Fahrenheit  thermometer  is  generally  used  in  the  United  States  and  England.  Tables  will  be 
found  in  this  work  for  the  interconversion  of  the  various  scale  readings  (Table  31). 

59.  The  thermometer  is  a  valuable  instrument  for  the  mariner,  not  only  by  reason  of  the  aid  it 
affords  him  in  judging  meteorological  conditions  from  the  temperature  of  the  air  and  the  amount  of 
moisture  it  contains,  but  also  for  the  evidences  it  furnishes  at  times,  through  the  temperature  of  the  sea 
water,  of  the  ship's  position  and  the  proVjable  current  that  is  being  encountered. 

60.  The  thermometers  employed  in  determining  the  temperature  of  the  air  (wet  and  dry  bulb) 
and  of  the  water  at  the  surface,  should  be  mercurial,  and  of  some  standard  make,  with  the  graduation 

etched  upon  the  glass  stem;  they  should  be  compared 
with  accurate  standards,  and  not  accepted  if  their  read- 
ings vary  more  than  1°  from  the  true  at  any  point  of 
the  scale. 

61.  The  dry-bulb  thermometer  gives  the  tempera- 
ture of  the  free  air.  The  wet-bulb  thermometer,  an 
exactly  similar  instrument  the  bulb  of  which  is  sur- 
rounded by  an  envelope  of  moistened  cloth,  gives  what 
is  known  as  the  temperature  of  evaporation,  whi(;h  is 
always  somewhat  less  than  the  temperature  of  the  free 
air.  From  the  difference  of  these  two  temperatures  the 
observer  may  determine  the  proximity  of  the  air  to 
saturation;  that  is,  how  near  the  air  is  to  that  point 
at  which  it  will  l)e  obliged  to  precipitate  some  of  its 
moisture  (water  vapor)  in  the  form  of  liquid.  With 
the  envelope  of  the  wet  \)\\\h  removed,  the  two  ther- 
mometers should  read  precisely  the  same;  otherwi.se 
hey  are  practically  useless. 

The  two  thermometers,  the  wet  and  the  dry  bulb, 
should  be  hung  within  a  few  inches  of  each  other,  and 
the  surroundings  should  be  as  far  as  possible  identical. 
In  ]iractice  the  two  thermometers  are  generally  inclosed 
within  a  small  lattice  case,  such  as  that  shown  in  figure 
6;  the  case  should  be  placed  in  a  j)osition  on  deck 
remote  from  any  source  of  artificial  heat,  sheltered 
from  the  direct  rays  of  the  .«un,  and  from  the  rain  and 
spray,  but  freely  exposed  to  the  circulation  of  the  air; 
the  door  shouUl  hi  kept  closed  except  during  the  ])roc- 
ess  of  reading.  The  cloth  envelope  of  the  wet  bulb 
should  be  a  single  thickness  of  line  muslin,  tightly 
stretched  over  the  bulb,  and  tied  with  a  fine  thread. 
The  wick  which  serves  to  carry  the  water  from  the 
cistern  to  the  bulb  should  consist  of  a  few  threads  of 
lamp  cotton,  and  should  be  of  sufficient  length  to  admit  of  two  or  three  inches  being  coiled  in  the  cistern. 
The  muslin  envelope  of  the  wet  bulb  should  V)e  at  all  times  thoroughly  moist,  but  not  dripping. 

When  the  temperature  of  the  air  falls  to  32°  F.  the  water  in  the  wick  freezes,  the  capillary  action 
is  at  an  end,  the  bull)  in  con.sequence  soon  becomes  quite  dry,  and  the  thermometer  no  longer  shows 
the  temperature  f)f  evaporation.  At  such  times  the  ImP)  should  be  thoroughly  wetted  with  ice-cold 
water  shortly  before  the  time  of  observation,  using  for  this  purpose  a  camel's  hair  brush  or  feather;  by 


Fig.  6. 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


25 


this  process  the  temperature  of  the  wet  bulb  is  temporarily  raised  above  that  of  the  dry,  but  only  for  a 
brief  time,  as  the  water  quickly  freezes;  and  inasmuch  as  evaporation  takes  place  from  the  surface  of 
the  ice  thus  formed  precisely  as  from  the  surface  of  the  water,  the  thermometer  will  act  in  the  same  way 
as  if  it  had  a  damp  bulb.  The  wet-bulb  thermometer  can  not  properly  read  higher  than  the  dry,  and 
if  the  reading  of  the  wet  bulb  should  be  the  higher,  it  may  always  be  attributed  to  imperfections  in  the 
instruments. 

62.  Knowing  the  temperature  of  the  wet  and  dry  bulbs,  the  relative  humidity  of  the  atmosphere 
at  the  time  of  observation  may  be  found  from  the  following  table: 


Tempera- 
ture of  the 
air,  dry- 

r)ifference  between  dry-bulb  and  wet-bulb  readings. 

bulb  ther- 
mometer. 

1° 

2° 

3° 

40 

5° 

6° 

7° 

.8° 

9° 

10° 

o 

Perct. 

Perct. 

Per  ct. 

Per  ct. 

Per  ct. 

Perct. 

Per  ct. 

Per  ct. 

Per  ct. 

Per  ct. 

24 

87 

75 

62 

50 

38 

26 

26 

88 

76 

65 

63 

42 

30 

28 

89 

78 

67 

56 

45 

34 

24 

30 

90 

79 

68 

58 

48 

38 

28 

32 

90 

80 

70 

61 

51 

41 

32 

23 

34 

90 

81 

72 

63 

53 

44 

35 

.  27 

36 

91 

82 

73 

64 

55 

47 

38 

30 

22 

38 

92 

83 

75 

66 

57 

50 

42 

34 

26 

40 

92 

84 

76 

68 

59 

52 

44 

37 

30 

22 

42 

92 

84 

77 

69 

61 

54 

47 

40 

33 

26 

44 

92 

85 

78 

70 

63 

56 

49 

43 

36 

29 

46 

93 

85 

79 

72 

65 

58 

51 

45 

38 

32 

48 

93 

86 

79 

73 

66 

60 

53 

47 

41 

35 

50 

93 

87 

80 

74 

67 

61 

55 

49 

43 

37 

52 

94 

87 

81 

75 

69 

63 

57 

51 

46 

40 

54 

94 

88 

82 

76 

70 

64 

59 

53 

48 

42 

56 

94 

88 

82 

77 

71 

65 

60 

55 

50 

44 

58 

94 

89 

83 

78 

72 

67 

61 

56 

51 

46 

60 

94 

89 

84 

78 

73 

68 

63 

58 

53 

48 

62 

95 

89 

84 

79 

74 

69 

64 

59 

54 

50 

64 

95 

90 

85 

79 

74 

70 

65 

60 

56 

51 

66 

95 

90 

85 

80 

75 

71 

66 

61 

57 

53 

68 

95 

90 

85 

61 

76 

71 

67 

63 

58 

54 

70 

95 

90 

86 

81 

77 

72 

68 

64 

60 

55 

72 

95 

91 

86 

82 

77 

73 

69 

65 

61 

57 

74 

95 

91 

86 

82 

78 

74 

70 

66 

62 

58 

76 

95 

91 

87 

82 

78 

74 

70 

66 

63 

59 

78 

96 

91 

87 

83 

79 

75 

71 

67 

63 

60 

80 

96 

92 

87 

83 

79 

75 

72 

68 

64 

61 

82 

96 

92 

88 

84 

80 

76 

72 

69 

65 

62 

84 

96 

92 

88 

84 

80 

77 

73 

69 

66 

63 

86 

96 

92 

88 

84 

81 

77 

73 

70 

67 

63 

88 

96 

92 

88 

85 

81 

77 

74 

71 

67 

64 

90 

96 

92 

88 

85 

81 

78 

74 

71 

68 

65 

The  table  may  be  readily  understood.  For  example,  if  the  temperature  of  the  air  (dry  bulb)  be 
60°,  and  the  temperature  of  evapoi'ation  (wet  bulb)  be  56°,  the  difference  being  4°,  look  in  the  column 
headed  "Temperature  of  the  air"  for  60°,  and  for  the  figures  on  the  same  line  in  column  headed  4°; 
here  78  will  be  found,  which  means  that  the  air  is  78  per  cent  saturated  with  water  vapor;  that  is,  that 
the  amount  of  water  vapor  present  in  the  atmosphere  is  78  per  cent  of  the  total  amount  that  it  could 
carry  at  the  given  temperature  (60°).  This  total  amount,  or  saturation,  is  thus  represented  by  100,  and 
if  there  occurred  any  irtcrease  of  the  quantity  of  vapor  beyond  this  point,  the  excess  would  be  precipi- 
tated in  the  form  of  liquid.  Over  the  ocean's  surface  the  relative  humidity  is  generally  about  90  per 
cent,  or  even  higher  in  the  doldrums;  over  the  land  in  dry  winter  weather  it  may  fall  as  low  as  40  per 
cent. 

63.  The  sea  water  of  which  the  temperature  is  to  be  taken  should  be  drawn  from  a  depth  of  3 
feet  below  the  surface,  the  liucket  used  being  weighted  in  order  to  sink  it.  The  bulb  of  the  thermome- 
ter should  remain  immersed  in  the  water  at  least  three  minutes  before  reading,  and  the  reading  should 
be  made  with  the  bulb  immersed. 

THE  LOG  BOOK. 

64.  The  Log  Book  is  a  record  of  the  ship's  cruise,  and,  as  such,  an  important  accessory  in  the  navi- 
gation. It  should  afford  all  the  data  from  which  the  position  of  the  ship  is  established  by  the  method 
of  dead  reckoning;  it  should  also  comprise  a  record  of  meteorological  oteervations,  which  should  be 
made  not  only  for  the  purpose  of  fortelling  the  weather  during  the  voyage,  luit  also  for  contribution  to 
the  general  fund  of  knowledge  of  marine  meteorology. 

65.  A  convenient  form  for  recording  the  data,  which  is  employed  for  the  log  books  of  United  States 
naval  vessels,  is  shown  on  page  26;  beside  the  tabulated  matter  thus  arranged,  to  which  one  page  of  the 
book  is  devoted,  a  narrative  of  the  miscellaneous  events  of  the  day,  written  and  signed  by  the  proper 
officers,  appears  upon  the  ojipcjsite  page. 


26 


INSTRUMENTS    AND    ACCESSORIES    IN    NAVIGATION. 


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INSTRUMEJSTTS    AND    ACCESSORIES    IN    NAVIGATION. 


27 


66.  For  the  most  part,  the  nature  of  the  information  called  for,  with  the  method  of  recording  it, 
will  be  apparent.     A  brief  explanation  is  here  given  of  "such  points  as  seem  to  require  it. 

67.  The  Wind. — In  recording  the  force  of  the  wind  the  scale  devised  by  the  late  Admiral  Sir  F. 
Beaufort  is  employed.  According  to  this  scale  the  wind  varies  from  0,  a  calm,  to  12,  a  hurricane,  the 
greatest  velocity  it  ever  attains.  In  the  lower  grades  of  the  scale  the  force  of  the  wind  is  estimated 
from  the  speed  imparted  to  a  man-of-war  of  the  early  part  of  the  nineteenth  centurj^  sailing  full  and  by; 
in  the  higher  grades,  from  the  amount  of  sail  which  the  same  vessel  could  carry  when  closehauled. 
The  scale,  with  the  estimated  A-elocity  of  the  wind  in  both  statute  and  nautical  miles  per  hour,  is  as 
follows: 


Conditions. 

Velocity. 

Mean  pressure 

in  pounds 

per  square 

foot. 

Foree  of  wind. 

Statute  miles  per 
hour. 

Nautical  miles  per 
hour. 

0.— Calm 

Full-rigged  ship,  all  sails  set,  no  headway. 

.lust  sufficient  to  give  steerage  way 

Speed  of  1  or2knots,  "full  and  by" 

Speed  of  3  or  4  knots,  "  full  and  by  " 

Speed  of  5  or  6  knots,  "full  and  by" 

All  plain  sail,  "  full  and  by" 

0  to    3 
8 
13 
18 
23 
28 
34 
40 
48 

56 

65 

75 

90  and  over. 

0  to    2. 6 
6.9 
11.3 
15.6 
20.0 
24.3 
29.6 
34.7 
41.6 

48.6 

56.4 

65.1 

78. 1  and  over. 

0  03 

1.— Light  air 

2.— Light  breeze 

3.— Gentle  breeze 

4.— Moderate  breeze . . 

0.23 
0.62 
1.2 
1.9 
2  9 

6.— Strong  breeze 

7.— Moderate  gale  — 
8.— Fresh  gale 

9. — Strong  gale 

10.— Whole  gale 

11.— Storm 

Topgallantsails  over  .single-reefed  topsails 

4.2 
5  9 

Treble-reefed  topsails  (or  reefed  upper- 
top.sails  and  courses). 

Close-reefed  topsails  and  courses  (or  lower 
topsails  and  courses). 

Close-reefed  main  topsail  and  reefed  fore- 
sail (or  lower  main  topsail  and  reefed 
foresail). 

8.4 
11.5 
15.5 

20.6 

12. — Hurricane 

Under  bare  poles 

29  6          , 

68.  When  steaming  or  sailing  with  any  considerable  speed,  the  apparent  direction  and  force  of 
the  wind,  as  determined  from  a  vane,  flag,  (jr  pennant  aboard  ship,  may  differ  materially  from  the  true 
direction  and  force,  the  reason  being  that  the  air  appears  to  come  from  a  direction  and  with  a  force 
dependent,  not  only  upon  the  wind  itself,  but  also  upon  the  motion  of  the  vessel.  For  instance, 
suppose  that  the  wind  has  a  velocity  of  20  knots  an  hour  (force  4),  and  take  the  case  of  two  vessels, 
each  steaming  20  knots,  the  first  with  the  wind  dead  aft,  the  second  with  the  wind  dead  ahead.  The 
former  vessel  will  be  moving  with  the  same  velocity  as  the  air  and  in  the  same  direction;  the  velocity 
of  the  wind  relatively  to  the  ship  will  thus  be  zero;  on  the  vessel  an  apparent  calm  will  prevail  and  the 
I^ennant  will  hang  up  and  down.  The  latter  vessel  will  be  moving  with  the  same  velocity  as  the  air,  but 
in  the  opposite  direction;  the  relative  velocity  of  the  two  will  thus  be  the  sum  of  the  two  velocities,  or  40 
knots  an  hour,  and  on  the  second  vessel  the  wind  will  apparently  have  the  velocity  corresponding  very 
nearly  with  a  fresh  gale.  Again,  it  might  be  shown  that  in  the  case  of  a  vessel  steaming  west  at  the 
rate  of  20  knots,  with  the  wind  blowing  from  north  with  the  velocity  of  20  knots  an  hour,  the  velocity 
with  which  the  air  strikes  the  ship  as  a  result  of  the  combined  motion  will  be  28  knots  an  hour,  and 
the  direction  from  which  it  comes  will  be  NW.  If,  therefore,  the  effect  of  the  the  speed  of  the  ship  is 
neglected  the  wind  will  be  recorded  as  NW.,  force  6,  when  in  reality  it  is  north,  force  4. 

In  order  to  make  a  proper  allowance  for  this  error  and  arrive  at  the  true  direction  and  force  of  the 
wind.  Table  32  may  be  entered  with  the  ship's  speed  and  the  apparent  direction  and  force  of  the  wind 
as  arguments,  and  the  true  direction  and  force  wall  be  found. 

69.  AVeather. — To  designate  the  weather  a  series  of  symbols  devised  by  the  late  Admiral  Beaufort 
is  employed.     The  system  is  as  follows: 


b. — Clear  blue  sky. 
c. — Clouds. 

d. — Drizzing,  or  light  rain. 
/. — Fog,  or  foggy  weather. 
g. — Cloomy,  or  dark,  stormy-looking  weather. 
^.— Hail. 
I. — Lightning. 
?». — Misty  weather. 
0. — Overcast. 


p. — Passing  showers  of  rain. 
q. — Squally  weather. 
r. — Eainy  weather,  or  continuous  rain 
s. — Snow,  or  snowv  weather. 
^— Thunder. 
u. 

r. — Visibility  of  distant  objects. 
v. — Wet,  or  heavy  dew. 
z. — Hazv. 


Ugly  appearances,  or  threatening  weather. 
Visib 


To  indicate  great  intensity  of  any  feature,  its  symbol  may  be  underlined;  thus:  r.,  heavy  rain. 

70.  ("LorDS. — The  following  are  the  principal  forms  of  clouds,  named  in  the  order  of  the  altitude 
above  the  earth  at  which  they  usually  occur,  beginning  with  the  most  elevated.  The  symbols  by  which 
each  is  designated  follows  its  name: 

1.  CiRKUs,  (d). ^Detached  clouds,  delicate  and  fibrous  looking,  taking  the  form  of  feathers, 
generally  of  a  white  color,  sometimes  arranged  in  belts  which  cross  a  portion  of  the  sky  in  great  circles, 
and,  by  an  effect  of  perspective,  converging  toward  one  or  two  opposite  points  of  the  horizon. 

2.  Cirro-Stratus,  [CL-S.). — A  thin,  whitish  sheet,  sometimes  completely  covering  the  sky  and 
only  giving  it  a  whitish  appearance,  or  at  others  presenting,  more  or  less  distinctly,  a  formation  like  a 
tangled  web.     This  sheet  often  produces  halos  around  the  sun  and  moon. 

3.  CiRRO-CuMULUs,  {Ci.-Cu.). — Small  globular  masses  or  white  flakes,  having  no  shadows,  or  only 
very  slight  shadows,  arranged  in  groups  and  often  in  lines. 

4.  Alto-Cumulus,  {A.-Cu.). — Rather  large  globular  masses,  white  or  grayish,  partially  shaded, 
arranged  in  groups  or  lines,  and  often  so  closely  packed  that  their  edges  appear  confused.  The  detached 
masses  are  generally  larger  and  more  compact  at  the  center  of  the  group;  at  the  margin  they  form  into 
finer  flakes.     They  often  spread  themselves  out  in  lines  in  one  or  two  directions. 


28  INSTRUMENTS    AND    ACCESSORIES    IN   NAVIGATION. 

5.  Alto-Strati's,  (^1.-»S'.)- — A  thick  sheet  of  a  gray  or  bhiish  color,  showing  a  brilliant  patch  in  the 
neighborhood  of  the  sun  or  moon,  and  which,  without  causing  halos,  may  give  rise  to  corome.  This 
form  goes  through  all  the  changes  like  the  Cirro-Stratus,  but  its  altitude  is  only  half  so  great. 

6.  STRATO-CrMiLrs,  {S.-Ch.). — I^rge  globular  masses  or  rolls  of  dark  cloud,  frequently  covering  the 
whole  sky,  especially  in  winter,  and  occasionally  giving  it  a  wavy  appearance.  The  layer  of  Strato- 
Cumulus  is  not,  as  a  ^jple,  very  thick,  and  patches  of  blue  sky  are  often  visible  through  the  intervening 
spaces.  All  sorts  of  transitions  between  this  form  and  the  Alto-Cumulus  are  noticeable.  It  may  be 
distinguished  from  Nimbus  by  its  globular  or  rolled  appearance  and  also  because  it  does  not  bring  rain. 

7.  Nimbus,  (N.). — Rain  clouds;  a  thick  layer  of  dark  clouds,  without  shape  and  with  ragged  edges, 
from  which  continued  rain  or  snow  generally  falls.  Through  the  openings  of  these  clouds  an  upper 
layer  of  Cirro-Stratus  or  Alto-Stratus  may  almost  invariably  be  seen.  If  the  layer  of  Nimbus  separates 
into  shreds  or  if  small  loose  clouds  are  visible  floating  at  a  low  level  underneath  a  large  nimbus,  they 
may  be  described  as  Fracto-Nimlms  (Fr.-N. ),  the  "scud "  of  sailors. 

8.  Cumulus,  (Cm.). — Wool-pack  clouds;  thick  clouds  of  which  the  upper  surface  is  dome-shaped 
and  exhibits  protuberances,  while  the  base  is  horizontal.  When  these  clouds  are  opposite  the  sun  the 
surfaces  usually  presented  to  the  observer  have  a  greater  brilliance  than  the  margins  of  the  protuber- 
ances. When  the  light  falls  aslant,  they  give  deep  shadows;  when,  on  the  contrary,  the  clouds  are  on 
the  same  side  as  the  sun,  they  appear  dark,  with  bright  edges.  The  true  Cumulus  has  clear  superior 
and  inferior  limits.  It  is  often  broken  up  by  strong  winds,  and  the  detached  portions  undergo  continual 
changes.     These  may  be  distinguished  by  the  name  of  Fracto-Cumulus  (Fr.-(1*«.). 

9.  CuMULO-NiMBus,  ( Cn.-N. ). — The  thunder-cloud  or  shower-cloud;  heavy  masses  of  clouds  rising  in 
the  form  of  mountains,  turrets,  or  anvils,  generally  having  a  sheet  or  screen  of  fibrous  appearance  above, 
and  a  mass  of  clouds  similar  to  Nimbus  underneath.  From  the  base  there  usually  fall  local  showers 
of  rain  or  of  snow  (occasionally  hail  or  soft  hail). 

10.  Stratus,  (»S'.  ). — A  horizontal  sheet  of  lifted  fog;  when  this  sheet  is  broken  up  into  irregular 
shreds  by  the  wind  or  by  the  summits  of  mountains,  it  may  be  distinguished  by  the  name  of  Fracto- 
Stratus  (Fr.-S.). 

71.  In  the  scale  for  the  amount  of  clouds  0  represents  a  sky  which  is  cloudless  and  10  a  sky  which 
is  completely  overcast. 

72.  State  of  Sea. — The  state  of  the  sea  is  expressed  by  the  following  system  of  symbols: 

B. — Broken  or  irregular  sea.  M. — Moderate  sea  or  swell. 

C. — Chopping,  short,  or  cross  sea.  R. — Rough  sea. 

Cr.^Ground  swell.  »S'. — Smooth  sea. 

H. — Heavy  sea.  T. — Tide-rips. 
L. — Long  rolling  sea. 


THE    COMPASS    EREOR.  29 


CHAPTER    III 
THE  COMPASS  EKEOE. 


CAUSES    OF   THE    ERROT. 

73.  When  two  magnets  are  near  enough  together  to  exert  a  mutual  intiuence,  their  properties  are 
such  as  to  cause  those  poles  which  possess  similar  magnetism  to  repel,  and  those  which  possess  magnet- 
ism of  opposite  sorts  to  attract  one  another. 

The  earth  is  an  immense  natural  magnet,  having  in  each  hemisphere  a  pole  lying  in  the  neighbor- 
hood of  the  geographical  pole,  though  not  exactly  coincident  therewith;  consequently,  when  a  magnet, 
such  as  that  of  a  compass,  is  allowed  to  revolve  freely  in  a  horizontal  plane,  it  will  so  place  itself  as  to 
be  i>arallel  to  the  lines  of  magnetic  force  in  that  plane  created  1)y  the  earth's  magnetic  poles,  the 
end  which  we  name  north  pointing  to  the  north,  and  the  south  end  in  the  opposite  direction.  The 
north  end  of  the  compass — north-seeking,  as  it  is  sometimes  designated  for  clearness — will  be  that  end 
Avhich  has  opposite  polarity  to  the  earth's  north  magnetic  pole,  this  latter  possessing  the  same  sort  of 
magnetism  as  the  so-called  south  pole  of  the  comjiass. 

74.  By  reason  of  the  fact  that  the  magnetic  pole  differs  in  position  from  the  geographical  pole,  the 
compass  needle  will  not  indicate  true  directions,  but  each  compass  point  will  differ  from  the  correspond- 
ing true  point  by  an  amount  dependent  upon  the  angle  between  the  geographical  and  the  magnetic  pole 
at  the  position  of  the  observer.  The  amount  of  this  difference,  expressed  in  angular  measure,  is  the 
Variation  of  the  Compass  (sometimes  called  also  the  Declination,  though  this  term  is  seldom  employed  by 
navigators). 

The  variation  not  only  changes  as  one  travels  from  point  to  point  on  the  earth,  being  different  in 
different  localities,  but,  as  it  has  Ijeen  found  that  the  earth's  magnetic  poles  are  in  constant  motion,  it 
undergoes  certain  changes  from  year  to  year.  In  taking  account  of  the  error  it  produces,  the  navigator 
nmst  therefore  be  sure  that  the  variation  used  is  correct  not  only  for  the  place,  but  also  for  the  time 
under  consideration.  The  variation  is  subject  to  a  small  diurnal  fluctuation,  but  this  is  not  a  material 
consideration  with  the  mariner. 

75.  Besides  the  error  thus  produced  in  the  indications  of  the  compass,  a  further  one,  due  to  Local 
Attraction,  may  arise  from  extraneous  influences  due  to  natural  magnetic  attraction  in  the  vicinity  of  the 
vessel.  Instances  of  this  are  quite  common  when  a  ship  is  in  port,  as  she  may  be  in  close  jiroximity  to 
vessels,  docks,  machinery,  or  other  masses  of  iron  or  steel.  It  is  also  encountered  at  sea  in  localities  where 
the  mineral  substan<'es  in  the  earth  itself  possess  magnetic  qualities — as,  for  example,  at  certain  places  in 
Lake  Superior  and  at  others  off  the  coast  of  Australia.  When  due  to  the  last-named  cause,  it  may  be  a 
source  of  great  danger  to  the  mai'iner,  but,  fortunately,  the  number  of  localities  suVjject  to  local  attraction 
is  limited.  The  amount  of  this  error  can  seldom,  if  ever,  be  determined;  if  known,  it  might  properly 
be  included  with  the  variation  and  treated  as  a  part  thereof. 

76.  In  addition  to  the  variation,  the  compass  ordinarily  has  a  still  further  error  in  its  indications, 
which  arises  from  the  effect  exerted  upon  it  by  masses  of  magnetic  metal  within  the  ship  itself.  This 
is  known  as  the  Deviation  of  the  Compass.  For  reasons  that  will  be  explained  later,  it  differs  in  amount 
for  each  heading  of  the  ship,  and,  further,  the  character  of  the  deviations  undergo  modification  as  a 
vessel  proceeds  from  one  geographical  locality  to  another. 

APPLYING  THE  COMPASS  ERROR. 

77.  From  what  has  been  explained,  it  may  be  seen  that  there  are  three  methods  by  which  bearings  or 
courses  may  be  expressed:  (a)  true,  when  they  refer  to  the  angular  distance  from  the  earth's  geographical 
meridian;  \h)  magnetic,  when  they  refer  to  the  angular  distance  from  the  earth's  magnetic  meridian, 
and  must  be  corrected  for  variation  to  be  converted  into  true;  and  (c)  by  compass,  when  they  refer  to 
the  angular  distance  from  the  north  indicated  ))y  the  compass  on  a  given  heading  of  the  ship,  and  must 
be  corrected  for  the  deviation  on  that  heading  for  conversion  to  magnetic,  and  for  both  deviation  and 
variation  for  conversion  to  true  bearings  or  courses.  The  process  of  applying  the  errors  under  all  circum- 
stances is  one  of  which  the  navigator  must  make  himself  a  thorough  master;  the  various  problems  of 
conversion  are  constantly  arising;  no  course  can  be  set  nor  liearing  plotted  without  involving  the  applica- 
tion of  this  problem,  and  a  mistake  in  its  solution  may  produce  serious  consequences.  The  student  is 
therefore  urged  to  give  it  his  most  careful  attention. 


30 


THE    COMPASS    ERROR. 


7§.  When  the  effect  of  a  compass  error,  whether  arising  from  variation  or  from  deviation,  is  to 
draw  the  north  end  of  the  compass  needle  to  the  right,  or  eastward,  the  error  is  named  east,  or  is 
marked  +;  when  its  effect  is  to  draw  the  north  end  of  the  needle  to  the  left  or  westward,  it  is  named 
west,  or  marked  — . 

Figures  7  and  8  represent,  respectively,  examples  of  easterly  and  westerly  errors.      In  both  cases 

consider  that  the  circles  rep- 
resent theobserver's  horizon, 
N  and  S  being  the  correct 
north  and  south  points  in 
each  case.  If  N^ and  S'  repre- 
sent the  corresponding  pomts 
indicated  by  a  compass  whose 
needle  is  deflected  by  a  com- 
pass error,  then  in  the  first 
qa.'-e,  the  north  end  of  the 
needle  being  drawn  to  the 
right  or  east,  the  error  will 
Ije  easterly  or  positive,  and 
in  the  second  case,  the  north 
end  of  the  needle  being  drawn 
to  the  left  or  west,  the  com- 
pass error  will  be  westerly  or 
negative. 

Considering  figure  7,  if 

we  assume  the  easterly  error  to  amount  to  one  point,  it  will  be  seen  that  if  a  direction  of  N.  by  W.  is 
indicated  by  the  compass,  the  correct  direction  should  be  north,  or  one  point  farther  to  the  right.  If 
the  compass  indicates  north,  the  correct  bearing  is  N.  by  E. ;  that  is,  still  one  point  to  the  right. 
If  we  follow  around  the  whole  card,  the  same  relation  will  be  found  in  every  case,  the  corrected  bearing 
being  always  one  point  to  the  right  of  the  compass  bearing.  Conversely,  if  we  regard  figure  8,  assuming 
the  same  amount  of  westerly  error,  a  compass  bearing  of  N.  by  E.  is  the  equivalent  of  a  correct  bearing 
of  north,  which  is  one  point  to  the  left;  and  this  rule  is  general  throughout  the  circle,  the  corrected 
direction  being  always  to  the  left  of  that  shown  by  the  compass. 

79.  Having  once  satisfied  himself  that  the  general  rule  holds,  the  navigator  may  save  the  necessity 
of  reasoning  out  in  each  case  the  direction  in  which  the  error  must  be  applied,  and  need  only  charge 
his  mind  with  some  single  formula  which  will  cover  all  cases.     Such  a  one  is  the  following: 
When  tlie  correct  direction  is  to  tite  right,  the  error  is  east. 

The  words  correct-right-east,  in  such  a  case,  would  be  the  key  to  all  of  his  solutions.  If  he  had  a 
compass  course  to  change  to  a  corrected  one  with  easterlj^  deviation,  he  would  know  that  to  obtain  the 
result  the  error  must  be  applied  to  the  right;  if  it  were  desired  to  change  a  correct  course  to  the  one  indi- 
cated by  compass,  the  error  being  westerly,  the  converse  presents  itself — the  correct  must  be  to  the 
left — the  uncorrected  will  therefore  be  to  the  right;  if  a  correct  bearing  is  to  be  compared  with  a  com- 
pass bearing  to  find  the  compass  error,  when  the  correct  is  to  the  right  the  error  is  east,  or  the  reverse. 
§0.  It  must  be  remembered  that  the  word  east  is  equivalent  to  right  in  dealing  with  the  compass 
error,  and  west  to  left,  even  though  they  involve  an  apparent  departure  from  the  usual  rules.  If  a 
vessel  steers  NE.  by  compass  with  one  point  easterly  error,  her  corrected  course  is  NE.  by  E. ;  but  if 
she  steers  SE.,  the  corrected  course  is  not  SE.  by  E.,  but  SE.  by  S.  Another  caution  may  be  necessary 
to  avoid  confusion;  the  navigator  should  always  regard  himself  as  facing  the  point  under  consideration 
when  he  applies  an  error;  one  point  westerly  error  on  South  will  bring  a  corrected  direction  to  S.  by 
E. ;  but  if  we  applied  one  point  to  the  left  of  South  while  looking  at  the  compass  card  in  the  usual 
way — north  end  up — S.  by  W.  would  be  the  point  arrived  at,  and  a  mistake  of  two  points  would  be  the 
result. 

§1.  In  the  foregoing  explanation  reference  has  been  made  to  "  correct"  directions  and  "  compass 
errors"  without  specifying  "magnetic"  and  "true"  or  "variation"  and  "deviation."  This  has  been 
done  in  order  to  make  the  statements  apply  to  all  cases  and  to  enable  the  student  to  grasp  the  subject 
in  its  general  bearing  without  confusion  of  details. 

Actually,  as  has  already  been  pointed  out,  directions  given  may  be  true,  magnetic,  or  by  compass. 
By  applying  variation  to  a  magnetic  bearing  we  correct  it  and  make  it  true,  by  applying  deviation  to  a 
compass  bearing  we  correct  it  to  magnetic,  and  by  applying  to  it  the  combined  deviation  and  variation 
we  correct  it  to  true.  Whichever  of  these  operations  is  undertaken,  and  whichever  of  the  errors  is 
considered,  the  process  of  correction  remains  the  same;  the  correct  direction  is  always  to  the  right, 
when  the  error  is  east,  by  the  amount  of  that  error. 

Careful  study  of  the  following  examples  will  aid  in  making  the  subject  clear: 

Examples:  A  bearing  taken  by  a  compass  free  from  deviation  is  ,^.  76°  H;  variation,  5°  W. ; 
required  the  true  bearing.     N.  71°  E. 

A  bearing  taken  by  a  similar  compass  is  NW.  bv  W.  i  W. ;  variation,  \  pt.  W. ;  requiretl  the  true 
bearing.     NW.  by  W.  f  W. 

A  vessel  steers  S.  27°  ¥j.  bv  compass;  deviation  on  that  heading,  3°  W. ;  variation  in  the  locality, 
12°  E. ;  required  the  true  course.     S.  18°  E. 

A  vessel  steers  S.  bv  W.  §  W. ;  deviation,  \  pt.  W. ;  variation,  1  pt.  E. ;  required  the  true  course. 
SSW.  \  W. 

It  is  desired  to  steer  the  magnetic  course  N.  38°  W.;  deviation,  4°  E. ;  required  the  course  by  com- 
pass.    N.  42°  W.  ' 

The  true  course  between  two  points  is  found  to  be  W.  \  N. ;  variation  \\  pt.  E. ;  no  deviation; 
required  the  compass  course.     W.  f  S. 

True  course  to  be  made,  N.  55°  E. ;  deviation,  7°  E.;  variation,  14°  W.;  required  the  course  by 
compass.     N.  62°  E. 


THE    COMPASS    ERROR.  31 

A  vessel  passing  a  range  whose  direction  is  known  to  be  S.  20°  W.,  magnetic,  observes  the  bearing 
by  compass  to  be  S.  2°  E. ;  required  the  deviation.     22°  E. 

The  sun's  observed  bearing  l)y  compass  is  S/i89°  E. ;  it  is  found  by  calculation  to  be  N.  84°  E.  (true) ; 
variation,  8°  W.;  required  the  deviation.     1°  E. 

FINDING  THE   COMPASS   EBBOB.  ^ 

§2.  The  variation  of  the  compass  for  any  giveiJ^locality  is  found  from  the  charts.  A  nautical 
chart  always  contains  information  from  which  the  navigator  is  enabled  to  ascertain  the  variation  for 
any  place  within  the  region  embraced  and  for  any  year.  Beside  the  information  thus  to  be  acquired 
from  local  charts,  special  charts  are  published  showing  the  variation  at  all  points  on  the  earth's  surface. 

83.  The  deviation  of  the  compass,  varying  as  it  does  for  every  ship,  for  every  heading,  and  for 
every  geographical  locality,  must  be  determined  by  the  navigator,  for  which  purpose  various  methods 
are  available. 

Whatever  method  is  used,  the  ship  must  be  swung  in  azimuth  and  an  observation  made  on  each  of 
the  headings  upon  which  the  deviation  is  required  to  be  known.  If  a  new  iron  or  steel  ship  is  being 
swung  for  the  first  time,  observations  should  be  made  on  each  of  the  thirty-two  points.  At  later 
swings,  especially  after  correctors  have  been  applied,  or  in  the  case  of  wooden  ships,  sixteen  points 
will  suffice — or,  indeed,  only  eight.  In  case  it  is  not  practicable  to  make  observations  on  exact  compass 
points,  they  should  be  made  as  near  thereto  as  practicable  and  platted  on  the  Napier  diagram  (to  be 
explaine)'!  hereafter),  whence  the  deviations  on  exact  points  may  be  found. 

84.  In  swinging  ship  for  deviations  the  vessel  should  be  on  an  evei^  keel  and  all  movable  masses 
of  iron  in  the  vicinity  of  the  compass  secured  as  for  sea.  The  vessel,  upon  being  placed  on  any  heading, 
should  be  steadied  there  for  three  to  four  minutes  before  the  observation  is  made  in  order  that  the 
compass  card  may  come  to  rest  and  the  magnetic  conditions  assume  a  settled  state.  To  assure  the 
greatest  accuracy  the  ship  should  first  be  swung  to  starboard,  then  to  port,  and  the  mean  of  the  two 
deviations  on  each  course  taken.  Ships  may  be  swung  under  their  own  steam,  or  with  the  assistance 
of  a  tug,  or  at  anchor,  where  the  action  of  the  tide  tends  to  turn  them  in  azimuth  (though  in  this  case 
it  is  difficult  to  get  them  steadied  for  the  recjuisite  time  on  each  heading),  or  at  anchor,  by  means  of 
springs  and  hawsers. 

85.  The  deviation  of  all  compasses  on  the  ship  may  be  obtained  from  the  same  swing,  it  being 
required  to  make  observations  with  the  standard  only.  To  accomplish  this  it  is  necessary  to  record  the 
ship's  head  by  all  compasses  at  the  time  of  steadying  on  each  even  point  of  the  standard;  applying 
the  deviation,  as  ascertained,  to  the  heading  by  standard,  gives  the  magnetic  heads,  with  which  the 
direction  of  the  ship's  head  by  each  other  compass  may  be  compared,  and  the  deviation  thus  obtained. 
Then  a  complete  table  of  deviations  may  be  constructeii  as  explained  in  article  94. 

86.  There  are  four  methods  for  ascertaining  the  deviations  from  swinging;  namely,  by  reciprocal 
hearings,  by  bearings  of  the  sun,  by  ranges,  and  by  a  distant  object. 

87.  Reciproc.vl  Bearings. — One  observer  is  stationed  on  shore  with  a  spare  compass  placed  in  a 
position  free  from  disturbing  magnetic  influences;  a  second  observer  is  at  the  standard  compass  on 
board  ship.  At  the  instant  when  ready  for  observation  a  signal  is  made,  and  each  notes  the  bearing 
of  the  other.  The  bearing  by  the  shore  compass,  reversed,  is  the  magnetic  bearing  of  the  shore  station 
from  the  ship,  and  the  difference  between  this  and  the  bearing  by  the  ship's  standard  compass  repre- 
sents the  deviation  of  the  latter. 

In  determining  the  deviations  of  compasses,  placed  on  the  fore-and-aft  amidship  line,  when  the 
distribution  of  magnetic  metal  to  starboard  and  port  is  symmetrical,  the  shore  compass  may  be  replaced 
by  a  dumb  compass,  or  pelorus,  or  bv  a  theodolite  in  which,  for  convenience,  the  zero  of  the  horizontal 
graduated  circle  may  be  termed  north;  the  reading  of  the  shore  instrument  will,  of  course,  not  represent 
magnetic  directions,  but  by  assuming  that  they  do  we  obtain  a  series  of  fictitious  deviations,  the  mean 
value  of  which  is  the  error  common  to  all.  Upon  deducting  this  error  from  each  of  the  fictitious  devia- 
tions, we  obtain  the  correct  values. 

If  ship  and  shore  observers  are  provided  with  watches  which  have  been  compared  with  one 
another,  the  times  may  be  noted  at  each  observation,  and  thus  afford  a  means  of  locating  errors  due  to 
misunderstanding  of  signals. 

88.  Bearings  of  the  Sun. — In  this  method  it  is  required  that  on  each  heading  a  bearing  of  the 
sun  be  observed  by  compass  and  the  time  noted  at  the  same  moment  by  a  chronometer  or  watch.  By 
means  which  will  be  explained  in  Chapter  XIV,  the  true  bearing  of  the  sun  may  be  ascertained  from 
the  known  data,  and  this,  compared  with  the  compass  bearing,  gives  the  total  compass  error;  deducting 
from  the  compass  error  the  variation,  there  remains  the  deviation.  The  variation  used  may  be  that 
given  by  the  chart,  or,  in  the  case  of  a  compass  affected  only  by  symmetrically  placed  iron  or  steel,  may 
be  considered  equal  to  the  mean  of  all  the  total  errors.  Other  celestial  bodies  may  be  observed  for  this 
purpose  in  the  same  manner  as  the  sun. 

This  method  is  important  as  being  the  only  one  available  for  determining  the  compass  error  at  sea. 

89.  Ranges. —In  many  localities  there  are  to  be  found  natural  or  artificial  range  marks  which  are 
clearly  distinguishable,  anil  which  when  in  line  lie  on  a  known  magnetic  bearing.  By  steaming  about 
on  different  headings  and  noting  the  compass  bearing  of  the  ranges  each  time  of  crossing  the  line  that 
they  mark,  a  series  of  deviations  may  be  obtained,  the  deviation  of  each  heading  being  equal  to  the 
difference  between  the  compass  and  the  magnetic  bearing. 

90.  Distant  Object. — A  conspicuous  object  is  selected  which  must  be  at  a  considerable  distance 
from  the  ship  and  upon  which  there  should  be  some  clearly  defined  point  for  taking  bearings.  The 
direction  of  this  object  by  compass  is  observed  on  successive  headings.  Its  true  or  magnetic  bearing  is 
then  found  and  compared  with  the  compass  bearings,  whence  the  deviation  is  obtained. 

The  true  or  the  magnetic  bearing  may  be  taken  from  the  chart.  The  magnetic  bearing  may  also  be 
found  by  setting  up  a  compass  ashore,  free  from  foreign  magnetic  disturbance,  in  range  with  the  object 
and  the  ship,  and  observing  the  bearing  of  the  object;  or  the  magnetic  bearing  maybe  assumed  to  be  the 
mean  of  the  compass  l)earings. 


32 


THE    COMPASS    ERROK. 


In  choosing  an  oliject  for  use  in  this  method  care  must.be  taken  that  it  is  at  such  a  distance  that  its 
bearing  from  the  shii)does  not  practically  differ  as  the  vessel  swings  in  azimuth.  If  the  ship  is  swung 
at  anchor,  the  distance  should  l)e  not  less  than  6  miles.  If  swung  under  way,  the  object  must  be  so  far 
that  the  parallax  (the  tangent  of  which  may  be  considered  equal  to  half  the  diameter  of  swinging 
divided  by  the  distance)  shall  not  exceed  about  30'. 

91.  in  all  of  the  inethods  described  it  will  be  found  convenient  to  arrange  the  results  in  tabular 
form.  In  one  column  record  the  ship's  head  by  standard  compass,  and  aljreast  it  in  successive  colunms 
the  observations  from  which  the  deviation  is  determined  on  that  heading,  and  finally  write  the  deviation 
itself.  When  the  result  of  the  swing  has  been  worked  up  another  table  is  constructed  showing  simply 
the  lieadings  and  the  corresponding  deviations.  This  is  known  as  the  Deriation  Table  of  the  compass. 
If  compensation  is  to  l)e  attempted,  this  table  is  the  basis  of  the  o])eration;  if  not,  the  deviation  tables 
of  the  standard  and  steering  compass  should  be  posted  in  such  place  as  to  be  accessible  to  all  i^ersons 
concerned  with  the  navigation  of  the  ship. 

92.  Let  it  lie  assumed  that  a  deviation  table  has  been  found  and  that  the  values  are  as  follows: 

Deviation  table. 


Ship's  head  ht 

Devia- 

Ship's head  by 
standard  compass. 

Devia- 

Ship's head  by 

Devia- 

Ship's head  bv 

Devia- 

standard compas.s. 

tion. 

tion. 

standard  compass. 

tion. 

1  standard  compass. 

tion. 

North  .      .      . . 

o         / 

-  1  00 

-  1  50 

East 

E.byS... 

-19  55 
-22  00 

South 

S.  by  W  . . 

0  00 
+  10  20 

West 

o        / 

+19  30 

N.  by  E  . . . 

W.byN... 

+17  00 

NNE 

-  3  00 

ESE 

-23  30 

SSW 

+  17  00 

WNW 

+  13  00 

NE.  by  N . . 

-  5  15 

SE.  bv  E  . 

-24  00 

SW.byS. 

+21  50 

1          NW.byW. 

+11  10 

NE : 

-  7  10 

SE :.... 

-23  30 

SW 

+24  30 

'  NW 

+  7  40 

NE.  by  E . . 

-10  15 

SE.bvS.. 

-20  30 

SW.  bv  W 

T-26  20 

NW.  by  N  . 

+  5  05 

ENE 

-13  05 

SSE 

-16  00 

WSW  .... 

+25  00 

NNW 

+  3  00 

E.by  N  ... 

-17  10 

S.byE... 

-  8  50 

1 

W.bvS.. 

+23  30 

N.byW... 

+  1  00 

AVe  have  from  the  table  the  amount  of  deviation  on  each  compass  heading;  therefore,  knowing  the 
ship's  head  by  compass,  it  is  easy  to  pick  out  the  corresponding  deviation  and  thus  to  obtain  the  mag- 
netic heading.  But  if  we  are  given  the  magnetic  direction  in  which  it  is  desired  to  steer  and  have  to 
find  the  corresponding  compass  course,  the  problem  is  not  so  simple,  for  we  are  not  given  deviations 
on  magnetic  heads,  and  where  the  errors  are  large  it  may  not  be  assumed  that  they  are  the  same  as  on 
the  corresponding  compass  headings.  For  example,  with  the  deviation  ta])le  just  given,  suppose  it  is 
required  to  determine  the  compass  heading  corresponding  to  N.  79°  W.,  magnetic. 

The  deviation  corresponding  to  N.  79°  W.,  per  compass,  is  +  17°  00'.  If  we  apply  this  to  N.  79° 
W.,  magnetic,  we  have  S.  84°  W.  as  the  compass  course.  But,  consulting  the  table,  it  may  be  seen  that 
the  deviation  corresponding  to  S.  84°  W.,  per  compass,  is  +  21  J°,  and  therefore  if  Me  steer  that  course 
the  magnetic  direction  will  be  N.  74^°  AV.,  and  not  N.  79°  W.,  as  desired. 

A  way  of  arriving  at  the  correct  result  is  to  make  a  series  of  trials  until  a  course  is  arrived  at  which 
fulfills  the  conditions.     Thus,  in  the  example  given: 


Mag.  course  required 

Try  dev.  on  X.  79°  W.,  p.  c 


First  trial. 

N.  79°  W. 

17°  E. 


Trial  comp.  course S.  84°  AV. 

Dev.  on  S.  84°  W.,  p.  c 2U°  E. 


Mag.  course  made  good N.  74i°  A\'. 

Since  this  assumption  carries  the  course  4i°  too 
far  to  the  right,  assume  next  a  deviation  on  a 
course  5°  farther  to  the  left  than  tlie  one  used  here. 


Mag.  course  required 

Try  dev.  on  S.  79°  A\'.,  p. 


Trial  comp.  course 
Dev.  onS.  77i°  W. 


p.  c 


/Second  trial. 

N.  79°  AA'. 

.....         23^°  E. 


77 i°  W 
24°  E. 


Mag.  course  made  good X.  782°  AV. 

This  is  as  close  to  the  required  course  as  the  ship 
can  be  steered.  It  may  occur  that  further  trials 
will  be  necessarv  in  some  cases. 


93.  The  Xapier  Diagram. — A  much  more  expeditious  method  for  the  solution  of  this  problem  is 
afforded  by  the  Xapier  Diagram,  and  as  that  diagram  also  facilitates  a  number  of  other  operations  con- 
nected with  compass  work  it  should  be  clearly  understood  by  the  navigator.  This  device  admits  of  a 
graphic  representation  of  the  table  of  deviations  of  the  compass  by  means  of  a  curve;  besides  furnishing 
a  ready  means  of  converting  compass  into  magnetic  courses  and  the  reverse,  one  of  its  chief  merits  is 
that  if  the  deviation  has  been  determined  on  a  certain  number  of  headings  it  enables  one  to  obtain  the 
most  probable  value  of  the  deviation  on  any  other  course  that  the  ship  may  head.  The  last-named 
feature  renders  it  useful  in  making  a  table  of  deviations  of  compasses  other  than  the  standard  when  their 
errors  are  found  as  described  in  article  85. 


THE    COMPASS    ERROR. 


33 


94.  The  Napier  diagram  (fig.  9)  represents  the  margin  of  a  compass  card  cut  at  the  north  point  and 
straightened  into  a  vertical  line;  for  convenience,  it  is  usually  divided  into  two  sections,  representing, 
respectively,  the  eastern  and  western  semicircles.  The  vertical  line  is  of  a  convenient  length  and  di\ided 
into  thirty-two  equal  parts  corresponding  to  the  points  of  the  compass,  beginning  at  the  top  with  North 
and  continuing  around  to  the  right;  it  is  also  divided  into  360  degrees,  which  are  appropriately  marked. 


DEVIATION 

WEST 


DEVIATIOM 
EAST 


DEVIATION 
WEST 


DEVIATION 
EAST 


Fi(4.  9. 


The  vertical  line  is  intersected  at  each  compass  point  l)y  two  lines  inclined  to  it  at  an  angle  of  60°, 
that  line  which  is  inclined  upward  to  the  right  being  drawn  plain  and  the  other  dotted. 

To  pl(jt  a  curve  on  the  Napier  diagram,  if  the  deviation  has  been  observed  with  the  ship's  head  ou 
given  coi/(/)a.s-.s' courses  (as  is  usually  the  case  with  the  standard  compass),  measure  off  on  the  vertical 
scale  the  number  of  degrees  corresponding  to  the  deviation  and  lay  it  down — to  the  right  if  easterly  and 
to  the  left  if  westerly — on  the  dotted  line  passing  through  the  point  representing  the  ship's  head;  or,  if 
the  observation  was  not  made  on  an  even  point,  then  lay  it  down  on  a  line  drawn  parallel  to  the  dotted 
ones  through  that  division  of  the  vertical  line  which  represents  the  compass  heading;  if  the  deviation 
has  been  observed  with  the  ship  on  given  magnetic  courses  (as  when  deviations  by  steering  compass  are 
obtained  by  noting  the  ship's  head  during  a  swing  on  even  points  of  the  standard) ,  proceed  in  the  same 
way,  excepting  that  the  deviation  must  be  laid  down  on  a  plain  line  or  a  line  parallel  thereto.  Mark 
each  point  thus  obtained  with  a  dot  or  small  circle,  and  draw  a  free  curve  passing,  as  nearly  as  possible, 
through  all  the  points. 


224X0—0:";- 


-3 


34 


THE    COMPASS    ERROR. 


To  obtain  a  complete  curve,  a  suflicient  number  of  observations  should  be  taken  while  the  t^hip 
swings  through  an  entire  circle.  Generally,  observations  on  every  alternate  point  are  enough  to  estab- 
lish a  good  curve,  but  in  cases  where  the  maximum  deviation  reaches  40°  it  is  preferable  to  observe  on 
every  i)oint. 

The  curve  shown  in  the  full  line  on  figure  9  corresponds  to  the  table  of  deviations  given  in  article  92. 

From  a  given  compass  course  to  find  the  corresponding  magnetic  course,  through  the  point  of  the  vertical 
line  representing  the  given  compass  course,  draw  a  line  parallel  to  the  dotted  lines  until  the  curve  is 
intersected,  and  from  the  point  of  intersection  draw  another  line  parallel  to  the  plain  lines;  the  point  on 
the  scale  where  this  last  line  cuts  the  vertical  line  is  the  magnetic  course  sought.  The  correctness  of 
this  solution  will  be  ap])arent  when  we  consider  that  the  60°  triangles  are  e(iuilateral,  and  therefore  the 
distance  measured  along  the  vertical  side  will  equal  the  distance  measured  along  the  inclined  sides — 
that  is,  the  deviation;  and  the  direction  will  be  correct,  for  the  construction  is  such  that  magnetic 
directions  will  be  to  the  right  of  compass  directions  when  the  deviation  is  easterly  and  to  the  left  if 
westerly. 

From  a  given  magnetic  course  to  find  the  corresponding  compass  course,  the  process  is  I  Ik  same,  exce])ting 
that  the  first  line  drawn  should  follow,  or  be  parallel  to,  the  plain  lines,  and  the  second,  or  return  line, 
should  be  parallel  to  the  dotted;  and  a  proof  similar  to  that  previously  employed  will  show  the  correctness 
of  the  result.  As  an  example,  the  problem  given  in  article  92  may  be  solved  by  the  diagram,  and  the 
result  will  be  found  to  accord  with  the  solution  previously  given. 

THE  THEORY  OF  DEVIATION."  ' 

95.  Features  of  the  Earth's  MA(iNETisM. — It  has  already  been  stated  that  the  earth  is  an 
immense  natural  magnet,  with  a  pole  in  each  hemisphere  which  is  not  coincident  with  the  geographical 
pole;  it  has  also  a  magnetic  equator  which  lies  close  to,  but  not  coincident  with,  the  geographical 
equator. 

A  magnetic  needle  freely  suspended  at  a  point  on  the  earth's  surface,  and  undisturbed  by  any 
other  than  the  earth's  magnetic  influence,  will  lie  in  the  plane  of  the  magnetic  meridian  and  at  an 
angle  with  the  horizon  depending  upon  the  geographical  position. 

The  magnetic  elements  of  the  earth  which  must  be  considered  are  shown  in  figure  10.  The  earth's 
total  force  is  represented  in  direction  and  intensity  by  the  line  AB.  Since  compass  needles  are  mechan- 
ically arranged  to  move  only  in  a  horizontal  plane,  it  becomes 
necessary,  when  investigating  the  effect  of  the  earth's  mag- 
netism upon  them,  to  resolve  the  total  force  into  two  com- 
ponents which  in  the  figure  are  represented  by  AC  and  AD. 
These  are  known,  respectively,  as  the  horizontal  and  vertical 
components  oi  the  earth's  total  force,  and  are  usually  designated 
as  H  and  Z.  The  angle  CAB,  which  the  line  of  direction 
makes  with  the  plane  of  the  horizon,  is  called  the  magnetic 
inclination  or  dip,  and  denoted  by  0. 

It  is  clear  that  the  horizontal  comj)onent  will  reduce  to 
zero  at  the  magnetic  poles,  where  the  needle  points  directly 
downward,  and  that  it  will  reach  a  maximum  at  the  magnetic 
equator,  where  the  free  needle  hangs  in  a  horizontal  direction. 
The  reverse  is  true  of  the  vertical  component  and  of  the  angle 
of  dip. 

Values  representing  these  different  terms  may  be  found 
from  special  charts. 

96.  Induction;  Hard  and  Soft  Iron. — When  a  piece  of 
unmagnetized  iron  or  steel  is  brought  within  the  influence  of 
a  magnet,  certain  magnetic  properties  are  inunediately  imparted 
to  the  former,  which  itself  becomes  magnetic  and  continues  to 
remain  so  as  long  as  it  is  within  the  sphere  of  influence  of  the 
permanent  magnet;  the  magnetism  that  it  acquires  under  these 
circumstances  is  said  to  he  induced,  and  the  properties  of  induc- 
tion are  such  that  that  end  or  region  which  is  nearest  the  pole 
of  the  influencing  magnet  will  take  up  a  polarity  opposite  thereto.  If  the  magnet  is  withdrawn,  the 
induced  magnetism  is  soon  dissipated.  If  the  magnet  is  brought  into  proximity  again,  but  with  its 
opposite  pole  nearer,  magnetism  will  again  \)e  induced,  but  this  time  its  polarity  will  be  reversed.  A 
further  property  is  that  if  a  piece  of  iron  or  steel,  while  temporarily  possessed  of  magnetic  qualities 
through  induction,  be  subjected  to  blows,  twisting,  or  mechanical  violence  of  any  sort,  the  magnetism 
is  thus  made  to  acquire  a  permanent  nature. 

The  softer  the  metal,  from  a  physical  point  of  view,  the  more  quickly  and  thoroughly  will  induced 
magnetism  be  dissipated  when  the  source  of  influence  is  withdrawn;  hard  metal,  on  the  contrary,  is 
slow  to  lose  the  effect  of  magnetism  imparted  to  it  in  any  way.  Hence,  in  regarding  the  different  features 
which  affect  deviation,  it  is  usual  to  denominate  as  hard  iron  that  which  possesses  retained  magnetism 
of  a  stable  nature,  and  as  soft  iron  that  which  rapidly  accjuires  and  parts  with  its  magnetic  qualities 
under  the  varying  influences  to  which  it  is  subjected. 

97.  Magnetic  Properties  Acqutrkd  by  an  Iron  or  Steel  Vessel  in  Buildinc. — The  inductive 
action  of  the  earth's  magnetism  affects  all  iron  or  steel  within  its  influence,  and  the  amount  and 
permanency  of  the  magnetism  so  induced  depends  upon  the  position  of  the  metal  with  reference  to  the 
earth's  total  force,  upon  its  character,  and  upon  the  degree  or  hammering,  bending,  and  twisting  that  it 
undergoes. 


JforLxonttMl,   Forc^  -  H 


Fig.  10. 


o  As  it  is  probable  that  the  Btudent  will  not  have  practical  need  of  a  knowledge  of  the  theory  of  deviation  and  the 
compensation  of  the  compa.ss  until  after  he  has  mastered  all  other  subjects  pertaining  to  Navigation  and  Nautical 
Astronomy,  it  may  be  considered  preferable  to  omit  the  remainder  of  this  chapter  at  first  and  return  to  it  later. 


THE    COMPASS    EKKOE.  35 

An  iron  bar  held  in  the  line  of  the  earth's  total  force  instantly  becomes  magnetic;  if  held  at  an 
angle  thereto  it  would  acquire  magnetic  properties  dependent  for  their  amount  upon  its  inclination  to 
the  line  of  total  force;  when  held  at  right  angles  to  the  line  there  would  be  no  effect,  as  each  extremity 
would  be  equally  near  the  pf)les  of  the  earth  and  all  influence  would  be  neutralized.  If,  while  such  a 
bar  is  in  a  magnetic  state  through  inductive  action,  it  should  be  hammered  or  twisted,  a  certain  mag- 
netism of  a  permanent  character  is  impressed  upon  it,  which  is  never  entirely  lost  unless  the  bar  i& 
subjected  to  causes  ecpial  and  opposite  to  those  that  produced  the  first  effect. 

A  sheet  of  iron  is  affected  by  induction  in  a  similar  way,  the  magnetism  induced  l)y  the  earth 
diffusing  itself  over  the  entire  plate  and  separating  itself  into  regions  of  opposite  polarity  divided  by  a 
neutral  area  at  right  angles  to  the  earth's  line  of  total  force.  If  the  plate  is  hammered  or  bent,  this 
magnetism  takes  up  a  permanent  character. 

If  the  magnetic  mass  has  a  third  dimension,  and  assumes  the  form  of  a  ship,  a  similar  condition 
prevails.  The  whole  takes  up  a  magnetic  character;  there  is  a  magnetic  axis  in  the  direction  of  the  line 
of  total  force,  with  poles  at  its  extremities  and  a  zone  of  no  magnetism  perpendicular  to  it.  The  distri- 
bution of  magnetism  will  depend  upon  the  horizontal  and  vertical  components  of  the  earth's  force  in 
the  locality  and  upon  the  direction  of  the  keel  in  building;  its  permanency  will  depend  upon_  tho 
amount  of  "mechanical  violence  to  which  the  metal  has  been  subjected  by  the  riveting  and  other  inci- 
dents of  construction,  and  upon  the  nature  of  the  metal  employed. 

98.  Causes  that  Produce  Deviation. — There  are  three  influences  that  operate  to  produce  devia- 
tion; namely,  (o)  si(bpernutneni  magnetism;  (b)  transient  magnetism  induced  in  reHical  soft  iron,  and  (c) 
transient  magnetism  induced  in  horizontal  soft  iron.     Their  effect  will  be  explaineil. 

Suhpernianent  magnetism  is  the  name  given  to  that  magnetic  force  which  originates  in  the  ship  while 
building,  through  the  process  explained  in  the  preceding  article;  after  the  vessel  is  launched  and  has 
an  opportunity  to  swing  in  azimuth,  the  magnetism  thus  induced  will  suffer  material  diminution  until, 
after  the  lapse'  of  a  certain  time,  it  will  settle  down  to  a  condition  that  continues  practically  unchanged; 
the  magnetism  that  remains  is  denominated  subpermanent.  The  vessel  will  then  approximate  to  a 
permanent  magnet,  in  which  the  north  polarity  will  lie  in  that  region  which  was  north  in  building,  and 
the  south  polarity  (that  which  exerts  an  attracting  influence  on  the  north  pole  of  the  compass  needle), 
in  the  region  which  was  south  in  building. 

Transient  magnetism  induced  in  vertical  soft  iron  is  that  developed  in  the  soft  iron  of  a  vessel  through 
the  inductive  action  of  the  vertical  component  only  of  the  earth's  total  force,  and  i.-^  transient  in  nature. 
Its  value  or  force  in  any  given  mass  varies  with  and  depends  upon  the  value  of  the  vertical  component 
at  the  place,  and  is  proportional  to  the  sine  of  the  dip,  being  a  maximum  at  the  magnetic  pole  and  zero 
at  the  magnetic  equator. 

Transient  magnetism  induced  in  horizontal  soft  iron  is  that  developed  in  the  soft  iron  of  a  vessel  through 
the  inductive  action  of  the  horizontal  component  only  of  the  earth's  total  force,  and  is  transient  in 
nature.  Its  value  or  force  in  any  given  mass  varies  with  and  depends  upon  the  value  of  the  horizontal 
component  at  the  place,  and  is  proportional  to  the  cosine  of  the  dip,  being  a  maximum  at  the  magnetic 
equator  and  reducing  to  zero  at  the  magnetic  pole. 

The  needle  of  a  compass  in  any  position  on  board  ship  will  therefore  be  acted  upon  by  the  earth's 
total  force,  together  with  the  three  forces  just  described.  The  poles  of  these  forces  d(j  not  usually  lie  in 
the  horizontal  plane  of  the  compass  needle,  bTit  as  this  needle  is  constrained  to  act  in  a  horizontal  plane, 
its  movements  will  be  affected  solely  by  the  horizontal  component*?  of  these  forces,  and  its  direction  will 
be  determined  by  the  resultant  of  those  components. 

The  earth's  force  operates  to  retain  the  compass  needle  in  the  plane  of  the  magnetic  meridian,  but 
the  resultant  of  the  three  remaining  forces,  when  without  this  plane,  deflects  the  needle,  and  the 
amount  of  such  deflection  constitutes  the  deviation. 

99.  Classes  of  Deviation. — Investigation  has  developed  the  fact  that  the  deviation  produced  as 
described  is  made  up  of  three  parts,  which  are  known  respectively  as  semicircular,  qnadrantal,  and  con- 
stant deviation,  the  latter  being  the  least  important.  A  clear  understanding  of  the  nature  of  each  of 
these  classes  is  essential  for  a  comprehension  of  the  methods  of  compensation. 

100.  Semicircular  Deviation  is  that  due  to  the  combined  influence,  exerted  in  a  horizontal  plane,  of 
the  subpermanent  magnetism  of  a  ship  and  of  the  magnetism  induced  in  soft  iron  by  the  vertical  com- 
ponent of  the  earth's  force.  If  we  regard  the  effect  of  these  two  forces  as  concentrated  in  a  single 
resultant  pole  exerting  an  attracting  influence  upon  the  north  end  of  the  compass  needle,  it  may  be  seen 
that  there  will  be  some  heading  of  the  ship  whereon  that  pole  will  lie  due  north  of  the  needle  and 
therefore  produce  no  deviation;  now  consider  that,  from  this  position,  the  ship's  head  swings  in  azi- 
muth to  the  right;  throughout  all  of  the  semicircle  first  described  an  easterly  deviation  will  be  produced, 
and,  after  completing  180°,  the  pole  will  be  in  a  position  diametrically  opposite  to  that  from  which  it 
started,  and  will  again  exert  no  influence  that  tends  to  produce  deviation.  Continuing  the  swing, 
throughout  the  next  semicircle  the  direction  of  the  deviation  produced  will  be  always  to  the  westward, 
until  the  circle  is  completed  and  the  ship  returns  to  her  original  neutral  position.  From  the  fact  that 
this  disturbing  cause  acts  in  the  two  semicircles  with  equal  and  opposite  effect  it  is  given  the  name  of 
semicircular  deviation. 

In  figure  9,  a  curve  is  depicted  which  shows  the  deviations  of  a  semicircular  nature  separated  from 
those  due  to  other  disturbing  causes,  and  from  this  the  reason  for  the  name  will  be  apparent. 

101.  Returning  to  the  two  distinct  sources  from  which  the  semicircular  deviation  arises,  it  may 
be  seen  that  the  force  due  to  subpermanent  magnetism  remains  constant  regardless  of  tlie  geographical 
position  of  the  vessel;  but  since  the  horizontal  force  of  the  earth,  which  tends  to  hold  the  needle  in  the 
magnetic  meridian,  varies  with  the  magnetic  latitude,  the  deviation  due  to  subpermanent  magnetism 

varies  inversely  as  the  horizontal  force,  or  as  tt;  this  may  be  readily  understood  if  it  is  considered  that 

the  stronger  the  tendency  to  cling  to  the  direction  of  the  magnetic  meridian,  the  less  will  be  the  deflec- 
tion due  to  a  given  disturbing  force.  On  the  other  hand,  that  part  of  the  semicircular  force  due  to 
magnetism  induced  in  vertical  soft  iron  varies  as  the  earth's  vertical  force,  which  is  proportional  to  the 


36  THE    COMPASS    ERROR. 

sine  of  the  dip;  its  effect  in  producing  deviation,  as  in  the  preceding  case,  varies  inversely  as  the  earth's 
horizontal  force — that  is,  inversely  as  the  cosine  of  the  dip;  hence  the  ratio  representing' the  change  of 

deviation  arising  from  this  cause  on  change  of  latitude  is        f.,  or  tan  9. 

If,  then,  we  consider  the  change  in  the  semicircular  deviation  due  to  a  change  of  magnetic  latitude, 
it  will  be  necessary  tt>  separate  the  two  factors  of  the  deviation  and  to  remember  that  the  portion  pro- 

V    duced  bv  subpermanent  magnetism  varies  as      ,  and  that  due  to  vertical  induction  as  tan  0.     But  for 
\  '  H 

any  consideration  of  the  effect  of  this  class  of  deviation  in  one  latitude  only,  the  two  parts  may  be 

joined  together  and  regarded  as  having  a  single  resultant. 

102.  If  we  now  resume  our  former  assumption,  that  all  the  forces  tending  to  produce  semicircular 
deviation  are  concentrated  in  a  single  pole  exerting  an  attracting  influence  upon  the  north  pole  of  the 
compass,  we  maj'  consider  a  line  to  be  drawn  joining  that  theoretical  pole  with  the  center  of  the  com- 
pass, then  the  angle  made  by  this  line  with  the  keel  line  of  the  vessel,  measured  from  right  ahead, 
around  to  the  right  is  called  the  starboard  angle.  From  this  it  follows  that  the  disturbing  force  producing 
semicircular  deviation  may  be  considered  to  have  the  same  effect  as  a  single  magnet  whose  center  is  in 
the  vertical  axis  of  the  compass,  and  whose  south  pole  (attracting  to  the  north  pule  of  the  compass)  is  in 
the  direction  given  by  the  starboard  angle;  if,  therefore,  a  magnet  be  placed  with  its  center  in  the  ver- 
tical axis  of  the  compass,  its  north  (or  repelling)  pole  in  the  direction  of  the  starboard  angle,  and  its 
distance  so  regulated  that  it  exerts  upon  the  compass  a  force  equal  to  that  of  the  ship's  combined  sub- 
permanent  magnetism  and  vertical  induced  magnetism,  the  disturbing  effect  of  these  two  forces  will  be 
counterbalanced,  and,  so  far  as  they  are  concerned,  the  compass  deviations  will  be  corrected,  provided 
that  the  ship  does  not  change  her  magnetic  latitude. 

103.  It  is  evident  that  the  force  of  the  single  magnet  may  be  resolved  into  two  components — one 
fore-and-aft,  and  one  athwartship;  in  this  case,  instead  of  being  represented  by  a  single  magnet  with  its 
south  pole  in  the  starboard  angle,  the  semicircular  forces  will  be  represented  by  two  magnets,  one  fore- 
and-aft  and  the  other  athwartship,  and  compensation 
may  be  made  by  two  separate  magnets  lying  respec- 
tively in  the  directions  stated,  but  with  their  north 
or  repelling  poles  in  the  position  occupied  by  the 
south  or  attracting  poles  of  the  ship's  force. 

Figure  11  represents  the  conditions  that  have  been 
described.  If  O  be  the  center  of  the  compass,  XX'' 
"*  and  YY'',  respectively,  the  fore-and-aft  and  athwart- 
ship lines  of  the  ship,  and  OS  the  direction  in  which 
the  attracting  pole  of  the  disturbing  force  is  exerted, 
then  XOS  is  the  starboard  angle,  usually  designated 
a.  Now,  if  OP  be  laid  off  on  the  line  OS,  represent- 
ing the  amount  of  the  disturbing  force  according  to 
some  convenient  scale,  then  Oh  and  Oc,  respectively, 
represei^t,  on  the  same  scale,  the  resolved  directions 
of  that  force  in  the  keel  line  and  in  the  transverse 
line  of  the  ship.  Each  of  these  resolved  forces  will 
exert  a  maximum  effect  when  acting  at  right  angles 
to  the  needle,  the  athwartship  one  when  the  ship 
Yio.  11.  heads  north  or  south  by  compass,  and  the  longitu- 

dinal one  when  the  heading  is  east  or  west.  On  any 
other  heading  than  those  named  the  deviation  produced  by  each  force  will  be  a  fraction  of  its  maximum 
whose  magnitude  will  depend  upon  the  azimuth  of  the  ship's  head.  The  maximum  deviation  produced, 
therefore,  forms  in  each  case  a  basis  for  reckoning  all  of  the  various  effects  of  the  disturbing  force,  and  is 
called  a  coefficient. 

The  coefficient  of  semicircular  deviation  produced  by  the  force  in  the  fore-and-aft  line  is  called  B, 
and  is  reckoned  as  positive  when  it  attracts  a  north  pole  toward  the  bow,  negative  when  toward  the 
stern;  that  produced  by  the  athwartship  force  is  C,  and  is  reckoned  as  positive  to  starboard  and  nega- 
tive to  port.     These  coefficients  are  expressed  in  degrees. « 

Referring  again  to  figure  11,  it  will  be  seen  that: 

Oc. 


or  (what  may  be  shown  to  be  the  same  thing): 


tan  a-^^^, 


,  sm  C. 

tan  a=  ,  -- 
sin  B 


and  when  the  maximum  deviations  are  small,  this  becomes: 

tan  '^1'=    , 

X) 

Since  the  starboard  angle  is  always  measured  to  the  right,  it  will  be  seen  that,  for  positive  values  of 
B  and  C,  a  will  Ije  between  0°  and  90°;  for  a  negative  B  and  a  positive  C,  between  90°  and  180°;  for 


a  It  should  be  remarked  that  in  a  mathematical  analysis  of  the  deviations,  it  would  be  necessar.v  to  distinguish  between 
the  approximate  coefficients,  B  and  C,  here  described,  as  also  A,  D,  and  E,  to  be  mentioned  later,  and  the  exact  coefficients 
denoted  by  the  corresponding  capital  letters  of  the  German  alphabet.  In  the  practical  discussion  of  the  subject  here  given, 
the  question  of  the  diflference  need  not  be  entered  into. 


THE    COMPASS    ERROE. 


37 


negative  values  of  both  B  and  C,  between  180°  and  270°;  and  for  a  positive  B  and  negative  0,  between 
270°  and  360°. 

104.  The  coefficient  B  is  approximately  equal  to  the  deviation  on  East;  or  to  the  deviation  on 
West  with  reversed  sign;  or  to  the  mean  of  these  two.  Thus  in  the  ship  having  the  table  of  deviations 
previously  given  (art.  92),  B  isequal  to  -19°  55',  or  to  —19°  80',  or  to  ^  (—19°  55'  —19°  30')=  -19°  43'. 

The  coefficient  C  is  approximately  equal  to  the  deviation  on  North;  or  to  the  deviation  on  South 
with  reversed  sign;  or  to  the  mean  of  these  two.  In  the  example  C  is  equal  to  —1°  00'  or  0°  00',  or 
i  (-1°  00'±0°  00')=  -0°  30'. 

105.  The  value  of  the  subpermanent  magnetism  remaining  practically  constant  under  all  condi- 
tions, it  will  not  alter  when  the  ship  changes  her  latitude;  but  that  due  to  induction  in  vertical  softiron 
undergoes  a  change  when,  by  change  of  geographical  position,  the  vertical  component  of  the  earth's 
force  assumes  a  different  value,  and  in  such  case  the  correction  by  means  of  one  or  a  pair  of  permanent 
magnets  will  not  remain  effective.  If,  however,  by  series  of  observations  in  two  magnetic  latitudes,  the 
values  of  the  coefficients  can  be  determined  under  the  differing  circumstances,  it  is  possible,  by  solving 
equations,  to  determine  what  effect  each  force  has  in  producing  the  semicircular  deviation;  having  done 
which,  the  subpermanent  magnetism  can  be  corrected  by  permanent  magnets  after  the  method  previ- 
ously described,  and  the  vertical  induction  in  soft  iron  can  be  corrected  by  a  piece  of  vertical  soft  iron 
placed  in  such  a  position  near  the  compass  as  to  produce  an  equal  but  opposite  force  to  the  ship's  vertical 
soft  iron.     This  last  corrector  is  called  a  Flinders  bur. 

Having  thus  opposed  to  each  of  the  component  forces  a  corrector  of  magnetic  character  identical  with 
its  own,  a  change  of  latitude  will  make  no  difference  in  the  effectiveness  of  the  compensation,  for  in  every 
case  the  modified  conditions  will  produce  identical  results  in  the  disturbing  and  in  the  correcting  force. 

106.  Qiiadrantal,  Deviation  is  that  which  arises  from  horizontal  induction  in  the  soft  iron  of  the 
vessel  through  the  action  of  the  horizontal  component  of  the  earth's  total  force.  Let  us  consider,  in  figure 
12,  the  effect  of  any  piece  of  soft  iron  which  is  symmetrical  with  respect  to  the  compass — that  is,  which 
lies  wholly  within  a  plane  passing  through  the  center  of  the  needle  in  either  a  fore-and-aft  or  an  ath wart- 
ship  direction.  It  may  be  seen  («)  that  such  iron  produces  no  deviation  on  the  cardinal  points  (for 
on  north  and  south  headings  the  fore-and-aft  iron,  though  strongly  magnetized,  has  no  tendency  to  draw 
the  needle  from  a  north-and-south  line,  while  the  athwartship 
iron,  being  at  right  angles  to  the  meridian,  receives  no  magnetic 
induction,  and  therefore  exerts  no  force;  and  on  east  and  west 
headings  similar  conditions  prevail,  the  athwartship  and  the 
fore-and-aft  iron  having  simply  exchanged  positions) ;  and  {li) 
the  direction  of  the  deviation  produced  is  opposite  in  successive 
quadrants.  The  action  of  unsymmetrical  soft  iron  is  not  (juite 
so  readily  apparent,  but  investigation  shows  that  part  of  its  effect 
is  to  produce  a  deviation  which  becomes  zero  at  the  inter-cardinal 
points  and  is  of  opposite  name  in  successive  quadrants.  From 
the  fact  that  deviations  of  this  class  change  sign  every  90° 
throughout  the  circle,  they  gain  the  name  of  qiiadraidal  deviations. 
One  of  the  curves  laid  down  in  the  Napier  diagram  (fig.  11)  is 
that  of  quadrantal  deviations,  whence  the  nature  of  this  disturb- 
ance of  the  needle  may  be  observed. 

107.  All  deviations  produced  by  soft  iron  may  be  considered 
as  fractions  of  the  maximum  deviation  due  to  that  disturbing 
influence;  and  consequently  the  maximum  is  regarded  as  a 
coefficient,  as  in  the  case  of  semicircular  deviations.  The  coeffi- 
cient due  to  symmetrical  soft  iron  is  designated  as  D,  and  is  Fui.  12. 
considered  positive  when  it  produces  easterly  deviations  in  the 

quadrant  between  North  and  P^ast;  the  coefficient  of  deviations  arising  from  unsymmetrical  soft  iron  is 
called  E,  and  is  reckoned  as  positive  when  it  produces  easterly  deviations  in  the  quadrant  between  NW. 
and  NE. ;  this  latter  attains  importance  only  when  there  is  some  marked  inetpiality  in  the  distribution 
of  metal  to  starboard  and  to  port,  as  in  the  case  of  a  compass  placed  off  the  midship  line. 

10§.  1)  is  approximately  equal  to  the  mean  of  the  deviations  on  NE.  and  SW. ;  or  to  the  mean  of 
those  on  SE.  and  NW.,  with  sign  reversed;  or  to  the  mean  of  those  means.  In  the  table  of  deviations 
given  in  article  92,  D  is  equal  to  \  {—1°  10' -  24°  30')  =  J- 8°  40';  or  to  h  (-i-23°  30' —  7°  40') 
=  -f  7°  55';  or  to  ^  ( 4-  8°  40'  +  7°  55')  =  —  8°  23'.  By  reason  of  the  nature  of  the  arrangement  of  iron 
in  a  ship,  D  is  almost  invariably  positive. 

E  is  approximately  P(iual  to  the  mean  of  the  deviations  on  North  and  South;  or  to  the  mean  of  tho.se 
on  East  and  West  with  sign  reversed;  or  to  the  mean  of  those  means.  In  the  example,  E  is  equal  to 
i  (-1°  00'±0°  00')  =  -0°  30';  or  to  \  (+  19°  55'-  19°  30')  =  +  0°  13';  or  to  i  (-0°  30' J-0°  13') 
=  _  0°  09'. 

109.  Quadrantal  deviation  does  not,  like  semicircular,  undergo  a  change  upon  change  of  magnetic 
latitude;  being  due  to  induction  in  horizontal  soft  iron,  the  magnetic  force  exerted  to  produce  it  is  propor- 
tional to  the  horizontal  component  of  the  earth's  magnetism ;  but  the  directive  force  of  the  needle  likewise 
depends  upon  that  same  component;  consequently,  as  the  disturbing  force  exerted  upon  the  needle 
increases,  so  does  the  power  that  holds  it  in  the  magnetic  meridian,  with  the  result  that  on  any  given 
heading  the  deflection  due  to  soft  iron  is  always  the  same. 

no.  Quadrantal  deviation  is  corrected  by  placing  masses  of  soft  iron  (usually  two  hollow  spheres 
in  the  athwartship  line,  at  equal  distances  on  each  side  of  the  compass),  with  the  center  of  mass  in  the 
horizontal  plane  of  the  needle.  The  distance  is  made  such  that  the  force  exerted  exactly  counteracts 
that  of  the  ship's  iron.  As  the  correcting  effect  of  this  iron  will,  like  the  directive  force  and  the  quad- 
rantal disturbing  force,  vary  directly  with  the  earth's  horizontal  component,  the  compensation  once 
properly  made  will  be  effective  in  all  latitudes. 

In  practice,  the  quadrantal  deviation  due  to  unsymmetrical  iron  is  seldom  corrected;  the  correction 
may  be  accomplished,  however,  by  placing  the  soft  iron  masses  on  a  line  which  makes  an  angle  to  the 
athwartship  line  through  the  center  of  the  card. 


38  THE    COMPASS    EEROR. 

111.  Constant  Deviation  is  due  to  induction  in  horizontal  soft  iron  unsymmetrically  placed  about  the 
compass.  It  has  already  been  explained  that  one  effect  of  such  iron  is  to  produce  a  quadrantal  <leviation, 
represented  by  the  coefficient  E;  another  effect  is  the  conMant  deviation,  so  called  because  it  is  uniform 
in  amount  and  direction  on  every  heading  of  the  ship.  If  plotted  on  a  Napier  diagram,  it  would  appear 
as  a  straight  line  parallel  with  the  initial  line  of  the  diagram. 

112.  Like  other  classes  of  deviation,  the  effect  of  the  disturbing  force  is  represented  by  a  coeffi- 
cient; this  coefficient  IS  designated  as  A,  and  is  considered  plus  for  easterly  and  minus  for  westerly  errors. 
It  is  approximately  equal  to  the  mean  of  the  deviations  on  any  number  of  equidistant  headings.  In  the 
case  previously  given,  it  might  be  found  from  the  four  headings,  North,  p]ast,  South,  and  West,  and 
would  then  be  equal  to  i  (  -1°  00^-19°  55^±0°  (KK-f  19°  3(K)=— 0°  2V;  or  from  all  of  the  32  headings, 
when  it  would  equal  -f  0°  16^. 

For  the  same  reason  as  in  the  case  of  E,  the  value  of  A  is  usually  so  small  that  it  may  be  neglected; 
it  only  attains  a  material  size  when  the  compass  is  placed  off  the  midship  line,  or  for  some  similar 
cause. 

113.  Like  quadrantal  deviation,  since  its  force  varies  with  the  earth's  horizontal  force,  the  con- 
stant deviation  will  remain  uniform  in  amount  in  all  latitudes. 

No  attempt  is  made  to  compensate  this  class  of  error. 

114.  Coefficients. — The  chief  value  of  coefficients  is  in  mathematical  analyses  of  the  deviations 
and  their  causes.  It  may,  however,  be  a  convenience  to  the  practical  navigator  to  find  their  approxi- 
mate values  by  the  methods  that  have  been  given,  in  order  that  he  may  gain  an  idea  of  the  various 
sources  of  the  error,  with  a  view  to  ameliorating  the  conditions,  when  necessary,  by  moving  the  bin- 
nacle or  altering  the  surrounding  iron.  The  following  relation  exists  between  tbe  coefficients  and  the 
deviation: 

d=A  +  B  sin  z'  +  C  cos  z'  +  D  sin  'Zi/  +  K  cos  2z^, 

where  d  is  the  deviation,  and  s/  the  ship's  heading  by  compass,  measured  from  compass  North. 

115.  Me.\n  Directive  Force. — The  effect  of  the  disturbing  forces  is  not  confined  to  causing  devi- 
ations; it  is  only  those  components  acting  at  right  angles  to  the  needle  which  oi)erate  to  produce 
deflection;  the  effect  of  those  acting  in  the  direction  of  the  needle  is  exerted  either  in  increasing  or 
diminishing  the  directive  force  of  the  compass,  according  as  the  resolved  component  is  northerly  or 
southerly. 

It  occurs,  with  the  usual  arrangement  of  iron  in  a  vessel,  that  the  mean  effect  of  this  action 
throughout  a  complete  swing  of  the  ship  upon  all  headings  is  to  reduce  the  directive  force — that  is, 
while  it  varies  with  the  heading  the  average  value  upon  all  azimuths  is  minus  or  southerly.  The  result 
of  such  a  condition  is  unfavorable  from  the  fact  that  the  compass  is  thus  made  more  "sluggish,"  is 
easily  disturbed  and  does  not  return  quickly  to  rest,  and  a  given  deflecting  force  produces  a  greater 
deviation  when  the  directive  force  is  reduced.  The  usual  methods  of  compensation  largely  correct  this 
fault,  but  do  not  entirely  do  so;  it  is  therefore  the  case  that  the  mean  combined  horizontal  force  of  earth 
and  ship  to  north  is  generally  less  than  the  horizontal  force  of  the  earth  alone;  but  it  is  only  in  extreme 
cases  that  this  deficiency  is  serious. 

116.  Heeling  Error. — This  is  an  additional  cause  of  deviation  that  arises  when  the  vessel  heels  to 
one  side  or  the  other.  Heretofore  only  those  forces  have  been  considered  which  act  when  the  vessel  is 
on  an  even  keel;  but  if  there  is  an  inclination  from  the  vertical  certain  new  forces  arise,  and  others 
previously  inoperative  become  effective.  These  forces  are  (a)  the  vertical  com])onent  of  the  subperma- 
nent  magnetism  acquired  in  building;  (b)  the  vertical  component  of  the  induced  magnetism  in  vertical 
soft  iron,  and  {(■)  the  magnetism  induced  by  the  vertical  component  of  the  earth's  total  force  in  iron 
which,  on  an  even  keel,  Mas  horizontal.  The  first  two  of  these  disturbing  causes  are  always  present, 
but,  when  the  ship  is  upright,  have  no  tendency  to  produce  deviation,  simply  exerting  a  downward 
pull  on  one  of  the  poles  of  the  needle;  the  last  is  a  new  force  that  arises  when  the  vessel  heels. 

The  maximum  disturbance  due  to  heel  occurs  when  the  ship  heads  North  or  South.  When  heading 
East  or  AVest  there  will  be  no  deviation  produced,  although  the  directive  force  of  the  needle  will  be 
increased  or  diminished.     The  error  will  increase  with  the  amount  of  inclination  from  the  vertical. 

117.  For  the  same  reason  as  was  explained  in  connection  with  semicircular  deviations,  that  part  of 

the  heeling  error  due  to  subpermanent  magnetism  will  vary,  on  change  of  latitude,  as     ,  while  that 

H 

due  to  vertical  induction  will  vary  as  tan  0.     In  south  magnetic  latitude  the  effect  of  vertical  induction 

will  be  opposite  in  direction  to  what  it  is  in  north. 

118.  The  heeling  error  is  corrected  by  a  ])ermanent  magnet  placed  in  a  vertical  position  directly 
under  the  center  of  the  compass.  Such  a  magnet  has  no  effect  upon  the  compass  when  the  ship  is 
upright;  but  since  its  force  acts  in  an  opjwsite  direction  to  the  force  of  the  ship  which  causes  heeling 
error,  is  equal  to  the  latter  in  amount,  and  is  exerted  under  the  same  conditions,  it  affords  an  effective 
compensation.  For  similar  reasons  to  those  affecting  the  compensation  of  B  and  C,  the  correction  by 
means  of  a  permanent  magnet  is  not  general,  and  nmst  be  rectified  upon  change  of  latitude. 

PRACTICAL  COMPENSATION. 

119.  In  the  course  of  explanation  of  the  different  classes  of  deviation  occasion  has  been  taken  to 
state  generally  the  various  methods  of  compensating  the  errors  that  are  produced.  The  practical 
methods  of  applying  the  correctors  will  next  be  given. 

120.  Order  of  Correction. — The  following  is  the  order  of  steps  to  be  followed  in  each  case.  It 
is  assumed  that  the  vessel  is  on  an  even  keel,  that  all  surrounding  ma.sses  of  iron  or  steel  are  in  their 
normal  positions,  all  correctors  removed,  and  that  the  binnacle  is  one  in  which  the  semicircular 
deviation  is  corrected  by  two  sets  of  permanent  magnets  at  right  angles  to  each  other. 

1.  Place  quadrantal  correctors  by  estimate. 

2.  Correct  semicircular  deviations. 


THE    COMPASS    ERROR.  39 

3.  Correct  quadrantal  deviations. 

4.  Swing  ship  for  residual  deviations. 

The  heeling  corrector  may  be  placed  at  any  time  after  the  semicircular  and  quadrantal  errors  are 
corrected.     A  Flinders  bar  can  be  put  in  place  only  after  observations  in  two  latitudes. 

121.  The  ship  is  first  placed  on  some  magnetic  cardinal  point.  If  North  or  South,  the  only  force 
(theoretically  speaking)  which  tends  to  produce  deflection  of  the  needle  will  be  the  athwartship  com- 
ponent of  the  semicircular  force,  whose  effect  is  represented  by  the  coefficient  C  If  East  or  West,  the 
only  deflecting  force  will  be  the  fore-and-aft  component  of  the  semicircular  force,  whose  effect  is  repre- 
sented by  the  coefficient  B.  This  will  be  apparent  from  a  consideration  of  the  direction  of  the  forces 
producing  deviation,  and  is  also  shown  by  the  equation  connecting  the  terms  (where  A  and  E  are  zero) : 

(7  =  B  sin  2^  +  C  cos  2'  +  D  sin  2z'. 

If  the  ship  is  headed  North  or  South,  z'  being  equal  to  0°  or  180°,  the  equation  becomes  d  =  ±  C. 
If  on  East  or  West,  z'  being  90°  or  270°,  we  have  d  =  i  B. 

This  statement  is  exact  if  we  regard  only  the  forces  that  have  been  considered  in  the  problem,  but 
experience  has  demonstrated  that  the  various  correctors  when  in  place  create  certain  additional  forces 
by  their  mutual  action,  and  in  order  to  correct  the  disturbances  thus  accidentally  produced,  as  well  as 
those  due  to  regular  causes,  it  is  necessary  that  the  magnetic  conditions  during  correction  shall  approxi- 
mate as  closely  as  possible  to  those  that  exist  when  the  compensation  is  completed;  therefore  the  quad- 
rantal correctors  should  first  be  placed  on  their  arms  at  the  positions  which  it  is  estimated  that  they 
will  occupy  later  when  exactly  located.  An  error  in  the  estimate  will  have  but  slight  effect  under 
ordinary  conditions.  It  should  be  understood  that  the  placing  of  these  correctors  has  no  corrective 
effect  while  the  ship  is  on  a  cardinal  point.  Its  object  is  to  create  at  once  the  magnetic  field  with  which 
we  shall  have  to  deal  when  compensation  is  perfected. 

This  having  been  done,  proceed  to  correct  the  semicircular  deviation.  If  the  ship  heads  North  or 
South,  the  force  producing  deflection  is,  as  has  been  stated,  the  athwartship  component  of  the  semi- 
circular force,  which  is  to  be  corrected  by  permanent  magnets  placed  athwartships;  therefore  enter  in 
the  binnacle  one  or  more  such  magnets,  and  so  adjust  tlieir  height  that  the  heading  of  the  ship  by 
compass  shall  agree  with  the  magnetic  heading.  When  this  is  done  all  the  deviation  on  that  azimuth 
will  be  corrected. 

Similarly,  if  the  ship  heads  East  or  West,  the  force  producing  deviation  is  the  fore-and-aft  com- " 
ponent  of  the  semicircular  force,  and  this  is  to  be  corrected  by  entering  fore-and-aft  permanent  magnets 
in  the  binnacle  and  adjusting  the  height  so  that  the  deviation  on  that  heading  disappears. 

With  the  deviation  on  two  adjacent  cardinal  points  corrected,  the  semicircular  force  has  been  com- 
pletely compensated.  Next  correct  the  quadrantal  deviation.  Head  the  ship  NE.,  SH,  SW.,  or  NW. 
The  coefficients  B  and  C  having  been  reduced  to  zero  by  compensation,  and  2z' ,  on  the  azimuths  named, 
being  equal  to  90°  or  270°,  the  equation  becomes  d  =  =b  D.  The  soft-iron  correctors  are  moved  in  or 
out  from  the  positions  in  which  they  were  placed  by  estimate  until  the  deviation  on  the  heading  (all  of 
which  is  due  to  quadrantal  force)  disappears.     The  quadrantal  disturbing  force  is  then  compensated. 

122.  Deter.mixation  of  Magnetic  Headings. — To  determine  when  the  ship  is  heading  on  any 
given  magnetic  course,  and  thus  to  know  when  the  deviation  has  been  corrected  and  the  correctors  are 
in  proper  position,  four  methods  are  available: 

(a)  Swing  the  ship  and  obtain  by  the  best  available  method  the  deviations  on  a  sufficient  number 
of  compass  courses  to  construct  a  curve  on  the  Napier  diagram  for  one  quadrant,  and  thus  find  the  com- 
pass headings  corresponding  to  two  adjacent  magnetic  cardinal  points  and  the  intermediate  intercardinal 
point,  as  North,  NE.,  and  East,  magnetic."  Then  put  the  ship  successively  on  these  courses,  noting  the 
corresponding  headings  by  some  other  compass,  and  when  it  is  desired  to  head  on  the  various  magnetic 
azimuths  during  the  process  of  correction  the  ship  may  be  steadied  upon  them  by  the  auxiliary  com- 
pass. Variations  of  this  method  will  suggest  themselves  and  circumstances  may  render  their  adoption 
convenient.  The  compass  courses  corresponding  to  the  magnetic  directions  may  be  obtained  from 
observations  made  with  the  auxiliary  compass  itself,  or  while  making  observations  with  another  com- 
pass the  headings  by  the  auxiliary  may  be  noted  and  a  curve  for  the  latter  constructed,  as  explained 
in  article  94,  and  the  required  headings  thus  deduced. 

(6)  By  the  methods  to  be  explained  hereafter  (Chap.  XIV),  ascertain  in  advance  the  true  bearing 
of  the  sun  at  frequent  intervals  during  the  period  which  is  to  be  devoted  to  the  compensation  of  the 
compasses;  apply  to  these  the  variation  and  obtain  the  magnetic  bearings;  record  the  times  and 
bearings  in  a  convenient  tabular  form;  set  the  watch  accurately  for  the  local  apparent  time;  then 
when  it  is  required  to  steer  any  given  magnetic  course,  set  that  point  of  the  pelorus  for  the  ship's 
head  and  set  the  sight  vanes  for  the  magnetic  bearing  of  the  sun  corresponding  to  the  time  by  watch. 
Maneuver  the  ship  with  the  helm  until  the  sun  comes  on  the  sight  vanes,  when  the  azimuth  of  the 
ship's  head  will  be  that  which  is  required.  The  sight  vanes  must  be  altered  at  intervals  to  accord  with 
the  table  of  times  and  bearings. 

(c)  Construct  a  table  showing  times  and  corresponding  magnetic  bearings  of  the  sun,  and  also  set 
the  watch,  as  explained  for  the  previous  method.  Then  place  the  sight  vanes  of  the  azimuth  circle  of 
the  compass  at  the  proper  angular  distance  to  the  right  or  left  of  the  required  azimuth  of  the  ship's 
head;  leave  them  so  set  and  maneuver  the  ship  with  the  helm  until  the  image  of  the  sun  comes  on  with 
the  vanes.  The  courserwill  then  be  the  required  one.  As  an  example,  suppose  that  the  table  shows  that 
the  magnetic  azimuth  of  the  sun  at  the  time  given  by  the  watch  is  N.  87°  E.,  and  let  it  be  required  to 
head  magnetic  North;  when  placed  upon.this  heading,  therefore,  the  sun  must  bear  87°  to  the  right,  or 
east,  of  the  direction  of  the  ship's  head;  when  steady  on  any  course,  turn  the  sight  vane  to  the  required 
bearing  relative  to  the  keel.     If  on  N.  11°  W.,  for  example,  turn  the  circle  to  N.  76°  E.;  leave  the  vane 

"This  is  all  that  is  required  for  the  purposes  of  compensation,  but  if  there  is  opportunity  it  is  always  well  to  make  a 
complete  swing  and  obtain  a  full  table  of  deviations,  which  may  give  interesting  information  of  the  existing  magnetic 
conditions. 


40  THE    COMPASS    ERROR. 

undisturbed  and  alter  course  until  the  sun  comes  on.     The  magnetic  heading  is  then  North,  and  adjust- 
ment may  be  made  accordingly. 

(d)  When  ranges  are  available,  they  may  be  utilized  for  determining  magnetic  headings. 

123.  Summary  of  Ordinary  Corrections. — To  summarize,  the  following  is  the  process  of  correct- 
ing a  compass  for  a  single  latitude,  where  magnets  at  right  angles  are  employed  for  compensating  the 
semicircular  deviation  ^pd  where  the  disturbances  due  to  unsymmetrical  soft  iron  are  small  enough  to  be 
neglected: 

First.  All  correctors  being  clear  of  the  compass,  place  the  quadrantal  correctors  in  the  position 
which  it  is  estimated  that  they  will  occupy  when  adjilstment  is  complete.  The  navigator's  experience 
will  serve  in  making  the  estimate,  or  if  there  seems  no  other  means  of  arriving  at  the  probable  position 
they  may  be  placed  at  the  middle  points  of  their  supports. 

Second.  Steady  the  ship  on  magnetic  North,  East,  South,  or  West,  and  hold  on  that  heading  by  such 
method  as  seems  best.  By  means  of  permanent  magnets  alter  the  indications  of  the  compass  until  the 
heading  coincides  with  the  magnetic  course.  If  heading  North,  magnets  must  be  entered  N.  ends  to 
starboard  to  correct  easterly  deviation  and  to  port  to  correct  westerly,  and  the  reverse  if  heading 
South.  If  heading  East,  enter  N.  ends  forward  for  easterly  and  aft  for  westerly  deviations,  and  the 
reverse  if  heading  W^est.  (Binnacles  differ  so  widely  in  the  methods  of  carrying  magnets  that  details 
on  this  point  are  omitted.  It  may  be  said,  however,  that  the  magnetic  intensity  of  the  correctors  may 
be  varried  by  altering  either  their  number  or  their  distance  from  the  compass;  generally  si)eaking, 
several  magnets  at  a  distance  are  to  be  preferred  to  a  small  number  close  to  the  compass. ) 

Third.  Steady  the  ship  on  an  adjacent  magnetic  cardinal  point  and  correct  the  compass  heading 
by  permanent  magnets  to  accord  therewith  in  the  same  manner  as  described  for  the  first  heading. 

Fourth.  Steady  the  ship  on  an  intercardinal  point  (magnetic)  and  move  the  quadrantal  correctors 
away  from  or  toward  the  compass,  keeping  them  at  equal  distances  therefrom,  until  the  compass  and 
magnetic  headings  coincide. 

124.  The  compensation  being  complete,  the  navigator  should  proceed  immediately  to  swing  ship 
and  make  a  table  of  the  residual  deviations.  Though  the  remaining  errors  will  be  small,  it  is  seldom 
that  they  will  be  reduced  to  zero,  and  it  must  never  be  assumed  that  the  compass  may  be  relied  upon 
without  taking  the  deviation  into  account.  Observations  on  eight  equidistant  points  will  ordinarily 
suffice  for  this  purpose. 

^  125.  To  Correct  Semicircular  Deviation  avith  a  Single  Magnet. — In  certain  binnacles  provision 
is  made  for  correcting  the  semicircular  deviation  by  a  single  magnet  (or  series  of  magnets)  in  the  star- 
board angle,  the  magnet  tray  having  motion  in  azimuth  as  well  as  vertically.  In  this  case  the  i^rocess  of 
correcting  semicircular  deviation  is  somewhat  different  from  that  described  for  correction  by  rectangular 
magnets.     Either  of  the  two  following  methods  may  be  employed: 

(o)  By  computation  determine  the  starboard  angle.  An  approximate  method  for  doing  this  is 
given  in  article  103,  and  a  more  exact  one  may  be  found  in  works  treating  this  subject  mathematically. 
Head  the  ship  on  a  cardinal  point  (magnetic);  enter  the  magnets  in  the  tray  and  revolve  it  until  their 
N.  ends  lie  at  an  angular  distance  from  ahead  (measured  to  the  right)  equal  to  the  starboard  angle; 
raise  or  lower  the  tray  until  the  deviation  disappears. 

(6)  Head  the  ship  on  a  cardinal  point  (magnetic),  enter  the  magnets,  and  turn  the  tray  to  an  east- 
and-west  position,  the  N.  ends  in  such  direction  as  will  tend  to  reduce  the  deviation;  raise  or  lower  the 
tray  until  the  deviation  disappears.  Alter  course  90°  and  head  on  an  adjacent  magnetic  cardinal  point; 
observe  the  amount  of  deviation  that  the  compass  shows;  correct  half  of  this  by  altering  the  starboard 
angle  and  the  other  half  by  raising  or  lowering  the  tray.  Return  to  first  course,  note  deviation,  and 
correct  one-half  in  each  way,  as  before.  Continue  the  operation,  making  a  series  of  trials  until  the 
deviations  disappear  on  both  headings,  when  the  compensation  will  be  correct.  This  operation  may  be 
considerably  hastened  by  finding  the  first  position  of  the  magnets  from  a  rough  calculation  of  the 
starboard  angle  (art.  103). 

126.  Correcting  the  Heeling  Error. — The  heeling  error  may  be  corrected  by  a  method 
involving  computation,  together  with  certain  observations  on  shore.  A  more  practical  method,  however, 
is  usually  followed,  though  its  results  may  be  less  precise.  The  heeling  corrector  is  placed  in  its  vertical 
tube,  N.  end  uppermost  in  north  latitudes,  as  this  is  almost  invariably  the  required  direction;  the  ship 
being  on  a  course  near  North  or  South  and  rolling,  observe  the  vibrations  of  the  card,  which,  if  the 
error  is  material,  will  be  in  excess  of  those  due  to  the  ship's  real  motion  in  azimuth;  slowly  raise  or 
lower  the  corrector  until  the  abnormal  vibrations  disappear,  when  the  correction  will  be  made  for  that 
lalitude;  but  it  must  be  readjusted  upon  any  considerable  change  of  geographical  position. 

In  making  this  observation  care  must  be  taken  to  distinguish  the  vessel's  "j'awing"  in  a  seaway, 
from  the  apparent  motion  due  to  heeling  error;  for  this  reason  it  may  be  well  to  have  an  assistant  to 
w^atch  the  ship's  head  and  keep  the  adjuster  informed  of  the  real  change  in  azimuth,  by  which  means 
the  latter  may  better  judge  the  effect  of  the  heeling  error. 

In  the  case  of  a  sailing  vessel,  or  one  which  for  any  reason  maintains  a  nearly  steady  heel  for  a 
continuous  period,  the  amount  of  the  heeling  error  may  be  exactly  ascertained  by  observing  the  azi- 
muth of  the  sun,  and  corrected  with  greater  accuracy  than  is  possible  with  a  vessel  which  is  constantly 
rolling. 

127.  Flinders  Bar. — The  simplest  method  that  presents  itself  for  the  placing  of  the  Flinders 
bar  is  one  which  is  available  only  for  a  vessel  crossing  the  magnetic  equator.  Magnetic  charts  of  the 
world  show  the  geographical  positions  at  which  the  dip  becomes  zero — that  is,  where  a  freely  suspended 
needle  is  exactly  horizontal  and  where  there  exists  no  vertical  component  of  the  earth's  total  magnetic 
force.  In  such  localities  it  is  evident  that  the  factor  of  the  semicircular  deviation  due  to  vertical  induc- 
tion disappears  and  that  the  whole  of  the  existing  semicircular  deviation  arises  from  subpermanent 
magnetism.  If,  then,  w'hen  on  the  magnetic  equator  the  compass  be  carefully  compensated,  the  effect 
of  the  subpermanent  magnetism  will  be  exactly  opposed  by  that  of  the  semicircular  correcting  magnets. 
Later,  as  the  ship  departs  from  the  magnetic  equator,  the  semicircular  deviation  will  gradually  acquire 
a  material  value,  which  will  be  known  to  be  due  entirely  to  vertical  induction,  and  if  the  Flinders  bar 
be  so  placed  as  to  correct  it,  the  compensation  of  the  compass  will  be  general  for  all  latitudes. 


THE    COMPASS    ERROR.  41 

In  following  this  method  it  may  usually  be  assumed  that  the  soft  iron  of  the  vessel  is  symmetrical 
with  respect  to  the  fore-and-aft  line  and  that  the  Flinders  bar  may  be  placed  directly  forward  of  the 
compas^  or  directly  abaft  it,  disregarding  the  effect  of  components  to  starboard  or  port.  It  is  therefore 
merely  necessary  to  observe  whether  a  vertical  soft  iron  rod  must  be  placed  forward  or  abaft  the 
compass  to  reduce  the  deviation,  and,  having  ascertained  this  fact,  to  find  by  experiment  the  exact 
distance  at  which  it  completely  corrects  the  deviation. 

The  Flinders  bar  frequenth^  consists  of  a  bundle  of  soft  iron  rods  contained  in  a  case,  which  is 
secured  in  a  vertical  position  near  the  compass,  its  upper  end  level  with  the  plane  of  the  needles;  in 
this  method,  the  distance  remaining  fixed,  the  intensity  of  the  force  that  it  exerts  is  varied  by  increasing 
or  decreasing  the  number  of  rods;  this  arrangement  is  more  convenient  and  satisfactory  than  the 
employment  of  a  single  rod  at  a  variable  distance. 

128.  When  it  is  not  possible  to  correct  the  compass  at  the  magnetic  equator  there  is  no  ready 
practical  method  by  which  the  Flinders  bar  may  be  placed;  the  operation  will  then  depend  entirely  upon 
computation,  and  as  a  mathematical  analysis  of  deviations  is  beyond  the  scope  laid  out  for  this  work 
the  details  of  procedure  will  not  be  gone  into;  the  general  principles  involved  are  indicated,  and  students 
seeking  more  must  consult  the  various  works  that  treat  the  subject  fully. 

It  has  been  explained  that  each  coeflBcient  of  semicircular  deviation  ( B  and  C )  is  made  up  of  a  sub- 
permanent  factor  varying  as  vj  and  of  a  vertical  induction  factor  varying  as  tan  6.  If  we  indicate  by  the 
subscripts  ^  and  ,.,  respectively,  the  parts  due  to  each  force,  we  may  write  the  equations  of  the  coefficients: 

B=B,  X  j^  +  B,  X  tan  0;  and 

C  =  C,X^+C,  X  tane. 

Now  if  we  distinguish  by  the  subscripts  i  and  ^  the  values  in  the  first  and  in  the  second  position  of 
observation,  respectively,  of  those  quantities  that  vary  with  the  magnetic  latitude,  we  have; 

Bi  =  B,Xjj-  +  B,Xtan6„ 

B2  =  B,  X  JJ-+  B^  X  tan&,;  and 

C,  =  C,x4-  +  CvXtane„ 

C,  =  C,  X  jj-  4- ('v  X  tan  0.,. 

The  values  of  the  coefficients  in  both  latitudes  are  found  from  the  observations  made  for  deviations; 
the  values  of  the  horizontal  force  and  of  the  dip  at  each  place  are  known  from  magnetic  charts;  hence 
we  may  solve  the  first  pair  of  equations  for  B^  and  B,.,  and  the  second  pair  for  (\  and  C,.;  and  having 
found  the  values  of  these  various  coefficients,  we  may  correct  the  effects  of  B,  and  C^  by  permanent  mag- 
nets in  the  usual  way  and  correct  the  remainder — that  due  to  B^.  and  C, — by  the  Flinders  bar. 

Strictly,  the  Flinders  bar  should  be  so  placed  that  its  repelling  pole  is  at  an  angular  distance  from 
ahead  equal  to  the  "starboard  angle"  of  the  attracting  pole  of  the  vertical  induced  force,  this  angle 
depending  upon  the  coefficients  B^,  and  C^.;  but  since,  as  before  stated,  horizontal  soft  iron  may  usually 
be  regarded  as  symmetrical,  C».  is  assumed  as  zero  and  the  bar  placed  in  the  midshi]i  line. 

129.  To  Correct  Ad-itstment  on  Change  of  Latitude. — The  compensation  of  quadrantal  devia- 
tion, once  properly  made,  remains  effective  in  all  latitudes;  but  unless  a  Flinders  bar  is  used  a  correction 
of  the  semicircular  deviation  made  in  one  latitude  will  not  remain  accurate  when  the  vessel  has 
materially  changed  her  position  on  the  earth's  surface.  With  this  in  mind  the  navigator  must  make 
frequent  observations  of  the  compass  error  during  a  passage  and  must  expect  that  the  table  of  residual 
deviations  obtained  in  the  magnetic  latitude  of  compensation  will  undergo  considerable  change  as  that 
latitude  is  departed  from.  The  new  deviations  may  become  so  large  that  it  will  be  found  convenient 
to  readjust  the  semicircular  correcting  magnets.     This  process  is  very  simple. 

Wien  correctors  at  right  angles  are  used,  provide  for  steadying  tte>  ship,  by  an  auxiliary  compas^s  or 
by  the  pelorus,  upon  two  adjacent  magnetic  cardinal  points  (art.  l3^).  Put  the  ship  on  heading  North 
or  South  (magnetic),  and  raise  or  lower  the  athwartship  magnets  or  alter  their  number  until  the 
deviation  disappears;  then  steady  on  East  or  West  (magnetic)  and  similarly  adjust  the  fore-and-aft 
magnets.     Swing  ship  for  a  new  table  of  residual  deviations. 

When  correctors  in  the  starboard  angle  are  nsed,  arrange  as  before  for  heading  on  two  adjax-ent  cardinal 
magnetic  courses.  Steady  on  one  of  these,  observe  amount  of  compass  error,  correct  half  by  changing 
the  starboard  angle  and  half  by  raising  or  lowering  magnets;  steady  on  the  adjacent  cardinal  point  and 
repeat  the  operation.  Continue  until  adjustment  is  made  on  both  headings,  then  swing  for  residual 
deviations. 


42  PILOTING. 


CHAPTER  IV. 
PILOTING. 


130.  Definition'. — Piloting,  in  the  sense  given  the  word  by  modern  and  popular  usage,  is  the 
art  of  conducting  a  vessel  in  channels  and  harbors  and  along  coasts,  where  landmarks  and  aids  to 
navigation  are  available  for  fixing  the  position,  and  where  the  depth  of  water  and  dangers  to  navigation 
are  such  as  to  require  a  constant  watch  to  be  kejit  upon  the  vessel's  course  and  frequent  changes  to  be 
made  therein. 

131.  Reqiisites. — As  requisites  to  successful  piloting,  the  navigator  should  be  provided  with 
the  best  available  chart  of  the  locality  to  be  traversed,  together  with  the  sailing  directions  and  descrip- 
tions of  aids  to  navigation;  and  all  of  these  should  be  corrected  for  the  latest  information,  published  in 
notices  to  mariners  or  otherwise,  that  bear  upon  the  locality.  The  vessel  should  be  equipped  with  the 
usual  instruments  employed  in  navigation.  The  deep-sea  sounding-machine,  if  i)rovided,  should  be  ready 
for  use  when  there  is  a  chance  that  it  may  be  needed.  The  lead  lines  should  be  correctly  marked,  and 
as  shoal  water  is  entered  one  or  two  men  should  be  stationed  to  sound.  The  index  errors  of  the  sextants 
should  be  known,  and,  above  all,  there  should  be  at  hand  a  table  showing  correctly  the  deviation  of 
the  compass  on  each  heading. 

132.  Laying  the  Course. — Mark  a  point  upon  the  chart  at  the  ship's  position;  then  mark  another 
point  for  which  it  is  desired  to  steer;  join  the  two  by  a  line  drawn  with  the  parallel  ruler,  and,  main- 
taining the  direction  of  the  line,  move  the  ruler  until  its  edge  passes  through  the  center  of  the  compass 
rose  and  note  the  direction.  If  the  compass  rose  indicates  true  directions,  this  will  be  the  true  course, 
and  must  be  corrected  for  variation  and  deviation  ( by  applying  each  in  the  opposite  direction  to  its 
name)  to  obtain  the  compass  course;  if  it  is  a  magnetic  rose,  the  course  need  be  corrected  for  deviation 
only. 

Before  putting  the  ship  on  any  course  a  careful  look  should  be  taken  along  the  line  over  which  it 
leads  to  be  assured  that  it  clears  all  dangers. 

1 33.  Methods  of  Fixing  Position. — A  navigator  in  sight  of  objects  whose  positions  are  shown  ujjon 
the  chart  may  locate  his  vessel  by  either  of  the  following  methods:  («)  cross  bearings  of  two  known 
objects;  {h)  the  bearing  and  distance  of  a  known  object;  {(•)  the  bearing  of  a  known  object  and  the 
angle  between  two  known  objects;  {d)  two  bearings  of  a  known  object  separated  by  an  interval  of  time, 
with  the  run  during  that  interval;  [e]  sextant  angles  between  three  known  objects.  Besides  the  fore- 
going there  are  two  methods  by  which,  without  obtaining  the  precise  position,  the  navigator  may  assure 
himself  that  he  is  clear  of  any  particular  danger.  These  are:  (/)  the  danger  angle;  {g)  the  danger 
bearing. 

The  choice  of  the  method  will  be  governed  by  circumstances,  depending  upon  which  is  best  adapted 
to  prevailing  conditions. 

1 34.  Cross  Bearings  of  two  Known  Objects. — Choose  two  objects  whose  i^osition  on  the  chart 
can  ])e  unmistakably  identified  and  whose  respective  bearings  from  the  ship  differ,  as  nearly  as  possible, 
bv90°;  observe  the  bearing  of  each,  either  by  compass  or  pelorus,  taking  one  as  quickly  as  possible 
at\er  tlie  othep;  see  that  the  ship  is  on  an  even  keel  at  the  time  the  observation  is  made,  and,  if  using 
the  pelorus,  be  sure  also  that  she  heads  exactlj-  on  the  course  for  which  the  i)elorus  is  set.  Correct  the 
bearings  so  that  they  will  be  either  true  or  magnetic,  according  as  they  are  to  be  plotted  by  the  true  or 
magnetic  compass  rose  of  the  chart — that  is,  if  observed  by  compass,  api)ly  deviation  and  variation  to 

obtain  the  true  bearing,  or  deviation  only  to  obtain  the  magnetic;  if 

/"  /  observed  by  pelorus,  that  instrument  should  be  set  for  the  true  or  mag- 

n/ti.  netic  heading,  according  as  one  or  the  other  sort  of  reading  is  required, 

y/r\  and  no  further  correction  will  be  necessary.     Draw  on  the  chart,  by 

y^  I  means  of  the  parallel  rulers,  lines  which  shall  pass  through  the  respec- 

y^      \  five  objects  in  the  direction  that  each  was  observed  to  bear.     As  the 

/  \  shi%Ls  position  on  the  chart  is  known  to  be  at  some  point  of  each  of 

jT  \  the«  lines,  it  must  l>e  at  their  intersection,  the  only  point  that  fulfills 

^^/  )    c  botn  conditions. 

/\ ^"  figure  13,  if  A  and  B  are  the  objects  and  OA  and  OB  the  lines 

X     N.  (  passing  through  them  in  the  observed  directions,  the  ship's  position 

/  N.  I  will  be  at  O,  their  intersection. 

N.  1  *  135.  If  it  be  possible  to  avoid  it,  ol)jects  should  not  be  selected 

'  i     N.    ^  \  for  a  cross  bearing»which  subtend  an  angle  at  the  ship  of  less  than  30° 

\/  or  more  than  150°,  as,  when  the  lines  of  bearing  approach  parallelism, 

f^B  a  small  error  in  an  observed  bearing  gives  a  large  error  in  the  result. 

VTS.  For  a  similar  reason  objects  near  the  ship  should  be  taken  in  prefer- 

^     N  ence  to  those  at  a  distance. 

Fig.  13.  1 36.  When  a  third  object  is  available  a  bearing  of  that  may  be 

taken  and  ])lotted.    If  this  line  intersects  at  the  same  point  as  the  other 

two  (as  the  bearing  OC  of  the  object  C  in  the  figure),  the  navigator  may  have  a  reasonable  assurance 

that  his  "  fix  "  is  correct;  if  it  does  not.  it  indicates  an  error  somewhere,  and  it  may  have  arisen  from 

inaccurate  observation,  incorrect  determination  or  application  of  the  deviation,  or  a  fault  in  the  chart. 


PILOTING. 


43 


V-t;:: 


Fui.  15. 


137.  What  may  be  considered  as  a  form  of  this  method  can  be  used  when  only  one  known  object 
is  in  sight  by  taking,  at  the  same  instant  as  the  bearing,  an  altitude  of  the  sun  or  other  heavenly  l)ody 
and  noting  the  time;  work  out  the  sight  and  obtain  the  Sumner  line  (as  explained  in  Chapter  XV),  and 
the  intersection  of  this  with  the  direction-line  from  the  object  will  give  the  observer's  position  in  the 
same  way  as  from  two  terrestrial  bearings. 

13§.  Bearing  and  Distance  of  a  Known  Object. — When  only  one  object  is  available,  the  ship's 
position  may  be  found  by  observing  its  bearing  and  distance.  Follow  the  preceding  method  in  the  mat- 
ters of  taking,  correcting,  and  plotting  the  bearing;  then,  on  this 
line,  lay  off  the  distance  from  the  object,  which  will  give  the 
point  occupied  by  the  observer.  In  figure  1-i,  if  A  represents  the 
object  and  AO  the  bearing  and  distance,  the  position  sought  will 
be  at  O. 

139.  It  is  not  ordinarily  easy  to  find  directly  the  distance 
of  an  object  at  sea.  The  most  accurate  method  is  when  its  height 
is  known  and  it  subtends  a  fair-sized  angle  from  the  ship,  in 
which  case  the  angle  may  be  measured  by  a  sextant,"  and  the 
distance  computed  or  taken  from  a  table.  Table  83  of  this  work 
gives  distances  up  to  5  miles,  corresponding  to  various  heights 
and  angles.  Captain  Lecky's  "Danger  Angle  and  Offshore  Dis- 
tance Tables"  carries  the  computation  much  further.  The  use 
of  this  method  at  great  distances  must  not  be  too  closely  relied 
upon,  as  small  errors,  such  as  those  due  to  refraction,  may  throw 
out  the  results  to  a  material  extent;  but  it  affords  an  excellent  approximation,  and  as  this  method  of  fixing 
position  is  employed  only  when  no  other  is  available  the  best  possible  approximation  has  to  suflice. 

In  measuring  vertical  angles,  strictness  requires  that  the 
observation  should  be  so  made  that  the  angle  at  the  foot  of  the 
object  should  equal  90°  and  that  the  triangle  be  a  right  triangle, 
as  OMN,  figure  15,  where  the  line  OM  is  truly  horizontal,  and 
not  as  in  the  triangle  O^MN,  where  the  condition  is  not  fulfilled. 
This  error  is  inapprecial>le,  however,  save  at  very  close  dis- 
tances, when  it  may  be  sufficiently  corrected  by  getting  down 
as  low  as  possible  on  board  the  vessel,  so  that  the  eye  is  near 
the  water-line.  One  condition  exists,  however,  where  the 
error  is  material — that  shown  in  figure  16,  where  the  visible 
shorjp-line  is  at  M^,  a  considerable  distance  from  M,  the  point 
vertically  below  the  summit.  In  this  case  there  is  nothing  to 
mark  M  in  the  observer's  eye,  and  it  is  essential  that  all  angles 
be  measured  from  a  point  dose  down  to  the  water-line. 

If  a  choice  of  objects  can  be  made,  the  best  results  will  l)e 
obtained  by  observing  that  one  which  subtends  the  greatest 
angle,  as  small  errors  will  then  have  the  least  effect. 

There  is  another  method  for  determining  the  distance  of 
an  o)>ject,  Avhich  is  available  under  certain  circumstances.  This  consists  in  observing,  from  a  position 
aloft,  the  angle  between  the  object  and  the  line  of  the  sea  horizon  beyond.  By  reference  to  Table  34 
will  be  found  the  distance  in  yards  corresponding  to  different  angles  for  various  heights  of  the  observer 
from  20  to  120  feet.  The  method  is  not  accurate  beyond  moderate  distances  (the  table  being  limited  to 
5,000  yards)  and  is  obviously  only  available  for  finding  the  distance  of  an  isolated  object,  such  as  an 
islet,  vessel,  or  target,  over  which  the  horizon  may  be  seen.  In  employing  this  method  the  higher  the 
l)osition  occupied  by  the  observer  the  more  precise  will  be  the  results. 

140.  In  observing  small  angles,  such  as  those  that  occur  in  the  methods  just  described,  it  is  some- 
times convenient  to  measure  them  on  and  off  the  limb  of  the  sextant.  Firet  look  at  the  bottom  of  the 
object  and  reflect  the  top  down  into  coincidence;  then  look  through  the  transparent  part  of  the  horizon 
glass  at  the  top  and  bring  the  bottom  up  by  its  reflected  ray.  The  mean  of  the  two  readings  will  be  the 
true  angle,  the  index  correction  having  been  eliminated  by  the  operation. 

141.  When  the  methods  of  finding  distance  by  a  vertical  or  a  horizon  angle  are  not  available,  it 
must  be  obtained  by  such  means  as  exist.  Fstimate  the  distance  by  the  appearance;  take  a  sounding,  and 
note  where  the  depth  falls  upon  the  line  of  bearing;  at  night,  if  atmospheric  conditions  are  normal, 
consider  that  the  distance  of  a  light  when  sighted  is  equal  to  its  maximum  range  of  visibility,  remem- 
l^ering  that  its  range  is  stated  for  a  height  of  eye  of  15  feet;  or  employ  such  method  as  suggests  itself 
under  the  circumstances,  regarding  the  result,  however,  as  an  approximation  only. 

142.  The  Bearing  of  a  Known  Object  and  the  Ancjle  between  two  Known  Objects. — This 
method  is  seldom  employed,  as  the  conditions  always  permit  of  cross  bearings  being  taken,  and  the 
latter  is  generally  considered  preferable. 

Take  a  bearing  of  a  known  object  by  compass  or  pelorus  and  observe  the  sextant  angle  between  some 
two  known  objects.  The  line  of  bearing  is  plotted  as  in  former  methods.  In  case  one  of  the  objects  of 
the  observed  angle  is  that  whose  bearing  is  taken,  the  angle  is  applied,  right  or  left  as  the  case  may  be, 
to  the  bearing,  thus  giving  the  direction  of  the  second  object,  which  is  plotted  from  the  compass  rose 
and  parallel  rulers.  If  the  object  whose  bearing  is  taken  is  not  one  of  the  objects  of  the  angle,  lay  off 
the  angle  on  a  three-armed  proti-actor,  or  piece  of  tracing  paper,  and  swing  it  (keeping  the  legs  or  lines 
always  over  the  two  objects)  until  it  ])asses  over  the  line  of  bearing,  which  defines  the  position  of  the 
ship;  there  will,  except  in  special  cases,  be  two  points  of  intersection  of  the  line  with  the  circle  thus 
described,  and  the  navigator  must  know  his  position  with  sufficient  closeness  to  judge  which  is  correct. 

143.  Two  Bearin(;s  of  a  Known  Object. — This  is  a  most  useful  method,  which  is  frequently 
employed,  certain  special  cases  arising  thereunder  being  particularly  easy  of  application.     The  process 


iThe  use  of  the  sextant  is  explained  in  Chapter  VIII. 


44 


PILOTING. 


is  to  take  a  careful  bearing  and  at  the  same  moment  read  the  patent  log;  then,  after  running  a  convenient 
distance,  take  a  second  bearing  and  again  read  the  log,  the  difference  in  readings  giving  the  intervening 
run;  when  running  at  a  known  speed,  the  time  interval  will  also  afford  a  means  for  determining  the 
distance  run. 

The  problem  is  as  follows:  In  figure  17,  given  OA,  the  direction  of  a  known  object,  A,  at  the  first 
observation;  PA,  the  direction  at  the  second  observation;  and  01*,  the  distance 
•  traversed  between  the  two;  to  find  AP,  the  distance  at  the  second  observation. 
Knowing  the  angle  PC) A,  the  angular  distance  of  the  object  from  right  ahead 
at  the  first  bearing;  OPA,  the  angular  distance  from  right  astern  at  the  secontl 
bearing;  and  OP,  the  distance  run;  we  have  by  Plane  Trigonometry: 

PAO  =  180°-  (POA  +  OPA) ;  and 


AP  =  OP  X 


sin  POA 
sin  PAO* 


If,  as  is  frequently  the  case,  we  desire  to  know  the  distance  of  passing  abeam^ 
we  have: 

AQ  =  AP  X  sin  OPA. 

Tables  5A  and  5B  give  solutions  for  this  problem,  the  former  for  intervals 
of  bearing  of  quarter  points,  the  latter  for  intervals  of  two  degrees.  The  first 
column  of  each  of  these  tables  gives  the  value  of  AP,  the  distance  of  the  ship 
from  the  observed  object  at  the  time  of  taking  the  last  bearing,  for  values  of 
OP  equal  to  unity;  that  is,  for  a  run  V)etween  bearings  of  1  mile.  The  second 
P       1-  column  gives  AQ,  the  distance  of  the  object  when  it  bears  abeam,  likewise  for 

a  value  of  OP  of  1  mile.     When  the  run  between  bearings  is  other  than  1  mile, 
the  number  taken  from  the  table  must  be  used  as  a  multiplier  of  that  run  to  give  the  required  distance. 
Example:  A  vessel  steering  north  takes  a  bearing  of  a  light  XW.  J  W. ;  then  runs  4.3  miles,  when 
the  bearing  is  found  to  be  WSW.     Required  the  distance  of  the  light  at  the  time  of  the  second  bearing. 
Difference  between  course  and  first  bearing,  4i  pts. 
Difference  between  course  and  second  bearing,  10  pts. 
Multiplier  from  first  column,  Table  5A,  0.88. 
4.3  miles  X  0.88  =  3.8  miles,  distance  at  second  bearing. 
Example:  A  vessel  on  a  course  S.  52°  E.  takes  the  first  bearing  of  an  object  at  S.  26°  E.,  and  the 
second  at  S.  2°  W.,  running  in  the  interval  0.8  mile.     Required  the  distance  at  which  she  will  pass 
abeam. 

Difference  between  course  and  first  bearing,  26°. 
Difference  between  course  and  second  bearing,  54°. 
Multiplier  from  second  column.  Table  5B,  0.79. 
0.8  mile  X  0.79  =  0.6  mile,  distance  of  passing  abeam. 
144.     As  has  been  said,  there  are  certain  special  cases  of  this  problem  where  it  is  exceptionally 
easy  of  application;  these  arise  when  the  multiplier  is  equal  to  unity,  and  the  distance  run  is  therefore 
equal  to  the  distance  from  the  object.     When  the  angular  distance  on  the  bow 
at  the  second  bearing  is  twice  as  great  as  it  was  at  the  first  bearing,  the  distance 
of  the  object  from  the  ship  at  fiecond  bearing  is  equal  to  the  run,  the  multiplier 
being  1.0.     For  if,  in  figure  18,  when  the  ship  is  in  the  first  position,  O,  the  ol)ject 
A  bears  ar°on  the  bow,  and  at  the  second  position,  P,  2cir°,  we  have  in  the  triangle 
APO,  observing  that  APO  =  180°  —  2ix,  and  POA  =  tx: 

PAO  =  180°  -(POA  -r-  APO), 
=  180°-(cr  +  180°-2a), 
=  a. 

Or,  since  the  angles  at  O  and  at  A  are  equal  to  each  other,  the  sides  OP  and  AP 
are  equal,  or  the  distance  at  second  bearing  is  equal  to  the  run.  This  is  known 
as  doubling  the  angle  on  the  buic. 

145.  A  case  where  this  holds  good  is  familiar  to  every  navigator  as  the  botv 
and  beambearing,  where  the  first  bearing  is  taken  when  the  object  is  broad  on 
the  bow  (four  points  or  45°  from  ahead)  and  the  second  when  it  is  abeam  (eight 
points  or  90°  from  ahead);  in  that  case  the  distance  at  second  bearing  and  the 
distance  abeam  are  identical  and  etiual  to  the  run  between  bearings. 

146.  When  the  first  bearing  is  26i°  from  ahead,  and  the  second  45°,  the 
distance  at  which  the  object  irill  be  passed  abeam  will  equal  the  run  between  bear- 
ings; this  may  be  proved  by  computation  or  by  reference  to  the  tables  and  is  a 

very  convenient  fact  to  remember,  as  it  shows  the  navigator  at  once,  it  about  to  pass  a  point,  how  wide 
a  berth  he  is  going  to  give  the  offiying  dangers. 

147.  There  is  a  graphic  method  of  solving  this  problem  that  is  considered  by  some  more  convenient 
than  the  use  of  multipliers.  Draw  upon  the  chart  the  lines  OA  and  PA  (fig.  19),  pa^^sing  through  the 
object  on  the  two  observed  bearings;  set  the  dividers  to  the  distance  run,  OP;  lay  down  the  parallel 
rulers  in  a  direction  parallel  to  the  course  and  move  them  toward  or  away  from  the  observed  object 
until  some  point  is  found  where  the  distance  between  the  lines  of  bearing  is  exactly  equal  to  the 
distance  between  the  points  of  the  dividers;  in  the  figure  this  occurs  when  the  rulers  lie  along  the  line 


PILOTING. 


45 


Fig.  19. 


OP,  and  therefore  O  represents  the  position  of  the  ship  at  the  first  bearing  and  P  at  the  second.     For 
any  other  positions  O^P',  O'^P^',  the  condition  is  not  fulfilled. 

14§.  Another  jiraiihic  solution  is  given  by  the  Dintance  Finder,  devised  by  Lieut.  J.  B.  Blish,  U.  S. 
Navy.  This  consists  of  a  semicircle  whose  circumference  is  graduated  in  degrees.  Two  pieces  of  thread, 
made  to  swing  aljout  a  pin-head  at  the  center,  are  laid  down  to 
represent  the  lines  of  bearing,  and  ease  in  measuring  distances  is 
afforded  l)y  series  of  cross  lines  similar  to  those  on  a  piece  of  profile  ^  ^ 
paper. 

149.  The  methoil  of  obtaining  position  by  two  bearings  of  the 
same  object  is  one  of  great  value,  by  reason  of  the  fact  that  it  is 
frequently  necessary  to  locate  the  ship  when  there  is  but  one  land- 
mark in  sight.  Careful  navigators  seldom,  if  ever,  miss  the  opjwr- 
tunity  for  a  bow  and  beam  bearing  in  passing  a  light-house  or  other 
well-plotted  ol:)ject;  it  involves  little  or  no  trouble,  and  always  gives 
a  feeling  of  added  security,  however  little  the  position  may  be  in 
doubt.  If  about  to  pass  an  object  abreast  of  whii-h  there  is  a 
danger — a  familiar  example  of  which  is  when  a  light-house  marks  a 
point  off  which  are  rocks  or  shoals — a  good  assurance  of  clearance 
should  l:)e  obtained  before  bringing  it  abeam,  either  by  doubling 
the  angle  on  the  bow,  or  by  using  the  26i°-45°  bearing;  the  latter 
has  the  advantage  over  the  former  if  the  object  is  sighted  in  time 
to  permit  of  its  use,  as  it  may  be  assumed  that  the  45°  (bow)  bear- 
ing will  always  be  observed  in  any  event,  and  this  gives  the  distance 
al>eam  directly,  saving  the  necessity  of  plotting  the  position  at 
second  Ijearing  (as  obtained  by  .doubling  the  angle)  and  then  carry- 
ing it  forward. 

150.  It  nuist  be  remembered  that,  however  convenient,  the 
fix  obtained  by  two  bearings  of  the  same  object  will  be  in  error  unless 
the  course  and  distance  are  correctly  estimated,  the  course  "made 
good"  and  the  distance  "over  the  ground"  being  required.  Difficulty  will  occur  in  estimating  the 
exact  course  when  there  is  bad  steering,  a  cross  current,  or  when  a  ship  is  making  leeway;  errors  in 
the  allowed  run  will  arise  when  she  is  being  set  ahead  or  back  by  a  current  or  when  the  logging  is 
inaccurate.  To  take  a  not  extreme  case,  a  vessel  making  10  knots  through  the  water,  running  against  a 
2-knot  tide,  will  overestimate  her  distance  one-fifth  of  its  true  amount  in  taking  a  bow  and  beam  bear- 
ing if  no  allowance  is  made  for  the  tide,  or  she  will  underestimate  her  distance  by  one-fifth  of  its 
apparent  amount  if  going  with  the  same  tide.  Therefore,  if  in  a  current  of  any  sort,  due  allowance 
must  be  made,  and  it  should  be  remembered  that  more  dependence  can  be  placed  upon  a  position  fixed 
by  simultaneous  bearings  or  angles,  when  two  or  more  objects  are  available,  than  by  two  bearings  of  a 
single  ol)ject. 

151.  Sextant  Anules  between  Three  Known  Objects. — This  method,  involving  the  solution  of 
the  three-}ioint  2)rof>len>,  will,  if  the  objects  be  well  cho.sen,  give  the  most  accurate  results  of  any.  It  is 
largely  employed  in  surveying,  because  of  its  precision;  and  it  is  especially  valuable  in  navigation, 
because  it  is  not  subject  to  errors  arising  from  imperfect  knowledge  of  the  compass  error,  improper  log- 
ging, or  the  effects  of  current,  as  are  the  methods  previously  described. 

Three  objects  represented  on  the  chart  are  selected  and  the  angles  measured  with  sextants  of 
known  index  error  between  the  center  one  and  each  of  the  others.  Preferably  there  should  be  two 
observers  and  the  two  angles  be  taken  sinuiltaneously,  but  one  observer  may  fii-st  take  the  angle  which 
is  changing  more  slowly,  then  take  the  other,  then  repeat  the  first  angle,  and  consider  the  mean  of  the 
first  and  last  observations  as  the  value  of  the  first  angle.  The  position  is  usually  plotted  by  means  of 
the  three-armed  protractor,  or  station-jwinter  (see  art.  432,  Chap.  XVII).  Set  the  right  and  left 
angles  on  the  instrument,  and  then  move  it  over  the  chart  until  the  three  beveled  edges  pass  respectively 
and  simultaneously  through  the  three  objects.  The  center  of  the  instrument  will  then  mark  the  ship's 
position,  which  may  be  pricked  on  the  chart  or  marked  with  a  pencil  point  through  the  center  hole. 
When  the  three-armed  protractor  is  not  at  hand,  the  tracing-paper  protractor  will  prove  an  excellent 
substitute,  and  may  in  some  cases  be  preferable  to  it,  as,  for  instance,  when  the  objects  angled  on  are 
so  near  the  observer  as  to  be  hidden  by  the  circle  of  the 
instrument.  A  graduated  circle  printed  upon  tracing 
l)aper  j^ermits  the  angles  being  readily  laid  off,  but  a 
plain  ])iece  of  tracing  paper  may  be  used  and  the  angles 
marked  by  means  of  a  small  protractor.  The  tracing- 
paper  protractor  pernnts  the  laying  down,  for  simultane- 
ous trial,  of  a  number  of  angles,  where  special  accuracy  is 
s>ought. 

1.52.  The  three-point  problem,  by  which  results  are 
obtained  in  this  method,  is:  "To  find  a  point  such  that 
three  lines  drawn  from  this  point  to  three  given  points 
shall  make  given  angles  with  each  other. 

Let  A,  B,  and  C,  in  figure  20,  be  three  fixed  objects  on 
shore,  and  from  the  ship,  at  D,  suppose  the  angles  CDB 
and  ADB  are  found  equal,  respectively,  to  40°  and  60°. 

With  the  complement  of  CDB,  50°,  draw  the  lines 
BE  and  CE;  the  point  of  intersection  will  be  the  center 
of  a  circle,  on  some  point  of  whose  circumference  the 
ship  must  be.  Then,  with  the  complement  of  the  angle  ADB,  30°,  draw  the  lines  AF  and  BF,  meeting 
at  F,  which  point  will  be  the  center  of  another  circle,  on  some  point  of  whose  circumference  the  ship 
must  be.  Then  D,  the  point  of  intersection  of  the  circumference  of  the  two  circles,  will  be  the  position 
of  the  ship. 


Fig.  20. 


46 


PILOTIKG, 


The  correctness  of  this  sohation  may  be  seen  as  follows:  Take  the  first  circle,  DBC;  in  the  triangle 
EBC,  the  angle  at  E,  the  center,  cquah  i80°— 2x50°=  2  (90°  -50° ),  twice  the  complement  of  50°,  which 
is  twice  the  observed  angle;  now  if  the  angle  at  the  center  subtended  by  the  chord  BC'  equals  twice  the 
observed  angle,  then  the  angle  at  any  point  on  the  circumference  subtended  by  that  chord,  which  equals 
half  the  angle  at  the  center,  eiiuals  the  observed  angle;  so  the  required  condition  is  fulfilled.  Should 
either  of  the  angles  exceed  90°,  the  excess  of  the  angle  over  90°  must  be  laid  off  on  the  opposite  side  of 
the  lines  joining  the  stations. 

153.  It  may  be  seen  that  the  intersection  of  the  circles  becomes  less  sharp  as  the  centers  'E  and  F 
approach  each  other;  and  finally  that  the  problem  becomes  indeterminate  when  the  centers  coincide, 
that  is,  when  the  three  observed  points  and  the  observer's  position  all  fall  upon  the  same  circle;  the 
two  circles  are  then  identical  and  there  is  no  intersection;  such  a  case  is  called  a  "revolver,"  because 
the  protractor  will  revolve  around  the  whole  circle,  everywhere  passing  through  the  observed  points. 
The  avoidance  of  the  revolver  and  the  employment  of  large  angles  and  short  distances  form  the  keys 
to  the  selection  of  favorable  objects. 

Generally  speaking,  the  observer,  in  judging  which  objects  are  the  best  to  be  taken,  can  picture 
in  his  eye  the  circle  passing  through  the  three  points  and  note  whether  it  comes  near  to  his  own 
position.  If  it  does,  he  must  reject  one  or  more  of  the  objects  for  another  or  others.  It  should  be 
remembered  that  he  must  avoid  not  only  the  condition  where  the  circle  passes  exactly  through  his 
position  (when  the  problem  is  wholly  indeterminate),  but  also  all  conditions  approximating  thereto, 
for  in  such  cases  the  circles  will  intersect  at  a  very  acute  angle,  and  the  inevitable  small  errors  of  the 
observation  and  plotting  will  produce  large  errors  in  the  resulting  fix. 

Without  giving  an  analysis  of  reasons,  which  may  be  found  in  various  works  that  treat  the 
problem  in  detail,  the  following  may  be  enumerated  as  the  general  conditions  which  result  in  a  (/ood  fix: 

(a)  When  the  center  object  of  the  three  lies  between  the  observer  and  a  line  joining  the  other  two, 
or  lies  nearer  than  either  of  the  other  two.  , 

(b)  When  the  sum  of  the  right  and  left  angles  is  equal  to  or  greater  than  180°. 

(c)  When  two  of  the  objects  are  in  range,  or  nearly  so,  and  the  angle  to  the  third  is  not  less  than  30°. 

(d)  When  the  three  objects  are  in  the  same  straight  line. 

A  condition  that  limits  all  of  these  is  that  angles  should  be  large — at  least  as  large  as  30° — excepting 
in  the  case  where  two  objects  are  in  range  or  nearly  so,  and  then  the  other  angle  must  be  of  good  size. 
When  possible,  near  objects  should  be  used  rather  than  distant  ones.  The  navigator  should  not  fall  into 
the  error  of  assuming  that  objects  which  would  give  good  cuts  for  a  cross  bearing  are  necessarily 
favorable  lor  the  three-point  solution. 

In  a  revolver,  the  angle  formed  by  lines  drawn  from  the  center  object  to  the  other  two,  added  to 
the  sum  of  the  two  observed  angles,  equals  180°.  A  knowledge  of  this  fact  may  aid  in  the  choice  of 
objects. 

If  in  doubt  as  to  the  accuracy  with  which  the  angles  will  plot,  a  third  angle  to  a  fourth  object  may 
be  taken.  Another  way  to  make  sure  of  a  dou1)tful  fix  is  to  take  one  compass 
bearing,  by  means  of  which  even  a  revolver  may  be  made  to  give  a  good 
position. 

154.  The  Danger  Angle. — When  running  in  sight  of  the  land,  it  is 
frequently  of  the  greatest  importance  for  the  navigator  to  assure  himself  that 
the  course  leads  clear  of  outlying  dangers,  and  the  Danger  Angle  affords  a  con- 
venient means  of  so  doing.  There  are  two  sorts  of  danger  angles — the  hori- 
zontal angle  taken  between  two  objects,  and  the  vertical  angle  of  a  single  one. 
The  former  will  be  first  described. 

155.  Suppose,  in  figure  21,  that  a  vessel  standing  along  the  coast  on  the 
course  indicated  nmst  pass  an  offshore  danger  between  two  well-marked 
objects,  A  and  B,  and  that,  allowing  a  safe  margin,  it  is  desired  to  approach 
no  closer  than  the  point  O.  Through  the  points  A,  B,  and  O  draw  a  circle, 
by  the  usual  methods  of  geometry,  and  observe  that  no  portion  of  the  danger 
lies  without  the  circle.  Measure  the  angle  AOB  with  a  protractor,  and  con- 
sider this  the  danger  angle;  as  the  ship  draws  near,  take  frequent  observa- 
tions with  a  sextant  of  the  angle  subtended  by  the  objects  A  and  B.  As 
long  as  the  angle  is  less  than  the  danger  angle  the 
ship  is  without  the  circle;  but  if  the  angle  increases 
to  the  amount  of  the  danger  angle,  she  is  on  the 
circle,  and  should  at  once  sheer  off  to  avoid  approach- 
ing closer.  The  reason  will  be  evident  from  the  con- 
sideration that  all  angles  AOB,  AO'B,  AO'^B,  AC^B, 
subtended   at  points  on  the  circumference  of    the 

circle  by  the  chord  AB,  are  equal. 

1 56.  The  vertical  danger  angle  is  an  application  of  the  same  principle 
where  there  is  in  sight  only  one  well-charted  object  and  that  is  of  known  height. 
Draw  a  circle  with  that  object  as  a  center  and  of  such  radius  that  no  neighboring 
dangei"s  lie  beyond  its  circumference;  note,  from  Table  33,  the  vertical  angle 
which  is  subtended  by  the  known  height  at  the  distance  chosen  as  a  radius, 
and,  by  frequent  observations  in  i)assing,  make  sure  that  this  danger  angle  is 
not  exceeded.  By  a  simple  modification,  a  ship  passing  inshore  of  an  isolated  z 
rock  or  shoal  could  be  navigated  clear  by  means  of  a  vertical  danger  angle  which 
was  not  allowed  to  decrease  below  that  corresponding  to  a  safe  distance. 

Considerations  governing  the  taking  of  vertical  angles  are  given   in  the 
description  of  finding  position  by  one  bearing  and  the  distance  (arts.  139,  140).  Y'' 

157.  The  Danger  Bearing. — This  is  a  method  by  which  the  navigator  is 
warned  by  a  compass  bearing  when  the  course  is  leading  into  danger.     Suppose 
a  vessel  to  be  steering  a  course,  as  indicated  in  figure  22,  along  a  coast  which  must  not  be  approached 
within  a  certain  distance,  the  landmark  A  being  a  guide.     Let  the  navigator  draw  through  A  the  line 


A 


Fig.  22. 


PILOTING.  47 

XA,  clear  of  the  danger  at  all  points,  and  note  its  direction  bj-  the  compass  rose;  then  let  frequent 
bearings  be  taken  as  the  ship  proceeds,  and  so  long  as  the  bearings,  YA,  ZA,  are  to  the  right  of  XA  he 
may  be  assured  that  he  is  on  the  left  or  safe  side  of  the  lines. 

If,  as  in  the  case  given,  there  is  but  one  object  in  sight  and  that  nearly  ahead,  it  would  be  very 
difficult  to  get  an  exact  position,  but  this  method  would  always  show  whether  or  not  the  ship  was  on  a 
good  course,  and  would,  in  consequence,  be  of  the  greatest  value.  And  even  if  there  were  other  objects 
visible  by  which  to  get  an  accurate  fix  it  would  be  a  more  simple  matter  to  note,  by  an  occasional  glance 
over  the' sight-vane  of  the  pelorus  or  compass,  that  the  ship  was  making  good  a  safe  course  than  to  be 
put  to  the  necessity  of  plotting  the  position  each  time. 

15§.  It  will  occasionally  occur  that  two  natural  objects  will  so  lie  that  when  in  range  they  mark 
a  danger  bearing;  advantage  should  be  taken  of  all  such,  as  they  are  easier  to  observe  than  a  compass 
bearing;  but  if  in  a  locality  with  which  the  navigator  has  not  had  previous  acquaintance  the  compass 
bearing  of  all  ranges  should  be  observed  and  compared  with  that  indicated  on  the  chart  in  order  to 
make  sure  of  the  identity  of  the  objects.  The  utility  of  ranges,  either  artificial  or  natural,  as  guides  in 
navigation  is  well  recognized. 

159.  SouNDiX(iS. — The  practice  should  be  followed  of  employing  one  or  two  leadsmen  to  take  and 
report  soundings  continuously  while  in  shoal  water  or  in  the  vicinity  of  dangers.  The  soundings  must 
not  be  regarded  as  fixing  a  position,  but  they  afford  a  check  upon  the  positions  obtained  by  other 
methods.  An  exact  agreement  with  the  soundings  on  the  chart  need  not  be  expected,  as  there  may  be 
some  little  inaccuracies  in  reporting  the  depth  on  a  shij)  moving  with  speed  through  the  water,  or  the 
tide  may  cause  a  discrepancy,  or  the  chart  itself  may  lack  perfection;  but  the  soundings  should  agree  in 
a  general  way,  and  a  marked  departure  from  the  characteristic  bottom  shown  on  the  chart  should  lead 
the  navigator  to  verify  his  position  and  proceed  with  caution;  especially  is  this  true  if  the  water  is  more 
shoal  than  expected. 

160.  But  if  the  soundingsinshallow  water  when  landmarks  are  in  sight  serve  merely  as  an  auxiliary 
guide,  those  taken  (usually  with  the  patent  sounding  machine  or  deep-sea  lead)  when  there  exist  no 
other  means  of  locating  the  ])osition,  fulfill  a  nuich  more  important  purpose.  In  thick  weather,  when 
approaching  or  running  close  to  the  land,  and  at  all  times  when  the  vessel  is  in  less  than  100  fathoms 
of  water  and  her  pf)sition  is  in  doubt,  soundings  should  be  taken  continuously  and  at  regular  intervals, 
and,  with  the  character  of  the  bottom,  systematically  recorded.  By  laying  the  soundings  on  tracing 
paper,  along  a  line  which  represents  the  track  of  the  ship  according  to  the  scale  of  the  chart,  and  then 
moving  the  i)aper  over  the  chart,  keeping  the  various  courses  parallel  to  the  corresponding  directions 
on  the  chart,  until  the  observed  soundings  agree  with  those  laid  down,  the  ship's  position  will  in  general 
be  quite  well  determined.  While  some  localities,  by  the  sharpness  of  the  characteristics  of  their 
soundings,  lend  themselves  better  than  others  to  accurate  determinations  by  this  method,  there  are  few 
places  where  the  mariner  can  not  at  least  keep  out  of  danger  by  the  indications,  even  if  they  tell  him  no 
more  than  that  the  time  has  come  when  he  must  anchor  or  lie  off  till  conditions  are  more  favorable. 

161.  Lights. — Before  coming  within  range  of  a  light  the  navigator  should  ac(iuaint  himself  with 
its  characteristics,  so  that  when  sighted  it  will  be  recognized.  The  charts,  sailing  directions,  and  light 
lists  give  information  as  to  the  color,  character,  and  range  of  visibility  of  the  various  lights.  Care  should 
be  taken  to  note  all  of  these  and  compare  them  when  the  light  is  seen.  If  the  light  is  of  the  flashing, 
revolving,  or  occulting  variety  the  duration  of  its  periods  should  be  noted  to  identify  it.  If  a  fixed 
light,  a  method  that  may  be  employed  to  make  sure  that  it  is  not  a  vessel's  light  is  to  descend  several 
feet  inunediately  after  sighting  it  and  observe  if  it  disappears  from  view;  a  navigation  light  will  usually 
do  so,  excepting  in  misty  weather,  while  a  vessel's  light  will  not.  The  reason  for  this  is  that  naviga- 
tion lights  are  as  a  rule  sufficiently  powerful  to  be  seen  at  the  farthest  point  to  which  the  ray  can  reach 
without  being  interrupted  by  the  earth's  curvature.  They  are  therefore  seen  at  the  first  moment  that 
the  ray  reaches  an  observer  on  a  ship's  deck,  and  are  cut  off  if  he  lowers  the  eye.  A  vessel's  light,  on 
the  other  hand,  is  usually  limited  by  its  intensity  and  does  not  carry  beyond  a  distance  within  which  it 
it  is  visible  at  all  heights. 

Care  nuist  be  taken  to  avoid  being  deceived  on  first  sighting  a  light,  as  there  are  various  errors  into 
which  the  inexperienced  may  fall.  The  glare  of  a  powerful  light  is  often  seen  beyond  the  distance  of 
visibility  of  its  direct  rays  by  the  reflection  downward  from  particles  of  mist  in  the  air;  the  same  mist 
may  also  cause  a  white  light  to  have  a  distinctly  reddish  tinge,  or  it  may  obscure  a  light  except  within 
shoVt  distances.  AVhen  a  light  is  picked  up  at  the  extreme  limit  at  which  the  height  of  the  observer 
will  permit,  a  fixed  light  may  appear  flashing,  as  it  is  seen  when  the  ship  is  on  the  crest  of  a  wave,  and 
lost  when  in  the  hollow. 

Many  lights  are  made  to  show  different  colors  in  different  sectors  within  their  range,  and  by  con- 
sulting his  chart  or  books,  the  navigator  may  be  guided  by  the  color  of  the  ray  in  which  he  finds  himself; 
in  such  lights  one  color  is  generally  used  on  bearings  whence  the  approach  is  clear,  and  another  covers 
areas  where  dangers  are  to  be  encountered. 

The  visibility  of  lights  is  usually  stated  for  an  assumed  height  of  the  observer's  eye  of  15  feet,  and 
must  be  modified  accordingly  for  any  other  height.  But  it  should  be  remembered  that  atmospheric  and 
other  conditions  considerably  affect  the  visibility,  and  it  nmst  not  he  positively  assumed,  on  sighting  a 
light,  even  in  perfectly  clear  weather,  that  a  vessel's  distance  is  equal  to  the  range  of  visibility;  it  may  be 
either  greater  or  less,  as  the  path  of  a  ray  of  light  near  the  horizon  receives  extraordinary  deflection  under 
certain  circumstances;  the  conditions  governing  this  deflection  are  discussed  in  article  301,  Chapter  X. 

162.  Buoys. — While  buoys  are  valuable  aids,  the  mariner  should  always  employ  a  certain  amount 
of  caution  in  being  guided  by  them.  In  the  nature  of  things  it  is  never  possible  to  be  certain  of  finding 
buoys  in  correct  position,  or,  indeed,  of  finding  them  at  all.  Heavy  seas,  strong  currents,  ice,  or  collisions 
with  passing  vessels  may  drag  them  from  their  places  or  cause  them  to  disappear  entirely,  and  they  are 
especially  imcertain  in  unfrequented  waters,  or  those  of  nations  that  do  not  keep  a  good  lookout  upon 
their  aids  to  navigation.  When,  therefore,  a  buoy  marks  a  place  where  a  ship  must  be  navigated  with 
caution,  it  is  well  to  have  a  danger  angle  or  bearing  as  an  additional  guide  instead  of  placing  too  much 
dependence  upon  the  buoy  being  in  place. 

Different  nations  adopt  different  systems  of  coloring  for  their  buoys;  an  important  feature  of 
many  such  systems,  including  those  adopted  by  the  United  States  and  various  other  great  maritime 


48  PILOTING. 

nations  (though  not  all),  consists  in  placing  black  l)uoyH  to  be  left  on  the  starboard  hand  of  a  vessel 
(johu/  out  of  a  liarbor  or  fairway,  and  red  biioys  (the  color  of  the  port  side  light)  on  the  port  hand.  ,In 
these  various  systems  the  color  and  character  of  the  buoy  are  such  as  to  denote  the  special  purpose  for 
which  it  is  employed. 

163.  Fogs  and  Fog  Signals. — As  with  lights,  the  navigator  should,  in  a  fog,  acquaint  himself 
with  the  characteristics  of  the  various  sound  signals  which  he  is  likely  to  pick  up,  and  when  one  is 
heard,  its  jjeriods  sh<Jbld  be  timed  and  comjjared  with  those  given  in  the  light  lists  to  insure  its  proper 
identity. 

Experiment  has  demonstrated  that  sound  is  convej'ed  through  the  atmosphere  in  a  very  uncertain 
way;  that  its  intensity  is  not  always  increased  as  its  origin  is  approached,  and  that  areas  within  its  range 
at  one  time  will  seem  silent  at  another.  Add  to  these  facts  the  possibility  that,  for  some  cause,  the 
signal  may  not  be  working  as  it  should  be,  and  we  have  reason  for  observing  the  rule  to  proceed  with 
the  utmost  caution  when  running  near  the  land  in  a  fog. 

The  best  guide  is  the  lead,  and  that  should  be  kept  going  constantly.  The  method  of  plotting 
soundings  descril^ed  in  article  160  will  give  the  most  reliable  position  that  is  obtainable.  Moreover, 
the  lead  will  warn  the  navigator  of  the  approach  to  shallow  water,  when,  if  his  position  is  at  all  in 
doubt,  it  is  wisest  to  anchor  before  it  becomes  too  late. 

"When  running  slowly  in  a  fog  (which  caution,  as  well  as  the  law,  requires  that  one  should  do)  it 
must  be  borne  in  mind  that  the  relative  effect  of  current  is  increased;  for  instance,  the  angle  of  deflec- 
tion from  the  course  caused  by  a  cross-set  is  greater  at  low  than  at  high  speed. 

It  is  worth  remembering  that  when  in  the  vicinity  of  a  bold  bluft"  shore  vessels  are  sometimes 
warned  of  a  too  close  approach  by  having  their  own  fog  signals  echoed  back  from  the  cliffs;  in<leed,  from 
a  knowledge  of  the  velocity  of  sound  (art.  314,  Chap.  XI)  it  is  possible  to  gain  some  rough  idea  of  the 
distance  in  such  a  case. 

164.  Tides  and  Currents.  « — The  information  relating  to  the  tides  given  on  the  chart  and  in  other 
publications  should  be  studied,  as  it  is  of  importance  for  the  navigator  to  know  not  only  the  height  of 
the  tide  above  the  plane  of  reference  of  the  chart,  but  also  the  direction  and  force  of  the  tidal  current. 

The  plane  of  reference  adopted  for  soundings  varies  with  different  charts;  on  a  large  number  it  is 
that  of  mean  low  water,  and  as  no  plane  of  reference  above  that  of  mean  low  water  is  ever  employed, 
the  navigator  may  with  safety  refer  his  soundings  to  that  level  when  in  doubt. 

When  traversing  waters  in  which  the  depth  exceeds  the  vessel's  draft  by  but  a  small  margin, 
account  must  be  taken  of  the  fact  that  strong  winds  or  a  high  barometer  may  cause  the  water  to  fall 
below  even  a  very  low  plane  of  reference.  On  coasts  where  there  is  much  diurnal  inequality  in  the 
tides,  the  amount  of  rise  and  fall  can  not  be  depended  upon,  and  additional  caution  is  necessary. 

A  careful  distinction  should  be  made  between  the  vertical  rUe  and  fall  of  the  tide,  which  is  marked 
at  the  transition  periods  by  a  stationary  height,  or  stand,  and  the  tidal  current,  which  is  the  horizontal 
transfer  of  water  as  a  result  of  the  difference  of  level,  producing  the  flood  and  ehb,  and  the  intermediate 
condition,  or  slack.  It  seldom  occurs  that  the  turn  of  the  tidal  stream  is  exactly  coincident  with  the 
high  and  low  water,  and  in  some  channels  the  current  may  outlast  the  vertical  movement  which  pro- 
duces it  by  as  much  as  three  hours,  the  effect  being  that  when  the  water  is  at  a  stand  the  tidal  stream 
is  at  its  maximum,  and  when  the  current  is  slack  the  rise  or  fall  is  going  on  with  its  greatest  rapidity. 
Care  must  be  taken  to  avoid  confounding  the  two.  Usually,  more  complete  data  is  furnished  in  charts 
and  tide  tables  regarding  the  rise  and  fall,  and  it  frequently  occurs  that  the  information  regarding  the 
tidal  current  is  comparatively  meager;  the  mariner  must  therefore  take  every  means  to  ascertain  for 
himself  the  direction  and  force  of  the  tidal  and  other  currents,  either  from  the  set  shown  between  suc- 
cessive well-located  jiositions  of  the  ship,  or  by  noting  the  ripple  of  the  water  around  buoys,  islets,  or 
shoals,  the  direction  in  which  vessels  at  anchor  are  riding,  and  the  various  other  visible  enacts  of  the 
current. 

Current  arrows  on  the  chart  must  not  be  regarded  as  indicating  absolutely  the  conditions  that  are 
to  be  encountered.  They  represent  the  mean  of  the  direction  and  force  observed,  but  the  observations 
upon  which  they  are  based  may  not  be  complete,  or  there  may  be  reasons  that  bring  about  a  departure 
from  the  normal  state. 

Generally  speaking,  the  rise  and  fall  and  strength  of  current  are  at  their  minimum  along  straight 
stretches  of  coast  upon  the  open  ocean,  while  bays,  bights,  inlets,  and  large  rivers  operate  to  augment 
the  tidal  effects,  and  it  is  in  the  vicinity  of  these  that  one  finds  the  highest  tides  and  strongest  currents. 
The  navigator  need  therefore  not  be  surprised,  in  cruising  along  a  coast,  to  notice  that  his  vessel  is  set 
more  strongly  toward  or  from  the  shore  in  passing  an  indentation,  and  that  the  evidences  of  tide  will 
appear  more  marked  as  he  nears  its  mouth. 

1 65.  Charts.  & — The  chart  should  be  carefully  studied,  and  among  other  things  all  of  its  notes  should 
be  read,  as  valuable  information  may  be  given  in  the  margin  which  it  is  not  practicable  to  place  upon 
the  chart  abreast  the  locality  affected. 

The  mariner  will  do  well  to  consider  the  source  of  his  chart  and  the  authority  upon  which  it  is  based. 
He  will  naturally  feel  the  greatest  confidence  in  a  chart  issued  by  the  Government  of  one  of  the  more 
important  maritime  nations  which  maintains  a  well-equipped  office  for  the  especial  purpose  of  acquiring 
and  treating  hydrographic  information.  He  should  note  the  character  of  the  survey  from  which  the 
chart  has  been  constructed;  and,  finally,  he  should  be  especially  careful  that  the  chart  is  of  recent  issue 
or  bears  correction  of  a  recent  date — facts  that  should  always  be  clearly  shown  upon  its  face. 

It  is  well  to  proceed  with  caution  when  the  chart  of  the  locality  is  based  upon  an  old  survey,  or  one 
whose  source  does  not  carry  with  it  the  presumption  of  accuracy.  Even  if  the  original  survey  was  a 
good  one,  a  sandy  bottom,  in  a  region  where  the  currents  are  strong  or  the  seas  heavy,  is  liable  to 
undergo  in  time  marked  changes;  and  where  the  depth  is  affected  by  the  deposit  or  removal  of  silt,  as 
in  the  vicinity  of  the  estuaries  of  large  river  systems,  the  behavior  is  sometimes  most  capricious.  Large 
blank  spaces  on  the  chart,  where  no  soundings  are  shown,  may  be  taken  as  an  indication  that  no  sound- 

oSee  also  Chapter  XX.  bSee  also  article  86  and  following  articles,  Chapter  II. 


PILOTING.  49 

ings  were  made,  and  are  to  be  regarded  with  suspicion,  especially  if  the  region  abounds  in  reefs  or  pin- 
nacle rocks,  in  which  case  only  the  the  closest  sort  of  a  survey  can  be  considered  as  revealing  all  the 
dangers.     AH  of  these  facts  must  be  duly  weighed. 

When  navigating  by  landmarks  the  chart  of  the  locality  which  is  on  the  largest  scale  should  be 
used.  The  hydrography  and  topography  in  such  charts  appear  in  greater  detail,  and — a  most  important 
consideration — bearings  and  angles  may  be  plotted  with  increased  accuracy. 

166,  Records. — It  will  be  found  a  profitable  practice  to  pay  careful  attention  to  the  recording  of 
the  various  matter  relating  to  the  piloting  of  the  ship.  A  notebook  should  be  kept  at  hand  on  deck  or 
on  the  bridge,  in  which  are  to  be  entered  all  bearings  or  angles  taken  to  fix  the  position,  all  changes  of 
course,  important  soundings,  and  any  other  facts  bearing  upon  the  navigation.  (This  book  should  be 
different  from  the  one  in  which  astronomical  sights  and  offshore  navigation  are  worked.)  The  entries, 
though  in  memorandum  form,  should  be  complete;  it  should  be  clear  whether  bearings  and  courses  are 
true,  magnetic,  or  by  compass;  and  it  is  especially  important  that  the  time  and  patent  log  reading  should 
be  given  for  each  item  recorded.  The  value  of  this  book  will  make  itself  apparent  in  various  directions; 
it  will  afford  accurate  data  for  the  writing  of  the  ship's  log;  it  will  furnish  interesting  information  for 
the  next  run  over  the  same  ground;  it  will  provide  a  means  by  which,  if  the  ship  be  shut  in  by  fog, 
rain,  or  darkness,  or  if  there  be  difficulty  in  recognizing  landmarks  ahead,  the  last  accurate  fix  can  be 
plotted  and  brought  forward;  and,  finally,  if  there  should  be  a  mishap,  the  notebook  would  furnish 
evidence  as  to  where  the  trouble  has  been. 

The  chart  on  which  the  work  is  done  should  also  be  made  an  intelligible  record,  and  to  this  end 
the  pencil  marks  and  lines  should  not  be  needlessly  numerous,  heavy,  or  long.  In  plotting  bearir\gs, 
draw  lines  only  long  enough  to  cover  the  probable  position.  Mark  intersections  or  positions  by  drawing 
a  small  circle  around  them,  and  writing  neatly  abreast  them  the  time  and  patent  log  reading.  Indicate 
the  courses  and  danger  bearings  by  full  lines  and  mark  them  appropriately,  preferably  giving  both 
magnetic  (or  true)  and  compass  directions.  A  great  number  of  lines  extending  in  every  direction  may 
lead  to  confusion;  however  remote  the  chance  may  seem,  the  responsibilities  of  piloting  are  too  serious 
to  run  even  a  small  risk. 

Finally,  on  anchoring,  record  and  plot  the  position  by  bearings  or  angles  taken  after  coming  to; 
observe  that  the  berth  is  a  safe  one,  or,  if  in  doubt,  send  a  boat  to  sound  in  the  vicinity  of  the  ship  to 
make  sure. 

22489—03 4 


50 


THE    SAILINGS. 


CHAPTER  V. 

THE  SAILINGS. 


167.  In  considering  a  ship's  position  at  sea  with  relerence  to  any  other  place,  either  one  that  has 
been  left  or  one  toward  which  the  vessel  is  bound,  five  terms  are  involved — the  Course,  the  Distance, 
the  Difference  of  Latitude,  the  Difference  of  Longitude,  and  the  Departure. "^  The  solutions  of  the  various 
problems  that  arise  from  the  mutual  relation  of  these  quantities  are  called  Sailings. 

16§.  Kinds  of  Sailin(js. — When  the  only  quantities  involved  are  the  course,  distance,  difference 
of  latitude,  and  departure,  the  process  iw  denominated  Plane  Sailing.  In  this  method  the  earth  is 
regarded  as  a  plane,  and  the  operation  prt)ceeds  as  if  the  vessel  sailed  always  on  a  perfectly  level  sur- 
face. When  two  or  more  courses  are  thus  considered,  the^-  are  comV)ined  by  the  method  ot  Traverse 
Sailing.  It  is  evident  that  the  number  of  miles  of  latitude  and  departure  can  thus  be  readily  deduced; 
but,  while  one  mile  always  equals  one  minute  in  difference  of  latitude,  one  mile  of  departure  corre- 
sponds to  a  difference  of  longitude  that  will  vary  with  the  latitude  in  which  the  vessel  is  sailing.  Plane 
sailing,  therefore,  furnishes  no  solution  where  difference  of  longitude  is  considered,  and  for  such  solu- 
tion resort  must  be  had  to  one  of  several  methods,  which,  by  reason  of  their  taking  account  of  the 
spherical  figure  of  the  earth,  are  called  Spherical  Sailings. 

When  a  vessel  sails  on  an  east  or  west  course  along  a  parallel  of  latitude,  the  method  of  converting 
departure  into  difference  of  longitude  is  called  Parallel  Sailing.  When  the  course  is  not  east  or  w-est, 
and  thus  carries  the  vessel  through  various  latitudes,  the  conversion  may  be  made  either  by  Middle 
Latitude  Sailing,  in  which  it  is  assumed  that  the  whole  run  has  been  made  in  the  mean  latitude,  or  by 
Mercator  Sailing,  in  which  the  principle  involved  in  the  construction  of  the  Mercator  chart  (art.  38, 
Chap.  II)  is  utilized. 

Great  Circle  Sailing  deals  with  the  courses  and  distances  between  any  two  points  when  the  track 
followed  is  a  gre^t  circle  of  the  terrestial  sphere.  A  modification  of  this  method  which  is  adopted 
under  certain  circumstances  is  called  (Jonipositc  Sailing. 

PLANE  SAILING. 

169.  In  Plane  Sailing,  the  curvature  of  the  earth  being  neglected,  the  relation  between  the  elements 
1-'  of  the  rhumb  track  joining  any  two  points  may  be  considered  from  the  plane 
right  triangle  formed  by  the  meridian  of  the  place  left,  the  parallel  of  the  place 
arrived  at,  and  the  rhumb  line.  In  figure  23,  T  is  the  point  of  departure; 
T^,  the  point  of  destination;  Tn,  the  meridian  of  departure;  T^n,  the  parallel 
of  destination;  and  XT'*,  the  rhumb  line  between  the  points.  Let  C  repre- 
sent the  course,  T^Tn;  Dist.,  the  distance,  TT^;  DL,  the  difference  of  latitude, 
Tn;  and  Dep.,  the  departure,  T^/i.  Then  from  the  triangle  TT^h,  we  have 
the  following: 

8inC=^; 
Dist. ' 


cos  C 


DL. 
Diet.' 


Fig.  23. 


tanC=^. 


From  these  equations  are  derived  the  following  formulse  for  working  the  various  problems  that  may 
arise  in  Plane  Sailing: 


Given. 


Required. 


Course  and  distance . 


("Difference  of  latitude . . . 
(Departure 


Difference  of  latitude  jfCourse 
and  departure. 


Distance - 


Course  and  difference  of   [Distance., 
latitude.  I  [Departure 


Formulse. 


D  L    =Dist.  cosC.    Log  D  L  =  log  Dist. + log  cos  C. 
Dep.  =Di8t.  sin  C.   Log  Dep.  =log  Dist.  +  log  sin  C. 


TanC=?^P-. 
D  L 

Dist.  =5^. 
sinC 


Dist. 
Dep. 


_  DL 
cos  C 
=D  L  tan  C. 


Log  tan  C= log  Dep.— log  D  L. 
Log  Dist. = log  Dep.  —log  sin  C. 

Log  Dist.  =log  D  L  —  log  cos  C. 
LogDep.=log  D  L-flogtanC. 


(I  For  the  definition  of  tliese  terms,  see  article  6,  Chapter  1. 


THE    SAILINGS. 


51 


Given. 


Course  and  departure. 


Required. 

I  Distance 
Difference  of  latitude. 


Distance  and   difference  y        ^"    '" 
of  latitude.  '  \  Departure 


Distance  and  departure. 


I  Course 
Difference  of  latitude. 


Formulae. 


Dist. 


Dep. 
sin  C 

D  L   =5^. 
tan  C 


Log  Dist.  =  log  Dep.  —log  sin  C. 
Log  D  L  =log  Dep.  —log  tan  C. 


^"^^=Di^ 


Log  cos  C=log  D  L  —log  Dist. 
Dep.  =Dist.  sin  C.    LogDep.  =  log  Dist. + log  sin  C. 


SinC=;^fP: 
Dist. 


Log  sin  C= log  Dep.  —log  Dist. 
D  L   =Dist.  cosC.    Log  D  L  =logDist.+logcosC. 


1  70.  The  solution  of  the  plane  right  triangle  may  be  accomplished  either  by  Plane  Trigonometry,  by 
Traverse  Tables,  or  by  construction.  If  the  former  method  is  adopted,  the  logarithms  of  numbers  may 
be  found  in  Table  42,  and  of  the  functions  of  angles  in  Table  44.  A  more  expeditious  method  is  avail- 
able, however,  in  the  Traverse  Tables,  which  give  by  inspection  the  various  solutions.  Table  1  contains 
values  of  the  various  parts  for  each  unit  of  Di.«t.  from  1  to  300,  and  for  each  quarter-point  (2°  49'),  of  C; 
Table  2  contains  values  for  each  unit  of  Dist.  from  1  to  600,  and  for  each  degree  of  C.  The  method  of 
solving  by  construction  consists  in  laying  down  the  various  given  terms  by  scale  upon  a  chart  or  plain 
paper,  and  measuring  thereon  the  terms  required. 

171.  Of  the  various  problems  that  may  arise,  the  first  two  given  in  the  foregoing  table  are  of  much 
the  most  frequent  occurrence.  In  the  first,  the  given  quantities  are  course  and  distance,  and  those  to  be 
found  are  difference  of  latitude  and  departure;  this  is  the  case  where  a  navigator,  knowing  the  distance 
run  on  a  given  course,  desires  to  ascertain  the  amount  made  good  to  north  or  south  and  to  east  or 
west.  In  the  second  case  the  conditions  are  reversed;  this  arises  where  the  course  and  distance  between 
two  points  are  to  be  obtained  from  their  known  difference  of  latitude  and  departure. 


Example:  A  ship  sails  SW.  byW.,  244  miles, 
made  good. 

By  Computation. 


Dist. 
C 

DL 

Dist. 
C 


244 
56°  15' 

135.6 

244 

56°  15' 


log  2.38739 

log  cos  9.74474 


2.13213 


log         ^^ 

log  2.38739 

log  sin   9.91985 


Required  the  <lifference  of  latitude  and  the  departure 

Bi/  Inspection. 

In  Table  1,  find  the  course  SW.  by  W.  (5  points);  it 
occurs  at  the  bottom  of  the  page,  therefore  take  the  names 
of  the  columns  from  the  bottom  as  well;  opposite  244  in 
the  Dist.  column  will  be  seen  Lat.  135.6  and  Dep.  202.9. 


Dep.       202.9        log 


2.30724 


Example:  A  ship  sails  N.  5°  E.,  188  miles.     Required  the  difference  of  latitude  and  the  departure. 


By  Computation. 


Dist. 
C 

DL 

Dist. 
C 

Dep. 


188 

5° 

187.3 

188 
5° 

16.4 


log         2.27416 
log  cos  9.99834 


log 


2.27250 


By  Inspection. 

In  Table  2,  find  the  course  5°;  it  occurs  at  the  top  of  the 
page,  therefore  take  the  names  of  the  columns  from  the 
top;  opposite  188  in  the  Dist.  column  will  be  seen  Lat. 
187.3  and  Dep.  16.4. 


log         2.27416 
log  sin   8.94030 


log 


1.21446 


Example:  A  vessel  is  bound  to  a  port  which  is  136  miles  to  the  north  ami  203  miles  to  the  west  of 
her  position.     Required  the  course  and  distance. 

By  Inspection. 

Enter  Table  1  and  turn  the  pages  until  a  course 
is  found  whereon  the  numbers  136  and  203  are 
found  abreast  each  other  in  the  columns  marked 
respectively  Lat.  and  Dep.  This  occurs  most  nearly 
at  the  course  for  5  points,  the  angle  being  taken 
from  the  bottom,  because  the  appropriate  names 
of  the  columns  are  found  there.  The  course  is 
therefore  NW.  by  W.  Interpolating  for  interme- 
diate values,  the  corresponding  number  in  tke 
Dist.  column  is  about  244.3. 


By  Computation. 

Dep.                         203        log         2.30750 
DL                           136        log         2.13354 

C      (N.)  56°  11'  (\V.) 

log  tan  0.17396 

Dep.                         203 
C                        56°  11' 

log         2.30750 
log  sin  9.91951 

Dist. 


244.3 


log 


2.38799 


52 


THE    SAILINGS. 


Example:  A.s  the  result  of  a  day's  run  a  vessel  changes  latitude  244  miles  to  the  south  and  makes  a 
departure  of  171  miles  to  the  east.     What  is  the  course  and  distance  made  good? 

By  Inspection. 

Enter  Table  2  and  the  nearest  agreement  will 
be  found  on  course  (S.)  35°  (E. ),  the  appropriate 
names  being  found  at  the  top  of  the  page.  The 
nearest  corresponding  Dist.  is  298  miles. 


By  Computation. 

Dep.                        171 
DL                       •   244 

log  2.23300 
log         2.38739 

C       (S.)  35°02^  (E.) 

log  tan  9.84561 

Dep.                        171 
C                       35°  02' 

log  2.23300 
log  sin  9.75895 

Dist, 


297.9 


log 


2.47405 


TRAVERSE  SAILING. 

1 72.  A  Traverse  is  an  irregular  track  made  by  a  ship  in  sailing  on  several  different  courses,  and  the 
method  of  Traverse  Sailing  consists  in  finding  the  difference  of  latitude  and  departure  corresponding  to 
several  courses  and  distances  and  reducing  all  to  a  single  equivalent  course  and  distance.  This  is  done 
by  determining  the  distance  to  north  or  south  and  to  east  or  west  made  good  on  each  course,  taking  the 
algebraic  sum  of  these  various  differences  of  latitude  and  departure  and  finding  the  course  and  distance 
corresponding  thereto.  The  work  can  be  most  expeditiously  performed  by  adopting  a  tabular  form  for 
the  computation  and  using  the  traverse  tables. 

Example:  A  ship  sails  SSE.,  15  miles;  SE.,  34  miL>s;  W.  by  S.,  16  miles;  WNW.,  89  miles;  S.  by  E., 
40  miles.     Required  the  course  and  distance  made  good. 


Courses. 

Dist. 

N. 

s. 

E. 

w. 

SSE. 

15 

13.9 

5.7 

SE. 

34 

24.0 

24.0 

W.  by  S. 

16 

3.1 

15.7 

WNW. 

39 

14.9 

36.0 

S.  by  E. 

40 

39.2 

7.8 

14.9 

80.2 

37.5 

51.7 

S.  by  W. 

66.8 

14.9 

37.5 

65.3 

14.2 

The  result  of  the  various  courses  is,  therefore,  to  carry  the  vessel  S.  by  W.,  66.8  miles  from  her  origrnal 
position. 

PARALLEL    SAILING. 

173.  Thus  far  the  earth  has  been  regarded  as  an  extended  plane,  and  its  spherical  figure  has  not 
been  taken  into  account;  it  has  thus  been  impossible  to  consider  one  of  the  important  terms  involved — 
namely,  difference  of  longitude.  Parallel  Sailing  is  the  simplest  of  the  various  forms  of  Spherical  Sailing, 
being  the  method  of  interconverting  departure  and  difference  of  longitude  when  the  ship  sails  upon  an 
east  or  west  course,  and  therefore  remains  always  on  the  same  parallel  of  latitude. 

In  figure  24  T  and  T'  are  two  places  in  the  same  latitude;  P,  the  adjacent  pole; 
TT'',  the  arc  of  the  parallel  of  latitude  through  the  two  places;  MM^,  the  corre- 
sponding arc  of  the  equator  intercepted  between  their  meridians  PM  and  PM'; 
and  TT',  the  departure  on  the  parallel  whose  latitude  is  TCM  =  OTC,  and  whose 
radius  is  OT. 

Let  DLo  represent  the  arc  of  the  equator  MM^,  which  is  the  measure  of 
MPM',  the  difference  of  longitude  of  the  meridians  PM  and  PM'';  R,  the  equa- 
torial radius  of  the  earth,  CM  =  CT;  r,  the  radius  OT  of  the  parallel  TT'';  and  L, 
the  latitude  of  that  parallel. 

Then,  since  TT'  and  MM'  are  similar  arcs  of  two  circles,  and  are  therefore 
-^proportional  to  the  radii  of  the  circles,  we  have: 


TT'   ^  OT. 
MM'      CM' 

From  the  triangle  COT,  r  =  R  cos  L;  lience 
Dep. R  cos  L 


or, 


Dep.  _  r 
DLo  ~R' 


DLo 


R 


or,  DLo  =  Dep.  sec.  L;  or,  Dep.  =  DIxi  cos  L. 


Thus  the  relations  are  expressed  between  minutes  of  longitude  and  miles  of  departure. 

174.  Two  cases  arise  under  Parallel  Sailing:  First,  where  the  difference  of  longitude  between  two 
places  on  the  same  parallel  is  given,  to  find  the  departure;  and,  second,  where  the  departure  is  given, 
to  find  the  difference  of  longitude. 


THE    SAILINGS.  53 

/ 

In  working  these  problems,  the  computation  can  be  made  by  logarithms;  but  the  traverse  tables 
may  more  conveniently  be  employed.     Kemembering  that  those  tables  are  based  upon  the  formuhe, 

DL=Dist.  cos  C,  and  Uist.=DL  sec  C, 
we  may  substitute  for  the  column  marked  Lat.  the  departure,  for  that  marked  Dist.  the  difference  of 
longitude,  and  for  the  courses  at  top  and  bottom  of  the  page  the  latitude.     The  tables  then  become 
available  for  making  the  required  conversions. 

Example:  A  ship  in  the  latitude  of  49°  30'  sails  directly  east  until  making  good  a  difference  of 
longitude  of  3°  30'.     Required  the  departure. 

By  Computation.  By  Inspection. 

L            49°  30'        log  cos  9.81254  Enter  Table  2  with  the  latitude  as  C  and  the  difference 

DLo             210'        log         2.32222  of  longitude  as  Dist.     As  the  table  is  calculated  only  to 

single  degrees,  we  must  find  the  numbers  in  the  pages  of 

Dep.         136. 4         log         2.13476  49°  and  50°  and  take  the  mean.     Corresponding  to  Dist. 

210  in  the  former  is  Lat.  137.8,  and  in  the  latter  Lat.  135.0. 
The  mean,  which  is  the  required  departure,  is  136.4. 

Example:  A  ship  in  the  latitude  of  38°  sails  due  west  a  distance  of  215.5  miles.  Required  the 
difference  of  longitude. 

By  Computation.  By  Inspection. 

L  38°        log  sec    0.10347  Entering  Table  2  with  the  latitude,  38°,  as  a  course, 

Dep.  215.  5        log  2.33345  corresponding  with  the  number  215.5  in  column  of  Lat., 

is  273.5  in  the  column  of  Dist.     This  is  therefore  the 

y^j    /      273'.  5        log  2.43692  required  difference  of  longitude,  being  equal  to  4°  33'. 5. 

JJ1.0  ^    40  33/    5 

MIDDLE   LATITUDE    SAILING. 

175.  When  a  ship  follows  a  course  obliquely  across  the  meridian  the  latitude  is  constantly 
changing,  and  the  method  of  converting  departure  and  difference  of  longitude  T)y  Parallel  Sailing,  just 
described,  ceases  to  be  applicable. 

In  figure  25,  T  is  the  point  of  departure;  T',  the  point  of  destination ;  P,  ? 
the  earth's  pole;  TT',  the  rhumb  tracrk;  r^TT',  the  course;  Tn,  «iT',  the 
respective  parallels  of  latitude;  and  MM',  the  equator. 

The  difference  of  longitude  between  T  and  T'  is  MPM',  wliich  may 
be  measured  by  the  arc  of  the  equator,  MM',  intercepted  between  their 
meridians.  This  corresponds  to  a  departure  Tn  in  the  latitude  of  T,  and 
to  the  smaller  departure  T'rzi  in  the  higher  latitude  of  T';  but  since  the 
vessel  neither  makes  all  of  the  departure  in  the  latitude  T,  nor  all  of  it 
in  the  latitude  T',  the  departure  actually  made  in  the  passage  must  have 
some  intermediate  value  between  these  extremes.  Dividing  the  total 
difference  of  longitude  into  a  number  of  equal  parts  MPwii,  hjjPhIj,  etc., 
of  such  small  extent  that,  for  the  purposes  of  conversion,  the  change  of 
latitude  corresponding  to  each  may  be  neglected,  we  have  the  total 
departure  made  up  of  the  sum  of  a  number  of  small  departures,  each 
equal  to  the  same  difference  of  longitude,  but  each  different  from  the 
other.  These  will  be  c/j  r^  in  the  latitude  T,  d^  r^  in  the  latitude  ?•,, 
etc.     Hence  we  have:  „       ^_ 

MM'=d,  r-i  sec  MT-|-f?2  ''21  sec  m,  rj  +  da  r^,  sec  7U2  r^,  +  etc.  *-'• 

Now,  if  LL'  be  a  parallel  of  latitude  lying  midwav  between  Tn  and  T'jij,  since  there  will  be  as  many 
of  the  small  parts  lying  above  as  below  it,  and  since  for  moderate  distances  the  ratio  to  be  employed  in 
the  conversion  of  departure  and  difference  of  longitude  may  be  regarded  as  varying  directly  with  the 
latitude,  it  maybe  assumed  for  such  distances  that  the  sum  of  all  of  the  different  small  departures 
equals  the  single  departure  between  the  meridians  measured  in  the  latitude  LL',  and  therefore  that  the 
departure  obtained  by  the  method  of  plane  sailing  on  any  course  may  be  converted  into  difference  of 
longitude  by  multiplying  by  the  secant  of  the  Middle  Latitude. 

The  niethod  of  conversion  based  upon  this  assumption  is  denominated  Middle  lAtitude  Sailing,  and 
by  reason  of  its  convenience  and  simplicity  is  usually  employed  for  short  distances,  such  as  those  covered 
by  a  vessel  in  a  day's  run. 

176.  In  Middle  Latitude  Sailing,  having  found  the  mean  of  the  latitudes,  the  solution  is  identical 
with  that  of  Parallel  Sailing  (art.  173),  substituting  the  Middle  Latitude  for  the  single  latitude  therein 
employed. 

177.  It  niay  be  remarked  that  the  Middle  Latitude  should  not  be  used  when  the  latitudes  are  of 
opposite  name;  if  of  different  names  and  the  distance  is  small,  the  departure  may  be  assumed  equal  to 
the  difference  of  longitude,  since  the  meridians  are  sensibly  parallel  near  the  equator;  but  if  the  distance 
is  great  the  two  portions  of  the  track  on  opposites  of  the  equator  must  be  treated  separatelv. 

]  Example:  A  ship  in  Lat.  42°  30'  N.,  Long.  58°  51'  W.,  sails  SE.  by  S.,  300  miles.     Required  the 
latitude  and  longitude  arrived  at. 

From  Table  1:  Course  SE.  by  S.,  Dist.,  300,  we  find  Lat.,  249.4  S.  (4°  09'.4),  Dep.,  166.7  E. 

Latitude  left,  42°  30'.0  N.  Latitude  left,  42°  30'  N. 

DL,  4    09  .4  S.  Latitude  arrived  at,  38    21    N. 


Latitude  arrived  at,  38    20  .6  N.  2)80    51 


Mid.  latitude,  40    25    N. 


54 


THE    SAILINGS. 


/^~V 


Enter  Table  2  with  the  middle  latitude,  40°,  as  a  course;  the  difference  of  longitude  (DLst. )  cor- 
responding to  the  departure  (Lat.)  166.7  is  217.6;  entering  with  41°,  it  is  220.9;  the  mean  is  219.2 
(3°  39'. 2).  ^ 

KjA      Longitude  left,  58°  51'.0  W. 

DLo,  3    39 .2  E.  * 


Longitude  arrived  at,  55    11  .8  W. 
Example:  A  ship  in  I^t.  39°  42'  S.,  Long.  3°  31'  E.,  sails  S.  42°  W. 


tude  and  longitude  arrived  at. 
From  Table  2:  Course,  S.  42° 
Latitude  left, 
DL, 


236  miles.     Required  the  lati- 


^ 


W.,  Dist.,  236  miles;  we  find  I^t.,  175.4  S.  (2°  55'.4),  Dep.,  157.9  W. 
39°  42'.0  S.  Latitude  left,  39°  42'  S. 

2    55  .4  S.  Latitude  arrived  at,  42    37    S. 


I^atitude  arrived  at,  42    37  .4  S. 


2)82     19 


Mid.  latitude,  41     09    S. 

From  Table  2:  Mid.  Lat.. (course),  41°,  Dep.  (Lat.),  157.9;  we  find  DLo  (Dist.),  209.3  (3= 

Longitude  left,  3°  31'.0  E.  • 

DLo,  3    29  .3  W. 


29'.3). 


Longitude  arrived  at,  0    01  .7  E. 
Example:  A  vessel  leaves  Lat.  49°  57'  N.,  Long.  15°  16'  W.,  and  arrives  at  T^at.  47°  18'  N.,  Long. 
20°  10'  AV.     Required  the  course  and  distance  made  good. 

Latitude  left,  49°  57'  N.  Longitude  left,  15°  16'  W. 

Latitude  arrived  at,  47    18  N.  Longitude  arrived  at,  20    10  W. 

l^L,  {^°159'}S-  ^'^'        ■  {%S'K 

2)97°  15'  N. 
Mid.  latitude,  48    38  N. 

From  Table  2:  Mid.  Lat.  (course),  49°,  DLo  (Dist.),  294;  we  find  Dep.  (Lat.),  192.9. 
From  Table  2:  DL  159  S.,  Dep.  192.9  W.,  we  find  course  S.  51°  W.,  Dist.,  251  miles. 
17§.  The  assumption  upon  which  Middle  Latitude  sailing  is  based — that  the  conversion  may  be 
made  as  if  the  whole  distance  were  sailed  upon  a  parallel  midway  between  the  latitudes  of  departure  and 
destination — while  sufficiently  accurate  for  moderate  distances,  may  be  materially  in  error  where  the 
distances  are  large.  In  such  case,  either  the  method  of  Mercator  Sailing  (art.  179)  must  be  employed, 
or  else  the  correction  given  in  the  following  table  should  be  applied  to  the  mean  latitude  to  obtain  what 
may  be  termed  the  latitude  of  conversion,  being  that  latitude  in  which  the  required  conditions  are 
accurately  fulfilled.     The  table  is  computed  from  the  formula: 

cos  Lc=— , 

■m 

where  Lc  represents  the  latitude  of  conversion,  and  /  and  m  are  respectively  the  differences  of  latitude 
and  of  meridional  parts  (art.  39,  Chap.  II)  between  the  latitudes  of  departure  and  destination. « 


Mid. 
Lat. 

Difference  of  latitude. 

Mid. 
Lat. 

1° 

2°          3° 

4° 

6° 

6° 

7°         8° 

9° 

10°       12° 

14° 

16° 

18° 

20° 

o 

15 

18 
21 

/ 

-86 
-67 
-54 

-85 
-67 
-54 

/ 
-84 
-66 
-53 
-44 
-29 
-21 
-15 
-11 
-  7 

/ 

-83 
-65 
-52 
-42 
-29 
-21 
-14 
-10 

-  6 

-  3 

-  1 

-  1 
0 
1 
2 

/ 

-81 
-63 
-51 

/ 

-79 
-61 
-49 

/ 
-76 
-59 
-47 
-38 
-24 
-17 

-73 
-56 
-44 
-.36 
-23 
-15 

/ 

-69 
-53 
-42 
-33 
-20 
-12 

/ 
-65 
-50 
-39 

-56 
-43 
-32 

/ 
-46 
-34 
-24 

/ 

-34 
-23 

-15 

/ 

-21 

-12 

-  5 

1 

11 

18 

' 
-     6 

1 
7 

o 

15 
18 
21 
24 
30 
35 

24 
30 
35 

-44  1  —44 
-31    -30 
-23   -22 

-41 
-28 
-19 
-13 

-  8 

-  5 

-40 
-26 
-18 
-12 

-  7 

-  3 
0 
2 
3 
4 
5 
6 

-31 1  -24 
-18   -12 
-10   -  5 

-17 

-  6 

2 

8 

14 

20 

-  8 
1 

10 
T6 
22 
28 

12 
21 

28 

■    40 
45 

50 

-17 
-12 

-  8 

-  5 

-  4 

-  3 

-16 

-10 

-  5 

-  1 
2 
4 
5 

7 
8 
9 

-  8 

-  3 

1 

-  6 

-  1 
3 

-  4 
1 
6 
10 
13 
14 
17 
18 
20 

2 

7 
12 

25 
31 

38 

34 
41 
49 

40 
45 
50 

55 
58 
60 

-  5 

-  3 

-  3 

-  4 
-3 

-  2 

—  2 
0 
1 
2 
3 
4 

5 
7 
8 
9 
11 
12 

7 
10 
11 
13 
14 
16 

17 
20 
22 

25 
29 
32 

35 
39 
43 

46 
51 
55 
60 
65 
71 

58 
64 
69 

55 
58 
60 

62 
64 
66 

-  3   -  2    -  1 

-  2   -  1         0 
-2-1'       0 

25 
27 
30 

35 
38 
42 

46 
50 
55 

75 
81 
89 

62 
64 
66 

68 
70 
72 

-  1:       0;       1 

-1           0:          1 

0        0        2 

2 
3 
4 

5 
5 

7 

8 

10 

10 
12 
13 

14 
16 
18 

18 
20 
23 

22 
25 

?8 

33 
37 
41 

46 
51 

57 

61 
67 
76 

78 
87 
97 

98 
109 
123 

68 
70 
72 

a  The  statement  often  made,  that  the  latitude  of  conversion  is  always  greater  than  the  middle  latitude,  is  not  correct 
when  the  compression  of  the  earth  is  taken  into  account,  as  an  inspection  of  the  table  will  show;  that  statement  is  based 
upon  an  assumption  that  the  earth  is  a  perfect  sphere,  and  it  was  iipon  that  assumption  that  a  table  which  appeared  in  early 

editions  of  this  work  was  computed.    The  value  of  the  compression  adopted  for  this  table  is  -  . 


THE    SAILINGS. 


55 


Example:  A  vessel  sails  from  Lat.  10°  13'  S.  to  Lut.  20°  2K  S.,  making  a  departure  of  432  miles. 
Required  the  difference  of  longitude. 
Latitude  left,  10°  13'   S. 

Latitude  arrived  at,     20    21     S. 


2)30    34 


For  Mid.  Lat.  15°  and  Diff.  of  Lat.  10°,  ('orrection,  —65' 


Mid.  latitude. 
Correction, 

15     17    S. 
-  1    05 

14°     12' 
432 

445'.  6 

log  sec 
log 

log 

Lc, 

14''-12     S. 

L<, 
Dep. 

DLo 

.01348 
2.63548 

2.64896 

MERCATOR   SAILING. 

1 79.  Mercator  Sailing  is  the  method  by  which  values  of  the  various  elements  are  determined  from 
<'onsidering  them  in  the  relation  in  which  they  are  .plotted  upon  a  chart  constucted  according  to  the 
Mercator  projection. 

180.  Upon  the  Mercator  chart  (art.  38,  Chap.  II),  the  meridians  being  parallel,  the  arc  of  a  par- 
allel of  latitude  is  shown  as  equal  to  the  corresponding  arc  of  the  equator;  the  length  of  every  such 
arc  is,  therefore,  expanded;  and,  in  order  that  the  rhumb  line  may  appear  as  a  straight  line,  the  merid- 
ians are  also  expanded  by  such  amount  as  is  necessary  to  preserve,  in  any  latitude,  the  proper  propor- 
tion existing  between  a  unit  of  latitude  and  a  unit  of  longitude.  The  lengths  of  small  portions  of  the 
meridian  thus  increased  are  called  meridional  parts  (art.  39,  Chap.  II),  and  these,  computed  for  every 
minute  of  latitude  from  0°  to  80°,  form  the  Table  of  Meridional  Parts  (Table  3), 
by  means  of  which  a  INIercator  chart  may  be  constructed  and  all  problems  of 
Mercator  Sailing  may  be  solved. 

In  the  triangle  ABC  (fig.  26),  the  angle  ACB  is  the  course,  C;  the  side  AC,  the  b 
distance,  Dist. ;  the  side  BC,  the  difference  of  latitude,  DL;  and  the  side  AB,  the 
departure,  Dep.  Then  corresponding  to  the  difference  of  latitude  BC  in  the  lati- 
tude under  consideration,  if  CE  be  laid  off  to  represent  the  meridional  difference 
of  latitude,  in,  completing  the  right  triangle  CEF,  EF  will  represent  the  differ- 
ence of  longitude,  DLo.  The  triangle  ABC  gives  the  relations  involved  in  Plane  dl 
Sailing  as  previously  described;  the  triangle  CEF  affords  the  means  for  the  con- 
version of  departure  and  difference  of  longitude  by  Mercator  Sailing. 

181.  To  find  the  arc  of  the  expanded  meridian  intercepted  between  any  two 
parallels,  or  the  meridional  difference  of  latitude,  when  both  places  are  on  the  same 
side  of  the  equator,  subtract  the  meridional  parts  of  the  lesser  latitude,  as  given 
by  Table  3,  from  the  meridional  parts  of  the  greater;  the  remainder  will  be  the 
meridional  difference  of  latitude;  but  if  the  places  are  on  different  sides  of  the 
equator,  the  sum  of  the  meridional  parts  will  be  the  meridional  difference  of 
latitude. 

1§2.  To  solve  the  triangle  CEF  by  the  traverse  tajbles  it  is  only  necessary  to  substitute  merid- 
ional difference  for  Lat.,  and  difference  of  longitude  for  Dep.  Where  long  distances  are  involved, 
<-arrying  the  computation  beyond  the  limits  of  the  traverse  table,  as  frequently  occurs  in  this  method, 
either  of  two  means  may  be  adopted :  the  problems  may  be  worked  by  the  trigonometrical  formulae, 
using  logarithms,  or  the  given  quantities  involved  may  all  be  reduced  b}'  a  common  divisor  until  they 
fall  within  the  traverse  table,  and  the  results,  when  obtained,  correspondingly  increased.  The  former 
method  is  generally  preferable,  especially  when  the  distances  are  quite  large  and  accurate  results  are 
sought.     The  formulae  for  the  various  conversions  are  as  follows: 


tan  C=5^;  DLo=m  tan  C;  r/i=DLo  cot  C. 


Example:  A  ship  in  Lat.  42°  3('  N.,  Long.  58°  51'  W.,  sails  SE.  by  S.,  300  miles, 
latitude  and  longitude  arrived  at. 

From  Table  1:  Course,  SE.  by  S.,  Dist,  300;  we  find  Lat.  249.4  S.  (4°  09/4). 

Latitude  left,  42°  30'. 0  N.  Merid.  parts,   +2806.4 

DL,  4    09  .4  S. 


Required  the 


Latitude  arrived  at,    38    20  .6  N. 


Merid.  parts, 
m, 


2480.4 


DLo 


By  Computation. 
326.0         log 


33°  45' 


;    217'.8 
\3°  37'.  8 


2.51322 
og  tan  9.82489 


log 


2.33811 


326.0 

By  Inspection. 

Enter  Table  1,   course  3  points;  since  the  quantities 
involved  exceed  the  limits  of  the  table,  divide  by  2; 

abreast  '|(Lat.),  163.0,  find     g—  (Dep.),  108.9;  hence 
DLo=217'.8  or  3°  37'.8. 


Longitude  left, 
DLo, 


58°  51'.0  W, 
3    37  .8  E. 


Longitude  arrived  at,  55    13  .2  W. 


56 


THE    SAILINGS. 


Example:  A  ship  in  Lat.  4°  37'  S.,  Ix)ng.  21°  05'  W.,  sails  N.  14°  W.,  450  miles.     Required  th« 
latitude  and  longitude  arrived  at. 

From  Table  2:  Course,  (N.)  14°  (W.),  Dist.,  450;  we  find  Lat.  436.6  N.  (7°  16'.6). 


Latitude  left,             4°  37'.0  S. 
i)L,                              7    16  .6  N. 

Merid.  parts,  -f  275.4 

Latitude  arrived  at,  2    39  .6  N. 

Merid.  parts,  -f  159.0 

m,                        434.4 

tation. 

By  Inspection. 

DLo 


434.4 


14' 


log         2.63789  From  Table  2:  Course,  14°,  m  (Lat.),  434.4,  we  tind 

log  tan  9.39677  DLo  (Dep. )  108'. 3  W.,  or  1°  48'. 3. 


{v 


108'.  3 
'  48'. 3 


log 


2.03466 


Longitude  left, 
DLo, 


21°  05'.0  W. 
1    48  .3  W. 


Longitude  arrived  at,  22    53  .3  W. 

Example:  Required  the  course  and  distance  by  rhumb  line  from  a  jwint  in  Lat.  42°  03'  N.,  Long. 
70°  04'  W.,  to  another  in  Lat.  36°  59'  N.,  Long.  25°  10'  W. 


Lat.  departure,     42°  03'  N. 
Lat.  destination,  36    59   N. 


DL 


Merid.  pts.,  -f  2770.1 
Merid.  pts.,  —2377.3 


Long,  departure,     70°  04'  W. 
Long,  destination,  25    10  W. 


/  5°  04'1  g 
\      304'/^- 
DLo      2694 
m         392.8 

(E.) 

m,             392.8 

log        3.43040 
log        2.59417 

DLo 

C  (S.)  81°  42' 
DL             304' 

log  tan    .83623 

log  sec   .84056 
log        2.48287 

/44°  54'\t 
\    2694'/^ 


Dist. 


2106 


log       3.32343 


The  course  is  therefore  S.  81°  42'  E.,  and  the  distance  is  2,106  miles.  Since  the  figures  involved 
are  so  large,  it  is  best  to  employ  only  the  method  by  computation.  The  formula  by  which  the  Dist.  is 
obtained  comes  from  Plane  Sailing. 

GREAT   CIRCLE    SAILING. 


1§3.  The  shortest  distance  between  any  two  points  on  the  earth's  surface  is  measured  by  the  arc  of 
the  great  circle  which  passes  through  those  points;  and  the  method  of  sailing  in  which  the  arc  of  a  great 
circle  is  employed  for  the  track  of  the  vessel,  taking  advantage  of  the  fact  that  it  is  the  shortest  route 
possible,  is  denominated  (ireat  Circle  Sailing. 

184.  It  frequently  happens  when  a  great  circle  route  is  laid  down  that  it  is  found  to  lead  across 
the  land,  or  to  carry  the  vessel  into  a  region  of  dangerous  navigation  or  extreme  cold  which  it  is  expe- 
dient to  avoid;  in  such  a  case  a  certain  parallel  should  be  fixed  upon  as  a  limit  of  latitude,  and  a  route 
laid  down  such  that  a  great  circle  is  followed  as  far  as  the  limiting  parallel,  then  the  parallel  itself,  and 
finally  another  great  circle  to  the  port  of  destination.  Such  a  modification  of  the  great  circle  method  is 
called  Composite  Sailing. 

1§5.  The  rhiuah  line  (art.  6,  Chap.  I)  also  called  the  loxodromic  curve,  which  cuts  all  the  meridi- 
ans at  the  same  angle,  has  been  largely  employed  as  a  track  by  navigators  on  account  of  the  ease  with 
which  it  may  be  laid  down  on  a  Mercator  chart.  But  as  it  is  a  longer  line  than  the  great  circle  between 
the  same  i)oints,  intelligent  navigators  of  the  jiresent  day  use  the  latter  wherever  practicable.  On  the 
Mercator  chart,  however,  the  arc  of  a  great  circle  joining  two  points  (unless  both  are  on  the  equator  or 
both  on  the  same  meridian)  will  not  be  projected  as  a  straight  line,  but  as  a  curve  which  seems  to  be 
longer  than  the  rhumb  line;  hence  the  shortest  route  appears  as  a  circuitous  one,  and  this  is  doubtless 
the  reason  that  a  wider  use  of  the  great  circle  has  not  been  made. 

It  should  be  clearly  understood  that  it  is  the  rhumb  line  which  is  in  fact  the  indirect  route,  and 
that  in  following  the  great  circle  the  vessel  is  always  heading  for  her  port,  exactly  as  if  it  were  in  sight, 
while  on  the  course  which  is  shown  as  a  straight  hue  on  the  Mercator  chart  the  vessel  never  heads  for 
her  port  until  at  the  very  end  of  the  voyage. 

186.  The  method  of  great  circle  sailing  is  of  especial  value  to  steamers,  as  such  vessels  need  not, 
in  the  choice  of  a  route,  have  regard  for  the  winds  to  the  same  extent  as  must  a  sailing  vessel ;  but  even  in 
navigating  vessels  under  sail  a  knowledge  of  the  great  circle  cour.se  may  proveof  great  value.  For  example, 
suppose  a  ship  to  be  bound  from  Sydney  to  Valparaiso;  the  first  great  circle  course  is  SE.  by  S.,  while 
the  Mercator  course  is  almost  due  east.     The  distance  is  748  miles  shorter  by  the  former  route  (if  the 


THE    SAILINGS.  57 

p;reat  circle  is  followed  throughout,  though  this  would  lead  to  a  latitude  of  61°  S.).  With  the  wind  at 
E.  J  S.  the  ship  would  lie  nearer  to  the  Mercator  course  on  the  starboard  tack,  assuming  that  she  sailed 
within  six  points  of  the  wind;  but  if  she  took  that  tack  she  would  be  increasing  her  distance  from  the 
port  of  destination  by  45  miles  in  every  10  that  she  sailed;  while  on  the  port  tack,  heading  one  point 
farther  from  the  rhumb,  the  gain  toward  the  port  would  be  9i  miles  out  of  every  10.  Any  course 
between  East  and  SSW.  would  be  better  than  the  Mercator  course;  and  if  the  wind  were  anything  to 
the  eastward  of  SE.  by  S.,  the  ship  would  gain  by  taking  the  port  tack  in  preference  to  the  starboard. 

1§7.  As  the  great  circle  makes  a  different  angle  with  each  meridian  that  is  crossed,  it  becomes 
necessary  to  make  frequent  changes  of  the  ship's  course;  in  practice,  the  course  is  a  series  of  chords 
joining  the  various  points  on  the  track  line. 

If,  while  endeavoring  to  follow  a  great  circle,  the  ship  is  driven  from  it,  as  by  unfavorable  weather, 
it  will  not  serve  the  purpose  to  return  to  the  old  track  at  convenience,  but  it  is  required  that  another 
great  circle  l)e  laid  down,  joining  the  actual  position  in  which  the  ship  finds  herself  with  the  port  of 
destination. 

1§S.  The  methods  of  determining  the  great  circle  course  may  be  divided  generally  into  four 
classes;  namely,  by  Great  Circle  Hailiny  Charts,  by  Computation,  by  the  methods  of  the  Time  Azimuth, 
and  by  Graphic  Approximations. 

1 89.  Great  Circle  Sailing  Charts. — Of  the  available  methods,  that  by  means  'of  charts  espe- 
cially constructed  for  the  purpose  is  considered  greatly  superior  to  all  others. 

A  series  of  great  circle  .sailing  charts  covering  the  navigable  waters  of  the  globe  is  published  by  the 
United  States  Hydrographic  Office.  Being  on  the  gnoinonic  projection  (art.  43,  Chap.  II),  all  great 
circles  are  represented  as  straight  lines,  and  it  is  only  necessary  to  join  any  two  points  by  such  a  line  to 
represent  the  great  circle  track  between  them.  The  courses  and  distance  are  readily  obtainable  by  a 
method  explained  on  the  charts.  The  track  may  be  transferred  to  a  chart  on  the  Mercator  projection 
by  plotting  a  number  of  its  points  by  their  coordinates  and  joining  them  with  a  curved  line. 

The  navigator  who  contemplates  the  use  of  great  circle 
tracks  will  find  it  of  the  greatest  convenience  to  be  pro- 
vided with  these  gnomonic  charts  for  the  regions  which 
his  vessel  is  to  traverse. 

190.  By  CoMPiTATiON. — This  method  consists  in  de- 
termining a  series  of  points  on  the  great  circle  by  their 
coordinates  of  latitude  and  longitude,  plotting  them  upon 
a  Mercator  chart,  and  tracing  the  curve  that  joins  them. 
The  first  point  determined  is  the  vertex,  or  point  of  highest 
latitude,  even  when,  as  sometimes  occurs,  it  falls  without 
that  portion  of  the  great  circle  which  joins  the  points  of 
departure  and  destination.  Fig.  27. 

In  figure  27,  A  represents  the  point  of  departure;  B,  the 
point  of  destination;  AV'B,  the  great  circle  joining  them,  with  its  vertex  at  V;  and  P,  the  pole  of  tlie 
earth. 

Let  Ca  =  PAB,  the  initial  course; 

Cb  =  PBA,  the  final  courser 
La  ,  Lv,  Lb  =  the  latitudesof  the  respective  points  A,  V,  B  =  (90°  —  PA),  (90°  —  PV),  (90°  -  PB). 
Loab,  Loav,  Lobv  =  the  differences  of  longitude  between  A  and  B,  A  and  V,  B  and  V,  respectively,  = 
APB,  APV,  BPV. 
D  =  the  great  circle  distance  between  A  and  B;  and 
q>  —  an  auxiliary  angle  introduced  for  the  computation. 
We  then  have: 

tan  cp  —  cos  Loab  cot  Lb; 
cot  Ca  =  cot  Loab  cos  (La  +  <p)  cosec  cp; 
cot  D  =  cos  Ca  tan  (La  +  ^); 
cos  Lv  =  sin  Ca  cos  La; 
cot  Loav  =  tan  Ca  sin  L  a  . 

Bv  these  formul.T  are  determined  the  initial  course  and  the  total  distance  by  great  circle;  also  the 
latitude  of  the  vertex  and  its  longitude  with  respect  to  A.  By  interchanging  the  subscript  letters  a  and 
B  throughout,  we  should  ol)tain  the  final  course,  and  the  longitude  of  the  vertex  with  respect  to  B;  also 
the  same  total  distance  and  latitude  of  the  vertex  as  before. 

In  performing  this  computation,  strict  regard  must  be  had  to  the  signs  of  the  quantities.  If  the 
points  of  departure  and  destination  are  in  different  latitudes,  the  latitude  of  one  of  these  points  must  he 
regarded  as  negative  with  respect  to  the  other,  and  they  must  be  marked  with  opposite  signs.  Should 
Loav  or  Lobv  assume  a  negative  value,  it  indicates  that  the  vertex  does  not  lie  between  A  and  B,  and  is 
to  be  laid  off  accordingly. 

To  find  other  points  of  the  great  circle,  M,  N,  etc. ,  let  their  latitudes  be  represented  by  L  m  ,  L  jj ,  etc. , 
and  their  longitudes  from  the  vertex  by  Lovj:,  Lovx,  etc.;  then 

tan  Lji  =  tan  Lv  cos  Lovm  ;  or,  cos  Lovm  =  tan  Lm  cot  L  v; 
tan  Ln  =  tan  Lv  cos  Lo v.\ ;  or,  cos  Lo vn  =  tan  L  x  cot  v ; 

and  so  on.  By  these  formulpe  intervals  of  longitude  from  the  vertex  of  5°,  10°,  or  any  amount,  may  be 
assumed,  and  the  corresponding  latitudes  deduced;  or  any  latitude  may  be  assumed  and  its  correspond- 
ing interval  of  longitude  from  the  vertex  found.  Two  positions  will  result  from  each  solution,  and  the 
appropriate  ones  may  be  chosen  by  keeping  in  mind  the  signs  involved. 


68 


THE    SAILINGS. 


Example:  Given  two  places,  one  in  Lat.  40°  X.,  Long.  70°  AV.,  the  other  in  Lat.  30°  S.,  Long.  10° 
W.,  find  the  great  circle  distance  between  them;  also  the  initial  course,  and  the  longitude  of  equator 
crossing. 

La  =  4-40°;  Lb  =  -30°;  Loab=60°. 

Loab  60°  cos  9.69897..  cot  9.76144 

Lb  -  30°         fot  (-)    .23856 

La  +40°  cos  9.88425  sin  9.80807 

<p  -  40°  54'  tan  (-)  9.93753.. co8ec(-)  .18393 

(La  +  <p)   -     0°  54'  cos  9.99995  tan  (-)  8.19616 

Ca  131°  24'  orS.48°36'E cot     (-)9.94532  cos  {-)  9.82041   sin  9.87513  tan  (-)    .05472 

P  89°  24'  or  5,364  miles cot  8.01657 

Ly  +   54°  56'  CDS  9.75938 

Loav  -   53°  54' ...cot  (-)9.86279 

The  initial  course  is  therefore  S.  48°  36'  E.,  and  the  distance  5,364  nautical  miles.  (It  may  be 
found  that  the  course  by  rhumb  line  is  S.  38°  45'  E.  and  the  distance  5,751  miles.)     The  vertex  of  the 

freat  circle  is  in  Lat.  54°  56'  N.,  and  is  53°  54'  in  longitude  from  the  point  A,  in  a  direction  away  from 
\\  hence  it  is  in  Long.  123°  54'  W.     To  find  the  longitude  of  equator  crossing  let  Lm  =  0°;  then  in  the 
^nation, 

cos  LovM=tan  Lm  cot  Lv, 

since  tan  Lm  equals  zero,  cos  I^oi  also  equals  zero,  or  the  longitude  interval  from  the  vertex  is  90°,  which 
is  evident  from  the  properties  of  the  great  circle;  thtjrefore  the  longitude  of  equator  crossing  is 
123°  54'  W.— 90°=33°  54'  W. 

191.  By  Time  Azimtth  Methods. — A  convenient  method  of  obtaining  the  initial  and  final  courses 
in  great  circle  sailing  is  afforded  by  the  tables  and  graphic  methods  which  are  prepared  for  the  solution 
of  the  Tone  Azimuth  problem  (art.  359,  Chap.  XIV).  It  will  be  found  by  comi)arison  that  if  the  lati- 
tude of  the  point  of  departure  be  substituted  for  the  latitude  of  the  observer  in  that  problem,  the  latitude 
of  destination  for  the  declination  of  the  celestial  body,  and  the  longitude  interval  for  the  hour  angle,  the 
solution  for  the  initial  course  will  coincide  with  that  for  the  azimuth;  by  interchanging  the  latitudes  of 
the  points  of  departure  and  destination  the  final  course  will  be  similarly  obtained.  Advantage  may 
thus  be  taken  of  the  various  methods  provided  for  facilitating  the  determination  of  the  azimuth  to  ascer- 
tain the  great  circle  courses  from  one  jwint  to  another. 

192.  By  Graphic  Approximations. — Of  the  numerous  methods  that  fall  w'ithin  this  class  only  two 
need  be  given. 

193.  By  the  use  of  a  TerreKtrial  Globe  the  two  given  points  tetween  which  the  great  circle  track 
is  required  may  be  joined  by  the  shortest  line  between  them,  either  by  means  of  a  piece  of  thread  or 
by  moving  the  globe  until  they  are  brought  to  the  fixed  horizon  which  is  usually  provided;  the  coordi- 
nates of  the  various  points  of  the  track  are  then  transferred  to  the  chart.  The  number  of  minutes  of 
arc,  as  measured  on  the  scale  of  the  horizon  between  the  points,  equals  the  number  of  miles  of  distance; 
if  there  be  no  horizon,  the  measure  may  be  made  by  a  thread  along  the  equator  or  a  meridian. 

194.  The  Method  of  Professor  Airy  consists  in  drawing  on  the  chart  a  rhumb  line  joining  the  two 
points,  and  erecting  at  its  middle  point  a  perpendicular;  the  following  table  should  then  be  entered 
with  the  middle  latitude  as  an  argument,  and  the  "corresponding  parallel"  of  latitude  taken  out 
(noting  whether  it  is  the  same  or  opposite  in  name  to  the  middle  latitude);  where  this  parallel  is  inter- 
sected by  the  perpendicular  that  was  drawn  will  be  the  center  from  which  may  be  swept  an  arc  approx- 
imately representing  the  great  circle  between  the  two  points. 


Middle  lati- 

Correspond- 

Name. 

Middle  lati- 

Correspond- 

Name. 

tude. 

ing  parallel. 

tude. 

o 

ing  parallel. 

o 

o       / 

o        / 

20 

81  13 

Opposite. 

52 

11  33 

Opposite. 

22 

78  16 

Do. 

54 

6  24 

Do. 

24 

74  59 

Do. 

56 

1  13 

Do. 

26 

71  26 

Do. 

58 

4  00 

Same. 

28 

67  38 

Do. 

60 

9  15 

Do. 

30 

63  37 

Do. 

62 

14  32 

Do. 

32 

59  25 

Do. 

64 

19  50 

Do. 

34 

55  05 

Do. 

66 

25  09 

Do. 

36 

50  36 

Do. 

68 

30  30 

Do. 

38 

46  00 

Do. 

70 

35  52 

Do. 

40 

41  18 

Do. 

72 

41  14 

Do. 

42 

36  31 

Do. 

74 

46  37 

Do. 

44 

31  38 

Do. 

76 

52  01 

Do. 

46 

26  42 

Do. 

78 

57  25 

Do. 

48 

21  42 

Do. 

80 

62  51 

Do. 

50 

16  39 

Do. 

THE    SAILINGS.  59 

COMPOSITE  SAILING. 

195.  It  has  already  been  stated  that  when,  for  any  reason,  it  is  impracticable  or  imadvisable  to 
follow  the  great  circle  track  to  its  highest  altitude,  a  limiting  parallel  is  chosen  and  the  route  moditied 
accordingly.     This  method  is  denominated  Composite  Sailing. 

196.  The  shortest  track  between  points  where  a  fixed  latitude  is  not  exceeded  is  made  up  as 
follows: 

1.  A  great  circle  through  the  point  of  departure  tangent  to  the  limiting  parallel. 

2.  A  course  along  the  parallel. 

3.  A  great  circle  through  the  point  of  destination  tangent  to  the  limiting  parallel. 

The  composite  track  may  be  determined  by  Oreat  Circle  Sailing  Chart,  by  CompuUUion,  or  by 
Graph ic  Approximation. 

197.  On  a  Great  Circle  Sailing  Chart,  draw  lines  from  the  points  of  departure  and  destination, 
respectively,  tangent  to  the  limiting  parallel;  transfer  these  great  circles  to  a  Mercator  chart  in  the 
usual  manner,  by  the  coordinates  of  several  points,  including  in  each  case  the  point  of  tangency  to  the 
parallel.  Follow  the  first  great  circle  to  the  parallel;  then  follow  the  parallel;  then  the  second  great 
circle.  Determine  great  circle  courses  and  distances  from  the  gnomonic  chart  as  thereon  described; 
determine  the  distance  along  the  parallel  by  Parallel  Sailing. 

19§.  Bi/  computation,  the  problem  consists  in  finding  the  great  circles  which  pass,  respectively, 
through  the  points  of  departure  and  destination  and  have  their  vertices  in  the  latitude  of  the  limiting 
parallel.     Resuming  the  designation  of  terms  already  employed  (art.  190),  we  have: 

cos  LovA=tan  La  cot  Lv  ; 
cos  LovB=tan  Lb  cot  Lv  ; 

where  Lova  and  Lovb  represent  the  distances  in  longitude  from  A  and  from  B  to  the  respective  points  of 
tangencv;  other  features  of  each  of  the  great  circles  mav  be  determined  in  the  usual  manner. 

Example:  A  vessel  in  Lat.  30°  S.,  Long.  18°  W.,  is*  bound  to  a  point  in  Lat.  39°  S..  Long.  145°  E., 
and  it  is  decided  not  to  go  south  of  the  parallel  of  55°  S.  Find  the  longitude  of  reaching  that  parallel 
and  the  longitude  at  which  it  should  be  left. 

La    =30°  S.;     Lb    =39°  8.;     Lv=55°S. 
Loa  =18°  W.;  Lob  =145°  E. 

La     30°  tan  9.76144         L„     39°  tan  9.90837 

Ly     55°  cot  9.84523         Lv     55°  cot  9.84523 


LovA  66°  09^  E.  cos  9.60667         Lovb  55°  27'  W.  cos  9.75360 
Loa    18    00    W.  Lob  145    00  E. 


Lov    48    09    E.  Lov    89    33    E. 

199.  A  graphic  approximation  to  the  composite  track  may  be  obtained  by  drawing  a  straight  line 
between  the  given  points  on  a  Mercator  chart  and  erecting  at  its  middle  point  a  perpendicular,  which 
shoulii  be  extended  until  it  intersects  the  limiting  parallel.  Then  through  this  intersection  and 
the  two  points  describe  the  arc  of  a  circle,  and  this  will  approximate  to  the  shortest  distance  within  the 
assigned  limit  of  latitude. 

200.  A  terrestrial  glol^e  may  be  employed  for  the  determination  of  the  composite  track;  the 
method  of  its  use  will  suggest  itself. 

201.  Another  approximation  is  obtained  by  joining  the  two  points  with  a  single  great  circle, 
and  following  this  to  its  intersection  with  the  limiting  parallel;  thence  sailing  along  the  parallel  until 
the  great  circle  is  again  intersected;  then  resuming  the  circle  and  following  it  to  the  destination. 


60  DEAD   RECKONING. 


chaptp:r  vl 

dead  keckoning. 


203.  Dead  Reckoning  is  the  process  by  which  the  position  of  a  ship  at  any  instant  is  found  by 
applying  to  the  last  well-determined  position  the  run  that  has  since  been  made,  using  for  the  purpose 
the  ship's  course  and  the  distance  indicated  by  the  log. 

203.  Positions  by  dead  reckoning,  also  spoken  of  as  positions  by  account,  differ  from  those 
determined  by  bearings  of  terrestrial  objects  or  by  observations  of  celestial  bodies  in  being  less  exact, 
as  the  correctness  of  dead  reckoning  depends  upon  the  accuracy  of  the  estimate  of  the  run,  and  this  is 
always  liable  to  be  at  fault  to  a  greater  or  less  extent.  The  course  made  good  by  a  ship  may  differ  from 
that  which  it  is  believed  that  she  is  making  good,  by  reason  of  imperfect  steering,  improper  allowance 
for  compass  error  and  leeway,  and  the  effects  of  unknown  currents;  the  allowed  distance  over  the 
ground  may  be  in  error  on  account  of  inaccurate  logging  and  unknown  currents. 

Notwithstanding  its  recognized  defects  as  comparetl  with  the  more  exact  methods,  the  dead 
reckoning  is  an  invaluable  aid  to  the  mariner.  It  affords  him  a  means  of  plotting  the  position  of  the 
ship  at  any  desired  time  between  astronomical  determinations;  it  also  gives  him  an  approximate 
position  at  the  moment  of  taking  astronomical  observations  which  is  a  great  convenience  in  working  up 
those  observations;  and  finally  it  affords  the  only  available  means  of  determining  the  location  of  a 
vessel  at  sea  during  those  periods  (which  may  continue  for  several  days  together)  when  the  weather  is 
such  as  to  render  the  observation  of  celestial  bodies  an  impossibility. 

204.  Taking  Departure. — Before  losing  sight  of  the  land,  and  preferably  while  objects  remain  in 
good  view,  it  is  the  duty  of  the  navigator  to  take  a  departure;  this  consists  in  fixing  the  position  of  the 
ship  by  the  best  means  available  (Chap.  IV),  and  using  this  position  as  the  origin  for  dead  reckoning. 
There  are  two  methods  of  reckoning  the  departure.  The  first  and  simpler  consists  in  taking  from  the 
chart  the  latitude  and  longitude  of  the  position  found,  and  applying  the  future  run  thereto.  The  other 
requires  that  the  bearing  and  distance  of  an  object  of  known  latitude  and  longitude  be  found;  the 
position  of  the  object  then  forms  the  basis  of  the  reckoning,  and  the  reversed  direction  of  the  bearing, 
with  the  distance,  forms  the  first  course  and  distance;  thus  it  may  be  considered  that  the  ship  starts  from 
the  position  of  the  object  and  sails  to  the  position  where  the  bearing  was  taken;  the  correction  for 
deviation  in  such  a  case  should  be  that  due  to  the  heading  of  the  ship  when  the  bearing  was  taken. 
Each  time  that  a  new  position  is  determined  it  is  used  as  a  new  departure  for  the  dead  reckoning. 

This  meaning  of  the  term  departure  should  not  be  confounded  with  the  other,  which  refers  to  the 
distance  run  toward  east  or  west. 

205.  Methods. — The  working  of  dead  reckoning  merely  involves  an  application  of  the  methods  of 
Traverse  Sailing  (art.  172)  and  Middle  Latitude  Sailing  (art.  175),  as  explained  in  Chapter  V. 

The  various  compass  courses  are  set  down  in  a  column,  and  abreast  each  are  written  the  errors  by 
reason  of  which  the  course  steered  by  compass  differs  from  the  true  course  made  good  over  the  ground; 
thence  the  true  course  made  good  is  determined  and  recorded;  next,  the  distance  is  written  in,  and 
afterwards,  by  means  of  Tables  1  or  2  (according  as  the  courses  are  expressed  in  cjuarter  points  or 
degrees),  the  difference  of  latitude  and  departure  are  found,  separate  columns  being  kept  for  distances  to 
the  north,  south,  east,  and  west. 

When  the  position  of  the  ship  at  any  moment  is  required,  add  up  all  the  differences  of  latitude  and 
departure,  and  write  in  the  column  of  the  greater  the  difference  between  the  northing  and  southing, 
and  the  easting  and  westing.  Apply  the  difference  of  latitude  to  the  latitude  of  the  last  determined 
position,  which  will  give  the  latitude  by  D.  R.,  and  from  which  may  be  found  the  middle  latitude;  with 
the  middle  latitude  find  the  difference  of  longitude  corresponding  to  the  departure,  apjjly  this  to  the 
longitude  of  last  position,  and  the  result  will  be  the  longitude  by  D.  R. 

The  employment  of  the  tabular  form  will  be  found  to  facilitate  the  work  and  guard  against  errors. 
It  will  be  a  convenience  to  include  in  that  form  colunnis  showing  the  hour,  together  with  the  reading 
of  the  patent  log  (if  used)  each  time  that  the  course  is  changed  or  the  dead  reckoning  worked  up. 

The  employment  of  minutes  and  tenths  in  dead  reckoning  rather  than  minutes  and  seconds  is 
recommended. 

E.XAMPLE:  A  vessel  under  sail  heading  NE.  f  E.  (on  which  course  deviation  is  \  pt.  Easterly)  takes 
departure  from  Cape  Henry  light-house  (see  Appendix  IV  for  position ),  bearing  SSVV.  ^  A\\  per  compass, 
distant  1.4  miles.  She  then  sails  on  a  series  of  courses,  with  errors  and  distances  as  indicated  below; 
wind  about  SE.  by  E.  Required  the  position  by  dead  reckoning;  also  the  course  and  distance  made 
good  by  dead  recokning. 


DEAD   RECKONING. 


61 


Comp.  course. 

Var. 

Dev. 

Leeway. 

Error. 

True  course. 

Dist.    i      N. 

s. 

E. 

w. 

D. 

NNE.  1  E. 

iw. 

iE. 

i  w. 

NNE.  i  E. 

1.4 

1.3 

0.6 

NE.  1  E. 

*w. 

iE. 

iw. 

iw. 

NE.  i  E. 

27.6 

18.5 

20.5 

S.  by  W. 

*vv. 

0 

iE. 

iw. 

S.  f  W. 

31.5  1 

81.2 

4.6 

ENE. 

iw. 

iE. 

iW. 

f  w. 

NE.  bv  E.  i  E. 

14.2  1     7.3 

12.2 

S.  iE. 

iW. 

0 

^E. 

0 

S.  i  E. 

11.0  ! 

11.0 

0.5 

NE.  i  N. 

i\\. 

iE. 

i  W. 

iw. 

NE.  by  N. 

87.0 

72.3 

48.3 

99.4 

42.2 

82.1 

4.6 

Made  good, 

NE.  i  E. 

96.5 

57.2 

77.5 

97.0 

Point  of  departure, 
Run, 

Bv  D.  K. 


Latitude. 
36°  55^6  N. 

57  .2  N.       Mid.  L.,  37° 


37    52  .8  N. 


Longitude. 

76°  00^5  W. 

1    37  .OE. 

74    23  .5  W. 


Example:  A  steamer's  position  by  observation  at  noon,  patent  log  reading  27.3,  is  Lat.  49°  15''  N., 
Long.  7°  32'  W.  Thence  she  steers  S.  82°  W.  ( per  compass ) ,  the  total  compass  error  on  that  course  being 
20°  W.,  until  12.30,  at  which  time,  patent  log  reading  33.9,  the  course  is  changed  to  S.  80°  W.  (p.  c), 
same  error.  At  4.12,  patent  log  80.5,  sights  are  taken  from  which  it  is  found  that  the  true  longitude  is 
8°  46'  W.,  and  the  compass  error  19°  W.  At  6.15,  patent  log  reading  6.1,  a  sight  is  taken  from  which 
it  is  found  that  the  true  latitude  is  48°  34'  30"  N.  At  8  j).  m.  the  patent  log  reads  27.5.  Required  the 
positions  by  D.  R.  at  each  sight  and  at  8  o'clock. 


Time. 

Comp.  course. 

Error. 

True  course. 

Pat.  Log. 

Dist. 

S. 

w. 

D. 

Noon, 

12.30 

4.12 

6.15 
8.00 

8.  82°  W. 
8.  80°  W. 

8.  80°  W. 
8.  80°  AV. 

20°  W. 
20°  W. 

19°  W. 
19°  W. 

8.  62°  W. 
8.  60°  W. 

8.  61°  W. 
S.  61°  W. 

27.3 
33.9 
80.5 

6.1 
27.5 

6.6 
46.6 

25.6 
21.4 

3.1 
23.3 

5.8 
40.3 

70.3 
34.1 
27.9 

26.4 
12.4 
10.4 

46.1 
22.4 
18.7 

By  obs.  at  noon, 
Run  to  4.12  sight. 

Latitude. 
49°  15'.0  N. 
26.4  S. 

Mid. 
Mid. 
Mid. 

L.,  49° 
L.,  49° 

L.,  48° 

Longitude. 
7°  32'.0  W 
1      10.3  W 

By  D.  R.  at  4.12  sight. 

48 

48.6  N. 
12.4  8. 

8 

42.3  W 

By  obs.  at  4.12  sight, 
Run  to  6.15  sight. 

8 

46.0  W 

34.1  W 

By  1).  R.  at  6.15  sight. 

48 

36.2  N. 

9 

20.1  W 

By  obs.  at  6.15  sight, 
Run  to  8  p.  m., 

48 

34.5  N. 
10.4  8. 

27.9  W 

By  1).  R.  at  8  p.  m.,  48     24.1  N.  9     48.0  W. 

206.  Allowance  for  Current. — When  a  vessel  is  sailing  in  a  known  current  whose  strength  may 
be  estimated  with  a  fair  degree  of  accuracy,  a  more  correct  position  may  be  arrived  at  by  regarding  the 
set  and  drift  of  the  current  as  a  course  and  distance  to  be  regularly  taken  account  of  in  the  dead 
reckoning. 

Example:  A  vessel  in  the  Gulf  Stream  at  a  point  where  the  current  is  estimated  to  set  N.  48°  E.  at 
the  rate  of  1.8  miles  an  hour,  sails  8.  3°  W.  (true),  making  9.5  knots  an  hour  through  the  water  for 
S^  30"".     Middle  latitude  35°.     Required  the  course  and  distance  made  good. 


True  course.            Dist. 

N. 

S.                  E.                W. 

D. 

Run 
Current 

Made  good 

8.  3°  W. 

N.  48°  E. 

8.  6°  E. 

33.3 
6.3 

29.3 

4.2' 

33.3                           1.7 

i      i.7 

3.6 

29. 1     ;      3. 0 

62 


DEAD    RECKONING. 


207.  Finding  the  Current. — It  is  usual,  upon  obtaining  a  gocnl  position  by  observation  (as  the 
navigator  usually  does  at  noon),  to  compare  that  position  with  the  one  obtained  by  dead  reckon- 
ing, and  to  attribute  such  discrepancy  as  may  be  found  to  the  effects  of  current.  It  has  already  been 
pointed  out  that  other  causes  than  the  motion  of  the  water  tend  to  make  the  dead  reckoning  inaccurate, 
80  that  it  must  not  be  assumed  that  currents  proper  are  thus  determined  with  complete  correctness. 

Current  is  said  to  have  set  and  drift,  referring  respectively  to  the  direction  toward  which  it  is  flow- 
ing and  the  velocity  ^<'!th  which  it  moves. 

It  is  evident  that,  in  calculating  current  by  the  method  of  comparing  positions  by  observation  with 
those  by  account,  the  navigator  must  limit  himself  to  the  periods  during  which  the  (lead  reckoning  has 
been  brought  forward  independently,  without  receiving  any  corrections  due  to  new  points  of  departure. 
In  ca.se  it  is  desired  to  find  the  current  covering  a  period  during  which  fresh  departures  have  been  used, 
as  from  noon  to  noon,  find  the  algebraical  sums  of  all  the  differences  of  latitude  and  longitude  from  the 
table,  and  apply  these  to  the  latitude  and  longitude  of  original  departure — that  of  the  preceding 
noon;  this  gives  the  position  from  the  ship's  run  proper,  and  the  difference  between  this  and  the  posi- 
tion by  observation  gives  the  set  and  drift  for  the  twenty-four  hours;  if  an  allowance  has  been  made 
for  current,  as  explained  in  the  preceding  article,  that  must  l)e  omitted  in  bringing  up  the  position 
which  is  to  take  account  of  the  run  only. 

20§.  Day's  Run. — It  is  usual  to  calculate,  each  day  at  noon,  the  ship's  total  run  for  the  preceding 
twenty-four  hours.  Having  the  positions  at  noon  of  esu-h  day,  the  course  and  distance  between  them  is 
found  as  explained  in  article  175,  Chapter  V.  The  position  by  observation  is  used  in  each  case,  if  such 
has  been  found;  otherwise,  the  position  by  dead  reckoning. 

Example:  At  noon,  January  22,  the  position  of  a  vessel  by  observation  was  Lat.  35°  ICK  N.,  Long. 
134°  01^  W.  During  the  next  24  hours,  tlie  run  by  account  was  60.1  miles  north  and  153.2  miles  east. 
At  noon,  January  23,  the  position  by  observation  was  Lat.  36°  03^  N.,  Long.  131°  14^  VV.  Required 
the  position  by  D.  R.  at  the  latter  time;  also  the  run  and  current  for  the  24  hours. 


Bv  obs.,  noon,  22d, 
Run, 

Latitude. 
35°  10^0  N.     1 
1     00.1  N. 

Mid. 
Dep. 

D, 
Dep. 

L.,  36° 
,  153.2  E. 
189.4  E. 

22.4  W.j 
,   18.1  W.j 

Langittide. 
134°0r.0W. 
3    09  .4  E. 

By  D.  R.,  noon,  23d, 
By  obs.,  noon,  23d, 

36    10  .IX. 
36    03  .ON.     1 

130  51.6W. 

131  14  .OW. 

Current, 

6  .9  R.     1 

22.4W. 

Current  for  24  hours,  6.9  S.,  18.1  W.=  S.  69°  W.,  19.4  miles. 
Current  per  ho\ir,  S.  69°  W.,  0.8  mile. 


By  obs.,  noon,  23d, 
By  obs.,  noon,  22d, 

Run, 


Latitude. 
36°  03^0  N. 
35    10  .ON. 

0    53  .0  N. 


Mid.  L.,  36° 
}D,       167.0  E. 
Dep.,  135.1 


Longittide. 
131°  14'.0W. 
134    01  .OW. 

2    47  .0  E. 


Run  for  24  hours,  53.0  N.,  135.1  E.=N.  68°  E.,  146  miles. 


DEFINITIONS    RELATING    TO    NAUTICAL    ASTRONOMY. 


63 


CHAPTER  VII. 
DEFINITIONS  RELATING  TO  NAUTICAL  ASTRONOMY. 


209.  Nautical  Astronomy,  or  Celo-Xavigafio)i,  has  been  defined  (art.  8,  Chap.  I)  as  that  branch  of 
the  science  of  Navigation  in  which  the  position  of  a  ship  is  determined  by  the  aid  of  celestial  objects — 
the  sun,  moon,  planets,  or  stars. 

210.  The  Celestial  Sphere. — An  observer  upon  the  surface  of  the  earth  appears  to  view  the 
heavenly  bodies  as  if  they  were  situated  upon  the  surface  of  a  vast  hollow  sphere,  of  which  his  eye  is 
the  center.  In  realit\^  we  know  that  this  apparent  vault  has  no  existence,  and  that  we  can  determine 
only  the  relative  directions  of  the  heavenly  bodies — not  their  distances  from  each  other  or  from  the 
observer.  But  by  adopting  an  imaginary  spherical  surface  of  an  infinite  radius,  the  eye  of  the  observer 
being  at  the  center,  the  places  of  the  heavenly  bodies  can  be  projected  upon  this  Celestial  Sphere,  or  Celes- 
tial Concave,  at  points  where  the  lines  joining  them  with  the  center  intersect  the  surface  of  the  sphere. 
Since,  however,  the  center  of  the  earth  should  be  the  point  from  which  all  angular  distances  are  meas- 
ured, the  observer,  by  transferring  himself  there,  will  find  projected  on  the  celestial  sphere,  not  only  the 
heavenly  bodies,  but  the  imaginary  points  and  circles  of  the  earth's  surface.  The  actual  position  of  the 
observer  on  the  surface  will  be  projected  in  a  point  called  the  zenith;  the  meridians,  equator,  and  all  other 
lines  and  points  may  also  be  projected. 

211.  An  observer  on  the  earth's  surface  is  constantly  changing  his  position  with  relation  to  the 
celestial  bodies  projected  on  the  sphere,  thus  giving  to  the  latter  an  apparent  motion.  This  is  due  to 
three  causes:  first,  the  diurnal  motion  of  the  earth,  arising  from  its  rotation  upon  its  axis;  second,  the 
annual  motion  of  the  earth,  arising  from  its  motion  about  the  sun  in  its  orbit;  and  third,  the  actual 
motion  of  certain  of  the  celestial  bodies  themselves.  The  changes  produced  by  the  diurnal  motion  are 
different  for  observers  at  different  points  upon  the  earth,  and  therefore  depend  upon  the  latitude  and 
longitude  of  the  observer.  But  the  changes  arising  from  the  other  causes  named  are  independent  of  the 
observer's  position,  and  may  therefore  be  considered  at  any  instant  in  their  relation  to  the  center  of  the 
earth.  To  this  end  the  elements  necessary  for  any  calculation  are  tabulated  in  the  Xuritical  Almanac 
from  data  based  upon  laws  which  have  been  found  by  long  series  of  observations  to  govern  the  actual  and 
apparent  motion  of  the  various  bodies. 

212.  The  Zenith,  of  an  observer  on  the  earth's  surface  is  the  point  <^>f  the  celestial  sphere  vertically 
overhead.     The  Nadir  is  the  point  vertically  beneath. 

213.  The  Celestial  Horizon  is  the  great  circle  of  the  celestial  sphere  formed  by  passing  a  plane 
through  the  center  of  the  earth  at  right  angles  to  the  line  which  joins  that  point  with  the  zenith  of  the 
observer.  The  celestial  horizon  differs  somewhat 
from  the  Visible  Horizon,  which  is  that  line  appearing 
to  an  observer  at  sea  to  mark  the  intersection  of  earth 
and  sky.  This  difference  arises  from  two  causes: 
first,  the  eye  of  the  observer  is  always  elevated  above 
the  sea  level,  thus  permitting  him  a  range  of  vision 
exceeding  90°  from  the  zenith;  and  second,  the 
observer's  position  is  on  the  surface,  instead  of  at  the 
center  of  the  earth.  These  causes  give  rise,  respec- 
tively, to  dip  of  the  horizon  and  parallax,  which  will 
be  explained  later  (Chap.  X). 

214.  In  figure  28  the  celestial  sphere  is  considered 
to  be  projected  upon  the  celestial  horizon,  represented 
by  NESW. ;  the  zenith  of  the  observer  is  projected  at 
Z,  and  that  pole  of  the  earth  which  is  elevated  above 
the  horizon,  assumed  for  illustration  to  be  the  north 
pole,  appears  at  P,  the  Elevated  Pole  of  the  celestial 
sphere.     The  other  pole  is  not  shown  in.the  figure. 

215.  The  Equinoctial,  or  Celestial  Equator,  is  the 
great  circle  formed  by  extending  the  plane  of  the 
earth's  equator  until  it  intersects  the  celestial  sphere. 
It  is  shown  in  the  figure  in  the  line  EQW.  The  equi- 
noctial intersects  the  horizon  in  E  and  W,  its  east  and 
west  points. 

216.  Hour  Circles,  Declination  Circles,  or  Celestial  Meridians  are  great  circles  of  the  celestial  sphere 
passing  through  the  poles;  they  are  therefore  secondary  to  the  equinoctial,  and  may  be  formed  by 
extending  the  planes  of  the  respective  terrestrial  meridians  until  they  intersect  the  celestial  sphere.  In 
the  figure,  PW,  PS,  PE,  are  hour  circles,  and  that  one,  PS,  which  contains  the  zenith  and  is  therefore 
formed  by  the  extension  of  the  terrestrial  meridian  of  the  observer,  intersects  the  horizon  in  N  and  S,  its 
north  and  south  points. 

217.  Vertical  Circles,  or  Circles  of  Altitude,  are  great  circles  of  the  celestial  sphere  which  pass  through 
the  zenith  and  nadir;  they  are  therefore  secondary  to  the  horizon.  In  the  figure,  ZH,  WZE,  NZS,  are 
projections  of  such  circles;  the  vertical  circle  NZS,  which  passes  through  the  poles,  coincides  with  the 


Fig 


64  DEFINITIONS    RELATING    TO    NAUTICAL    ASTRONOMY. 

meridian  of  the  observer.  The  vertical  cintle  WZE,  whose  plane  is  at  right  angles  to  that  of  the  merid- 
ian, intersects  the  horizon  in  its  eastern  and  western  points,  and,  iheretV)re,  at  the  points  of  intersection 
of  the  equinoctial;  this  circle  ia  distinguished  as  the  Prime  Vertk-al. 

21 S.  The  Declination  of  any  point  in  the  celestial  sphere  is  its  angular  distance  from  the  equinoctial, 
measiured  upon  the  hour  or  declination  circle  which  passes  through  that  jxtint;  it  is  designated  as  North 
cr  South  according  to  the  direction  of  the  point  from  the  equinoctial;  it  is  customary  to  regard  north 
declinations  as  positive  (~r ),  and  south  declinations  as  negative  ( ~ ).  In  the  figure,  DM  is  the  declina- 
tion of  the  point  M.     Declination  upon  the  celestial  sphere  corresponds  with  latitude  upon  the  earth. 

219.  The  Polar  Distance  of  any  point  is  its  angular  distance  from  the  jjole  (generally,  the  elevated 
pole  of  an  observer),  measured  upon  the  hour  or  declination  circle  passing  through  the  point;  it  must 
therefore  equal  90°  minus  the  declination,  if  measured  from  the  pole  of  the  same  name  as  the  declina- 
tion, or  90°  pins  the  declination,  if  measured  from  the  pole  of  opposite  name.  The  polar  distance  of  the 
point  M  from  the  elevated. pole,  P,  is  PM. 

220.  The  Altitude  of  any  point  in  the  celestal  sphere  is  its  angular  distance  from  the  horizon, 
measured  upon  the  vertical  circle  passing  through  the  point;  it  is  regarded  as  positive  when  the  body 
is  on  the  same  side  of  the  horizon  as  the  zenith      The  altitude  of  the  point  ]\I  is  HM. 

5-21.  The  ZenitJi  Distance  of  any  ])oint  is  its  angular  distance  from  the  zenith,  measured  upon  the 
vertical  circle  passing  through  the  ]>oint;  the  zenith  distance  of  any  point  which  is  above  the  horizon  of 
an  observer  must  therefore  equal  90°  )nimis  the  altitude.     The  zenith  distance  of  M,  in  the  figure,  is  ZM. 

222.  The  Hour  Angle  of  any  point  is  the  angle  at  the  pole  between  the  meridian  of  the  observer 
and  the  hour  circle  passing  through  that  point;  it  may  also  be  regarded  as  the  arc  of  the  equinoctial 
intercepted  between  those  circles.  It  is  measured  tuward  the  west  as  a  positive  direction  through  the 
twenty-four  hours,  or  360  degrees,  which  constitute  the  interval  between  the  successive  returns  to  the 
meridian,  due  to  the  diurnal  rotation  of  the  earth,  of  any  point  in  the  celestial  sphere.  The  hour  angle  of 
M  is  the  angle  C^PD,  or  the  arc  QD. 

223.  The  Azimuth  of  a  point  in  the  celestial  sphere  is  the  angle  at  the  zenith  between  the  meridian 
of  the  observer  and  the  vertical  circle  passing  through  the  point;  it  may  also  be  regarded  as  the  arc  of 
the  horizon  intercepted  between  those  circles.  It  is  measured  from  either  the  north  or  the  south  point 
of  the  horizon  (usually  that  one  of  the  same  name  as  the  elevated  pole)  to  the  east  or  west  through  180°, 
and  is  named  accordingly;  as,  N.  60°  W.,  or  S.  120°  W.  The  azimuth  of  M  is  the  angle  NZH,  or  the  arc 
NH,  from  the  north  point,  or  the  angle  SZH,  or  the  arc  SH,  from  the  south  point  of  the  horizon. 

224.  The  Amplitude  of  a  point  is  the  angle  at  the  zenith  between  the  prime  vertical  and  the  vertical 
circle  of  the  point;  it  is  measured  from  the  east  or  the  west  jioint  of  the  horizon  through  90°,  as  W.  30° 
N.  It  is  closely  allied  with  the  azimuth  and  may  always  be  deduced  therefrom.  In  the  figure,  the 
amplitude  of  H  is  the  angle  WZH,  or  the  arc  WH.  The  amplitude  is  only  used  with  reference  to  points 
in  the  horizon. 

225.  The  Ecliptic  is  the  great  circle  representing  the  path  in  which,  by  reason  of  the  annual  revo- 
lution of  the  earth,  the  sun  appears  to  move  in  the  celestial  sphere;  the  plane  of  the  ecliptic  is  inclined 
U)  that  of  the  equinoctial  at  an  angle  of  23°  21 Y,  and  this  inclination  is  called  the  obliquity  of  the  ecliptic. 
The  ecliptic  is  represented  by  the  great  circle  CVT. 

226.  The  Equinoxes  are  those  points  at  which  the  ecliptic  and  the  equinoctial  intersect,  and  when 
the  sun  occupies  either  of  these  positions  the  days  and  nights  are  of  equal  length  throughout  the  earth. 
The  Vernal  Equinox  is  that  one  at  which  the  sun  appears  to  an  observer  on  the  earth  when  passing  from 
southern  to  northern  declination,  and  the  Aidumnal  Equinox  that  one  at  which  it  appears  when  passing 
from  northern  to  southern  declination.  The  Vernal  Equinox  is  also  designated  as  the  Ftrst  Point  of  Aries, 
and  is  used  as  an  origin  for  reckoning  right  ascension;  it  is  indicated  in  the  figure  at  V. 

227.  The  Solstitial  Points,  or  Solstices,  are  points  of  the  ecliptic  at  a  distance  of  90°  from  the  equinoxes, 
at  which  the  sun  attaiiis  its  highest  declination  in  each  hemisphere.  They  are  called  respectively  the 
Summer  and  the  Winter  Solstice,  according  to  the  season  in  whicn  the  sun  appears  to  pass  these  points  in 
its  path. 

22S.  The  Right  Ascension  of  a  point  is  the  angle  at  the  pole  between  the  hour  circle  of  the  point 
and  that  of  the  First  Point  of  Aries;  it  may  also  be  regarded  as  the  arc  of  the  equinoctial  intercepted 
between  those  circles.  It  is  measured  from  the  First  Point  of  Aries  to  the  eastward  as  a  positive 
direction,  through  twenty-four  hours  or  360  degrees.     The  right  ascension  of  the  point  M  is  YD. 

229.  Celestial  Latitude  is  measured  to  the  north  or  south  of  the  ecliptic  upon  great  circles  secondary 
thereto.  Celestial  Longitude  is  measured  upon  the  ecliptic  from  the  First  Point  of  Aries  as  an  origin, 
being  regarded  as  positive  to  the  eastward  throughout  360°. 

230.  Coordinates. — In  order  to  define  the  position  of  a  jwint  in  space,  a  system  of  lines,  angles,  or 

planes,  or  a  combination  of  these,  is  used  to  refer  it  to  some  fixed 
line  or  plane  adopted  as  the  primitive;  and  the  lines,  angles,  or 
l)lanes  by  which  it  is  thus  referred  are  called  coordinates. 

231.  In  figure  29  is  shown  a  system  of  rectilinear  coordinates 
for  a  plane.  A  fixed  line  FE  U  chosen,  and  in  it  a  definite  point  C, 
as  the  origin.  Then  the  position  of  a  point  A  is  defined  by  CB  =  x, 
the  distance  from  the  origin,  C,  to  the  foot  of  a  perpendicular  let 

■ fall  from  A  on  FE;  and  by  AB  =  y,  the  length  of  the  perpendicular. 

The  distance  x  is  called  the  abscissa  and  y  the  ordinate.     Assuming 
two  intersecting  right  lines  FE  and  HI  as  standard  lines  of  refer- 
ence, the  location  of  the  point  A  is  defined  by  regarding  the  dis- 
FiG.  29.  tances  measured  to  the  right  hand  of  HI  and  above  FE  af>  positive; 

those  to  the  left  hand  of  HI  and  below  FE  as  negative. 
An  exemplification  of  this  system  is  found  in  the  chart,  on  which  FE  is  represented  by  the  equator, 
Hi  by  the  prime  meridian;  the  coordinates  x  and  y  being  the  longitude  and  latitude  of  the  point  A. 


DEFINITIONS    RELATING    TO    NAUTICA-L    ASTEONOMY.  65 

332.  The  great  circle  is  to  the  sphere  wliat  tlie  straight  line  is  to  the  i)lane;  hence,  in  order  to 
define  the  position  of  a  point  on  the  surface  of  a  sphere,  some  great  circle  must  be  selected  as  the 
primary,  and  some  particular  point  of  it  as  the  origin.  Thus,  in  figure  30,  which  represents  the  case  of  a 
sphere,  some  fixed  great  circle,  CBQ,  is  selected  as  the  axis  and  called  the 
primary;  and  a  point  C  is  chosen  as  the  origin.  Then  to  define  the  pos-ition 
of  any  point  A,  the  abscissa  x  equals  the  distance  from  C  to  the  point  B, 
where  the  secondary  great  circle  through  A  intersects  the  primary;  the 
ordinate  y  equals  the  distance  of  A  from  the  primary  measured  on  the 
secondary — that  is,  x  —  C-B  and  //  =  AB. 

233.  In  the  case  of  the  earth,  the  primary  selected  is  the  equator  (its 
])lane  being  j)erpendicular  to  the  earth's  axis),  and  upon  this  are  measured 
the  abscissa',  while  upon  the  secondaries  to  it  are  measured  the  ordinates  of 
all  points  on  the  earth's  surface.  The  initial  point  for  reference  on  the 
equator  is  determined  by  the  prime  meridian  chosen,  West  longitudes  and 
North  latitudes  being  called  positive,  East  longitudes  and  South  latitudes, 
negativt'. 

234.  In  the  case  of  the  celestial  si)here,  there  are  four  systems  of  coor- 
dinates in  use  for  defining  the  position  of  any  point;  these  vary  according  to  the  circle  adopted  as  the 
primary  and  the  point  used  as  an  origin.     They  are  as  follows: 

1.  Altitude  and  azimuth. 

2.  Declination  and  hour  angle. 

3.  Declination  and  right  ascension. 

4.  Celestial  latitude  and  longitude. 

235.  In  the  system  of  Altitude  and  Azimuth,  the  primary  circle  is  the  celestial  horizon,  the  seconda- 
ries to  which  are  the  vertical  circles,  or  circles  of  altitude.  The  horizon  is  intersected  by  the  celestial 
meridian  in  its  northern  and  southern  points,  of  which  one — usually  that  adjacent  to  the  elevated  pole — is 
selected  as  an  origin  for  reckoning  coordinates.  The  azimuth  indicates  in  Avhich  vertical  circle  the  point 
to  be  defined  is  found,  and  the  altitude  gives  the  position  of  the  point  in  that  circle.  In  figure  28  the 
point  M  is  located,  according  to  this  system,  by  its  azimuth  NH  and  altitude  HM. 

236.  In  the  system  of  Dedination  and  Hour  Angle,  the  primary  circle  is  the  equinoctial,  the  seconda- 
ries to  which  are  the  circles  of  declination,  or  hour  circles.  The  pcjint  of  origin  is  that  poiht  of  inter- 
section of  the  equinoctial  and  celestial  meridian  which  is  above  the  horizon.  The  hour  angle  indicates 
in  which  declination  circle  the  point  to  be  defined  is  found,  and  the  declination  gives  the  position  of 
the  point  in  that  circle.  In  figure  28  the  point  M  is  located,  according  to  this  system,  by  its  hour  angle 
QD  and  declination  DM. 

237.  Inthe  system  of  Dedination  and  Right  Ascension,  the  primary  and  secondaries  are  the  same  as  in 
the  system  just  described,  but  the  point  of  origin  differs,  being  assumed  to  be  at  the  First  Point  of  Aries,  or 
vernal  equinox.  The  right  ascension  indicates  in  which  declination  circle  the  point  to  be  defined  may 
be  found,  and  the  declination  gives  the  position  in  that  circle.  In  figure  28  the  point  M  is  located  by  YD, 
the  right  ascension,  and  DM,  the  declination.  It  should  be  noted  that  this  system  differs  from  the 
preceding  in  that  the  position  of  a  point  is  herein  referred  to  a  fixed  point  in  the  celestial  sphere  and  is 
independent  of  the  zenith  of  the  observer  as  well  as  of  the  position  of  the  earth  in  its  diurnal  motion, 
while,  in  the  system  of  declination  and  hour  angle,  both  of  these  are  factors  in  determining  the  coordinates. 

23§.  In  the  system  of  Celestial  Latitude  and  Longitude,  the  primary  circle  is  the  ecliptic;  the  point 
of  origin,  the  First  Point  of  Aries.  The  method  of  reckoning  by  this  system,  which  is  of  only  slight 
importance  in  Nautical  Astronomy,  will  appeaj  from  the  definitions  of  celestial  latitude  and  longitude 
already  given  (art.  229). 

22489—03 5 


66 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 


CHAPTER   VIII. 

INSTRUMENTS  EMPLOYED  IN  NAUTICAL  ASTRONOMY. 


THE  SEXTANT. 

239.  The  sextant  if?  an  instrument  fur  measuring  the  angle  between  two  o))jeets  by  Itringing  into 
coincidence  at  the  eye  of  the  observer  rays  of  light  received  directly  from  the  one  and  by  reflection  from 
the  other,  the  measure  being  afforded  by  the  inclination  t)f  the  reflecting  surfaces.  By  reason  of  its 
small  dimensions,  its  accuracy,  and,  above  all,  the  fact  that  it  does  not  recjuire  a  permanent  or  a  stable 
mounting  but  is  available  for  u.se  under  the  conditions  existing  on  shipboard,  it  is  a  most  important 
instrument  for  the  purposes  of  the  navigator.  While  the  sextant  is  not  capable  of  the  same  degree  of 
accuracy  as  fixed  instruments,  its  measurements  are  sufficiently  exact  for  navigation. 

240.  Description. — A  usual  form  of  the  sextant  is  represented  in  figure  31.  The  frame  is  of  brass 
or  some  similar  alloy.     The  graduated  arc,  AA,  generally  of  silver,  is  marked  in  approi)riate  divisions; 

in  the  finer  sextants,  each  divir 
sion  represents  10^,  and  the 
vernier  affords  a  means  of 
reading  to  10^'.  A  wooden 
handle,  H,  is  provided  for 
holding  the  instrument.  The 
index  mirror,  31,  and  horizon 
mirror,  m,  are  of  plate  glass, 
and  are  silvered,  though  the 
upper  half  of  the  horizon  glass 
is  left  plain  to  allow  direct  rays 
to  pass  through  unobstructed. 
To  give  greater  distinctness  to 
the  images,  a  small  telescope, 
E,  is  placed  in  the  line  of 
sight;  it  is  supported  in  a  ring, 
K,  which  can  he  moved  by  a 
screw  in  a  direction  at  right 
angles  to  the  plane  of  the  sex- 
tant, thus  shifting  the  axis  of 
the  telescope,  and  therefore  the 
plane  of  reflection;  this  plane, 
however,  always  remains  par- 
allel to  that  of  the  instrument, 
the  motion  of  the  telescope 
being  intended  merely  to  regu- 
late the  relative  brightness  of 
the  direct  and  reflected  images.  In  the  ring  K  are  small  screws  for  the  purpose  tif  adjusting  the  tele- 
scope by  making  its  axis  parallel  with  the  plane  of  the  sextant.  The  vernier  is  carried  on  the  end  of  an 
index  bar  pivote<l  beneath  the  index  mirror,  M,  and  thus  travels  along  the  graduated  scale,  affording  a 
measure  for  any  change  of  inclination  of  the  index  mirror;  a  reading  glass,  11,  attached  to  the  index  bar 
and  turning  upon  a  pivot,  S,  facilitates  the  reading  of  vernier  aiul  scale.  The  index  mirror,  31,  is  attached 
to  the  head  of  the  index  bar,  with  its  suil'ace  perjiendicular  to  the  plane  of  the  instrument;  an  adjust- 
ing screw  is  fitted  at  the  back  to  permit  of  adjustment  to  the  peritendicular  i)lanc.  The  fixed  gla.'^s  m, 
half  silvered  and  half  plain,  is  called  the  horizon  glass,  as  it  is  through  this  tiiat  the  horizon  is  observed 
in  measuring  altitudes  of  celestial  bodies;  it  is  provided  with  screws,  by  which  its  perpendicularity  to 
the  i)lane  of  the  instrument  may  l>e  adjusted.  At  I'  and  Q  are  colored  glasses  of  different  shades, which 
may  be  used  separately  or  in  comlMnation  to  protect  tlie  eye  from  th  3  intense  light  of  the  sun.  In  order 
to  observe  with  accuracy  and  make  the  images  come  i)recisely  in  contact,  a  tanijent-screir,  B,  is  fixed  to 
the  index,  by  means  of  which  the  latter  may  be  moved  with  great;-r  ))recision  than  by  hand;  but  this 
screw  does  not  act  until  the  index  is  fixed  by  the  screw  C  at  the  back  of  the  sextant;  when  the  index 
is  to  be  moved  any  considerable  amount,  the  screw  C  is  loosened;  when  it  is  brought  near  to  its  required 
position  the  screw  must  be  tightened,  and  the  index  may  then  be  moved  gradually  by  the  tangent-screw. 
Besides  the  telescope,  E,  the  instrument  is  usually  provided  with  an  inverting  telescope,  I,  and  a 
tube  without  glasses,  F;  also,  with  a  cap  carrying  colored  glasses,  which  may  be  put  on  the  eye-end  of 
the  telescope,  thus  dispensing  with  the  necessity  for  the  use  of  the  colored  shades,  Pand  Q,  and  elimina- 
ting any  possible  errors  which  might  arise  from  nonparallelism  of  their  surfaces. 

341.  The  rerm«r  is  an  attachment  for  facilitating  the  exact  reading  of  the  scale  of  a  sextant,  by 
which  aliquot  parts  of  the  smallest  divisions  of  the  graduated  scale  are  measured.  The  principle  of  the 
sextant  vernier  is  identical  with  that  of  the  barometer  vernier,  a  complete  description  of  which  will 
be  found  in  article  51,  Chapter  II.    The  arc  of  a  sextant  is  usually  divided  into  120  or  more  parts,  each 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY.  67 

division  representing  1°;  each  of  these  degree  divisions  is  further  subdivided  to  an  extent  dependent 
upon  the  accuracy  of  reading  of  which  the  sextant  is  capable.  In  the  instruments  for  finer  work,  the 
divisions  of  the  scale  correspond  to  10'  each,  and  the  vernier  covers  a  length  corresponding  to  59  such 
divisions,  which  is  subdivided  into  60  parts,  thus  permitting  a  reading  of  ICK';  all  sextants,  however,  are 
not  so  closely  graduated. 

Whatever  the  limits  of  subdivision,  all  sextants  are  fitted  with  verniers  which  contain  one  more 
division  than  the  length  of  scale  covered,  and  in  which,  therefore,  scale-readings  and  vernier-readings 
increase  in  the  same  direction — toward  the  left  hand.  To  read  any  sextant,  it  is  merely  necessary  to 
observe  the  scale  divi.sion  next  below,  or  to  the  right  of,  the  zero  of  the  vernier,  and  to  add  thereto  the 
angle  corresponding  to  that  division  of  the  vernier  scale  which  is  meet  nearly  in  exact  coincidence  with 
a  division  of  the  instrument  scale. 

242.  Optical  Principle. — When  a  ray  of  light  is  reflected  from  a  plane  surface,  the  angle  of  inci- 
dence is  equal  to  the  angle  of  reflection.  From  this  it  ^^ 
may  be  proved  that  when  a  ray  of  light  undergoes  two 
reflections,  in  the  same  plane  the  angle  between  its 
first  and  its  last  direction  is  equal  to  twice  the  inclina- 
tion of  the  i-eflecting  surfaces.  Upon  this  fact  the  con- 
struction of  the  sextant  is  based. 

In  figure  32  let  B  and  C  represent  respectively  the 
index  mirror  and  horizon  mirror  of  a  sextant;  draw 
EF  perpendicular  to  B,  and  CF  perpendicular  to  C; 
then  the  angle  CFB  represents  the  inclination  of  the 
two  mirrors.  Suppose  a  ray  to  proceed  from  A  and 
undergo  reflection  at  B  and  at  C,  its  last  direction  I  leing 
CD;  then  ADC  is  the  angle  between  its  first  and  last 
directions,  and  we  desire  to  prove  that  ADC  =  2  CFB. 

From  the  eciuality  of  the  angles  of  incidence  and  ^m   3'> 

reflection: 

ABE  =  EBC,  and  ABC  =  2  EBC; 
BCF  ^  FCD,  and  BCD  =  2  BCF. 
From  Geometry: 

ADC  =  ABC  -  BCD  =  2  (EBC  -  BCF)  =  2  CFB, 

which  is  the  relation  that  was  to  be  pro'^ed. 

24;?.  In  the  sextant,  since  the  index  mirror  is  immovably  attached  to  L.ie  index  arm,  which  also 
carries  the  vernier,  it  follows  that  no  change  can  occur  in  the  inclination  between  the  index  mirror  and 
the  horizon  mirror,  excepting  such  as  is  registered  l)y  the  travel  of  the  vernier  upon  the  scale. 

If,  when  the  index  mirror  is  so  placed  that  it  is  nearly  parallel  with  the  horizon  mirror,  an  observer 
direct  the  telescope  toward  some  well-defined  object,  there  will  be  seen  in  the  field  of  view  two  separate 
images  of  the  object;  and  if  the  inclination  of  the  index  mirror  be  slightly  changed  bv  moviug  the  index 
bar,  it  will  be  seen  that  while  one  of  the  images  remains  fixed  the  other  moves.  'The  fixed  image  is 
the  direct  one  seen  through  the  unsilvered  part  of  the  horizon  glass,  while  the  movable  image  is  due  to 
rays  reflected  by  the  index  and  horizon  mirrors.  When  the  two  images  coincide  these  mirrors  m^^t  be 
parallel  (assuming  that  the  object  is  sufficiently  distant  to  disregard  the  space  which  separates  the  mir- 
rors);  in  this  position  of  the  index  mirror  the  vernier  indicates  the  true  zero  of  the  scale.  If,  however, 
instead  of  observing  a  single  object,  the  instrument  is  so  placed  that  the  direct  ray  from  one  object 
appears  in  coin<'idence  with  the  reflected  ray  of  a  second  object,  then  the  true  angle  between  the  objects 
will  be  twice  the  angle  of  inclination  between  the  mirrors,  or  twice  the  angle. measured  by  the  vernier 
from  the  true  zero  of  the  scale.  To  avoid  the  necessity  of  doubling  the  angle  on  the  scale,  the  latter  is 
so  marked  that  each  half  degree  appears  as  a  whole  degree,  whence  its  indications  give  the  whole  anple 
directly. 

244.  AD.irsTMENTS  OF  THE  Sextaxt. — The  theory  of  the  sextant  requires  that,  for  accurate  indi- 
cations, the  following  conditions  be  fulfilled: 

(o)  The  two  surfaces  of  each  mirror  and  shade  glass  must  be  parallel  plants. 

{h)  The  graduated  arc  or  limb  must  be  a  plane,  and  it:;  graduations,  as  well  as  those  of  the  vernier, 
must  be  exact. 

(c)  The  axis  must  be  at  the  center  of  the  limb,  and  perpendicular  to  the  plane  thereof. 

(d)  The  index  and  horizon  gla.sses  must  be  perpendicular,  and  the  line  of  sight  parallel,  to  the 
plane  of  the  limb. 

Of  these,  only  the  last  named  ordinarily  require  the  attention  of  the  navigator  who  is  to  make  use  of 
the  sextant;  the  others,  which  may  be  called  the  perrnaueiit  adjvstinenl.^,  should  be  made  before  the 
instrument  leaves  the  hands  of  the  maker,  and  with  careful  use  will  never  be  dranged. 

245.  The  Adjustmi'iit  of  the  Index  Mirror  consists  in  making  the  reflecting  surface  of  tiiis  mirror 
truly  perpendicular  to  the  jtlane  of  the  sextant.  In  onltr  to  test  this,  set  the  index  iv  ar  the  middle  of 
the  arc,  then,  placing  the  eye  very  nearly  in  the  plane  of  the  sextant  and  close  to  the  index  mirror, 
observe  whether  the  direct  image  of  the  arc  and  its  image  reflected  from  the  mirror  appear  to  form  one 
continuous  arc;  if  so,  the  glass  is  perpendicular  to  the  plane  of  the  sextant;  if  the  reflected  image  appears 
to  droop  from  the  arc  seen  directly,  the  glass  leans  backward;  if  it  seems  to  rise,  the  glass  leans  forward. 
The  adjustment  is  made  by  the  screws  at  the  back  of  the  mirror. 

246.  The  Adjmtment  of  the  Horizon  Mirror  consists  in  making  the  reflecting  surface  of  this  i.iirror 

gerpendicular  to  the  plane  of  the  sextant.  The  index  mirror  having  been  adjusted,  if,  in  revolving  it 
y  means  of  the  index  arm,  there  is  found  one  position  in  which  it  is  parallel  to  the  horizon  glass,  then 
the  latter  must  also  be  perpendicular  to  the  plane  of  the  sextant.  In  order  to  test  this,  put  in  the  tele- 
scope and  direct  it  toward  a  star;  move  the  index  until  the  reflected  image  appears  to  pass  the  direct 
image;  if  one  ymsses  directly  over  the  other  the  mirrors  must  be  parallel;  if  one  passes  on  either  side  of 
the  other  the  horizon  glass  needs  adjustment,  which  is  accomplished  by  means  of  the  screws  attached. 


68  INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 

The  sea  horizon  may  also  be  used  for  making  this  adjustment.  Hold  the  sextant  vertically  and 
bring  the  direct  and  the  reflected  images  of  the  horizon  line  into  coincidence;  then  incline  the  sextant 
until  its  plane  makes  l)ut  a  small  angle  with  the  horizon;  if  the  images  still  coincide  the  glasses  are 
parallel;  if  not,  the  horizon  glass  needs  adjustment. 

247.  The  Adjustineiit  of  the  Telescope  must  be  so  made  that,  in  measuring  angular  distances,  the  line 
of  sight,  or  axis  oit  th«  telescope,  shall  be  parallel  to  the  plane  of  the  instrument,  as  a  deviation  in  that 
respect,  in  measuring  large  angles,  will  occasion  a  considerable  error.  To  avoid  such  error,  a  tele.scope  is 
employed  irv  which  are  placed  two  wires,  ])arallel  to  each  other  and  equidistant  from  the  center  of  the 
telescope;  by  means  of  these  wires  the  adjuMtment  may  be  made.  Screw  on  the  telescope,  and  turn  the 
tube  containing  the  eyeglass  till  the  wires  are  parallel  to  the  plane  of  tlie  instrument;  then  select  two 
dearly-defined  objects  whose  angular  distance  must  be  not  less  than  90°,  because  an  error  is  more  easily 
discovered  when  the  distance  is  great;  bring  the  reflected  image  of  one  object  into  exact  eoincideuce 
with  the  direct  image  of  the  other  at  the  inner  wire;  then,  by  altering  slightly  the  ])osition  of  the  instru- 
ment, make  the  objects  appear  on  the  other  wire;  if  the  contact  still  remains  perfect,  the  axis  of  the 
telescope  is  in  its  right  situation;  but  if  the  two  objects  aj)pear  to  separate  or  lap  over  at  the  outer  wire 
the  telescope  is  not  parallel,  and  it  must  be  rectified  by  turning  one  of  the  two  screws  of  the  ring  into 
which  the  telescope  is  screwed,  having  previously  unturned  the  other  screw;  by  repeating  this  operation 
a  few  times  the  contact  will  be  precisely  the  same  at  both  wires,  and  the  axis  of  the  telescope  will  be 
parallel  to  the  plane  of  the  instrument. 

Another  method  of  making  this  adjustinent  is  to  place  the  sextant  upon  a  tal>le  in  a  horizontal 
position,  look  along  the  plane  of  the  limb,  and  make  a  mark  upon  a  wall,  or  other  vertical  surface,  at  a 
distance  of  about  20  feet;  draw  another  mark  above  the  first  at  a  distance  equal  to  the  height  of  the  axis 
of  the  telescope  above  the  plane  of  the  limb;  then  so  a<ljust  the  telescope  that  the  upper  mark,  as 
viewed  through  the  telescope,  falls  midway  between  the  wires.  Some  sextants  are  accompanied  by 
small  sights  whose  height  is  exactly  equal  to  the  distance  between  the  telescope  and  the  plane  of  the 
limb;  by  the  use  of  these,  the  necessity  for  employing  the  second  mark  is  avoided  and  the  adjustment; 
can  be  very  accurately  made. 

24§.  The  errors  which  arise  from  defects  in  what  have  been  denominated  the  permanent  adjustments 
of  the  sextant  may  be  divided  into  three  classes,  namely:  Errors  due  to  faulty  centering  of  the  axes, 
called  eccentricity;  errors  of  graduation;  and  errors  arising  from  lack  of  parallelism  of  surfaces  in  index 
mirror  and  in  shade  glasses- 

The  errors  due  to  eccentricity  and  faulty  graduation  are  constant  for  the  same  angle,  and  should  be 
determined  once  for  all  at  some  place  where  proper  facilities  for  doing  the  work  are  at  hand;  these 
errors  can  only  be  ascertained  by  measuring  known  angles  with  the  sextant.  If  angles  of  10°,  20°,  30°, 
40°,  etc.,  are  first  laid  off  with  a  theodolite  or  similar  instrument  and  then  measured  by  the  sextant,  a 
table  of  errors  of  the  sextant  due  to  eccentricity  and  faulty  graduation  may  be  made,  and  the  error  at 
any  intermediate  angle  found  by  interpolation;  this  table  will  include  the  error  of  graduation  of  the 
theodolite  and  also  the  error  due  to  inaccurate  reading  of  the  sextant,  but  such  errors  are  small.  Another 
method  for  determining  the  combined  errors  of  eccentricity  and  graduation  is  by  measuring  the  angular 
distance  between  stars  and  comparing  the  observed  and  the  computed  arc  between  them,  but  this  process 
is  liable  to  inaccuracies  by  reason  of  the  uncertainty  of  allowances  for  atmospheric  refraction. 

Errors  of  graduation,  when  large,  may  be  detected  by  "stepping  off "  distances  on  the  graduated 
arc  with  the  vernier;  place  the  zero  of  the  vernier  in  exact  coincidence  with  a  division  of  the  arc,  and 
observe  whether  the  final  division  of  the  vernier  also  coincides  with  a  division  of  the  arc;  this  should  be 
tried  at  numerous  positions  of  the  graduated  limb,  and  the  agreement  ought  to  be  perfect  in  every  case. 

The  error  due  to  a  prismatic  index  mirror  may  be  found  by  measuring  a  certain  unchangeable  angle, 
then  taking  out  the  glass  and  turning  the  upper  edge  down,  and  measuring  the  angle  again;  half  the  dif- 
ference of  these  two  measures  will  be  the  error  at  that  angle  due  to  the  mirror.  From  a  number  of  meas- 
ures of  angles  in  this  manner,  a  table  similar  to  the  one  for  eccentricity  and  faulty  graduation  can  be 
made;  or  the  two  tables  may  be  combined.  When  possible  to  avoid  it,  however,  no  sextant  should  be 
used  in  which  there  is  an  index  mirror  which  produces  a  greater  error  than  that  due  to  the  probable  error 
of  reading  the  scale.  Mirrors  having  a  greater  angle  than  2'^  between  their  faces  are  rejected  for  use  in 
the  United  States  Navy.  Index  mirrors  may  be  roughly  tested  by  noting  if  there  is  an  elongated  image 
of  a  well-defined  point  at  large  angles. 

Since  the  error  due  to  a  prismatic  horizon  mirror  is  included  in  the  index  correction  (art.  2-19),  and 
consequently  applied  alike  to  all  angles,  it  may  be  neglected. 

Errors  due  to  prismatic  shade  glasses  can  be  determined  by  measuring  angles  with  and  without  the 
shade  glasses  and  noting  the  difference.  They  may  also  be  determined,  where  the  glasses  are  so  arranged 
that  they  can  be  turned  through  an  angle  of  180°,  by  measuring  the  angle  first  with  the  glass  in  its 
usual  position  and  then  reversed,  and  taking  the  mean  of  the  two  as  the  true  measure. 

249.  Index  Error. — The  Index  Error  of  a  sextant  is  the  error  of  its  indications  due  to  the  fact 
that  when  the  index  and  horizon  mirrors  are  parallel  the  zero  of  the  vernier  does  not  coincide  with 
the  zero  of  the  scale.  Having  made  the  adjustments  of  the  index  and  horizon  mirrors  and  of  the 
telescope,  as  previously  described,  it  is  necessary  to  find  that  point  of  the  arc  at  which  the  zero  of  the 
vernier  falls  when  the  two  mirrors  are  parallel,  for  all  angles  measured  by  the  sextant  are  reckoned  from 
that  point.  If  this  point  is  to  the  left  of  the  zero  of  the  limb,  all  readings  will  be  too  great;  if  to  the 
right  of  the  zero,  all  readings  will  be  too  small. 

If  desirable  that  the  reading  should  be  zero  when  the  mirrors  are  parallel,  place  the  zero  of  the 
vernier  on  zero  of  the  arc;  then,  by  means  of  the  adjusting  screws  of  the  horizon  glass,  move  that  glass 
until  the  direct  and  reflected  images  of  the  same  object  coincide,  after  which  the  perpendicularity  of 
the  horizon  glass  should  again  be  verified,  as  it  may  have  been  deranged  by  the  operation.  This  adjust- 
ment is  not  essential,  since  the  correction  may  readily  be  determined  and  applied  to  the  reading.  In 
certain  sextant  work,  however,  such  as  surveying,  it  will  be  very  convenient  to  be  relieved  of  the 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY.  69 

necessity  of  correcting  each  angle  observed.  The  sextant  should  never  be  relied  upon  for  maintaining 
a  constant  index  correction,  and  the  error  should  be  ascertained  frequently.  It  is  a  good  practice  to 
verify  the  correction  each  time  a  sight  is  taken. 

250.  The  Index  Correction  may  be  found  (a)  by  a  star,  {b)  by  the  sea  horizon,  and  (c)  by  the  sun. 

(a)  Bring  the  direct  and  reflected  images  of  a  star  into  coincidence,  and  read  off  the  arc.  The 
index  correction  is  numerically  equal  to  this  reading,  and  is  positive  or  negative  according  as  the  read- 
ing is  on  the  right  or  left  of  the  zero. 

(b)  The  same  method  may  be  employed,  substituting  for  a  star  the  sea  horizon,  though  this  will  be 
found  somewhat  less  accurate. 

(c)  Measure  the  apparent  diameter  of  the  sun  by  first  bringing  the  upper  limb  of  the  reflected 
image  to  touch  the  lower  limb  of  the  direct  image,  and  then  bringing  the  lower  limb  of  the  reflected 
image  to  touch  the  upper  limb  cf  the  direct  image. 

Denote  the  readings  in  the  two  cases  by  r  and  r^;  then,  if  S  =  apparent  diameter  of  the  sun,  and 
R  =  the  reading  of  the  sextant  when  the  two  images  are  in  coincidence,  we  have: 

r  =R  +  S, 
r'  =  R  -  S, 

R  =  ^(r  +  rO. 

As  R  rei^resents  the  error,  the  correction  will  be  —  R.  Hence  the  rule :  Mark  the  readings  when  on 
the  arc  with  the  negative  sign;  when  off,  with  the  positive  sign;  then  the  index  correction  is  one-half  the 
algebraic  sum  of  the  two  readings. 

Example:  The  sun's  diameter  is  measured  for  index  correction  as  follows:  On  the  arc,  31^  20^';  off 
the  arc,  33^  10^^.     Required  the  correction. 

On  the  arc,       -  31^  20^^ 
Off  the  arc,       -  33    10       ' 


1    50. 


I.  ('.,         -r-    0   55 

251.  From  the  equations  previously  given,  it  is  seen  that: 

8  =  i  (r-rO; 

hence,  if  the  observations  are  correct,  it  will  be  found  that  the  sun's  semidiameter,  as  given  in  the 
Nautical  Almanac  for  the  day  of  observation,  is  equal  to  one-half  the  algebraic  difference  of  the  readings. 
If  required  to  obtain  the  index  correction  with  great  precision,  several  observations  should  be  taken  and 
the  mean  used,  the  accuracy  being  verified  by  comparing  the  tabulated  with  the  observed  semidiameter. 
If  the  sun  is  low,  the  horizontal  semidiameter  should  be  observed,  to  prevent  the  error  that  may  arise 
from  unequal  refraction. 

252.  Use  of  the  Sextant. — To  measure  the  angle  between  any  two  visible  objects,  point  the  tele- 
scope toward  the  lower  one,  if  one  is  above  the  other,  or  toward  the  left-hand  one,  if  they  are  in  nearly 
the  same  horizontal  plane.  Keep  this  object  in  direct  view  through  the  unsilvered  part  of  the  horizon 
glass,  and  move  the  index  arm  until  the  image  of  the  other  object  is  seen  by  a  double  reflection  from  the 
index  mirror  and  the  silvered  portion  of  the  horizon  glass.  Having  gotten  the  direct  image  of  one 
object  into  nearly  exact  contact  with  the  reflected  image  of  the  other,  clamp  the  index  arm  and,  by 
means  of  the  tangent-screw,  complete  the  adjustment  so  that  the  contact  may  be  perfect;  then  read  the 
limbs. 

In  measuring  the  altitude  of  a  celestial  body  above  the  sea  horizon,  it  is  necessary  that  the  angle 
shall  be  measured  to  that  point  of  the  horizon  which  lies  vertically  beneath  the  object.  To  determine 
this  point,  the  observer  should  move  the  instrument  slightly  to  the  right  and  left  of  the  vertical,  swinging 
it  about  the  line  of  sight  as  an  axis,  taking  care  to  keep  the  object  in  the  middle  of  the  field  of  view. 
The  object  will  appear  to  describe  the  arc  of  a  circle,  and  the  lowest  point  of  this  arc  marks  the  true 
vertical. 

The  shade-glasses  should  be  employed  as  may  be  necessary  to  protect  the  eye  when  observing 
objects  of  dazzling  brightness,  such  as  the  sun,  or  the  horizon  when  the  sun  is  reflected  from  it  at  a  low 
altitude.  Care  must  be  taken  that  the  images  are  not  too  bright  or  the  eye  will  be  so  affected  as  to 
interfere  with  the  accuracy  of  the  observations. 

253.  Choice  of  Sextants. — The  choice  of  a  sextant  should  be  governed  by  the  kind  of  work  which 
is  required  to  be  done.  In  rough  work,  such  as  surveying,  where  angles  need  only  be  measured  to  the 
nearest  30'^  the  radius  may  be  as  small  as  6  inches,  which  will  permit  easy  reading,  and  the  instrument 
can  be  correspondingly  lightened.  Where  readings  to  10"  are  desired,  as  in  nice  astronomical  work,  the 
radius  should  be  about  7j  inches,  and  the  instrument,  to  be  strongly  built,  should  weigh  about  3  J  pounds. 

The  parts  of  an  instrument  should  move  freely,  without  binding  or  gritting.  The  eyepieces  should 
move  easily  in  the  telescope  tubes;  the  bracket  for  carrying  the  telescope  should  be  made  very  strong. 
It  is  frequently  found  that  the  parallelism  of  the  line  of  sight  is  destroyed  in  focusing  the  eyepiece, 
either  on  account  of  the  looseness  of  the  fit  or  because  of  the  telescope  bracket  being  weak.  The  vernier 
should  lie  close  to  the  limbs  to  prevent  parallax  in  reading.  If  it  is  either  too  loose  or  too  tight  at  either 
extremity  of  its  travel,  it  may  indicate  that  the  pivot  is  not  perpendicular.  The  balls  of  the  tangent- 
screw  should  fit  snugly  in  their  sockets,  so  that  there  may  be  no  lost  motion. 

Where  possible,  the  sextant  should  always  be  submitted  to  expert  examination  and  test  as  to  the 
accuracy  of  its  permanent  adjustments  before  acceptance  by  the  navigator. 

254.  Resilverinu  Mirrors. — Occasion  may  sometimes  arise  for  resilvering  the  mirrors  of  a 
sextant,  as  they  are  always  liable  to  be  damaged  by  dampness  or  other  causes.     For  this  purpose  some 


70  INSTRUMENTS    EMi-LOYED    IN    NAUTICAL    ASTRONOMY. 

clean  tin  foil  and  mercury  are  required.  Upon  a  piece  of  glass  about  4  inches  square  lay  a  piece  of 
tin  foil  whose  dimensions  exceed  by  about  a  quarter  of  an  inch  in  each  direction  those  of  the  glass  to  be 
silvered;  smooth  out  the  foil  carefully  by  rubbing;  put  a  small  drop  of  mercury  on  the  foil  and  spread 
it  with  the  finger  over  the  entire  surface,  being  careful  that  none  shall  find  its  Avay  untler  the  foil; 
then  put  on  a  few  more  drops  of  mercury  until  the  whole  surface  is  fluid.  The  glass  which  is  to  be 
silvered  having  been  carefully  cleaned,  it  should  l)e  laid  upon  a  piece  of  tissue  paper  whose  edge  just 
covers  the  edge  of  the  foil  and  transferred  carefully  from  the  paper  to  the  tin  foil,  a  gentle  pressure 
being  kept  upon  the  glass  to  avoid  the  formation  of  bubbles;  finally,  place  the  mirror  face  downward 
and  leave  it  in  an  inclined  position  to  allow  the  surjilus  mercury  to  flow  off,  the  latter  operation  being 
hastened  by  a  strip  of  tin  foil  at  its  lower  edge.  After  five  or  six  hours  the  tin  foil  around  the  edges 
may  be  removed,  and  the  next  day  a  coat  of  varnish  made  from  spirits  of  wine  and  red  sealing  wax 
should  l)e  applied.  For  a  horizon  mirror  care  must  be  taken  to  avoid  silvering  the  plain  half.  The 
mercury  drawn  from  the  foil  should  not  be  placed  with  clean  mercury  with  a  view  to  use  in  the  artificial 
horizon  or  the  whole  will  be  spoiled. 

255.  Octants  and  Quintants. — Properly  speaking,  a  sextant  is  an  instrument  whose  arc  covers 
one-sixth  of  a  complete  circle,  and  which  is  therefore  capable  of  measuring  an  angle  of  120°.  Other 
instruments  are  made  which  are  identical  in  princijile  with  the  sextant  as  heretofore  described,  and 
which  differ  from  that  instrument  only  in  the  length  of  the  arc.  These  are  the  octant,  an  eighth  of  a 
circle,  by  which  angles  may  be  measured  to  90°,  and  the  (jitinlant,  a  fifth  of  a  circle,  which  measures 
angles  up  to  144°.  The  distinction  between  these  instruments  is  not  always  carefully  made,  and  in 
such  matters  as  have  been  touched  upon  in  the  foregoing  articles  the  sextant  may  be  regarded  as  the 
type  of  all  kindred  reflecting  instruments. 

THE    ARTIFICIAL   HORIZON. 

256.  The  Artificial  Horizon  is  a  small,  rectangular,  shallow  basin  of  mercury,  over  which,  to  protect 
the  mercury  from  agitation  ])y  the  wind,  is  placed  a  roof  consisting  of  two  plates  of  glass  at  right  angles 

to  each  other.     The  mercury  affords  a  perfectly  horizontal  surface 

*\  which  is  at  the  same  time  an  excellent  mirror.     The  different  parts 

N.  of  an  artificial  horizon  are  furnished  in  a  compact  form,  a  metal 

\v  bottle  being  i)rovided  for  containing  the  mercury  when  not  in  use, 

N.  together  with  a  suitable  funnel  for  pouring. 

\v  If  MX,  in  figure  33,  is  the  horizontal  surface  of  the  mercury;  S^]} 

N^  a  raj'  of  light  from  a  celestial  object,  incident  to  the  surface  at  B; 

^  \^  BA  the  reflected  ray;  then  an  observer  at  A  will  receive  the  ray  BA 

\v  Nv  as  if  it  proceeded  from  a  point  S^^,  Avhose  angular  depression,  ^IBS''', 

N.  N.  below  the  horizontal  plane  is  equal  to  the  altitude,  ]MBS^,  of  the 

>v  ^A     object  above  that  plane.     If,  then,  SA  is  a  direct  ray  from  the  object 

N.  /        parallel  t~)  S'B,  an  observer  at  A  can  measure  with  the  sextant  the 

.      \^  /  angle  8A8''=  S'BS''=  2  S'BM,  by  bringing  the  image  cf  the  object 

N.  /  reflected  by  the  index  mirror  into  coincidence  with  the  image  S'' 

\^^       /  reflected  by  the  mercury  and  seen  through  the  horizon  glass.     The 

\/  instrumental  measure,  corrected  for  index  error,  will  be  double  the 

/»  apparent  altitude  of  the  body. 

/  The  sun's  altitude  will  be  measured  by  bringing  the  lower  limb 

/  of  one  image  to  touch  the  upper  liml)  of  "the  other.     Half  the  cor- 

/  reefed  instrumental  reading  will  l)e  the  apparent  altitude  of  the 

^./  sun's  loirer  or  upper  limb,  according  as  the  lower  or  upper  limb  of 

Pj^,    .>.>  the  reflected  image  was  the  one  employed  in  the  observation. 

In  observations  of  the  sun  with  the  artificial  horizon,  the  eye  is 
protected  by  a  single  dark  glass  over  the  eyepiece  of  the  telescope  through  which  direct  and  reflected 
rays  must  pass  alike,  thereby  avoiding  the  errors  that  might  possibly  arise  from  a  difference  in  the 
separate  shade  glasses  attached  to  the  frame  of  the  sextant. 

The  glasses  in  the  roof  over  the  mercury  should  be  made  of  plate-glass,  with  perfectly  parallel  faces. 
If  they  are  at  all  prismatic,  the  ol)served  altitude  will  l)e  erroneous.  The  error  may  be  removed  by 
observing  a  second  altitude  with  the  roof  reversed,  and,  in  general,  by  taking  one  halfVjf  a  set  of  obser- 
vations with  the  roof  in  one  ])osition  and  the  other  half  with  the  roof  reversed.  On  the  rare  occasions 
when  the  atmosphere  is  so  calm  that  the  unsheltered  mercury  Mill  remain  undisturbed,  most  satisfac- 
tory observations  may  be  made  by  leaving  off  the  roof. 

257.  In  setting  up  an  artificial  horizon,  care  should  be  taken  that  the  basin  is  free  from  dust  and 
other  foreign  matter,  as  small  particles  floating  upon  the  surface  of  the  mercury  interfere  with  a  perfect 
reflection.  The  basin  should  be  so  i)laced  that  its  longer  edge  lies  in  the  direction  in  which  the  observed 
body  will  bear  at  the  middle  of  the  observations.  The  spot  selected  for  taking  the  sights  should  lie  as 
free  as  possible  from  causes  which  will  produce  vibration  of  the  mercury,  and  precautions  should  be 
taken  to  shelter  the  horizon  from  the  wind,  as  the  mere  placing  of  the  roof  will  not  ordinarily  be  suf- 
ficient to  accomplish  this.  Embedding  the  roof  in  earth  serves  to  keep  out  the  wind,  while  setting  the 
whole  horizon  upon  a  thick  towel  or  a  piece  of  such  material  as  heavy  felt  usually  affords  ample  protec- 
tion from  wind,  tends  to  reduce  the  vibrations  from  mechanical  shoc^ks,  and  also  aids  in  keeping  out  the 
moisture  from  the  ground.  In  damp  climates  the  roof  should  lie  kept  dry  by  wiping,  or  the  moisture 
deposited  from  the  inclosed  air  will  form  a  cloud  upon  the  glass. 

Molasses,  oil,  or  other  viscous  fluid  may,  when  necessary,  be  employed  a.s  a  substitute  for  mercury. 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY.  71 

iiJ.jS.  Owing  to  the  perfection  of  manufacture  that  is  required  to  insure  accuracy  of  results  with  the 
artificial  horizon,  navigators  are  advised  to  accept  only  such  instrument  as  has  satisfactorily  stood  the 
necessary  tests  to  prove  the  correctness  of  its  adjustment  as  regards  the  glasses  of  the  roof. 

THE    CHRONOMETER. 

259.  The  Chronometer  is  simply  a  correct  time-measurer,  differing  from  an  ordinary  watch  in 
having  the  force  of  its  main-spring  rendered  uniform  by  means  of  a  variable  lever.  Owing  to  the  fact 
that  on  a  sea  voyage  a  chronometer  is  exposed  to  many  changes  of  temperature,  it  is  furnished  with  an^ 
expansion  balance,  formed  of  a  combination  of  metals  of  different  expansive  qualities,  which  produces 
the  required  compensation.  In  order  that  its  working  may  not  be  deranged  by  the  motion  of  the  ship 
in  a  seaway,  the  instrument  is  carried  in  gimbals. 

As  the  regularity  of  the  chronometer  is  essential  for  the  correct  determination  of  a  ship's  position, 
it  is  of  the  greatest  importance  that  every  precaution  be  taken  to  insure  the  accuracy  of  its  indications. 
There  is  no  more  certain  way  of  doing  this  than  to  provide  a  vessel  with  several  of  these  instruments — 
preferably  not  less  than  three — in  order  that  if  an  irregularity  develop  in  one,  the  fact  may  be  revealed 
V)y  the  others. 

260.  Care  of  Chronometers  ox  Shipboard. — The  box  in  which  the  chronometers  are  kept 
should  have  a  permanent  place  as  near  as  practicable  to  the  center  of  motion  of  the  ship,  and  where  it 
will  be  free  from  excessive  shocks  and  jars,  such  as  thos^e  that  arise  from  the  engines  or  from  the  firing 
of  heavy  guns;  the  location  should  be  one  free  from  sudden  and  extreme  changes  of  temperature,  and 
as  far  removed  as  possible  from  masses  of  vertical  iron.  The  box  should  contain  a  separate  compart- 
ment for  each  clironometer,  and  each  compartment  should  be  lined  with  baize  cloth  padded  with 
curled  hair,  for  the  double  purpose  of  reducing  shocks  and  ecpializing  the  temperature  within.  An 
outer  cover  of  l^aize  cloth  should  be  provided  for  the  lx)x,  and  this  should  be  changed  or  dried  out 
frequently  in  damp  weather.  The  chronometers  should  all  be  placed  with  the  XII  mark  in  the  same 
position. 

For  transportation  for  short  distances  by  hand,  an  instrument  should  he  rigidly  clamped  in  its 
gimbals,  for  if  left  free  to  swing,  its  performance  may  be  deranged  by  the  violent  oscillations  that  are 
imparted  to  it. 

For  transportation  for  a  considerable  distance,  as  l)y  express,  the  chronometer  should  l)e  allowed 
to  run  down,  and  should  then  be  dismounted  and  tlie  balance  corked. 

2611.  Since  it  is  not  possible  to  make  a  perfect  in.strument  which  will  be  uninfluenced  by  the  dis- 
turbing causes  incident  to  a  sea  voyage,  it  becomes  the  duty  of  the  navigator  to  determine  the  error  and 
to  keep  watch  upon  the  variable  rate  of  the  chronometer. 

The  error  of  tlte  dtronometer  .i>i  t\w  difference  l)etween  the  time  indicated  and  the  standard  time  to 
which  it  is  referred — usually  (ireonwich  mean  time. 

The  amount  the  chronometer  gai)!.^  or  loses  daily  is  the  daih/  rate. 

The  indications  of  a  chronometer  at  any  given  instant  require  a  correction  for  the  accumulated  error 
to  that  instant;  and  this  can  be  found  if  the  error  at  any  given  time,  together  with  the  daily  rate,  are 
known. 

262.  Winding. —Chronometers  are  ordinarily  constructed  to  run  for  56  hours  without  rew  inding, 
and  an  indicator  on  the  face  always  shows  how  many  hours  have  elapsed  since  the  last  winding.  To 
insure  a  uniiorm  rate,  they  mr.st  l)e  wound  regularly  every  day,  and,  in  order  to  avoid  the  serious  conse- 
quences of  their  running  down,  the  navigator  shoultl  take  some  means  to  guard  against  neglecting  this 
duty  thnnigh  a  fault  of  memory.  To  wind,  turn  the  clironometer  gently  on  its  sicle,  enter  the  key  in  its 
hole  and  ])ush  it  home,  steadying  the  instrument  with  the  hand,  and  wind  t(j  the  left,  the  last  half  turn 
being  made  so  as  to  bring  up  gently  against  the  stop.  After  winding,  cover  the  keyhole  and  return  the 
instrument  t(^  its  natural  position.  Chronometers  should  always  be  wound  in  the  same  order  tofirevent 
omissions,  and  the  jn-ecaution  taken  to  insjiect  the  indicators,  as  a  further  assurance  of  the  proper 
performance  of  the  oj)eralion. 

After  winding  each  day,  the  comparisons  should  Ix;  made,  and,  with  the  readings  of  the maximum- 
and-mininunn  thermometer  and  other  necessary  data,  recorded  in  a  book  kept  for  the  purpose. 

The  maximum-and-mininuuu  thermometer  is  one  so  arranged  that  its  highest  and  lowest  readings 
are  marked  by  small  steel  indices  that  remain  in  ]>lace  imtil  reset.  Every  chronometer  box  should  be 
provided  with  such  an  instrument,  as  a  knowledge  of  the  temperature  to  which  chronometers  have 
been  subjected  is  essential  in  any  analysis  of  tiie  rate.  To  draw  down  the  indices  for  the  purpose  of 
resetting,  a  magnet  is  used.    This  magnet  should  be  kept  at  all  times  at  a  distance  from  the  chronometers. 

263.  Comparison  of  Chronometers.— The  instrument  believed  to  be  the  best  is  regarded  as  the 
Standard,  and  each  other  is  compared  with  it.  It  is  usual  to  designate  the  Standard  as  A,  and  the 
others  as  B,  C,  etc.  Chronometers  a-e  made  to  beat  half-seconds,  and  any  two  may  be  compared  by 
following  the  beat  of  one  with  the  ear  and  of  the  other  with  the  eye. 

To  make  a  comparison,  say  of  A  and  B,  open  the  boxes  of  these  two  instruments  and  close  all 
others.  Cret  the  cadence  and,  commencing  when  A  has  just  completed  the  beat  of  some  even  5-second 
division  of  the  dial,  count  "half-one-half-two-half-three-half-four-half-five,"  glancing  at  B  in  time  to 
note  the  position  of  its  second-hand  at  the  last  count;  the  seconds  indicated  by  A  will  be  five  greater 
than  the  number  at  the  beginning  of  the  count.  The  hours  and  minutes  are  also  recorded  for  each 
chronometer,  and  the  subtraction  made.  A  good  check  upon  the  accuracy  is  afforded  by  repeating  the 
operation,  taking  the  tick  from  B. 

Where  necessary  for  exact  work,  it  is  possible  to  estimate  the  fraction  between  beats,  and  thus 
make  the  comparison  to  tenths  of  a  second;  but  the  nearest  half-second  is  sufficiently  exact  for  the 
purposes  of  ordinary  navigation  at  sea. 


72 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY. 


364.  The  following  form  represents  a  convenient  method  of  recording  comparisons: 
Stand.  A,  No.  777.  Chro.  B,  No.  1509.  Ghro.  C,  No.  1802, 


Date,  1903. 

Designation  of 
comparisvis. 

Chro.  B 

Chro.  C 

with 
Stand.  A. 

2ddifl. 

Therm. 

Bar. 

Remarks. 

Stand.  A.    ! 

Max. 

Mln. 

Air. 

Jan'uary 

1 

Stand.  A. 
B  and  C. 

Difference. 

h.  m.    s. 
1  13  40 
1  12  21.5 

s. 

h.    m.     s. 

1  14  20 

2  04  11 

«. 

0 

63 

o 

59 

o 

60 

// 
30.07 

Fomid    errors 
by    t i m e - 
ball. 

1  18^5 

11  10  09 

2 

Stand.  A. 
B  and  C. 

Difference. 

1  16  30 
1  15  10 

+  1.5 

1  17  00 

2  06  51.5 

-0.5 

64 

58 

57 

30.12 

Left    New 
York    for 
San    Juan, 
P.  R. 

1  20 

11  10  08.  5 

265.  The  second  difference  in  the  form  is  the  difference  between  the  comparisons  of  the  same 
instruments  for  two  successive  days.  When  a  vessel  is  equipped  with  only  one  chronometer  there  is 
nothing  to  indicate  any  irregularity  that  it  may  develop  at  sea — and  even  the  best  instruments  may 
undergo  changes  from  no  apparent  cause.  When  there  are  two  chronometers,  the  second  difference, 
which  is  equal  to  the  algebraic  difference  between  their  daily  rates,  remains  uniform  as  long  as  the  rates 
remain  uniform,  but  changes  if  one  of  the  rates  undergoes  a  change;  in  such  a  case,  there  is  no  means 
of  knowing  which  chronometer  has  departed  from  its  expected  performance,  and  the  navigator  must 
proceed  with  caution,  giving  due  faith  to  the  indications  of  each.  If,  however,  there  are  three  chro- 
nometers, an  irregularity  on  the  part  of  one  is  at  once  located  by  a  comparison  of  the  second  differ- 
ences. Thus,  if  the  predicted  rates  of  the  chronometers  were  such  as  to  give  for  the  second  difference  of 
A  — B,  + 1'.5,  and  of  A  —  C,  —0^.5,  suppose  on  a  certain  day  those  differences  were  -;-4*.5  and  — 0'.5, 
respectively;  it  would  at  once  be  suspected  that  the  irregularity  was  in  B,  and  that  that  chronometer 
had  lost  3*  on  its  normal  rate  during  the  preceding  day.  Suppose,  however,  the  second  differences 
were  -f  4^5  and  +2^.5;  it  would  then  be  apparent  that  A  had  gained  3^ 

266.  Temperature  Curves. — Notwithstanding  the  care  taken  to  eliminate  the  effect  of  a  change 
of  temperature  upon  the  rate  of  a  chronometer,  it  is  rare  that  an  absolutely  perfect  compensation  is 
attained,  and  it  may  therefore  be  assumed  that  the  rates  of  all  chronometers  vary  somewhat  with  the 
temperature.  Where  the  voyage  of  a  vessel  is  a  long  one  and  marked  changes  of  climate  are  encoun- 
tered, the  accumulated  error  from  the  use  of  an  incorrect  rate  may  be  very  material,  amounting  to  sev- 
eral minutes'  difference  of  longitude.  Careful  navigators  will  therefore  take  every  means  to  guard 
against  such  an  error.  By  the  employment  of  a  temperature  curve  in  connection  with  the  chronometer 
rate  the  most  satisfactory  results  are  arrived  at. 

267.  There  should  be  furnished  with  each  chronometer  a  statement  showing  its  daily  rate  under 
various  conditions  of  temperature;  and  this  may  be  supplemented  by  the  observations  of  the  navigator 
during  the  time  that  the  chronometer  remains  on  board  ship.  AVith  all  available  data  a  temperature 
curve  should  be  constructed  which  will  indicate  graphically  the  performance  of  the  instrument.  It  is 
most  convenient  to  employ  for  this  purpose  a  piece  of  "profile  paper,"  on  which  parallel  lines  are  ruled 
at  equal  intervals  at  right  angles  to  each  other.  Let  each  horizontal  line  represent,  say,  a  degree  of  tem- 
perature, numbered  at  the  left  edge,  from  the  bottom  up;  draw  a  vertical  line  in  red  ink  to  represent 
the  zero  rate,  and  let  all  rates  to  the  right  be  plus,  or  gaining,  and  those  to  the  left  minus,  or  losing;  let 
the  intervals  between  vertical  lines  represent  intervals  of  rate  (as  one-tenth  of  a  second)  numbered  at 
the  top  from  the  zero  rate;  then  on  this  scale  plot  the  rate  corresponding  to  each  temperature;  when 
there  are  several  observations  covering  one  height  of  the  thermometer,  the  mean  may  be  used. 
Through  all  the  plotted  points  draw  a  fair  curve,  and  the  intersection  of  this  curve  with  each  tempera- 
ture line  gives  the  mean  rate  at  that  temperature.  The  mean  temperature  given  by  the  maximum  and 
minimum  thermometer  shows  the  rate  to  be  used  on  any  day. 

26§.  Hack  or  Comparing  Watch. — In  order  to  avoid  derangement,  the  chronometers  should 
never  be  removed  from  the  permanent  box  in  which  they  are  kept  on  shipboard.  When  it  is  desired  to 
mark  a  certain  instant  of  time,  as  for  an  astronomical  observation  or  for  obtaining  the  chronometer 
error  by  signal,  the  time  is  marked  by  a  "hack  "  (an  inferior  chronometer  used  for  this  purpose  only), 
or  by  a  comparing  watch.  Careful  comparisons  are  taken — preferably  both  before  and  afterwards — and 
the  chronometer  time  at  the  required  instant  is  thus  deduced.  The  correction  represented  by  the  chro- 
nometer time  minus  the  watch  time  (twelve  hours  being  added  to  the  former  when  necessary  to  make 
the  subtraction  possible)  is  referred  to  as  C  —  W. 

Suppose,  for  example,  the  chronometer  and  watch  are  compared  and  their  indications  are  as  follows: 

Chro.  t.,     5''27'"30» 
W.  T.,    -2   36    45.5 


C-W,       2    50   44.5 

If  then  a  sight  is  tak«n  when  the  watch  shows  3''  01"'  27.* 5,  we  have: 

W.  T.,        3"  01"  27^5 
C-W,  +2  50    44.5 

Chrn.t.,      5    52    12.0 


INSTRUMENTS    EMPLOYED    IN    NAUTICAL    ASTRONOMY.  73 

It  may  occur  that  the  values  of  C  —  W,  as  obtained  from  comparisons  before  and  after  marking  the 
desired  time,  will  vary;  in  that  case  the  value  to  be  used  will  be  the  mean  of  the  two,  if  the  time  marked 
is  about  midway  between  comparisons,  but  if  much  nearer  to  one  comparison  than  the  other,  allowance 
should  be  made  accordingly. 

Thus  suppose,  in  the  case  previously  given,  a  second  comparison  had  been  taken  after  the  sight  as 
follows: 

Chro.  t,       6M2»'45' 
W.  T.,     -3    21    59.5 


C-W,        2   50    45.5 

The  sight  having  been  taken  at  about  the  middle  of  the  interval,  the  C  —  W  to  be  used  would  be  the 
mean  of  the  two,  or  2''  50™  45*.  0. 

Let  us  assume,  however,  that  the  second  comparison  showed  the  following: 

Chro.t.,       6''38™25»  ^ 

W.  T.,     -3   47    39 

'  C-W,        2   50    46 

Then,  the  sight  having  been  taken  when  only  about  one-third  of  the  interval  had  elapsed  between 
the  first  and  second  comparisons,  it  would  be  assumed  that  only  one-third  of  the  total  change  in  the 
C  —  W  had  occurred  up  to  the  time  of  sight,  and  the  value  to  be  used  would  be  2**  50'"  45". 0. 

269.  It  is  considered  a  good  practice  always  to  subtract  watch  time  from  chronometer  time 
whatever  the  relative  values,  and  thus  to  employ  C  —  W  invariably  as  an  additive  correction.  It  is  equally 
correct  to  take  the  other  difference,  W  —  C,  and  make  it  subtractive;  it  may  sometimes  occur  that  a  few 
figures  will  thus  be  saved,  but  a  chance  for  error  arises  from  the  possibilitj'  of  inadvertently  using  the 
wrong  sign,  which  is  almost  impossible  by  the  other  method.  Thus,  the  following  example  may  be 
taken: 

rC,  10*  57'"  38'  W,  U"*  42"  35» 


Comparison 


Sight 


|W,        -11     42    35  C,         -10    57    38 


[C-W,     11     15    03  W-C,     0    44    57 

f\V,  11     50    21  W,  11     50    21 

I  C-W, +11     15    03  W-C-  0    44    57 


[C,  11     05    24  C,  n     05    24 


74  TIME    AND   THE    NAUTICAL    ALMANAC. 


CHAPTER  IX. 
TIME  AND  THE  NAUTICAL  ALMANAC. 


270.  The  subjects  of  Tinu  aii<l  the  Xauiical  Almanac  are  two  of  the  most  important  ones  to  be 
mastered  in  the  study  of  Nautical  Astronomy,  as  they  enter  into  every  oi>eration  for  the  astronomical 
determination  of  a  ship's  position.     They  will  be  treated  in  conjunction,  as  the  two  are  interdependent. 

METHODS  OF  RECKONING  TIME. 

271.  The  instant  at  which  any  point  of  the  celestial  sphere  is  on  the  meridian  of  an  observer  is 
termed  the  tramit,  cubni)iation,  or  meridian  passaye  of  that  point;  when  on  that  half  of  the  me.idian 
which  contains  the  zenith,  it  is  designated  as  superior  or  tipper  transit;  when  on  the  half  containing  the 
nadir,  as  inferior  or  lotcer  transit. 

272.  Three  different  kinds  of  time  are  employed  in  astronomy — (a)  apparent  or  mhn-  time,  [h]  mean 
time,  and  (e)  sidereal  time.  These  depend  ujwn  the  hour  angle  from  the  meridian  of  the  points  to  which 
they  respectively  refer.  The  point  of  reference  for  apparent  or  solar  time  is  the  Center  of  the  >Sun;  for 
mean  time,  an  imaginary  point  called  the  Mean  Sun;  and  for  sidereal  time,  the  Vernal  Equinox,  also  called 
the  First  Point  of  Aries. 

The  unit  of  time  is  the  Day,  which  is  the  period  between  two  successive  transits  over  the  same 
branch  of  the  meridian  of  the  point  of  reference.  The  day  is  divided  into  24  equal  parts,  called  Hours; 
these  into  (50  equal  parts,  called  Minutes,  and  these  into  60  equal  parts,  called  Seconds. 

273.  Apparent  or  Solar  Time. — The  hour  angle  of  the  center  of  the  sun  affords  a  measure  of 
Apparent  or  Solar  Time.  An  Apjiarcnt  or  Sular  Jkni  is  the  interval  of  time  between  two  successive  transits 
over  the  same  meridian  of  the  center  of  the  sun.  It  is  Ajyparent  Noou  when  the  suti's  hour  circle  coin- 
cides with  the  celestial  meridian.  This  is  the  most  natural  and  direct  measure  of  time,  and  the  unit  of 
time  adopted  by  the  navigator  at  sea  is  the  apparent  solar  day.  Apparent  noon  is  the  time  when  the 
latitude  can  be  most  readily  determined,  and  the  ordinary  method  of  determining  the  longitude  by  the 
sun  involves  a  calculation  to  deduce  the  apparent  time  first. 

Since,  however,  the  intervals  between  the  successive  leturns  of  the  sun  to  the  same  meridian  are  not 
equal,  apparent  time  can  not  be  taken  as  a  standard.  The  apparent  day  varies  in  length  from  two  causes: 
fii-st,  the  sun  does  not  move  in  the  equator,  the  great  circle  perpendicular  to  the  axis  of  rotation  of  the 
earth,  but  in  the  ecliptic;  and,  secondly,  the  sun's  motion  in  the  ecliptic  is  not  uniform.  Sometimes  the 
sun  describes  an  arc  of  57^  of  the  ecliptic,  and  sinnetimes  an  arc  of  hV  in  a  day.  At  the  points  where 
the  ecliptic  and  equinoctial  intersect,  the  direction  of  the  sun's  ajyparent  motion  is  inclined  at  an  angle 
of  23°  27'  to  the  equator,  while  at  the  solstices  it  moves  in  a  direction  parallel  to  the  equator. 

274.  Mean  Time. — To  avoid  the  irregularity  of  time  caused  by  the  want  of  uniformity  in  the  sun's 
motion,  a  fictitious  sun,  called  the  Mean  Sun,  is  supposed  to  move  in  the  equinoctial  with  a  imiform 
velocity  that  equals  the  mean  velocity  of  the  true  sun  in  the  ecliptic.  This  mean  sun  is  regarded  as  being  in 
coincidence  with  the  true  sun  at  the  vernal  equinox,  or  First  Point  of  Aries. 

Mean  Time  is  the  hour  angle  of  the  mean  sun.  A  Mean  Ihuj  is  the  interval  between  two  successive 
transits  of  the  mean  sun  over  the  meridian.  Mean  Noon  is  the  instant  when  the  mean  sun's  hour  circle 
coincides  with  the  meridian. 

Mean  time  lapses  uniformly;  at  certain  times  it  agrees  with  apparent  time,  while  sometimes  it  is 
behind,  and  at  other  times  in  advance  of  it.  It  is  this  time  that  is  measured  by  the  clocks  in  ordinary 
use,  and  to  this  the  chronometers  used  by  navigators  are  regulated. 

275.  The  difference  between  apparent  and  mean  time  is  called  the  Equation  of  Time;  l)y  this 
quantity,  the  conversion  from  one  to  the  other  of  these  times  may  be  made.  Its  magnitude  and  the 
direction  of  its  application  may  be  found  for  any  moment  from  the  Nautical  Almanac. 

270.  Sidereal  Ti.me. — Sidereal  Time  is  the  hour  angle  of  the  First  Point  of  Aries.  This  point, 
which  is  identical  with  the  vernal  equinox,  is  the  origin  of  all  coordinates  of  right  ascension.  Since  the 
position  of  the  point  is  fixed  in  the  celestial  si)here  and  does  not,  like  the  sun,  moon,  and  planets,  have 
actual  or  apparent  motion  therein,  it  shares  in  this  re.spect  the  i)roperties  of  the  fixed  stars.  It  may 
therefore  be  said  that  intervals  of  sidereal  time  are  those  which  are  measured  by  the  stars. 

A  Sideretd  Day  is  the  interval  between  two  successive  transits  of  the  First  Point  of  Aries  across 
the  same  meridian.  Sidereal  Xoon  is  the  instant  at  which  the  hour  circle  of  the  First  Point  of  Aries 
coincides  with  the  meridian.  In  order  to  interconvert  sidereal  and  mean  times  an  element  is  tabulated 
in  the  Nautical  Almanac.  This  is  the  Sidereal  Time  of  Mean  Noon,  which  is  also  the  Right  A.^cension 
of  the  Mean  Sun. 

277.  Civil  and  Astronomical  Ti.me. — The  Civil  Day  commences  at  midnight  and  comprises  the 
twenty-four  hours  until  the  following  midnight.  The  hours  are  counted  from  0  to  12,  from  midnight  to 
noon;  then,  again,  from  0  to  12,  from  noon  to  midnight.  Thus  the  civil  day  is  divided  into  two  periods 
of  twelve  hours  each,  the  first  of  which  is  marked  a.  m.  (ante  meridian),  while  the  last  is  marked  p.  m. 
(post  meridian) . 


TIME    AND    THE    NAUTICAL    ALMANAC. 


75 


The  Astronomical  or  Solar  Day  commences  at  noon  of  the  civil  day  of  the  same  date.  It  comprises 
twenty-four  hours,  reckoned  from  0  to  24,  from  noon  of  one  day  to  noon  of  the  next.  Astronomical  time 
(apparent  or  mean)  is  the  hour  angle  of  the  sun  (true  or  mean)  measured  to  the  westward  throughout 
its  entire  circuit  from  the  time  of  .its  upper  transit  on  one  day  to  the  same  instant  of  the  next. 

The  civil  day,  therefore,  begins  twelve  hours  before  the  astronomical  day,  and  a  clear  under- 
standing of  this  fact  is  all  that  is  required  for  intercon verting  these  times.     For  example: 

January  9,  2  a.  m.,  civil  time,  is  January  8,  14'',  astronomical  time. 

January  9,  2  p.  m.,  civil  time,  is  January  9,  2'',  astronomical  time. 

278.  Hour  Angle. — The  hour  angle  of  a  heavenly  body  is  the  angle  at  the  pole  of  the  celestial 
concave  between  the  declination  circle  of  the  heavenly  body  and  the  celestial 
meridian.    It  is  measured  by  the  arc  of  the  celestial  equator  between  the  decli- 
nation circle  and  the  celestial  meridian. 

In  figure  34  let  P  be  the  pole  of  the  celestial  sphere,  of  which  YMQ  is  the 
equator,  PQ,  the  celestial  meridian,  and  PM,  PS,  PV,  the  declination  circles  of 
the  mean  sun,  a  heavenly  body,  and  the  First  Point  of  Aries,  respectively. 

Then  QPM,  or  its  arc,  QM,  is  the  hour  angle  of  the  mean  sun,  or  the  mean  v< 
time;  QPS,  or  QS,  the  hour  angle  of  the  heavenly  body;  QPV,  or  QV,  the  hour 
angle  of  the  First  Point  of  Aries,  or  the  right  ascension  of  the  meridian,  both  of 
which  are  e(]uivalent  to  the  sidereal  time;   VPS,  or  YS,  the  right  ascension  of 
the  heavenly  body;  and  VPM,  or  V^I,  the  right  ascension  of  the  mean  sun. 

279.  Time  at  Different  ^Ieridians. — The  hour  angle  of  the  true  sun  at  any  meridian  is  called  the 
local  apparent  time;  that  of  the  mean  sun,  the  heal  vieaii  time;  that  of  the  First  Point  of  Aries,  the  local 
sidereal  time.  The  hour  angles  of  the  same  body  and  points  from  Greenwich  are  respectively  the  Green- 
vrich  apparent,  mean,  and  sidereal  times.  The  difference  between  the  local  time  at  any  meridian  and  the 
Greenwich  time  is  e(]ual  to  the  longitude  of  that  place  from  Greenwich  expressed  in  time;  the  conver- 
sion from  time  to  arc  may  be  effected  by  a  simple  mathematical  calculation  or  by  the  use  of  Table  7. 

In  comparing  corresponding  times  of  different  meridians  the  most  easterly  meridian  may  be  distin- 
guished as  that  at  which  the  time  is  greatest  or  latest. 

In  figure  35  P3I  and  PM^  represent  the  celestial  meridians  of  two  places; 
PS,  the  declination  circle  through  the  sun,  and  PG,  the  Greenwich  meridian; 
let  To  =  the  Greenwich  time  =  GPS; 

Tm  =  the  corresponding  local  time  at  all  places  on  the  meridian  PM  =  MPS ; 

Tji'^the  corresponding  local  time  at  all  places  on  the  meridian  PM''  = 
M^PS; 

Lo  —  west  longitude  of  meridian  PM  =  GPM ;  and 

Lo^  =  east  longitude  of  meridian  PM'  =  GPM'. 

If  west  longitudes  and  hour  angles  be  reckoned  as  positive,  and  east  lon- 
gitudes and  hour  angles  as  negative,  we  have: 

Lo  =  T«~T„;  and 
Lo'  =  To  — TmS  therefore, 
Lo  — Lo'  =  Tm— Tm. 

Thus  it  may  be  seen  that  the  difference  of  longitude  between  two  places  equals  the  difference  of 
their  local  times.     This  relation  may  be  shown  to  hold  for  any  two  meridians  whatsoever. 

Both  local  and  Greenwich  times  in  the  above  formula^  must  be  reckoned  westward,  always  from 
their  respective  meridians  and  from  O*"  to  24'';  in  other  words,  it  is  the  astronomical  time  which  should 
be  used  in  all  astronomical  computations. 

The  formula  Lo  =  Tg  — Tj,  is  true  for  any  kind  of  time,  solar  or  sidereal;  or,  in  general  terms, 
To  and  T>i  are  the  hour  angles  of  any  point  of  the  sphere  at  the  two  meridians  whose  difference  of 
longitude  is  Lo.     S  may  be  the  sun  (true  or  mean)  or  the  vernal  equinox. 

2§0.  Fi.vDiNG  THE  (jREENwicH  TiME. — Siuce  nearly  every  computation  made  by  the  navigator 
requires  a  knowledge  of  the  Greenwich  date  and  time  as  a  preliminary  to  the  use  of  the  Nautical 
Almanac,  the  first  operation  necessary  is  to  deduce  from  the  local  time  the  corresponding  (rreenwich 
date,  either  exact  or  approximate,  and  thence  the  Greenwich  time  expressed  astronomically. 

The  formula  is: 

To=Tm+Lo, 

remembering  that  west  longitudes  are  positive,  east  longitudes  are  negative.     Hence  the  following  rule 
for  converting  local  to  Greenwich  time: 

Having  expressed  the  local  time  astronomically,  add  the  longitude  if  west,  subtract  it  if  east;  the  result 
is  the  corresponding  Greenwich  time. 

•    Example:  In  longitude  81°  15'  \V.  the  local  time  is,  1879,  April,  15''  10''  17'"  30"  a.  m.     Required  the 
Greenwich  time. 

Local  Ast.  time,  April,   14''  22"  17"'  30" 
Longitude,  +     5   25    00 


Fig.  35. 


Greenwich  time, 


15     8   42    30 


Example:  In  longitude  81°  15'  E.  the  local  time  is,  August,  5^  2"  10"'  30^  p.  m.    Required  the  Green- 
wich time. 

Local  Ast.  time,  5''    2"  10'"  30' 

Longitude,  -     5   25    00 


Greenwich  time. 


4  20   45    30 


76  TIME    AND    THE    NAUTICAL    ALMANAC. 

I 
Example:  In  longitude  17°  28'  AV.  the  local  time  is,  May,  1"*  S*"  10™  p.  m.    Required  the  Greenwich 
time.  ^ 

Local  Agt.  time,  l"*  S**  10™  00' 

Longitude,  +    1    09    52 


_  Greenwich  time,  1   4    19    52 

Example:  In  longitude  125°  SO'  E.  the  local  time  ia,  May,  l"*  S*"  10™  30»  a.  m.  Required  the  Green- 
wich time. 

Local  Ast.  time,  April,    SO**  20"  10"'  30' 
Longitude,  —     8   22    00 

Greenwich  time,  30   11    48    30 

2§1.  From  the  preceding  article  we  have: 

To  =  Tm  +  Lo;  hence, 
Tm  =  Tg  —  Lo; 

thus  it  will  be  seen  that,  to  find  the  local  time  corresponding  to  any  Greenwich  time,  the  above  process 
is  simply  reversed. 

Since  all  observations  at  sea  are  referred  to  chronometers  regulated  to  Greenwich  mean  time,  and 
as  these  instruments  are  usually  marked  on  the  dial  from  0"  to  12",  it  becomes  necessary  to  distinguish 
whether  it  is  a.m.  or  p.m.  at  Greenwich.  Therefore,  an  approximate  knowledge  of  the  longitude  and 
local  time  is  necessary  to  determine  the  Greenwich  date. 

Example:  In  longitude  5"  00™  00*  W.,  about  3"  30"' p.m.  April  15th,  the  Greenwich  chronometer 
read  8"  25™,  and  was  fast  of  Gr.  time  3™  15^     Required  the  local  astronomical  time. 

Aprox.  local  time,       15"  3"  30™  Gr.  chro.,  8"  25™  00*  Gr.  Ast.  time  \b^,       8"  21™  45 

Longitude,  -f        5   00  Corr.,  —        3    15  Longitude,  —  5  00    00 


Approx.  Gr.  time,      15   8   30  Gr.  Ast.  time  15\      8  21    45  Local  Ast.  time  15*,      3   21    45 

Example:  In  longitude  5"  00™  00*  E.,  about  8  a.  m.  May  3d,  the  Gr.  chro.  read  3"  15™  20%  and  was 
fast  of  Gr.  time  3™  15*.     Required  the  local  astronomical  time. 

Approx.  local  time.  May,  2"  20"  Gr.  chro.,  3"  15™  20*  Gr.  Ast.  time  2'»,       15"  12™  05 

Longitude,  —    5  Corr.,  —    3    15  Longitude,  —    5  00    00 


Approx.  Gr.  time,  2    15  Gr.  Ast.  time  2"»,      15    12    05  Local  Ast.  time 2",     20    12    05 

THE   NAUTICAL   ALMANAC. « 

2§2.  The  American  Ephemeris  and  Nautical  Almanac  is  divided  into  four  parts,  a.s  follows:  Part  I, 
Ephemeris  for  the  meridian  of  Greenwich,  gives  the  ephemerides  of  the  sun  and  moon,  the  geocentric 
and  heliocentric  positions  of  the  major  planets,  the  sun's  coordinates,  and  other  fundamental  astronom- 
ical data  for  equidistant  intervals  of  Greenwich  mean  time;  Part  II,  Ephemeris  for  the  meridian  of 
Washington,  gives  the  ephemerides  of  the  fixed  stars,  sun,  moon,  and  major  planets  for  transit  over  the 
meridian  of  Washington;  Part  III,  Phenomena,  contains  predictions  of  phenomena  to  be  observed,  with 
data  ior  their  computation;  and  Part  IV,  Star  Numbers  and  other  data,  contains  matter  relating  to  cer- 
tain fixed  stars.  Tables  are  also  appended  for  the  interconversion  of  mean  and  sidereal  time  and  for 
finding  the  latitude  by  an  altitude  of  Polaris. 

The  American  Nautical  Almanac  is  a,  smaller  book  made  up  of  extracts  from  the  "  Ephemeris  and 
Almanac"  just  described,  and  is  designed  especially  for  the  use  of  navigators,  being  adapted  to  the 
meridian  of  Greenwich.  It  contains  the  positions  of  the  sun  and  moon,  the  distances  of  the  moon  from 
the  center  of  the  sun,  from  the  centers  of  the  four  most  conspicuous  planets,  and  from  certain  fixed 
stars,  together  with  the  ephemerides  of  the  planets  Mercury,  Venus,  Mars,  Jupiter,  and  Saturn,  and  the 
mean  places  of  150  fixed  stars;  solar  and  lunar  eclipses  are  described,  and  the  tables  for  the  interconversion 
of  mean  and  sidereal  time  and  for  finding  the  latitude  by  Polaris  are  included. 

The  elements  dependent  upon  the  sun  and  moon  are  placed  at  the  beginning  of  the  book, 
arranged  according  to  the  months  of  the  year;  eighteen  pages  are  devoted  to  each  month,  numbered  in 
Roman  notation  from  I  to  XVIII.  Of  these,  page  I  contains  the  Apparent  Right  Ascension  and  Declina- 
tion of  the  sun  and  the  Equation  of  Time  for  the  instant  of  Greenwich  apparent  noon;  throughout  the 
remaining  seventeen  pages  Greenwich  mean  time  forms  the  basis  of  reckoning.  Page  I  is  used  in  com- 
putations from  observations  that  depend  upon  the  time  of  the  sun's  meridian  passage,  at  which  instant 
the  local  apparent  time  is  0",  and  the  Greenwich  apimrent  time  is  equal  to  the  longitude,  if  west,  or  to 
24"  minus  the  longitude,  if  east;  this  page  therefore  affords  a  means  for  reducing  the  elements  for  such 
observations  from  a  knowledge  of  the  longitude  alone.  In  all  other  observations  the  calculation  is 
made  for  some  definite  instant  of  Greenwich  mean  time  (usually  as  noted  by  the  chronometer) ,  in  which 
case  Pages  II  to  XVIII  are  employed. 

2S3.  Rediction'  of  Elements. — The  reduction  of  elements  in  the  Nautical  Almanac  is  usually 
accomplished  by  Interpolation,  but  in  certain  cases  where  extreme  preiision  is  necessary  the  method  of 
Second  Differences  must  be  used. 


a  See  extracts  from  Ephemeris  and  Nautical  Almanac  for  1879,  Appendix  I. 


TIME    AND    THE    NAUTICAL    ALMANAC.  77 

The  Ephemeris,  being  computed  for  the  Greenwich  meridian,  contains  the  right  ascensions,  declina- 
tions, equations  of  time,  and  other  elements  for  given  equidistant  intervals  of  Greenwich  time.  Hence, 
before  the  value  of  any  of  these  quantities  can  be  found  for  a  given  local  time  it  is  necessary  to  determine 
the  corresponding  Greenwich  time.  Should  that  time  be  one  for  which  the  Nautical  Ahnanac  gives  the 
value  of  the  required  element,  nothing  more  is  necessary  than  to  employ  that  value.  But  if  the  time 
falls  between  the  Almanac  times,  the  required  quantity  must  be  found  by  interpolation. 

The  Almanac  contains  the  rate  of  change  or  difference  of  each  of  the  principal  quantities  for  some 
unit  of  time,  and,  unless  great  precision  is  required,  the  first  differences  only  need  be  regarded.  In 
order  to  use  the  difference  columns  to  advantage,  the  Greenwich  date  should  be  expressed  in  the  unit 
of  time  for  which  the  difference  is  given.  Thus,  for  using  the  hourly  differences,  the  Greenwich  tin.e 
should  be  expressed  in  hours  and  decimal  parts  of  an  hour;  when  using  the  differences  for  one  minute, 
the  time  should  be  in  minutes  and  decimal  parts  of  a  minute.  Instead  of  using  decimal  parts,  some  may 
prefer  the  use  of  aliquot  parts. 

Since  thequan titles  in  the  Almanac  are  approximate  numbers,  given  to  a  certain  decimal,  any  inter- 
polation of  a  lower  order  than  that  decimal  is  unneces.«ary  work.  Moreover,  since,  in  computations  at 
sea,  the  Greenwich  time  is  more  or  less  inexact,  too  great  refinement  need  not  be  sought  in  reducing  the 
Ahnanac  elements. 

Simple  interpolation  assumes  that  the  differences  of  the  quantities  are  proportional  to  the  differences 
of  the  times;  in  other  words,  that  the  differences  given  in  the  Almanac  are  constant;  this  is  seldom  the 
case,  but  the  error  arising  from  the  assumption  will  be  smaller  the  less  the  interval  between  the  times 
in  the  Almanac.  Hence  those  quantities  which  vary  most  irregularly  are  given  for  the  smallest  units 
of  time;  as  the  variations  are  more  regular,  the  units  for  which  the  differences  are  given  increase. 

In  taking  from  the  Almanac  the  elements  relating  to  the  fixed  stars  the  data  may  be  found  either 
in  the  table  which  gives  the  "mean  place"  of  each  star  for  the  year  or  in  that  which  gives  the 
"apparent  place  "  occupied  by  each  one  on  every  tenth  day  throughout  the  year.  As  the  annual  varia- 
tion of  position  of  the  fixed  stars  is  small,  the  results  will  not  vary  greatly  whichever  ta])le  may  be  used. 
Yet,  as  it  is  proper  to  seek  always  the  greatest  attainable  accuracy,  the  use  of  the  table  showing  the 
exact  positions  is  recommended.  That  table  is,  however,  published  in  the  "Ephemeris  and  Nautical 
Almanac"  only,  and  is  omitted  from  the  abridged  "  Nautical  Almanac;  "  hence,  where  the  larger  book 
is  not  at  hand,  the  tiible  of  mean  places  nmst  be  employed. 

2§4.  To  find  from  the  Nautical  Almanac  a  required  element  for  any  given  time  and  place,  it  is 
first  necessary  to  express  the  time  astronomically  and  to  convert  it  to  Greenwich  time  and  date.  Then 
take  from  the  Almanac,  for  the  nearest  given  precedivg  instant,  the  required  quantity,  together  with  its 
corresponding  "Diff.  for  l*"  "  or  "Diff.  for  1"","  noting  the  name  or  sign  in  each  cat^e;  for  the  sun  use 
Page  I  of  the  proper  month  in  the  Almanac  when  apparent  time  is  to  be  the  I)asi8  for  correction,  but 
otherwise  use  Page  II.  Multiply  the  "Diff.  for  l**"  by  the  number  of  hours  and  fraction  of  an  hour, 
or  the  "Diff.  for  1'""  by  the  number  of  minutes  and  fraction  of  a  minute,  corresponding  to  the  interval 
between  the  time  for  which  the  quantity  is  given  in  the  Almanac  and  the  time  for  which  required; 
apply  the  correction  thus  obtained,  having  regard  to  its  sign. 

A  modification  of  this  rule  may  be  adopted  if  the  time  for  which  the  quantity  is  desired  falls  con- 
siderably nearer  a  subsequent  time  given  in  the  Almanac  than  it  does  to  one  preceding;  in  this  case  the 
interpolation  may  be  made  backward,  the  sign  of  application  of  the  correction  being  reversed. 

Example:  At  a  place  in  longitude  81°  15' W.,  April  17,  1879,  find  the  sun's  declination  and  the 
equation  of  time  at  apj)arent  noon. 

Long.  =81°  15'  W.  G.  A.  T.  =  17'*  b^  25™  =  17'»  +  5\42. 

Eq.  t.,     17'»    0^  O-"  24\46 

Corr.,  +  3  .18 


Dec,  17"'0h, 
Corr., 

(-r) 

+ 

+ 
+ 

+ 

10° 

26'  42".  3  N 
4  46  .2 

Dec,  17'*  5'>  25™ 

10 

31    28  .5  N 

H.  D., 
G.  A.  T., 

52".  80 
5\42 

Corr., 

/  286".  18 
14'46".18 

Eq.  t,  17''5h25"',        0    27.64 

H.  D.,  +         0-\587 

G.  A.  T.,  +         5^.42 


Corr.,  -f  3M82 

{Subtract  from  apparent  time.) 

Example:  At  a  place  in  Long.  81°  15'  E.,  April  17,  1879,  find  the  sun's  declination  and  the  equation 
of  time  at  apparent  noon. 

Long.  =81°  15'  E.  G.  A.  T.  =  16'»  18"  35™  =  17*  —  5h.42. 

Dec,  17'*    0\         (  +  )  10°  26'42".3N.  Eq.  t.,  I71    0^  0"  24'.46 

Corr.,  -  4  46  .2  Corr.,  -         3.18 


Dec,  16*  18"  35™, 

10    21   56  .1  N. 

Eq.  t.,  16*  18"  35" 

H.  D., 
G.  A.  T., 

Corr., 

',     0    21  .28 

H.  D., 
G.  A.  T.^ 

+               52".  80 
—                  5".  42 

-f       0«.587 
-       5".  42 

Cor.\, 

(    286".  18 
\4'46".18 

—      3M82 

78 


TIME    AND    THE    NAUTICAL    ALMANAC. 


Example:  April  16,  1879,  at  U**  55""  30^  a.  m.,  local  mean  time,  in  Long.  81°  15'  W.,  required  the 
declination  and  semidiameter  of  the  sun,  the  equation  of  time,  and  the  right  ascension,  declination, 
horizontal  parallax,  and  semidiameter  of  the  moon  and  Jupiter. 


Local  mean  time, 
Longitude, 

Greenwich  mean  time. 


IS-i  23'>  55™  30" 
5"  25'"  00" 

16*    5"  20"' 30" 
16''    5"  20™.5 
16-1    5\34 


Dec,  0^  (  +  )  10°  05'  30''.  1  N. 
Corr.,         +  4   44  .  3 


For  the  Sun. 

S.  D.,  15'  58".  0 

(Same  as  at  G.  A.  Noon.) 


Dec., 

H.  D., 
G.  M.  T., 

Corr., 


10    10    14  .  4  N. 


53".  24 
5\  34 


Eq.  t, 
Corr., 

+ 

+ 

0'" 

10' 
3 

.15 
.  22 

Eq.  t., 

0 

13 

.37 

H.  D. 

G.  M. 

0\ 
5". 

604 
34 

+{ 


284".  30 
4'  44".  30 


Corr., 


+ 


3'.  22 


{Add  to  mean  time.  ] 


For  the  Moon. 


R.  A.,  5h, 
Corr., 

R.  A., 

M.  D., 
No.  min., 

Corr., 


•J'Jt'  14'"  39'.29 
+  38.31 


22    15    17  .60 


1».869 
20^.5 


Dec,  5'', 
Corr., 

Dec, 

M.  D., 
No.  mln., 


(-)  7°59'36".l  S. 
+  4  27  .1 

7  55  09  .0  S. 


]3".03 
20'". 5 


38'.31 


f     267".  12 
t  4'27".l 


Hor.  Par-.O!-, 
Corr., 

Hor.  Par., 

H.  D., 
G.  M.  T., 

Corr., 


5,5'  13".6 
7  .2 


l."34 
5i'.34 


S-D-.C, 
•Corr., 

S.  D., 

H.  D., 
G.  M.  T., 


15'  04".7 
1  .8 


15  02  .9 


-        0".34 


7".15  Corr., 


1".81 


R.  A.,0\       22"  26'"  ;^^  54 
Corr.,        +  9.71 


For  Jupiter. 

Dec,  0^      (-)  10°  40'  28".  0  S. 
Corr.,  +  53  .  6 


R.  A., 

H.  D.,       + 

G.  M.  T.,  + 

Corr.,        + 


22    26    45  .  25 


1".  819 
5\  34 


".  71 


Dec, 

H.  D., 
G.  M.  T., 

Corr. , 


10    39   34  .  4  S. 


10".  03 
5".  34 


Hor.  Par.,  16'^,         1".  6 


S.  D.,  16^  16".{ 


53".  6 


2§5.  Should  greater  precision  be  required  than  that  attainable  by  niraple  interpolation,  resort  must 
be  had  to  the  reduction  for  second  differences. 

The  differences  between  successive  values  of  the  quantities  given  in  the  Nautical  Almanac  are  called 
the  first  differences;  the  differences  between  successive  first  differences  are  called  the  second,  differences. 
Simple  interpolation,  which  satisfies  the  necessities  of  sea  computations,  assumes  the  first  differences  to 
be  constant;  but  if  the  variation  of  the  first  differences  be  regarded,  a  further  interpolation  is  required 
for  the  second  difference. 

The  difference  for  a  unit  of  time  in  the  American  Nautical  Almanac  abreast  any  element  expresses 
the  rate  at  which  the  element  in  changing  at  that  precise  instant  of  Greenwich  time.  Now,  regarding 
the  second  difference  as  constant,  the  first  difference  varies  uniformly  with  the  Greenwich  time;  there- 
fore it«  value  may  be  found  for  any  intermediate  time  by  simple  interpolation. 

Hence  the  following  rule  for  second  differences:  Employ  the  interpolated  value  of  th6  first  differ- 
ence which  corresponds  to  the  middle  of  the  interval  for  which  the  correction  is  to  be  computed. 

Example:  For  the  Greenwich  date  1879,  April,  10"*  18''  25'"  30",  find  the  moon's  declination. 


Dec,  18",  (-)26°  19'  41".l  S. 
Corr.,  +  2  .1 


First  diff.,  +  0".  044 
Corr.,         +0  .039 


Dec, 


26    19    39  .0  S. 


M.  D.,        4^0  .083 
No.  min.,  +25°'.5 


Second  diff.. 
Interval, 

Corr. , 


0".181 
f  Oh. 213 

+  0".039 


Corr. , 


2".  12 


The  difference  for  one  minute  being  4- 0".044  at  18'',  and  +0".225  at  19'',  the  difference  for  one 
minute  undergoes  a  change  of  4  0".181  during  one  hour.  The  time  for  which  it  is  desired  to  obtain  the 
difference  is  at  the  middle  instant  between  18*'  0'"  and  18''  25'".5 — that  is,  at  18''  12"'.  75,  or  its  equivalent, 
18''  213.  With  a  change  of  -f  0".181  in  one  hour,  the  change  in  0''.213  is  readily  obtainable;  correcting 
the  minute's  difference  at  18''. 0  accordingly,  the  proces '  of  correcting  the  declination  becomes  the  same 
as  in  simple  interpolation. 


TIME    AND    THE    NAUTICAL    ALMANAC.  79 

CONVERSION  OF  TIMES. 

iiS6.   Conversion  of  Time  is  the  process  by  which  any  instant  of  time  that  if<  defined  according  to  one 
system  of  reckoning  may  be  defined  according  to  some  other  system;  and  also 
by  Avhich  any  interval  of  time  expressed  in  units  of  one  system  may  be  con- 
verted into  units  of  another. 

287.  Sidereal  and  Meax  Times. — Mean  time  is  the  hour  angle  of  the 
Mean  Sun;  sidereal  time  is  the  hour  angle  of  the  First  Point  of  Aries.  Since 
the  Right  Ascension  of  the  Mean  Sun  is  the  angular  distance  between  the  hour 
circles  of  the  Mean  Sun  and  of  the  First  Point  of  Aries,  mean  time  may  be  con- 
verted into  sidereal  time  by  adding  to  it  the  Right  Ascension  of  the  Mean  Sun; 
and  similarly,  sidereal  time  may  be  converted  into  mean  time  by  subtracting  from 
it  the  Right  Ascension  of  the  ^fean  Sun. 

This  is  explained  in  figure  36,  vhich  represents  a  projection  of  the  celestial 
sphere  upon  the  equator.  If  P  be  the  pole;  QPQ',  the  meridian;  V,  the  First 
Point  of  Aries;  M,  the  position  of  the  mean  sun  (west  of  the  meridian);  then 
QPV,  or  the  arc  QV,  is  the  sidereal  time;  QPM,  or  the  arc  QM,  is  the  mean 
time;  and  VPM,  or  the  arc  VM,  is  the  Right  Ascension  of  the  Mean  Sun.     From  tl^s  it  will  appear  that: 

QV=QM+VM,  or 
Sidereal  f.me=Mean  time-j- Right  Ascension  of  Mean  Sun. 

If  the  mean  sun  be  on  the  opposite  side  of  the  meridian,  at  3F,  then  the  mean  time  equals 
24"— M^Q.     In  this  case: 

QV  =  VM'— M'Q,  or 
Sidereal  time=Right  Ascension  of  Mean  Sun  — (24''— Mean  time), 
=Right  Ascension  of  Mean  Sun -^ Mean  time— 24". 

Right  ascension  being  measured  to  the  east  and  hour  angle  to  the  west,  the  sidereal  time 
will  therefore  always  equal  the  sum  of  these  two;  but  24"  must  be  subtracted  when  the  sum  exceeds 
that  amount. 

From  the  preceding  equations,  we  also  have: 

QM=QV-VM;  and 
M^Q=VM'-QV,  or 

(24"-M'Q)  =  (24"+QV)-VM^ 

From  this  it  may  be  seen  that  the  mean  time  equals  the  sidereal  time  minus  the  Flight  Ascension 
of  the  Mean  Sun,  but  the  former  must  be  increased  by  24"  when  necessary  to  make  the  subtraction 
possible. 

28§.  Apparent  and  Mean  Times. — Apparent  time  is  the  angle  between  the  meridian  and  the 
hour  circle  which  contains  the  center  of  the  sun;  mean  time  is  the  angle  between  the  meridian  and  the 
hour  circle  which  contains  the  mean  sun.  Since  the  equation  of  time  ref>resents  the  angle  between 
the  hour  circles  of  the  mean  and  apparent  suns,  it  is  clear  that  the  conversion  of  mean  time  to  apparent 
time  may  be  accomplished  by  the  api)lication  of  the  ecpiation  of  time,  with  its  j>roper  sign,  to  the  mean 
time;  and  the  reverse  operation  by  the  application  of  the  same  quantity,  in  an  opposite  direction,  to  the 
apparent  time. 

The  resemblance  of  these  operations  to  the  interconversion  of  mean  and  sidereal  times  may  be 
observed  if,  in  figure  36,  we  assume  that  PV  is  the  hour  circle  of  the  true  sun,  PM  remaining  that  of  the 
mean  sun;  then  the  arc  Q3I  will  be  the  mean  time;  QV,  the  apparent  time;  and  VM,  the  equation  of 
time;  whence  \.e  have  as  before: 

QV  =  QM+VM,  or 
Apparent  time  —  ^lean  time  —  Equation  of  time; 
the  equation  of  time  will  be  positive  or  negative  according  to  the  relative  position-of  the  two  suns. 

2§9.  Sidereal  and  Mean  Time  Intervals. — The  sidereal  year  consists  of  366.25636  sidereal  days 
or  of  365.25636  mean  solar  days.  If,  therefore,  M  be  any  interval  of  mean  time,  ami  S  the  corresponding 
interval  of  sidereal  time,  the  relations  between  the  two  may  be  expressed  as  follows: 

Therefore,  S  =  1.0027379  M  =  M  +  . 0027379  M; 
M  =  0.9972696   S  =  S  -.0027304  S. 

If  M  =  24",  S  =  24"  +  3"'  56^6;  or,  in  a  mean  solar  day,  sidereal  time  gains  on  mean  time  3™  56'.6,  the 
gain  each  hour  being  9'. 8565. 

If  S  =  24",  M  =  24"  — 3"'  55'.9;  or,  in  a  sidereal  day,  mean  time  loses  on  sidereal  time  3'"  55'.9,  the 
loss  each  hour  being  9^.8296. 

If  'M  and  S  be  expressed  in  hours  and  fractional  parts  thereof, 

S  =  M  + 9^8565  M; 
M  =  S  -  9^8296  S. 

Tables  for  the  conversion  of  the  intervals  of  mean  into  those  of  sidereal  time  and  the  reverse  are 
based  upon  these  relations.  Tables  8  and  9  of  this  work  give  the  values  for  making  these  conversions, 
and  similar  tables  are  to  b^  found  in  the  Nautical  Almanac. 


80  TIME    AND    THE    NAUTICAL    ALMANAC. 

390.  To  Convert  Meax  Solar  ixto  Sidereal  Time. — Apply  to  the  local  mean  time  the  longitude, 
adding  if  west  and  subtracting  if  east,  and  thus  obtain  the  Greenwich  mean  time.  Take  from  tlie  Nau- 
tical Almanac  the  Right  Ascension  of  the  Mean  Sun  at  Greenwich  mean  noon,  and  correct  it  for  the 
Greenwich  mean  time  l)y  Table  9  or  by  the  hourly  difference  of  9". 857.  Add  to  the  local  mean  time  this 
corrected  right  a.scension,  rejecting  24''  if  the  sum  is  greater  than  that  amount.  The  result  will  be  the 
local  sidereal  time. 

Example:  April  ^2,  1879,  in  Long.  81°  15^  W.,  the  local  mean  time  is  2"  00"'  00»  p.  m.  Required 
the  corresponding  local  sidereal  time: 

L.  M.  T.,       22*'  2"  00"'  Oa-        R.  A.  M.  S.,  22»  0^  2"  00"'  41^24        L.  M.  T.,  2"  00'"  00^ 

Long.,     -t  5    25    00  Red.  for  7"  25""  (Tab.  9), -f         1     13.10        R.A.M.S.,    r    2    01    54.34 


G.M.T.,        22    7     25     00  R.  A.  M.  S.,  7"  25"',  2    01     54.34         L.  S.  T.,  4    01     54.34 

Example:  April  22,  1879,  in  Long.  75°  E.,  the  local  mean  time  is  4''  00"'  00"  a.  m.  Ketjuired  the 
local  sidereal  time. 

L.  M.  T.,    21'»  16"  00'"  00^  R.  A  M.  S.  21'»  0",  1"  56""  44^69        L.M.T.,    21"  16"  00"'  OO'' 

Long.,    -  5    00    00  Red.  for  11"  (Tab.  9),  ^  1    48.42        R.A.M.S.,4       1    58    33.11 

G.  M.  T.,  21    11    00    00  R.  A.  M.  S.,  11",  1    58    33  .11        L.  S.  T.,     21    17    58    33.11 

In  these  examples  the  reduction  of  the  R.  A.  M.  S.  has  formed  a  separate  operation  in  order  to 
make  clear  the  process.  It  would  be  as  accurate  to  add  together  directly  L.  M.  T.,  R.  A.  M.  S.,  and 
Red.,  and  the  work  would  thus  be  rendered  more  brief. 

291.  To  CoxvERT  Sidereal  ixto  Meax  Solar  Time. — Take  from  the  Nautical  Almanac  the 
Right  Ascension  of  the  Mean  Sun  for  Greenwich  mean  noon  of  the  given  astronomical  day,  and  apply 
to  it  the  reduction  for  longitude,  either  by  Table  9  or  by  the  hourly  difference  of  9^857,  and  the  result 
will  be  the  Right  Ascension  of  the  Mean  Sun  at  local  mean  noon,  which  is  equivalent  to  the  local 
sidereal  time  at  that  instant.  Subtract  this  from  the  given  local  sidereal  time  (adding  24"  to  the  latter 
if  necessary),  and  the  result  will  be  the  interval  from  local  mean  noon,  expressed  in  units  of  sidereal 
time.  Convert  this  sidereal  time  interval  into  a  mean  time  interval  by  subtracting  the  reduction  as 
given  by  Table  8  or  by  tlie  hourly  difference  of  9^830;  the  result  will  be  the  local  mean  time. 

Example:  April  22,  1879,  a.  m.,  in  Long.  75°  E.,  the  local  sidereal  time  is  17"  58"'  33M1.  AVhat  is 
the  local  mean  time? 

Astronomical  day,  April  21. 

L.  S.  T.,  17"  58-"  33M1  R.  A.  M.  S.,  Gr.  21"  0",  1"  56"'  44\69 

R.  A  M.S.,  —   1   55    55.41  Red.  for -5"  long.  (Tab.  9),  —  49.28 


Sid.  interval  from  L.  M.  noon,  16  02    37.70  R.  A.  M.  S.,  local  0",  1   55    55.41 

Red.  for  sid.  interval  (Tab.  8),         2    37  .70 


L.  M.  T.,  21",  16  00    00  .00 

Example:  April  22,  1879,  p.  m.,  at  a  place  in  Long.  81°  15^  W.,  the  sidereal  time  is  4"  01"'  54».34. 
What  is  the  corresponding  mean  time? 

Astronomical  day,  April  22. 

L.  S.  T.,  4"  01""  54'.34  R.  A.  M.  S  ,  Gr.  22"  0",  2"  00"'  4P.24 

R.  A.  M.  S.,  -  2  01    34  .63  Red.  for  +5"  25™  long.  (Tab.  9),  +       0    53  .39 


Sid.  interval  from  L.  M.  Noon,     2   00    19  .71  R.  A.  M.  S.,  local  0",  2    01    34  .63 

Red.  for  sid.  interval  (Tab.  8),  —       0    19  .71 

L.  M.  T.,  22",  2   00   00  .00 

392.  To  Covert  Mean  into  Apparent  Time  and  the  Reverse. — Find  the  Greenwich  time  corre- 
sponding to  the  given  local  time.  If  apparent  time  is  given,  find  the  Greenwich  apparent  time  and  take 
the  equation  of  time  from  Page  I  of  the  Almanac.  It  mean  time,  find  the  Greenwich  mean  time  and 
take  the  equation  of  time  from  Page  II.  Correct  the  equation  of  time  for  the  required  instant  and 
apply  it  with  its  proper  sign  to  the  given  time. 

IExample:  April  21,  1879,  in  Long.  81°  15^  W.,  find  the  local  apparent  time  corresponding  to  a  local 
mean  time  of  3"  05""  00'  p.  m. 

L.  M.  T.,    21"3"05"'00' 
Long.,     +        5  25    00 


G.  M.  T.,    21    8   30    00 


L.  M,  T.,    21"  3"  05"'  00" 
Eq.  t.,    +               1    22.01 

Eq.  t.,  0",     1'"  17.61 
Corr.,     +          4.40 

L.  A.  T.,    21    3   06    22.01 

.   Eq.t.,           1    22.01 

H.D.,     +         0\518 
G.M.T.,+         8".5 

Corr.,     +         f.403 
{Add  to  mean  time.) 


TIME    AND    THE    NAUTICAL    ALMANAC.  81 

Example:  April  3,  1879,  in  Long.  81°  15'  E.,  the  local  apparent  time  is  8''  45™  00'  a.  m.     Required 
the  mean  time. 

L.  A.  T.,  2^  20"  45"'  00'  L.  A.  T.,  2"  20"  45™  00'  Eq.  t.,  0",        3™  42'.46 

Long.,        -  5   25    00  Eq.  t.,        +  3    30.90  Corr.,  —      11  .56 


G.  A.  T.,  2    15    20    00  L.  M.  T.,  2    20  48    30.90  Eq.  t.,  3    30  .90 


H.  D.,        -  0'.754 

G.  M.  T.,  —       15''.33 


Corr.,         —        11\56 
{Add  to  apparent  time.) 

293.  To  Find  the  Hour  Angle  of  a  Body  from  the  Time,  and  the  Eeverse. — In  figure  36,  if  M 
and  M'  represent  the  positions  of  celestial  bodies  instead  of  those  of  the  mean  sun  as  before  assumed, 
then  the  hour  angles  of  the  bodies  will  be  Q  M  and  24''  -  M'  Q,  respectively,  and  their  right  ascen- 
sions will  be  V  M  and  V  M^ 

As  before,  we  have: 

Q  V     =  Q  M  +  V  M, 
,  =  V  M'  -  M'  Q; 

QM     =QV-VM; 
M'  Q  =  V  M'  -  V  Q,  or 

(24"  -  M'  Q)  =  (24"  +  Q  V)  -  Y  W. 

Substituting,  therefore,  hour  angle  of  the  body  for  mean  time,  and  right  ascension  of  the  body  for  Right 
Ascension  of  the  Mean  »S'u«,  the  rules  previously  given  for  the  conversion  of  mean  and  sidereal  times  will 
be  applicable  for  the  conversion  of  hour  angle  and  sidereal  time.  Thus,  the  sidereal  time  is  equal  to  the 
sum  of  the  right  ascension  of  the  body  and  its  hour  angle,  subtracting  24"  when  the  sum  exceeds  that 
amount;  and  the  hour  angle  equals  the  sidereal  time  minus  the  right  ascension  of  the  body,  24"  being 
added  to  the  former  when  necessary  to  render  the  subtraction  possible. 

Example:  In  Long.  81°  15'  W.',  on  April  25,  1879,  at  12"  10'"  30'  (astronomical)  mean  time,  find  the 
hour  angle  of  Sirius. 

L.  JVI.  T.,       12"  10"'  30'  L.  M.  T.,  12"  10°'  30" 

Long.,       +    5  25    00  R.  A.  M.  S.,  0",+    2   12    30.91 

Red.  (Tab.  9) ,  +  2    53.39 

G.  M.  T.,       17   35    30 


L.  S.  T.,  14  25    54.30 

R.  A.  Sirius,       —    6  39    49.83 


H.  A.  Sirius,  7   46    04.47 

Example:  May  9, 1879,  Arcturus  being  2"  27"'  42*.52  east  of  the  meridian,  find  the  local  sidereal  time 

24"  00"'  00*  H.  A.,       21"  32'°  17'.48 

H.  A.,     2  27    42.52  E.  R.  A.,    ^  14   10    11  .71 


H.  A.,  21    32    17.48  W.  L.  S.  T.,      11   42    29.19 

Or  thus: 

H.  A.,     -  2"27"'42'.52 

R.  A.,      +  14    10   11  .71 


L.  S.  T.,       11    42   29  .19 


22489—03 6 


82 


OOBRECTION    OF    OBSERVED    ALTITUDES. 


CHAPTER  X. 
OOEEEOTION  OF  OBSEEVED  ALTITUDES. 


294.  The  true  altitude  of  a  heavenly  body  at  any  place  on  the  earth's  surface  is  the  altitnde  of  its 
center,  as  it  would  be  measured  by  an  observer  at  the  center  of  the  earth,  above  the  plane  passed 
through  the  center  of  the  earth  at  right  angles  to  the  direction  of  the  zenith. 

Tne  obsen'ed  altitude  of  a  heavenly  body,  as  measured  at  sea,  may  be  converted  to  the  true  altitude 
by  the  application  of  the  following-named  corrections:  Index  Correction,  Dip,  Refraction,  ParallcLv,  and 
Semidiaynefer.  The  corrections  for  parallax  and  semidiameter  are  of  inappreciable  magnitude  in 
observations  of  the  fixed  stars,  and  with  planets  are  so  small  that  they  need  only  be  regarded  in  refined 
calculations.     In  observations  with  the  artificial  horizon  there  is  no  correction  for  dip. 

For  theoretical  accuracy,  the  corrections  should  be  applied  in  the  order  in  which  they  are  named, 
but  in  ordinary  nautical  practice  the  order  of  application  makes  no  material  difference,  except  in  the 
case  of  the  parallax  of  the  moon  as  explained  in  article  306. 

INDEX  CORRECTION. 

295.  This  correction  is  fully  explained  in  articles  249  and  250,  Chapter  VIII. 

REFRACTION. 

296.  It  is  known  by  various  experiments  that  the  rays  of  light  deviate  from  their  rectilinear 
course  in  passing  obliquely  from  one  medium  into  another  oi  a  different  density;  if  the  latter  be  more 
dense,  the  ray  will  be  bent  toward  the  perpendicular  to  the  line  of  junction  of  the  media;  if  less  dense, 
it  will  be  bent  away  from  that  perpendicular. 

The  ray  of  light  before  entering  the  second  medium  is  called  the  incident  ray ;  after  it  enters  the 

second  medium  it  is  called  the  refracted  ray,  and  the 
difference  of  direction  of  the  two  is  called  the  refraction. 
The  rays  of  light  from  a  heavenly  body  must  pass 
through  the  atmosphere  before  reaching  the  eye  of  an 
observer  upon  the  surface  of  the  earth.  The  earth's 
atmosphere  is  not  of  a  uniform  density,  but  is  most 
dense  near  the  earth's  surface,  gradually  decreasing  in 
density  toward  its  upper  limit;  hence  the  path  of  a  ray 
of  light,  by  passing  from  a  rarer  medium  into  one  of 
continually  increasing  density  becomes  a  curve,  which 
is  concave  toward  the  earth.  The  last  direction  of  the 
ray  is  that  of  a  tangent  to  the  curved  path  at  the  eye  of 
the  observer,  and  the  difftsrence  of  the  direction  of  the 
ray  before  entering  the  atmosphere  and  this  last  direc- 
tion constitutes  the  refraction. 

297.  To  illustrate  this,  consider  the  earth's  atmos- 
phere as  shown  in  figure  37;  let  SB  be  a  ray  from 
a  star  S,  entering  the  atmosphere  at  B,  and  bent  into 
the  curve  BA;  then  the  apparent  direction  of  the  star 
is  AS'',  the  tangent  to  the  curve  at  the  point  A,  the 
refraction  being  the  angle  between  the  lines  BS  and 
AS'.  If  CAZ  is  the  vertical  line  of  the  observer,  by  a 
law  of  Optics  the  vertical  plane  of  the  observer  which 
contains  the  tangent  AS''  must  also  contain  the  whole 
curve  BA  and  the  incident  ray  BS.  Hence  refraction 
increases  the  apparent  altitude  of  a  star  without  affect- 
ing its  azimuth. 

At  the  zenith  the  refraction  is  nothing.  The  less 
the  altitude  the  more  obliquely  the  rays  enter  the  atmosphere  and  the  greater  will  be  the  refraction.  At 
the  horizon  the  refraction  is  the  greatest. 

298.  The  refraction  for  a  mean  state  of  the  atmosphere  (barometer  30'",  Fahr.  thermometer  50°) 
is  given  in  Table  20  A;  the  combined  refraction  and  sun's  parallax  in  Table  20  B;  and  the  combined 
refraction  and  moon's  parallax  in  Table  24. 

Since  the  amount  of  the  refraction  depends  upon  the  density  of  the  atmosphere,  and  the  density 
varies  with  the  pressure  and  the  temperature,  which  are  indicated  by  the  barometer  and  thermometer, 
the  true  refra<;tion  is  found  by  applying  to  the  mean  refraction  the  corrections  to  be  found  in  Tables  21 
and  22;  these  are  deduced  from  Be&sel's  formuhe,  and  are  regarded  as  the  most  reliable  tables 
constructed.  It  should  be  remembered,  however,  that  under  certain  conditions  of  the  atmosphere  a 
very  extraordinary  deflection  occurs  in  rays  of  light  which  reach  the  observer's  eye  from  low  altitudes 


Fig.  37. 


CORRECTION    OE^    OBSERVED    ALTITUDES. 


83 


(that  is,  from  points  near  the  visible  horizon),  the  amount  of  which  is  not  covered  by  the  ordinary- 
corrections  for  pressure  and  temperature;  the  error  thus  created  is  discussed  under  IHp  (art.  301);  on 
account  of  it,  altitudes  less  than  10°  should  be  avoided. 

Example:  Required  the  refraction  for  the  apparent  altitude  5°,  when  the  thermometer  is  at  20° 
and  the  barometer  at  30'"  .67. 

The  mean  refraction  by  Table  20  A  is,  9^  52''' 

The  correction  for  height  of  barometer  is,  +  13 

The  correction  for  the  temperature,  +  42 


True  refraction,  10  47 

299.  The  correction  for  refraction  should  always  be  subtracted,  aa  also  that  for  combined  refraction 
and  parallax  of  the  sun;  the  correction  for  combined  refraction  and  parallax  of  the  moon  is  invariably 
additive. 

DIP. 

300.  Dip  of  the  Horizon  is  the  angle  of  depression  of  the  visible  sea  horizon  below  the  true  horizon, 
due  to  the  elevation  of  the  eye  of  the  observer  above  the  level  of  the  sea. 

In  figure  38  suppose  A  to  be  the  position  of  an 
observer  whose  height  above  the  level  of  the  sea  is 
AB.     CAZ  is  the  true  vertical  at  the  position  of  the 

observer,  and  AH  is  the  direction  of  the  true  hori-  \^  z 

zon,  S  being  an  observed  heavenly  body.  Draw 
ATH'  tangent  to  the  earth's  surface  at  T.  Disre- 
garding refraction,  T  will  be  the  most  distant  point 
visible  from  A.  Owing  to  refraction,  however,  the 
most  distant  visible  point  of  the  earth's  surface  is  h- 
more  remote  from  the  observer  than  the  point  T, 
and  is  to  be  found  at  a  point  T',  in  figure  39.  But 
to  an  observer  at  A  the  point  T''  will  appear  to  lie 
in  the  direction  of  AH''',  the  tangent  at  A  to  the  curve 
AT''.  If  the  vertical  plane  were  revolved  about  CZ 
as  an  axis,  the  line  AH  would  generate  the  plane  of 
the  true  horizon,  while  the  point  T'  would  generate 
a  small  circle  of  the  terrestrial  sphere  called  the 
ViMble  or  Sea  Horizon.  The  Dip  of  the  Horizon  is 
HAH",  being  the  angle  between  the  true  horizon  and 
the  apparent  direction  of  the  sea  horizon.  Values 
of  the  dip  are  given  in  Table  14  for  various  heights 
of  the  observer's  eye,  and  in  the  calculation  of  the 
table  allowance  has  been  made  for  the  effect  of  at- 
mospheric refraction  as  it  exists  under  normal  con- 
ditions. 


Fig.  38. 


301.  The  fact  must  be  emphasized,  however,  that 
under  certain  conditions  the  deflection  of  the  ray  in  its  path 
from  the  horizon  to  the  eye  is  so  irregular  as  to  give  a  value 
of  the  dip  widely  different  from  that  which  is  tabulated  for 
the  mean  state  of  atmosphere.  These  irregularities  usually 
occur  when  there  exists  a  material  difference  between  the 
temperature  of  the  sea  water  and  that  of  the  air,  and  they 
attain  a  maximum  value  in  calm  or  nearly  calm  weather, 
when  the  lack  of  circulation  permits  the  air  to  arrange  itself 
in  a  series  of  horizontal  strata  of  different  densities,  the 
denser  strata  being  below  when  the  air  is  warmer,  and  the 
reverse  condition  obtaining  when  the  air  is  cooler.  The 
effect  of  such  an  arrangement  is  that  a  ray  of  light  from  the 
horizon,  in  passing  through  media  of  different  densities, 
undergoes  a  refraction  quite  unlike  that  which  occurs  in  the 
atmosphere  of  much  more  nearly  homogeneous  density  that 
exists  under  normal  conditions. 

Various  methods  have  been  suggested  for  computing 
the  amount  of  dip  for  different  relative  values  of  tempera- 
ture of  air  and  water,  but  none  of  these  afford  a  satisfactory 
solution,  there  being  so  many  elements  involved  which  are  not  susceptible  of  determination  by  an 
observer  on  shipboard  that  it  will  always  be  difficult  to  arrive  at  results  that  may  be  depended  upon.  « 

As  the  amount  of  difference  between  the  actual  and  tabulated  values  of  the  dip  due  to  this  cause 
may  sometimes  be  very  considerable — reliable  observations  having  frequently  placed  it  above  10',  and 
values  as  high  as  32''  having  been  recorded — it  is  necessary  for  the  navigator  to  be  on  his  guard  against 
the  errors  thus  produced,  and  to  recognize  the  possible  inaccuracy  of  all  i  esults  derived  from  observations 
taken  under  unfavorable  conditions.  Without  attempting  to  give  any  method  for  the  determination  of 
the  amount  of  the  extraordinary  variation  in  dip,  the  following  rules  may  indicate  to  the  navigator  the 
conditions  under  which  caution  must  be  observed,  and  the  direction  of  probable  error: 

(a)  A  displacement  of  the  horizon  should  always  be  suspected  when  there  is  a  marked  difference 
between  the  temperatures  of  air  and  sea  water;  this  fact  should  be  especially  kept  in  mind  in  regions 
such  as  those  of  the  Red  Sea  and  the  Gulf  Stream,  where  the  difference  frequently  exists. 


Fig.  39. 


« A  sextant  attachment  devised  by  Lieutenant-Commander  J.  B.  Blish,  U.  S.  Navy,  enables  an  observer  to  measure  the 
actual  dip  at  any  time. 


84 


CORRECTION    OF    OBSERVED    ALTITUDES. 


(6)  The  error  in  the  tabulated  value  of  the  dip  will  increase  with  an  increase  in  the  difference  of 
temperature,  and  Mill  diminish  with  an  increase  in  the  force  of  the  wind. 

(c)  The  error  will  decrease  with  the  height  of  the  observer's  eye;  hence  it  is  expedient,  especially 
when  error  is  suspected,  to  make  the  observation  from  the  most  elevated  position  available. 

( d)  When  the  sea  water  is  colder  than  the  air  the  visible  horizon  is  raised  and  the  dip  is  decreased; 
therefore  the  true  al^tude  is  greater  than  that  given  by  the  use  of  the  ordinary  dip  table.  AVhen  the 
water  is  warmer  than  the  air,  the  horizon  is  depressed  and  the  dip  is  increased.  At  such  times  the 
altitude  is  really  less  than  that  found  from  the  use  of  the  table. 

The  same  cause,  it  may  be  mentioned  here,  affects  the  kindred  matter  of  the  visibility  of  objects. 
When  the  air  is  warmer,  terrestrial  objects  are  sighted  from  a  greater  distance  and  appear  higher  above 
the  horizon  than  under  ordinary  conditions.  When  the  water  is  warmer  than  the  air,  the  distance  of 
visibility  is  reduced,  and  terrestrial  objects  appear  at  a  less  altitude. 

302.  What  has  been.said  heretofore  about  the  dip  supposes  the  horizon  (o  be  free  from  all  inter- 
vening land  or  other  objects;  but  it  often  happens  that  an  observation  is  required  to  be  taken  from  a 
ship  sailing  along  shore  or  at  anchor  in  harbor,  when  the  sun  is  over  the  land  and  the  shore  is  nearer  the 
ship  than  the  visible  sea-horizon  would  be  if  it  were  unconfined;  in  this  case  the  dip  will  be  different  from 
that  of  Table  14,  and  will  be  greater  the  nearer  the  ship  is  to  that  point  of  the  shore  to  which  the  sun's 
image  is  brought  down.  In  such  case  Table  15  gives  the  dip  at  different  heights  of  the  eye  and  at 
different  distances  of  the  ship  from  the  land. 

303.  The  dip  is  always  to  be  subtracted  from  the  observed  altitude. 

PARALLAX. 

304.  The  parallax  of  a  heavenly  body  is,  in  general 
terms,  the  angle  between  two  straight  lines  drawn  to  the 
body  from  different  points.  But  in  Nautical  Astronomy 
geocentric  parallax  is  f.lone  considered,  this  being  the  differ- 
ence between  the  positions  of  a  heavenly  body  as  seen  at 
the  same  instant  from  the  center  of  the  earth  and  from  a 
])oint  on  its  surface. 

The  zenith  distance  of  a  body,  S  (fig.  40),  seen  from  A,  on 
tlie  surface  of  the  earth,  is  ZAS;  seen  from  C  it  is  ZCS;  the 
I)  irallax  is  the  difference  of  these  angles,  ZAS— ZCS=ASC. 

Parallax  in  altUnde  is,  then,  the  angle  at  the  heavenly 
iody  subtended  by  the  radius  of  the  earth. 

If  the  heavenly  body  is  in  the  horizon  as  at  H',  the 
ra  lius,  being  at  right  angles  to  AH'',  subtends  the  greatest 
possible  angle  at  the  star  for  the  same  distance,  and  this 
angle  is  called  the  horizontal  parallax.  The  parallax  is  less 
an  the  bodies  are  farther  from  the  earth,  as  will  be  evident 
Yicr.  40.  from  the  figure. 


Let  par.  =  parallax  in  altitude,  ASC; 

Z  =  SAZ,  the  apparent  zenith  distance  (corrected  for  refraction); 

R  =  AC,  the  radius  of  the  earth;  and 

D  =  CS,  the  distance  of  the  object  from  the  center  of  the  earth. 

Then,  since  SAC  =  180°  —  SAZ,  the  triangle  ASC  gives: 

R  sin  Z 


sm  par.  = 


D 


If  the  object  is  in  the  horizon  at  H^,  the  angle  AH^C  is  the  horizontal  parallax,  and  denoting  it  by 
H.  P.  the  right  triangle  AH''C  gives: 

sin  H.  P.  =  ^- 

Substituting  this  value  of  r^  i"  the  above,  . 

sin  par.  —  sin  H.  P.  sin  Z. 

If  h  =  SAH'',  the  apparent  altitude  of  the  heavenly  body,  then  Z  =  90°  —  /;;  hence, 

sin  par.  =  sin  H.  P.  cos  h. 

Since  par.  and  H.  P.  are  always  small,  the  sines  are  nearly  proportional  to  the  angles;  hence, 

par.  =  H.  P.  cos  h. 

305.  The  Nautical  Almanac  gives  the  horizontal  parallax  of  the  moon,  as  well  as  of  the  planets 
Mercury,  Venus,  Mars,  Jupiter,  Saturn,  Uranus,  and  Neptune. 


COERECTION    OF    OBSERVED    ALTITUDES.  85 

In  Table  16  will  be  found  the  values  of  the  sun's  parallax  for  altitude  intervals  of  5°  or  10°,  while 
Table  20  B  contains  the  combined  values  of  the  sun's  parallax  and  the  refraction.  In  Table  24  is  given 
the  parallax  of  the  moon,  combined  with  the  refraction,  at  various  altitudes  and  for  various  values  of 
the  horizontal  parallax. 

306.  Parallax  is  always  additive;  combined  parallax  and  refraction  additive  in  the  case  of  the 
moon,  but  eubtractive  for  the  sun. 

Aa  the  correction  for  parallax  of  the  moon  is  so  large,  it  is  essential  that  it  be  taken  from  the  table 
with  considerable  accuracy;  the  corrections  for  index  correction,  semidiameter,  and  dip  should  there- 
fore be  applied  first,  and  the  "approximate  altitude"  thus  obtained  should  be  used  as  an  argument  in 
entering  Table  24  for  parallax  and  refraction. 

SEMIDIAMETEB. 

307.  The  semidiameter  of  a  heavenly  body  is  half  the  angle  subtended  by  the  diameter  of  the 
visible  disk  at  the  eye  of  the  observer.  For  the  same  body  the  semidiameter  varies  with  the  distance; 
thus,  the  difference  of  the  sun's  semidiameter  at  different  times  of  the  year  is  due  to  the  change  of  the 
earth's  distance  from  the  sun;  and  similarly  for  the  moon  and  the  planets. 

In  the  case  of  the  moon,  the  earth's  radius  bears  an  appreciable  and  considerable  ratio  to  the  moon's 
distance  from  the  center  of  the  earth;  hence  the  moon  is  materially  nearer  to  an  observer  when  in  or 
near  his  zenith  than  when  in  or  near  his  horizon,  and  therefore  the  semidiameter,  besides  having  a 
menstrual  change,  has  a  semidiurnal  one  also. 

The  increase  of  the  moon's  semidiameter  due  to  increase  of  altitude  is  called  its  augmentation.  This 
reduction  may  be  taken  from  Table  18. 

The  semidiameters  of  the  sun,  moon,  and  planets  are  given  in  their  appropriate  places  in  the  Nautical 
Almanac. 

30§.  The  semidiameter  is  to  be  added  to  the  observed  altitude  in  case  the  lower  limb  of  the  body 
is  brought  into  contact  with  the  horizon,  and  to  be  subtracted  in  the  case  of  the  upper  limb.  When  the 
artificial  horizon  is  used,  the  limb  of  the  reflected  image  is  that  which  determines  the  sign  of  this  correc- 
tion, it  being  additive  for  the  lower  and  subtractive  for  the  upper. 

Example:  May  6, 1879,  the  observed  altitude  of  the  sun's  upper  limb  was  62°  10'  40'';  I.  C,  +  3'  10"; 
height  of  the  eye,  25  feet.     Required  the  true  altitude. 

Obs.  alt.  0,     62°  10'  40"     I.  C,  +  3'  10" 

Corr.,        -    18  04  

S.  D.  (NautAlm.),  -  15' 53" 


True  alt.,       61  52  36     dip  (Tab.  14),     -  4  54 

p.&r.   (Tab.  20  B),  -   27 

-21  14 

Corr.,  -18' 04" 

Example:  The  altitude  of  Sirius  as  observed  with  an  artificial    horizon  was  50°  59'  30";    I.  C, 
V  30".     Required  the  true  altitude. 


Obs.  2  alt. 

I.e., 

20  A) 

50° 

59'  30" 
1  30 

2)50 

58  00 

Obs.  alt., 
ref.  (Tab. 

25 

29  00 
2  02 

True  alt.. 

25 

26  58 

Example:  April  16,  1879,  observed  altitude  of  Venus  53°  26'  10";  I.  C,  +  2'  30";  height  of  eye,  20 
feet.     Required  the  true  altitude. 

Obs.  alt.  *,  53°  26'  10"  par.  (Tab.  17),    -r  0'  04"  Hor.  Par.  (Naut.  Aim.),  7" 

Corr.,       -  2  32  I.  C,  +  2  30 


53    23  38  -r2  34 

dip  (Tab.  14),      -  4'  23" 
ref.  (Tab.  20  A),-      43 


-  5  06 
Corr.,  -  2'  32" 


«6 


CORRECTION    OF    OBSERVED    ALTITUDES, 


Example:  May  6,  1879,  at  13*"  24™  G.  M.  T.,  the  observed  altitude  of  the  moon's  lower  limb  was  25° 
30'  30";  I.  C,  —1'  30";  height  of  eye,  20  feet.     Required  the  true  altitude. 


Oba.  alt.£,                  25°  30'  30" 
Istcorr.,                 +         10  57 

S.  D.  (Naut.  Aim.), 
Aug.  (Tab.  18), 

dip  (Tab.  14), 

I.e., 

+  16' 

42" 

08 

Hor.  Par. 

(Naut.  Aim.),  61' 

Approx.  alt.,               «    41   27 

p.  &  r.  (Tab.  24),  +         53  07 

True  alt.,                     26    34  34 

+  16 

-  4' 

—  1 

50 

23" 
30 

-    5 

53 

Ist  corr.. 

+  10'  57" 

Or,  the  following  modification 

may  be  adopted: 

Obs.  alt.C,            25°  30'  30" 
Istcorr.,          +           8  56 

S.  D., 
Aug., 

dip, 
ref., 

I.e., 

+  16'  42" 

+         08 

A-  16  50 

-  4' 23" 

-  2  01 

-  1   30 

H.  P. 

App. 

par.. 

3670" 
alt.,  25°  39' 

/    3308" 
155'  08" 

log  3.  56467 
cos  9. 95494 

Approx.  alt.,       25    39  26 
par.,                 +         55  08 

log  3.51961 

True  alt.,              26    34  34 

—    7 

54 

1st  corr., 

+    8' 

56" 

THE    CHRONOMETER    ERROR.  87 


CHAPTER    XI. 
THE  OHRONOMETEE  EREOR. 


309.  It  has  already  been  explained  (art.  261,  Chap.  VIII)  that  the  error  of  a  chronometer  is  the 
difference  between  the  time  indicated  by  it  and  the  correct  standard  time  to  which  it  is  referred;  and 
that  the  dailn  rate  is  the  amount  that  it  gains  or  loses  each  day.  In  practice,  chronometer  errors  are 
usually  stated  with  reference  to  Greenwich  mean  time.  It  is  not  required  that  either  the  error  or  the 
rate  shall  be  zero,  but  in  order  to  be  enabled  to  determine  the  correct  time  it  is  essential  that  both  rate 
and  error  be  known,  and  that  the  rate  shall  have  been  uniform  since  its  last  determination. 

310.  Determining  the  Rate. — Since  all  chronometers  are  subject  to  some  variation  in  rate  under 
the  changeable  conditions  existing  on  shipboard,  it  is  desirable  to  ascertain  a  new  rate  as  often  as  possible. 
The  process  of  obtaining  a  rate  involves  the  determination  of  the  error  on  two  different  occasions  sepa- 
rated by  an  interval  of  time  of  such  length  as  may  be  convenient;  the  change  of  error  during  this  interval, 
divided  by  the  number  of  days,  gives  the  daily  rate. 

Example:  On  March  10,  at  noon,  found  chronometer  No.  576  to  be  0™  32".5  fast  of  G.  M.  T. ;  on  March 
20,  at  noon,  the  same  chronometer  was  0"'  48*.0  fast  of  G.  M.  T.     What  was  the  rate? 

Error,  March  IC*  0\  +  0"'  32'.  5 

Error,  March  20<*  0^  -f-O    48  .  0 

Change  in  10  days,  +       15  .  5 

Daily  rate,  +         1'.55 

The  chronometer  is  therefore  gaming  1'.55  per  day. 

311.  Determining  Error  from  Rate. — The  error  on  any  given  day  being  known,  together  with 
the  daily  rate,  to  find  the  error  on  any  other  day  it  is  only  necessary  to  multiply  the  rate  by  the  number 
of  days  that  may  have  elapsed,  and  to  apply  the  product,  with  proper  sign,  to  the  given  error. 

Example:  On  December  17  a  chronometer  is  3'"  27^5  slow  of  G.  M.  T.  and  losing  0^.47  daily.  What 
is  the  error  on  December  26? 

Error  Dec.  17,-3'"  27'.5  Daily  rate,  —  0».47 

Correction,        —         4.2  No.  days,  9 


Error  Dec.  26,  -  3    31  .7  Corr.,  -  4  .23 

The  chronometer  is  therefore  f<Joiv  of  G.  M.  T.  on  Decem1)er  26,  3""  3P.7. 

312.  It  is  necessary  to  distinguish  between  the  signs  of  the  chronometer  correction  and  of  the 
chronometer  error.  A  chronometer  fast  of  the  standard  time  is  considered  as  having  a  positive  error, 
since  its  readings  are  positive  to  (greater  than)  those  of  an  instrument  showing  correct  time;  but  the 
same  chronometer  has  a  negative  correction,  as  the  amount  must  be  subtracted  to  reduce  chronometer 
readings  to  correct  readings. 

313.  Numerous  methods  are  available  for  determining  the  error  of  a  chronometer  in  port.  The 
principal  of  these  will  be  given. 

BY  TIME  SIGNALS. 

314.  In  nearly  all  of  the  important  ports  of  the  world  a  time  signal  is  made  each  day  at  some 
defined  instant.  In  many  cases  this  consists  in  the  dropping  of  a  time-ball — the  correct  instant  being 
given  telegraphically  from  an  observatorj'.  In  a  number  of  places  where  there  is  no  time-ball  a  signal 
may  be  received  on  the  instruments  at  the  telegraph  offices,  whereby  mariners  may  ascertain  the  errors 
of  their  chronometers.     Such  signals  are  to  be  had  in  almost  every  port  of  the  United  States. 

The  time  signal  may  be  given  by  a  gun-fire  or  other  sound,  in  which  case  allowance  must  be  made 
by  the  observer  for  the  length  of  time  necessary  for  the  sound  to  travel  from  the  point  of  origin  to  his 
position.  Sound  travels  1,090  feet  per  second  at  32°  F.,  and  its  velocity  increases  at  the  rate  of  1.15  feet 
per  second  with  each  degree  increase  of  temperature.     If  V  be  the  velocity  of  sound  in  feet  per  second 

at  the  existing  temperature,  and  D  the  distance  in  feet  to  be  traversed,  y  is  the  number  of  seconds  to 

be  subtracted  from  the  chronometer  reading  at  the  instant  of  hearing  the  signal,  to  ascertain  the  reading 
at  the  instant  the  signal  was  made. 

This  method  of  obtaining  the  chronometer  error  consists  in  taking  the  difference  between  the 
standard  time  and  chronometer  time  at  the  time  of  observation  and  marking  the  result  with  appropriate 
sign. 


88  THE    CHRONOMETER    ERROR. 

Example:  A  time-ball  drops  at  5^  0™  0%  G.  M.  T.,  and  the  reading  of  a  chronometer  at  the  same 
moment  is  4''  57"  52'.  5.     What  is  the  chronometer  error? 

G.  M.  T.,  5h  OO"'  00»  1 

Chro.  t.,  4  57    52  .5 


•  Chro.  error,  —        2    07  .5 

That  is,  chronometer  slow  2™  07'.  5;  chronometer  correction  additive. 

BY  TRANSITS. 

315.  The  most  accurate  method  of  finding  the  chronometer  correction  is  by  means  of  a  transit 
instrument  well  adjusted  in  the  meridian,  noting  the  times  of  transit  of  a  star  or  the  limbs  of  the  sun 
across  the  threads  of  the  instrument. 

At  the  instant  of  the  body's  passage  over  the  meridian<(\vire,  mark  the  time  by  the  chronometer. 
The  hour  angle  at  the  instant  is  O*";  therefore  the  local  sidereal  time  is  equal  to  the  right  ascension  of 
the  body  in  the  case  of  a  star,  or  the  local  apparent  time  is  O**  in  the  case  of  the  sun's  center.  By  con- 
verting this  sidereal  or  apparent  time  into  the  corresponding  mean  time  and  applying  the  longitude,  the 
Greenwich  mean  time  of  transit  is  given.  By  comparing  with  this  the  time  shown  by  chronometer  the 
error  is  found. 

Example:  1879,  May  9  (Ast.  day),  in  Long.  44°  39'  E.,  observed  the  transit  of  Arcturus  over  the 
middle  wire  of  the  telescope,  the  time  noted  by  a  chronometer  regulated  to  Greenwich  mean  time  being 
S*"  05'"  33^5.     Required  the  error. 

L.  S.  T.  (R.  A.  *),  14»     10"'  IP.  71 

Long.,  -      2      58    36 


G.  S.  T., 

R.  A.  M.  S.,  9^  0^      - 

11 
-     3 

11 
07 

35 
42 

.71 
.69 

Sid.  int.  from  0^ 
Reduction  (Tab.  8),  - 

8 

03 

1 

53. 
19. 

,02 

.27 

G.  M.  T., 
Chro.  t, 

8 
8 

02 
05 

33. 
33. 

.75 
,50 

Chro.  fast. 

2 

59. 

.  75 

Example:  June  25,  1879,  in  Long.  60°  E.,  observed  the  transit  of  both  limbs  of  the  eun  over  the 
meridian  wire  of  the  telescope,  noting  the  times  by  a  chronometer.  Find  the  error  of  the  chronometer 
on  G.  M.  T. 

Transit  of  western  limb,  S^   04"'  02^  5  Eq.  t.,  2'"  16^  72 

Tran-it  of  eastern  limb,  8     06    20  . 0  

H.  D.,  +  0\532 
Chro.  time,  loc.  app.  noon,       8     05     11  .25  Long.,  —  4'' 


8 

05 

11  . 

.25 

O" 

00" 
•    2 

'  00' 

14 

.59 

0 
4 

02 
00 

14 
00 

.59 

8 
8 

02 
05 

14 
11  . 

.59 
.25 

L.  A.  T.,  loc.  app.  noon,  0"   00"'  00'  Corr.,     —  2M28 

Eq.  t,  -        -     ^- 

Eq.  t.,   2"'  14^59 
L.  M.  T.,  loc.  app.  noon,  0    02     14  .59  Add  to  apparent  time. 

Long.,  - 

G.  M.  T.,  loc.  app.  noon, 
Chro.  time,  loc.  app.  noon, 

Chro.  fast,  2    56  .  66 

BY   A   SINGLE   ALTITUDE   iTIME    SIGHT). 

316.  The  problem  involved  in  this  solution,  by  reason  of  its  frequent  application  in  determining 
the  longitude  at  sea,  is  one  of  the  most  important  ones  in  Nautical  Astronomy.  It  consists  in  finding 
the  hour  angle  from  given  values  of  the  altitude,  latitude,  and  polar  distance.  The  hour  angle  thus 
obtained  is  converted  by  means  of  the  longitude  and  equation  of  time  in  the  case  of  the  sun,  or  longi- 
tude and  right  ascension  in  the  case  of  other  celestial  bodies,  into  Greenwich  mean  time;  and  this,  com- 
pared with  the  chronometer  time,  gives  the  error. 

317.  It  should  be  borne  in  mind  that  the  most  favorable  position  of  the  heavenly  body  for  time 
observations  is  when  near  the  prime  vertical.  When  exactly  in  the  prime  vertical  a  small  error  in  the 
latitude  produces  no  appreciable  effect.  Therefore,  if  the  latitude  is  uncertain,  good  results  may  be 
obtained  by  observing  the  sun  or  other  body  when  bearing  east  or  west.  If  observations  are  made  at 
the  same  or  nearly  the  same  altitude  on  eacli  side  of  the  meridian  and  the  mean  of  the  results  is  taken, 
various  errors  are  eliminated  of  which  it  is  otherwise  impossible  to  take  account,  and  a  very  accurate 
determination  is  thus  afforded. 

31§.  With  a  sextant  and  artificial  horizon  or  good  sea  horizon,  several  altitudes  of  a  body  should 
be  observed  in  quick  succession,  noting  in  each  case  the  time  as  shown  by  a  hack  chronometer  or  com- 
jMiring  watch  whose  error  upon  the  standard  chronometer  is  known.     Condensing  the  observation  into 


THE    CHRONOMETER    ERROR. 


89 


a  brief  interval  justifies  the  assumption  that  the  altitude  varies  uniformly  with  the  time.  A  very  satis- 
factory method  is  to  set  the  sextant  in  advance  at  definite  intervals  of  altitude  and  note  the  time  as  con- 
tact is  observed. 

319.  Correct  the  observed  altitude  for  instrumental  and  other  errors,  reducing  the  apparent  to  the 
true  altitude. 

If  the  sun,  the  moon,  or  a  planet  is  observed,  the  declination  is  to  be  taken  from  the  Nautical 
Almanac  for  the  time  of  the  observation.     If  the  chronometer  correction  is  not  approximately  known 

and  it  is  therefore  impossible 

X  jr to  determine  the  Greenwich 

mean  time  of  observation 
with  a  fair  degree  of  accu- 
racy, the  first  hour  angle 
found  will  be  an  approximate 
()ne;  thedeclination  corrected 
by  this  new  value  of  the  time 
will  i^roduce  a  more  exact 
value  of  the  hour  angle,  and 
the  operation  may  be  re- 
l)eated  until  a  sufficiently 
jirecise  value  is  determined. 
320.  In  figure  41  there 
are  given: 

AO  =  /*,   the  altitude   of 
the  body  O; 

DO  =  d,  the  declination; 
and 
QZ  =  L,  the  latitude  of  the  place. 

In  the  astronomical  triangle  POZ  there  may  be  found  from  the  foregoing: 
ZO  =  z,  the  zenith  distance  of  the  body,  =  90°  —  h; 
PO  =p,  the  polar  distance,  =  90°  it  d;  and 
PZ  =  co-L,  the  co-latitude  of  the  place,  =90°  —  L. 

From  this  data  it  is  required  to  find  the  angle  POZ,  the  hour  angle  of  the  body,  =  /. 
by  the  formula: 

.    2  1         COS  ^  (h-T-L+p)  sin  ^  {L+p  —h) 
SHI    5  r  — 


This  is  given 


If  we  let  8  =  J  {h-\-L  -\-p),  this  becomes: 


cos  L  sin  p 


sin  i  t  —  ■^  sec  L  cosec^  cos  »  sin  («  —  h). 

The  polar  distance  is  obtained  by  adding  the  declination  to  90°  when  of  different  name  from  the 
latitude  and  subtracting  it  from  90°  when  of  the  same  name.  Like  latitude  and  altitude  it  is  always 
I)ositive. 

If  the  sun  is  the  body  observed,  the  resulting  hour  angle  is  the  local  apparent  time  and  is  to  be 
taken  from  the  a.  m.  or  p.  m.  column  of  Table  44  according  as  the  altitude  is  observed  in  the  forenoon 
or  afternoon.  If  the  moon,  a  star,  or  a  planet  be  taken,  the  hour  angle  is  always  found  in  the  p.  m. 
column. 

Local  apparent  time  as  deduced  from  an  observation  of  the  sun  is  converted  to  local  mean  time  by 
the  application  of  the  equation  of  time;  then,  by  adding  the  longitude  if  west,  and  subtracting  it  if  east, 
the  Greenwich  mean  time  is  obtained. 

The  hour  angle  of  any  other  body,  added  to  its  right  ascension  when  it  is  west  of  the  meridian  at 
observation  or  subtracted  therefrom  when  east,  gives  the  local  sidereal  time,  which  may  be  reduced  to 
Greenwich  sidereal  time  by  the  application  of  the  longitude,  and  thence  to  Greenwich  mean  time  by 
methods  previously  explained. 

A  comparison  of  the  Greenwich  mean  time  with  the  chronometer  time  of  sight  gives  the  error  of 
the  chronometer. 

Example:  January  20,  1879,  p.  m.,  in  Lat.  48°  -iV  00^'  S.,  Long.  69°  03'  00"'  E.,  observed  a  series 
of  altitudes  of  the  sun  with  a  sextant  and  artificial  horizon;  mean  double  altitude,  59°  03''  10''',  images 
approaching;  mean  of  times  by  comparing  watch, 4*" 40™ 56*;  C — W,7''23"'25*;  index  correction,— 1^30'''; 
approximate  chronometer  correction,  —0'"  10'.     AVhat  was  the  exact  chronometer  error? 

W.  T.,  4''  40"'  56»     Obs.  2  alt.  Q,    59°  03'  10"    Dec,  20°  08'  26".  6  S.    Eq.  t.,         ll"  14'.60 

C_W,  ^      -     -„      -    - 


Chro 

t. 

0 

04 

21 

App. 

C. 

c. 

— 

0 

10 

7    23    25      I.  C. 


Q 


App.  G.  M.  T.,     0   04    11      Corr. 


S.  D.. 


p.  &  r., 
Corr.,  + 


— 

1  30 

2)59 

01  40 

29 

-1- 

30  50 
14  43 

29 

45  33 

^     16'  17" 

-      1'  34" 

H.  D., 
G.  M.  T. 

Corr. , 

Dec, 

P, 


32".  5 
0^.07 


H.  D.,         4-      0».74 
G.  M.  T.,  0\07 


+        2".  275       Corr.,  +    0^.052 

20°  08'  24".  3  8.    Eq.  t. ,  ll""  14^  7 


69°  51'  36" 


(Add  to  apparent 
time. ) 


14'  43" 


'90  THE    CHRONOMETER    ERROR. 


h 
h 

29° 

48 

69 

45'  33" 
41   00 
51   36 

sec 
cosec 

cos 
sin 

.18031 
.02740 

9.43631 
9.84483 

L.  A.  T., 

Eq.  t., 

L.  M.  T., 

Long., 

G.  M.  T., 
Chro.  t., 

Chro.  slow 

4" 

+ 

29" 
11 

'46'.  7 
14.7 

p 

4 
—4 

41 
36 

01.4 
12.0 

2)148 

•     74 
44 

18  09 

09  05 
23  32 

8 

0 
0 

04 
04 

49.4 
21.0 

2)19.48885 

,     0 

00 

28.4 

L.  A.T.,  4''29"'46».7  sin  J  <  9.74442 

Example:  May  18,  1879,  p.  m.,  in  Lat.  8°  03'  22"  S.,  Long.  34°  51'  57"  W.,  observed  a  series  of 
altitudes  of  the  star  Arcturus,  east  of  the  meridian,  using  artificial  horizon;  mean  double  altitude, 
60°  10';  mean  w^atoh  time,  0''  50-"  32';  C— W,  2"  20'"  59^5;  I.  C,  -f  2'  00".  Find  the  true  error  of  the 
chronometer. 

W.  T.,       6"  50"'  32^  Obs.  2  alt.  *,  60°  10'  00"  R.  A.  *,    14"  10"'  IP. 7 

C— W,      2   20    59.5  I.  C,        "         +  2   00 


Chro.  t.,    9   11    31.5  2)60    12  00 


30    06  00 
ref.,  -  1   41 


Dec.*,     19°  48' 33".  5  ^^ 
p,  109°  48'  34" 


h,  30    04   19 

h  30°  04'  19"  R.  A,  *,  14"  10™  11».7 

L  8    03   22  sec  .00431  H.  A.,  -     3   35    41 

p  109    48  34  cosec  .02650 


L.  S.  T., 


2)147    56   15  Long., 

t  73    58   08  cos  9.44116  G.  S.  T., 

(  —  /i  43    53   49  sin  9.84096  R.  A.  M.  S.,  0", 


H.  A.     3"  35'"  41'  E.         sin  ^  t  9.65647 


2)19.31293  Sid.  int.  from  0", 

Red.  (Tab.  8),       - 


G.  M.  T., 

Chro.  t., 


10  34 

+    2   19 

30.7 
27.8 

12  53 
-     3   43 

58.5 
11.7 

9   10 
-           1 

46.8 
30.2 

9  09 
9   11 

16.6 
31.5 

Chro.  fast,  2    14  .9 

BY  EaUAL  ALTITUDES. 

321.  The  method  of  observing  equal  altitwhs  of  the  same  body  on  opposite  sides  of  the  meridian 
is  usually  employed  for  accurate  determinations  of  the  chronometer  error  when  the  method  of  transits  is 
not  available. 

In  the  case  of  a  star,  the  mean  of  the  two  chronometer  times  corresponding  to  the  equal  altitudes 
is  the  chronometer  time  of  transit;  but  in  the  case  of  the  sun  the  mean  of  these  times  differs  somewhat 
from  the  time  of  transit,  since,  in  consequence  of  the  change  of  the  sun's  declination  between  the 
observations,  the  equal  altitudes  do  not  occur  at  equal  intervals  before  and  after  the  transit. 

The  small  correction  necessary,  when  the  sun  is  observed,  to  reduce  the  mean  of  the  times  to  the 
time  of  transit  ia  called  the  equation  of  equal  altitudes. 

322.  Equal  Altitudes  of  the  Sun.« — On  shore,  at  a  place  whose  longitude  is  accurately  known, 
and  whose  latitude  is  approximately  known,  observe,  with  an  artificial  horizon,  the  same  altitude  both 
before  and  after  meridian  passage,  as  near  the  prime  vertical  as  convenient  when  the  altitude  is  more 
than  10°,  noting  the  times.  In  low  latitudes  the  method  of  equal  altitudes  will  often  give  very  accurate 
results,  even  when  the  observations  are  quite  near  the  meridian. 

It  is  most  convenient,  as  well  as  conducive  to  accuracy,  to  take  the  observations  in  series,  setting 
the  sextant  in  advance  of  the  altitude  and  marking  the  time  at  the  instant  that  the  contact  is  observed; 
about  five  or  seven  sights  may  compose  a  series,  and  several  series  may  be  observed,  with  the  images  of 
the  sun  alternately  approaching  and  separating;  thus  the  mean  of  the  results  (working  each  series  of 
sights  separately)  will  eliminate  various  possible  errors.  Ten  minutes  of  double  altitude  will  usually 
be  found  a  convenient  interval  for  observing. 

The  sights  may  be  taken  on  opposite  sides  of  the  meridian  for  either  upper  or  lower  transit.  If  at 
upper  transit,  the  first  altitudes  are  taken  in  the  forenoon  and  the  times  recorded;  then  in  the  afternoon 
the  times  corresponding  to  the  same  altitudes  are  observed,  the  last  altitude  taken  in  the  morning  being 
the  first  to  come  on  in  the  afternoon;  series  taken  with  separating  images  in  the  forenoon  should  be 
observed  with  approaching  images  in  the  afternoon,  and  the  reverse.  If  the  time  of  lower  transit  is  to 
be  determined,  the  first  set  of  sights  is  taken  in  the  afternoon  of  one  day  and  the  second  set  in  the 
forenoon  of  the  next,  care  being  taken  as  beforer  to  observe  with  im^es  moving  in  opposite  directions 
on  opposite  sides  of  the  meridian. 

a  Chauvenet's  method. 


THE    CHRONOMETER    ERROR. 


91 


323.  The  mean  of  the  a.  m.  times  call  the  A.  M.  Chronometer  Time,  the  mean  of  the  p.  m. 
times,  the  P.  M.  Chronometer  Time.  If,  instead  of  noting  the  times  by  the  chronometer,  a  watch  is 
used  (compared  with  the  chronometer  both  before  and  after  each  observation),  it  will  generally  be 
found  necessary  to  make  an  allowance  for  its  gain  or  loss  on  the  chronometer,  so  as  to  obtain  the  exact 
difference  between  the  watch  and  chronometer  at  the  instant  of  observation.  The  difference  applied 
to  the  mean  of  the  watch  times  gives  the  mean  chronometer  time  the  same  as  would  have  been  found 
by  employing  the  chronometer  directly. 

The  half  sum  of  the  A.  M.  and  P.  M.  Chronometer  Times  is  the  Middle  Chronometer  Time;  the  P.  M. 
minus  the  A.  M.  time  in  the  case  of  observations  for  upper  transit,  or  the  A.  M.  minus  the  P.  M.  time 
for  lower  transit,  gives  the  Elapsed  Time.  Twelve  hours  should  be  added  to  the  chronometer  time  at 
second  observation  in  any  case  where  the  chronometer  has  passed  XII''  during  the  interval  between 
sights. 

Take  from  the  Nautical  Almanac,  page  I,  the  sun's  declination,  the  hourly  difference  of  declination, 
and  the  equation  of  time,  reducing  each  to  the  instant  of  local  apparent  noon  by  applying  the  differences 
due  to  the  longitude. 

Mark  ttorth  latitude  and  declination  +>  south  latitude  and  declination  — . 

Mark  hourly  difference  of  declination  when  tovmrd  north  -{-,  when  toward  south  — . 

Enter  Table  37  with  the  elapsed  time,  and  take  out  log  A  and  log  B,  prefixing  to  each  its  proper 
sign  as  given  in  the  table  at  the  head  of  the  page. 

To  log  A  add  the  logarithm  of  the  hourly  diff.  (Table  42)  and  the  log  tangent  of  the  latitude  (Table 
44).  Prefix  to  each  logarithm  the  sign  of  the  quantity  it  represents,  and  to  their  sum  the  sign  which 
results  from  the  algebraic  multiplication  of  the  quantities.  This  sum  is  the  logarithm  (Table  42)  of  the 
number  of  seconds  of  time  in  the  first  part  of  equation  of  equal  altitudes,  to  be  marked  +  or  — ,  like  its 
logarithm. 

To  log  B  add  the  logarithm  of  the  hourly  diff.  and  the  log  tangent  of  the  declination,  marking  the 
signs  as  before.  The  sum  is  the  logarithm  of  the  second  part  of  the  equation  of  equal  altitudes,  to  be 
marked  +  or  —  like  its  logarithm. 

Combine  the  two  parts,  having  regard  to  signs,  to  obtain  the  equation  of  equal  altitudes;  apply  this, 
with  proper  sign,  to  the  Middle  Chronometer  Time  and  the  result  is  the  Chronometer  Time  of  Local 
Apparent  Noon  or  Chronometer  Time  of  Local  Apparent  Midnight,  according  as  observations  were  taken  on 
opposite  sides  of  the  meridian  at  upper  or  at  lower  transit. 

Apply  the  equation  of  time  (adding  when  it  is  additive  to  mean  time,  otherwise  subtracting);  the 
result  is  the  Chronometer  Time  of  Local  Mean  Noon,  or  Midnight,  which,  if  the  chronometer  is  regulated 
to  local  time,  will  be  12''  0'"  0*  when  the  chronometer  is  right,  more  than  12''  when  fast,  less  than  12*" 
when  slow. 

If  the  chronometer  is  regulated  to  Greenwich  time,  apply  the  longitude  (in  time)  to  the  chronom- 
eter time  of  mean  noon  (subtracting  in  west,  adding  in  east  longitude) ;  the  result  will  be  more  or  less 
than  12'',  according  as  the  chronometer  is  fast  or  slow. 

Example:  April  13,  1879,  at  a  place  in  Lat.  30°  25^  N.,  Long.  5"  25"'  42'  W.,  observed  the  following 
equal  altitudes  of  the  sun  with  a  sextant  and  artificial  horizon,  noting  the  times  by  a  watch  compared 
Avith  a  chronometer  regulated  to  Greenwich  mean  time.     What  is  the  error  of  the  chronometer? 


A.  M.  COMPARISONS. 
Chro.,  2'>  22"  30» 

Watch, 


C-W, 


Chro., 
Watch, 

C-W, 


8  52 

02 

5  30 

28 

2''  56" 
9  26 

'30« 
02 

5  30 

28 

P.  M.  COMPARISONS. 

Chro.,  8'>  04='  30" 

Watch,  2    34    01 


C-W, 


Dec, 


9°  00'  54".  1  N. 


H.  D.  (13th),+54".40 
H.  D.  (14th), +54  .03 


WATCH,  A.  M. 
9h  12m  30s 

12  55 

13  20 

13  46 

14  10 


Chro., 
Watch, 

C-W, 

ALTS. 
91°  00' 

10 
20 
30 
40 


5  30 

29 

8"  33" 
3  03 

'30« 
01 

5  30 

29 

H.  D.  at  iioon,+ 
Long.,  + 


54".32 
5''.43 


Corr., 


Dec, 


(•294".96 
t  4'55".0 


9°  05'  49"  N. 


Dlfl.,  24  hrs.,-  0  .37 

Diff.,  1  hr.,    -0".015 
Diff.,  5''.43,     -0  .08 

H.D.atnoon,+54".32 


WATCH,  P.  M. 

2h  45"'  45" 
45    20 

44    55    Tab.  37  log  A(-)9.4445  logB(  +  )9.3193 

44    30    H.  D.    +54".32  log     (  +  )1.7350  log     (  +  )1.7350 

44    05   Lat.      +30°  25' tan     (+) 9.7687  d  + 9°6' tan    (  +  )9.2045 


Mean,  W.  T.,  A.  M., 
C-W, 

A.  M.  Chro.  T., 
P.  M.  Chro.  T., 


Mid.  Chro.  T., 
Eq.  eq.  alt., 

Chro.  t.  L.  A.  Noon, 
Eq.  t, 

Chro.  t.  L.  M.  Noon, 
Long., 

Chro.  fast. 


9hl3"- 

20" 

+  5 

30 

28 

2 

43 

48 

+  8 

15 

24 

2)10 

69 

12 

5 

29 

36 

- 

7.1 

5 

29 

28.9 

- 

0 

31.5 

5 

28 

67.4 

-  5 

25 

42.0 

Mean,  W.  T.,  P.  M. 
C-W. 

P.  M.  Chro.  T., 
A.  M.  Chro.  T., 

Elapsed  Time, 

Eq.  t., 

H.  D., 
Long., 


2h  44m  5.5*  1st   Part>-8».88  log     (_)0.9482 
+    5   30    29   2d    Part+1  .81 


log    (  +  )  0.2588 


16    24    Eq.  eq.l  _^  ^ 
43    48       alt.    / 


-    2    43    48       alt 


5    31    36 


0">  36'.02 


0«.65 
5h.43 


Corr., 
Eq.  t., 


{Minug  to  mean  time.) 


0   03    16.4 


92 


THE    CHRONOMETER    ERROR. 


324.  A  quicker  method  of  solving  the  same  problem «  is  available  when  results  are  not  required  to 
be  accurate  to  the  fraction  of  a  second. 

If  /i'  is  the  change  of  altitude  in  minutes  of  arc,  due  to  the  total  change  in  declination  in  the 
time  elapsed  between  sights  (the  latitude  and  hour  angle  remaining  the  same),  and  i'  the  number  of 
seconds  it  requires  for  the  sun  to  change  its  altitude  one  minute  of  arc,  then: 

•  1 

Equation  of  equal  altitudes  =7^h^  X  t' . 


Table  25  gives  the  change  of  altitude  of  an  object  arising  from  a  change  of  100  seconds  in  declination 
at  various  altitudes,  declinations,  and  latitudes.  By  multiplying  the  appropriate  quantity  taken  from 
this  table  by  the  total  change  of  declination  between  sights,  dividing  by  100,  and  converting  the  result 
from  seconds  to  minutes  of  arc,  //  is  found.     It  is  marked  with  the  sign  indicated  in  the  table. 

By  dividing  the  number  of  seconds  of  time  between  the  first  and  last  sights  of  one  of  the  series  by 
the  number  of  minutes  difference  of  altitude,  we  find  i' .  When  the  sights  are  taken  on  opposite  sides 
of  the  upper  meridian  t'  is  minus;  for  the  lower  meridian  it  is  plus. 

When  the  artificial  horizon  is  used,  if  i^  is  computed  on  a  basis  of  the  change  of  the  double  altitude, 
its  value  is  only  half  of  the  true  one  and  the  second  term  of  the  equation  becomes  h^  X  t^'  instead  of  as 
given  above. 

The  example  given  in  illustration  of  the  preceding  method  when  worked  by  this  method  is  as 
follows: 


Change  in  declination  between  sights  =  H.  D.  X  elapsed  time 
Change  in  altitude  due  to  lOO'^  declination  (Tab.  25)  =  +  56'^ 


54'''.32  X  5\53  =  300^'. 


V  = 


100  X  60 

2'»45'"45'  —  2''44°K)5" 


91°  40^  — 91°  00^ 
Eq.  equal  alt.  =  +  2.80  X  - 


100^ 
40' 


2\o 


=  -  2« 

7^oo. 


325.  If  equal  altitudes  of  a  planet  were  observed,  the  correction  due  to  change  of  declination  could 
be  computed  as  in  the  case  of  the  sun.  It  is  not  ordinarily  expedient  to  use  a  planet,  however,  for  if 
night  sights  are  to  be  taken  facility  of  working  would  make  it  preferable  to  employ  a  fixed  star. 

On  account  of  its  rapid  and  excessive  change  of  declination  the  moon  would  never  be  observed  for 
equal  altitudes. 

326.  Equal  Altitudes  op  a  Fixed  Star. — In  selecting  stars  for  this  observation,  it  is  to  be 
remarked  that  the  nearer  to  the  zenith  the  star  passes  the  less  may  the  elapsed  time  be;  and  when  a 
star  passes  exactly  through  the  zenith  the  two  altitudes  may  be  taken  within  a  few  minutes  of  each 
other.  But,  with  the  ordinary  sextants,  altitudes  near  90°  can  not  be  taken  with  the  artificial  horizon, 
as  the  double  altitude  is  then  nearly  180°.  A  limit  is  thus  placed  upon  the  extreme  altitude  that  it 
is  practicable  to  observe. 

The  sextant  should  be  set  and  the  coincidences  of  the  two  images  of  the  star  awaited,  as  in  the  case 
of  the  sun's  limb,  and  the  times  by  chronometer  or  watch  noted  as  usual. 

327.  Take  the  mean  of  the  times  before  the  meridian  passage  as  the  A.  M.  Chronometer  Time,  and 
the  mean  of  those  after  the  meridian  passage  as  the  P.  M.  Chronometer  Time.  The  mean  of  these  two 
(adding  12''  to  the  later  one  in  case  the  chronometer  has  passed  XII*"  in  the  interval  between  sights)  is 
the  Chronometer  Time  of  Star's  Transit.  At  the  instant  of  transit  the  local  sidereal  time  will  equal  the 
right  ascension  of  the  star  in  case  of  the  upper  transit,  or  it  will  equal  the  right  ascension  plus  12''  in 
case  of  the  lower  transit.  By  converting  local  sidereal  into  Greenwich  sidereal  and  thence  into  Green- 
wich mean  time  in  the  usual  way,  the  chronometer  error  is  found. 

Example:— June  8,  1879,  at  Cape  Town,  Lat.  33°  56'  S.,  Long.  18°  28'  40"  E.,  using  sextant  and  arti- 
ficial horizon,  observed  equal  altitudes  of  star  Antares  before  and  after  upper  transit,  as  stated  below. 
Required  the  chronometer  error  on  Greenwich  mean  time. 


Chro.  A.  M. 

7"  32'"  10^5 


32 
32 


35.0 
59.3 


Altitudes. 
125°  30^ 
40 
50 


A.  M. 
P.  M. 

Chro.  t.,          7 
Chro.  t.,        11 

32 
33 

34.9 
56.1 

2)19 

06 

31.0 

Chro. 
G.  M. 

t.  Transit,      9 
T.  Transit,      9 

33 
59 

15.5 
30.9 

Chro.  slow, 


26    15.4 


Chro.  P.  M. 
11"  34"'  20^3 
11     33     56.0 
11     33     32.0 

P.  M.  Chro.  t.. 

n 

33 

56.1 

L.  S.  T.(R.A.  *), 
Long., 

16" 

—   1 

22"' 
14 

03%5 
54.7 

G.  S.  T., 

R.  A.  M.  S.,  0", 

15 
—    5 

07 
05 

08.8 
59.4 

Sid.  int.  from  0", 
Red.  (Tab.  8), 

10 

01 

1 

09.4 
38.5 

G.  M.  T., 

9 

59 

30.9 

a  Suggested  by  Commander  W.  E.  Sewell,  U.  S.  Navy. 


THE    CHRONOMETER    ERROR.  93 

32§.  Degrek  of  Dependence. — An  error  of  5''  in  the  latitude  would  not  affect  the  corresponding 
part  of  the  equation  of  equal  altitudes  by  more  than  one-hundredth  of  its  amount  in  the  most  unfavorable 
case,  and  in  general  would  have  no  sensible  effect.  It  is  one  of  the  advantages  of  the  equal  altitude 
method,  therefore,  that  it  does  not  require  an  accurate  knowledge  of  the  latitude.  It  is  also  plain  that 
errors  in  the  longitude  affecting  the  declination  and  its  hourly  difference  produce  but  small  propor- 
tionate effects  upon  the  computed  equation.  The  absolute  error  of  the  chronometer  on  Greenwich  will 
be  affected  by  the  whole  error  in  the  longitude,  but  the  rate  v^dll  still  be  correct.  Hence,  we  conclude 
that  by  this  method  the  chronometer  may  be  accurately  rated  at  a  place  whose  latitude  and  longitude 
are  both  imperfectly  known. 

The  chief  source  of  error  is  in  the  observation  itself.  The  best  observers  with  the  sextant  can  not 
depend  on  the  noted  time  of  a  single  contact  within  0^.5,  and  hence  the  intervals  between  the  successive 
chronometer  times  (which,  if  observations  could  be  perfectly  taken,  would  be  sensibly  equal)  may 
differ  2".  But  the  greatest  probable  error  of  the  chronometer  time  of  sun's  or  star's  transit,  from  the 
mean  of  six  such  observations  on  each  side  of  the  meridian,  is  found  to  be  not  more  than  0*.2,  provided 
the  rate  of  the  chronometer  between  the  observations  is  uniform. 


94 


LATITUDE. 


CHAPTER  XII. 
LATITUDE. 


BY  MERIDIAN  ALTITUDE. 

329.  The  latitude  of  a  place  on  the  surface  of  the  earth,  being  its  angular  distance  from  the  equator, 
is  measured  by  an  arc  of  the  niieridian  between  the  zenith  and  the  equator;  hence,  if  the  zenith  distance 

of  any  heavenly  body  when  on  the  meridian  be  known,  together 
with  the  declination  of  the  body,  the  latitude  can  thence  be  found. 

Ivet  figure  42  represent  a  projection  of  the  celestial  sphere  on 
the  plane  of  the  meridian  NZS;  C,  the  center  of  the  sphere;  NS,  the 
horizon;  P  and  P',  the  poles  of  the  sphere;  QCQ'',  the  equator;  Z, 
the  zenith  of  the  observer.  Then,  by  the  above  definition,  ZQ  will 
be  the  latitude  of  the  observer;  and  NP,  the  altitude  of  the  elevated 
pole,  will  also  equal  the  latitude. 

Let  A  be  the  position  of  a  heavenly  body  north  of  the  equator, 
but  south  of  the  zenith;  QA  =  (/,  its  declination;  AS  =  /i,  its  altitude; 
and  ZA  =  2  =  9U°— /i,  its  zenith  distance. 

From  the  figure  we  have: 

QZ  =  QA4-AZ,  or 

Fig.  42.  •  ^y  attending  to  the  names  of  z  and  d,  marking  the  zenith  dis- 

tance north  or  south  according  as  the  zenith  is  north  or  south  of  the 
body,  the  above  equation  may  be  considered  general  for  any  position  of  the  body  at  upper  transit,  as 
A,  A^  A''. 

In  case  the  body  is  below  the  pole,  as  at  A''^^ — that  is,  at  its  lower  culmination — the  same  formula 
may  be  used  by  substituting  180°— d  for  d.     Another  solution  is  given  in  this  case  by  observing  that: 

NP  =  PA^''  +  NA^'^  or 
L=p  +  h. 

330.  A  common  practice  at  sea  is  to  commence  observing  the  altitude  of  the  sun's  lower  limb 
above  the  sea  horizon  about  10  minutes  before  noon,  and  then,  by  moving  the  tangent-screw,  to  follow 
the  sun  as  long  as  it  rises;  as  soon  as  the  highest  altitude  is  reached,  the  sun  begins  to  fall  and  the  lower 
limb  will  appear  to  dip.  When  the  sun  dips  the  reading  of  the  limb  is  taken,  and  this  is  regarded  as 
the  meridian  observation. 

It  will,  however,  be  found  more  convenient,  and  frequently  more  accurate,  for  the  observer  to  have 
his  watch  set  for  the  local  apparent  time  of  the  prospective  noon  longitude,  or  to  know  the  error  of  the 
watch  thereon,  and  to  regard  as  the  meridian  altitude  that  one  which  is  observed  when  the  watch  indi- 
cates noon.  This  will  save  time  and  try  the  patience  less,  for  when  the  sun  transits  at  a  low  altitude  it 
may  remain  "on  a  stand|"  without  appreciable  decrease  of  altitude  for  several  minutes  after  noon;  more- 
over, this  method  contributes  to  accuracy,  for  when  the  conditions  are  such  that  the  motion  in  altitude 
due  to  change  of  hour  angle  is  a  slow  one,  the  motion  therein  due  to  change  of  the  observer's  latitude 
may  be  very  material,  and  thus  have  considerable  influence  on  the  time  of  the  sun's  dipping.  This 
error  is  large  enough  to  take  account  of  in  a  fast-moving  vessel  making  a  course  in  which  there  is  a  good 
deal  of  northing  or  southing. 

In  observing  the  altitude  of  any  other  heavenly  body  than  the  sun,  the  watch  time  of  transit 
should  previously  be  computed  and  the  meridian  altitude  taken  by  time  rather  than  by  the  dip.  This 
is  especially  important  with  the  moon,  whose  rapid  motion  in  declination  may  introduce  still  another 
element  of  inaccuracy. 

331.  The  watch  time  of  transit  for  the  sun,  or  other  heavenly  body,  may  be  found  by  the  forms 
given  below,  knowing  the  prospective  longitude,  the  chronometer  error,  and  the  amount  that  the  watch 
18  slow  of  the  chronometer. 


For  the  Sun. 


For  other  Bodies. 


L.  A.  T.  noon. 

Long.  (+  if  west), 

G.  A.  T., 

Eq.  t., 

G.  M.  T., 

C.  C.  (sign  reversed) 

Chro.  time, 

C-W, 

Watch  time  noon, 


0"  00'"   OO" 


L.  S.  T.  transit, 

Long.  (+  if  west), 

G.  S.  T., 

R.  A.  M.  S.,  0\ 

Sid  int.  from  O*", 

Red.  (Tab.  8), 

G.  M.  T., 

C.  C.  (sign  reverse*!), 

Chro.  time, 

C-W, 

Watch  time  transit, 


( Right  ascension. ) 


LATITUDE.  95 

332.  From  the  observed  altitude  deduce  the  true  altitude,  and  thence  the  true  zenith  distance. 
Mark  the  zenith  distance  North  if  the  zenith  is  north  of  the  body  when  on  the  meridian,  South  it  the 
zenith  is  south  of  the  body. 

Take  out  the  declination  of  the  body  frorti  the  Nautical  Almanac  for  the  time  of  meridian  passage, 
having  regard  for  its  proper  sign  or  name. 

The  algebraic  sum  of  tlie  declination  and  zenith  distance  will  be  the  latitude.  Therefore,  add 
together  the  zenith  distance  and  the  declination  if  they  are  of  the  same  name,  but  take  their  difference  if  of 
opposite  names;  this  sum  or  difference  will  be  the  latitude,  which  will  be  of  the  same  name  as  the  greater. 

Example:  At  sea,  June  21,  1879,  in  Long.  60°  W.,  the  observed  meridian  altitude  of  the  sun's  lower 
limb  was  40°  4';  sun  bearing  south ;  I.  C.j  +  S'O'';  height  of  the  eye,  20  feet;  required  the  latitude. 


Obs.  alt., 
Corr., 

40° 

+ 

04^ 
13 

00'^ 
21 

S.  D., 
LC, 

dip, 
p.  <&r. 

+  15^ 

+  3 

46'^ 
00 

Dec, 

H.  D., 
Long., 

Corr., 

Dec, 

23°  27^  20^''.5 

,  +       0'''.32 
4". 

h, 

40 

17 

21 

+  18 

-  ¥ 

,  -     1 

46 

23'^ 
02 

2, 

49° 
23 

42^ 

27 

39'^  N. 
22  N. 

+        F''.28 

23°  27^  22^' 

L, 

73 

10 

01  N. 

-  5 

25 

Corr.,    +  13^  21'-' 

Example:  At  sea,  April  14, 1879,  in  Long.  140°  E.,  the  observed  meridian  altitude  of  the  sun's  lower 
limb  was  81°  W  30'^;  sun  bearing  north;  I.  C.,— 2'  30'-';  height  of  the  eye,  20  feet. 

Obs.  alt.,        81°  15'  30'^  S.  D.,    +  15'  59''  Dec,  9°  22'  35".4    N. 

Corr.,  +  8    59 


H.  D.,  +  54^.03 

h,  81     24    29  p.'&r.,  -     0    07  Long.,  -  9\33 

z,  8°  35'  31"  S.  p  r     504".  1 

d,  9     14    II   N.  -     7    00  *"""•'  \8'  24". I 


L,  0    38    40   N.  Corr.,    +     8'  59"  Dec,  9°  14'  11"      N. 

Example:  At  sea.  May  15,  1879,  Long.  0°,  the  observed  meridian  altitude  of  the  sun's  lower  limb 
was  30°  13'  10";  sun  bearing  north;  I.  C,  + 1'  30";  height  of  the  eye,  15  feet. 

Obs.  alt.,       30°  13'   10"  S.  D.,    +  15'  51"  Dec,  Gr.  0^,  18°  50'48".5  N. 

Corr.,  +         12    02  .     I.  C,     +     1     30 

h,  30    25     12  +  17    21 

z,  59°  34'  48"  S.  dip,       -     3'  48" 

d,  18    50    49    N.  p.&r.,  -     1     31 

L,  40    43    59    S.  -     5     19 

Corr.,    +  12'  02" 

Example:  January  1,  1879,  the  observed  meridian  altitude  of  Sirius  was  53°  23'  40",  bearing  south; 
I.  C.,  +  5'  0";  height  of  the  eye,  17  feet. 

Dec.  *,  16°  33'  04"  S. 


Obs.  alt., 
Corr. , 

53° 

+ 

23' 

40" 
15 

N. 
S. 

N. 

LC, 

dip, 
ref., 

Corr., 

+ 
+ 

5'  00" 

*, 

53 

23 

55 

43 

% 

36° 
16 

36' 
33 

05" 
04 

4  45 

0'  15" 

L» 

20 

03 

01 

Example:  June  13,  1879,  in  Long.  65°  W.,  and  in  a  high  northern  latitude,  the  meridian  altitude  of 
the  sun's  lower  limb  was  8°  16'  10",  below  the  pole;  height  of  the  eye,  20  feet;  I.  C,  0'  00". 
Greenwich  apparent  time  of  lower  culmination,  June  13,  !&"  20'"  (  =Long.  +12''). 

S.  D.,        -^r  15'  47"  Dec,  23°  13'    03".8    N. 

dip,  -    4  23 

p.  &T.,     -    6   12 


Obs.  alt., 
Corr.,   - 

8°  16'  10" 
5  12 

K 

8  21  22 

z, 
180°-(7, 

81°  38'  38"  S. 
156  44  36  N. 

75  05  58  N. 
Alternative  method, 
h,                      8°  21'  22" 
p,                    66  44  36 

10   35 


Corr.,        -h    5   12 


H.  D.,   + 
G.  M.  T., 

8".58 
16"  .33 

Corr.,   + -( 

2' 

140".  5 
20".  5 

Dec,      23° 

15' 

24" 

p,                     66° 

44' 

36" 

180°-J,    156° 

44' 

36" 

N. 


L,  75    05  58    N. 


96  LATITUDE. 

Example:  June  26,  1879,  in  Long.  80°  W.,  the  observed  meridian  altitude  of  the  moon's  upper  limb 
was  59°  6'  4(y',  bearing  south;  I.  C,  + 1'  ^'\  height  of  the  eye,  19  feet. 

G.  M.  T.,  Gr.  trans.,  5i>  27'».0  Dec.  (llh),     4°  51'  36".5  S. 

Corr.  for  Long  (Tab.  11),+        11  .0 


h,   59°  18'  00" 

Obs.  alt., 

I.  C, 

S.  D., 
Aug., 
dip, 

1st  Corr., 

+ 

59°  06'  40" 

z,   30°  42' 00"  N. 
d,     4  51  06  S. 

2' 00" 

L,  25  50  54  K. 

14 
4  16 

20  33 

18'  33" 

L.  M.  T.,  local  trans.,  5  38  .0 

Long.,  -*-   5  20  .0 


G.  M.  T.,  local  trans.,      +  10  58  .0 


M.  D., 
No.  min., 

+ 

15".07 

2n'.0 

Corr., 

30".l 

Dec, 

4°  51' 

06"   S. 

Approx.  alt.,  58°  48'  07" 

l>.<tr.  (Tab.  24),  +        29  53 


Example:  At  sea,  September  16,  1879,  in  Long.  75°  E.,  the  observed  meridian  altitude  of  Jupiter 

was  51°  2W  24'^  bearing  north;  I.  C,  -^3^  0''';  height  of  the  eye,  16  feet. 

Obs.  alt.,     51°  25' 24"                   par.,    +0'01"  G.  M.  T.,  Gr.  trans.,         10i>  49'».8  Dec,                      10°  44' 20".5    S. 

CJorr.,       -         1  41                     I.e.,    +3  00  Corr.  for  Long.,              -         0  .9  — .— — 

H.  D.,     •  -                6".58 

h,                  51    23  43                                  +3  01  L.  M.  T.,  local  trans.,       10    .50.7  G.  M.  T.,                              5'' .84 

— ^—                                    —  Long.,                             -   5   00  .0  • 

z,                  38°  36' 17"  S.               dip,     -3' 55"                                                          Corr.,  -              38".43 

d,       10  44  59  S.      ref.,  -  47  G.  M.  T.  local  trans.,    5' 50  .7  — — ^— 

Dec,  10°  44'  53"   S. 


L,        49  21  16  S.  -4  42 

•       H.  P.,  2".2 

Corr..  -1' 41"  par.  (Tab.  17)  ,        1" 

333.  Constant. — In  working  a  meridian  altitude,  especially  the  daily  noon  observation  of  the  sun, 
it  is  frequently  a  convenience  to  so  arrange  the  terms  of  the  problem  that  all  computation,  excepting 
the  application  of  the  observed  altitude,  is  completed  beforehand;  then  the  ship's  latitude  will  be  known 
immediately  after  the  sight  has  been  taken,  it  benig  necessarj^  only  to  add  or  subtract  the  altitude. 

It  is  assumed  that  the  noon  longitude  will  be  sufficiently  accurately  known  in  advance  to  enable  the 
navigator  to  correct  the  declination;  also  the  approximate  meridian  altitude  to  correct  the  parallax  and 
refraction;  if  the  latter  is  not  known,  it  may  readily  be  found  from  the  declination  and  approximate 
latitude. 

Generally  speaking, 

Lat.  =  Zenith  distance  —  Dec, 
=  90°  —  True  alt.  +  Dec, 
=  90°  -  (Obs.  alt.  +  Corr.)  +  Dec, 
=  (90°  -f  Dec.  -  Corr.)  -  Obs.  alt., 

in  which  the  quantity  (90°  -f  Dec.  —  Corr.)  may  be  termed  a  Constant  for  the  meridian  altitude  of  the 
day,  as  it  remains  the  same  regardless  of  what  the  observed  altitude  may  prove  to  be.  The  constant 
having  been  worked  up  before  the  observation  is  made,  the  latitude  will  be  known  as  soon  aa  the 
observed  altitude  is  applied. 

To  avoid  the  confusion  that  might  arise  from  the  necessity  of  combining  the  terms  algebraically 
according  to  their  different  names,  it  may  be  convenient  to  divide  the  problem  into  four  cases  and  lay 
down  rules  for  the  arithmftical  combination  of  the  terms,  disregarding  their  respective  names  as  follows: 

Case      I.  Lat.  and  Dec.  same  name,  Lat.  greater,  +  90°  +  Dec.  —  Corr.  —  Obs.  alt. 

Case    II.  Lat.  and  Dec.  same  name,  Dec.  greater,  —  90°  +  Dec.  +  Corr.  +  Obs.  alt. 

Case  III.  Lat.  and  Dec.  opposite  names,  +  90°  —  Dec.  —  Corr.  —  Obs.  alt. 

Case  IV.  Lat.  and  Dec.  same  name,  lower  transit,-!-  90°  —  Dec.  -f-  Corr.  +  Obs.  alt. 

The  correctness  of  such  an  arrangement  will  become  readily  apparent  from  an  inspection  of  figure  42. 
The  assumption  has  been  made  that  the  correction  to  the  observed  altitude  is  positive;  when  this  is 
not  true  the  sign  of  the  correction  must  be  reversed. 

As  examples  of  this  method,  the  first,  second,  third,  and  fifth  of  the  examples  previously  given 
illu-strating  the  meridian  altitude  will  be  worked,  using  the  constant;  the  details  by  which  Corr.  and 
Dec.  are  obtained  are  omitted,  being  the  same  as  in  the  originals. 

1st  Example.  2i>  Example.  3d  Example.  5th  Example. 

Case  I.  Case  II.  Case  III.  Case  I V. 

+  90°  00' 00'^  -90°  00' 00''  +90°  00' 00"  -f  90°  00' 0(7' 

Dec,         +  23  27  22  Dec,         -f  9  14  11  Dec,         -18   50  49  Dec,         -23   15  24 

Corr.,       -  13  21  Corr.,        -f         8  59  Corr.,        -        12  02  Corr.,       -f         5  12 

Constant, -4-113  14  01  Con8tant,-80  36  50  Constant,  +  70  57  09  Constant,+66  49  48 

Obs.  alt.,    -  40  04  00         Obs.  alt., -f  81   15  30         Obs.  alt., -30   13  10  Obs.  alt.,-^  8  16  10 


Lat.,  73   10  01  (N.)  Lat,  0  38  40  (N.)  Lat.,  40  43  59  (S.)  Lat.,  75  05  58 (N.) 


LATITUDE.  97 

BY  REDUCTION  TO  THE  MERIDIAN. 

334.  Should  the  meridian  observation  be  lost,  owing  to  clouds  or  for  other  reason,  altitudes  may  be 
taken  near  the  meridian  and  the  times  noted  by  a  watch  compared  with  the  chronometer,  from  which, 
knowing  the  longitude,  the  hour  angle  may  be  deduced. 

If  the  observations  are  within  26'"  from  the  meridian,  before  or  after,  the  correction  to  be  applied 
to  the  observed  altitude  to  reduce  it  to  the  meridian  altitude  may  be  found  by  inspection  of  Tables  26 
and  27.  Table  26  contains  the  variation  of  the  altitude  for  one  minute  from  the  meridian,  expressed  in 
seconds  and  tenths  of  a  second.  Table  27  contains  the  product  obtained  by  multiplying  the  square  of 
the  minutes  and  seconds  by  the  change  of  altitude  in  one  minute. 

Let  a  =  change  of  altitude  (in  seconds  of  arc)  in  one  minute  from  the  meridian: 
H  =  meridian  altitude; 
h   =  corrected  altitude  at  observation;  and 
t    =  interval  from  meridian  passage. 
The  value  of  the  reduction  to  the  meridian  altitude  of  each  altitude  is  found  by  the  formula: 

H  =  /*  ^  at-, 

a  being  found  in  table  26,  and  af  in  Table  27;  hence  the  following  rule: 

Find  the  hour  angle  of  the  body  in  minutes  and  seconds  of  time.  Take  from  Table  26  the  value  of 
a  corresponding  to  the  declination  and  the  latitude.  Take  from  Table  27  the  value  of  at^  corresponding 
to  the  fi  thus  found  and  to  the  interval,  in  minutes  and  seconds,  from  meridian  passage.  This  quantity 
will  represent  the  amount  necessary  to  reduce  the  corrected  altitude  at  the  time  of  observation  to  the 
corrected  altitude  at  the  meridian  pa-ssage;  it  is  always  additive  when  the  body  is  near  upper  transit, 
and  always  to  be  subtracted  when  near  lower  transit. 

If  the  mean  of  a  number  of  sights  is  to  be  taken,  determine  each  reduction  separately,  take  the 
mean  of  all  the  reductions,  and  apjily  it  U)  the  mean  of  the  altitud(!s;  it  is  incorrect,  in  such  a  case,  to 
take  the  mean  of  the  times  and  work  the  sight  with  this  single  value  of  t.  The  differences  of  altitude 
being  small,  the  parallax  and  refraction  will  be  sensibly  the  same  for  all,  and  one  computation  of  the 
correction  to  the  observed  altitude  will  suffice. 

Knowing  the  meridian  altitude,  the  latitude  is  to  be  found  as  previously  explained. 

335.  When  several  sights  are  taken,  the  most  expeditious  method  of  calculating  will  be  to  find 
first  the  watch  time  of  transit,  and  thence  obtain  the  hour  angle  of  each  observation  by  comparing  the 
watch  time  of  observation.  The  watch  time  of  transit  may  be  found  as  already  explained  (art.  331) 
for  computing  that  quantity  as  a  guide  in  taking  the  meridian  altitude,  but  the  hour  angle  thus  obtained 
is  subject  to  a  correction.  The  difference  l;etween  watch  time  of  transit  and  watch  time  of  observation 
^ives  the  watch  time — that  is,  the  mean  time — elapsing  between  transit  and  observation.  A  fixed  star 
covers  in  that  time  an  angle  corresponding  to  the  sidereal  and  not  to  the  mean  time  interval,  and  a 
reduction  should  be  made  accordingly  to  give  its  true  hour  angle  at  the  instant  of  observation.  A 
planet's  hour  angle  should  be  corrected  in  the  same  way  (for  we  may  disregard  its  very  small  change 
m  right  ascension).  The  correction  may  be  entirely  neglected  in  the  case  of  the  sun,  as  the  difference 
between  mean  and  apparent  time  intervals  is  immaterial.  The  reduction  of  the  hour  angle  in  the  ca.se 
of  the  moon  becomes  rather  cumbersome,  so  much  so  that  it  is  better  to  find  the  hour  angle  of  this  body 
by  the  more  usual  method  of  converting  watch  time  to  G.  M.  T.,  and  thence  to  L.  8.  T.,  and  finding 
the  difference  between  the  latter  and  the  R.  A.;  an  additional  reason  for  this  is  that  the  G.  M.  T.  of 
observation  must  be  known  exactly,  with  the  moon,  for  the  correction  of  the  declination  (art.  338). 

336.  Table  26  includes  values  of  the  latitude  up  to  60°,  and  those  of  the  declination  up  to  63°, 
thus  taking  in  all  frequented  waters  of  the  globe  and  all  heavenly  bodies  that  the  navigator  is  likely  to 
employ.  No  values  of  (i  are  given  when  the  altitudes  are  above  86°  or  below  6°,  as  the  method  of  reduc- 
tion to  the  meridian  is  not  accurate  when  the  body  transits  very  near  the  zenith,  and  the  altitudes 
themselves  are  questionable  when  very  low.  In  case  it  is  desired  to  find  the  change  of  altitude  in  one 
minute  from  noon  for  conditions  not  given  in  the  tables,  it  may  be  computed  by  the  formula: 

l'^9635  cos  L  cos  d 

sm  (L — a) 

In  working  sights  by  this  method  where  great  accuracy  is  required,  as  in  determining  latitudes  on 
shore  for  surveying  purposes,  it  is  well  to  compute  the  a  rather  than  to  take  it  from  the  table,  as  one 
is  thus  enabled  to  employ  the  value  as  found  to  the  second  decimal  jilace. 

Due  regard  must  be  paid  to  the  names  of  the  declination  and  latitude  in  working  this  formula;  if 
thev  are  of  opposite  names,  the  declination  is  negative,  and  L  and  d  should  be  added  together  to  obtain 
L— '(/. 

337.  Table  27  contains  values  of  af  up  to  the  limits  within  which  the  method  is  con.sidered  to 
apply  with  a  fair  degree  of  accuracy.  It  nuist  not  be  understood  that  the  plan  of  reduction  to  the 
meridian  is  not  available  for  wider  limits,  but  it  would  seem  ]ireferable  to  employ  the  tp^  cp"  formula, 
described  hereafter,  when  the  hour  angle  falls  beyond  that  for  which  the  table  is  computed.  On  the 
other  hand,  the  reduction  is  not  exact  in  all  cases  covered  by  the  table;  while  sufiiciently  so  for  sea 
navigation,  the  limits  given  are  far  too  wide  for  the  precise  determinations  required  in  surveying,  where 
the  aim  should  l)e  to  observe  bodies  under  such  conditions  that  the  total  reduction  a(^  shall  not  exceed  V. 

33§.  It  should  be  kept  clearly  in  mind  when  employing  the  method  of  reduction  to  the  meridian 
that  the  resulting  latitude  is  that  of  the  ship  at  the  instant  of  observation,  and  to  bring  it  up  to  noon 
the  run  nuist  be  applied.  The  declination  should  properly  be  corrected  for  the  instant  of  observation; 
with  the  sun  or  a  planet,  it  is  sufiiciently  accurate  to  use  the  declination  at  meridian  passage,  unless  the 
interval  from  the  meridian  be  quite  large;  but  the  moon's  declination  changes  so  rapidly  that  the  exact 
time  of  observation  nmst  be  used  in  its  correction  when  working  with  this  body. 

22489—03—7 


98 


LATITUDE. 


Ex.\mplk:  In  latitude  47°  S.,  having  previou.-^ly  worked  up  the  constant  for  meridian  altitude; 
78°  42^  10'^  observed  altitude  of  sun  near  meridian,' 31°  11'  50'';.Dec  11°  X.;  watch  time,  11"  40™  21% 
watch  fast  of  L.  A.  T.,  7*.     Find  the  latitude. 


Watch  time,   11"  40°' 21^ 


AVatch  fast, 

• 

07 

L. 

A.  T., 

11 

40 

14 

t, 

19'' 

I.46S 

Obs.  alt.,     31°  11^50'' 
at\  +        10  24 


a  (Tab.  26),      1.'''6 


Mer.  alt.,     31    22   14 
ConsUnt,     78   42   10 


a<2(Tab.27), 


Lat., 


47    19  56  8. 


l.'''0=   6^30'^ 
.  6=   3  54 

1.  6  =  10  24 


Example:  At  sea,  July  12,  1879,  in  Lat.  50°  N.,  Long.  40°  W.,  observed  circum-meridian  altitude  of 
the  sun's  lower  limb,  61°  48'  30^',  the  time  bv  a  chronometer  regulated  to  Greenwich  mean  time  being 
2"  41'"  39^;  chro.  corr.,  -2""  30';  I.  C,  —3'  O'';  height  of  the  eye,  15  feet.     Find  the  latitude. 


Chro.t., 
C.C, 

2h  4i« 
-          2 

'39' 
30 

Q 

Corr. , 

h, 

S.  D., 

dip, 
p.  &  r. 
L  C, 

Corr., 
h 

61° 

'  48'  30" 
8   31 

Dec, 

H.D., 

Long., 

Corr., 
Dec, 

22°  00'  23". 2  N. 

Eq.t., 

H.  D., 

Long., 

Corr., 

Eq.  t, 
{Suhtrac 
time. ) 

[Tab.  26),      2. 
2. 

(Tab.  27),  r^- 

5'"  17^99 

20".  7 

2".  7 

+        0^32 

2".  7 

G.M.T., 

Eq.t., 

2    39 
—          5 

09 
19 

61 

57   01 

-T 

15'  46" 

55".  9 

~           .86 

G.A.T., 
Long., 

,       2    33 
-  2    40 

50 
00 

) 

3   48 
0   27 
3   00 

21°  59'  27"     X. 

a  1 
at' 

5"'  18».9 

L.A.T., 

11    53 

50 

t, 

6 

10 

- 

7   15 

61°  57' 
1 

8   31 

01" 
35 

"5 

"0  =  1' 16" 
5  =  0   19 

H,      61    58  36 


1   35 


28    01    24  N. 
21    59  27  N. 


L,       50    00  51  X. 

Example:  May  31,  1879,  in  Lat.  30°  25'  X.,  Lonsf.  5"  25"'  42'  W.,  about  9  p.  m.,  observed  with  a 
sextant  and  artificial  horizon  a  series  of  altitudes  of  Spica;  mean  observed  double  altitude  98°  06'  34"; 
noted  times  as  enumerated  below  bv  a  watch  compared  with  a  chronometer  which  was  2"'  33''  fast  of 
G.  M.  T.;  C-W,  5"  29""  40^  I.  C,  -3'  00".     Find  the  latitude. 

R.  A.  *  (L.  S.  T.transit) ,     13"  18'"  52^2  Mean  2  all 


Long., 

G.  S.  T., 

R.  A.  M.  S.  Gr.  0", 

Sid.  int.  from  0", 
Red.  (Tab.  8), 

G.  M.  T., 

C.  C.  (sign  reversed), 

Chro.  time  transit, 
C— W, 

Watch  time  transit. 


+  5  25  42 


Watch  times. 
8"  31'"  18^0 
33  19.5 
36  07.0 
38  50.0 
41  07.5 
43  45.5 
45  46.0 
47  33.0 
51  12.5 


18   44 
4   34 

34.2 
26.9 

14   10 
2 

07  .3           re 
19.4 

;, 

14   07 

_U             9 

>              1               -^ 

47  .9 
33 

14    10 
-  5   29 

20.9 
40 

8   40    41 
Intervals  from  transit. 

Meantime. 
—  9'"  23^0 


21  .5 
34.0 
51.0 


-r  0  26.5 
3  04.5 

5  05.0 

6  52.0 
31 .5 


10 


Sid.  time. 
-  9™  24' 
7  23 

4  35 
1  51 

-0  27 
3  05 

5  06 

6  53 
10  33 


98° 

06'  34" 
3   00 

R.  A.  *, 
Dec, 

a  (Tab.  26), 

13"  18'"  52^2 

10°  32'  04"  S. 

98 

03   34 

2".5 

49 

01   47 
50 

49 

00   57 

at^  (Tab.  27). 

£o  05^  2!5   ' 

2'  56"  0'  44"  3'  40" 

1  49  0  27  2  16 

0  42  0  10  0  52 

0  07  0  01  0  08 

0  01  0  00  0  01 

0  19  0  04  0  23 

0  52  0  13  1  05 

1  35  0  23  1  58 
3  42  0  55  4  37 


h,        49°  00'  57" 
«<*,+     1  40 


H, 


49  02  37 

40  57  23  N. 

10  32  04  S. 

30  25  19  N. 


9)15  00 


1  40 


LATITUDE. 


99 


Example:  August  6,  1S79,  Lat.  59°  S.,  Long.  175°  27^  E.,  during  evening  twilight,  observed  an 
altitude  of  Achernar,  near  lower  transit,  26°  52';  watch  time,  4"  31"'  12^;  C  — W,  0"  18"'  07^;  chro.  fast  of 
G.  M.  T.,  12"'  42^;  I.  C,  -f  V  20^';  height  of  eye,  24  ft.  Find  hour  angle  by  both  methods;  thence  the 
latitude. 


R.   A.    JJC    -t-   12                   1        1  Oh  oom  1  Ka  A 

L.  S.  T.  lower  trans./     ^'^  ^^^    ^^  '^ 
Long.,                           -  11  41    48 

Watch  time, 
C-W, 

Chro.  t., 
C.  C, 

G.  M.  T.  5^ 
R.A.M.S.  Gr.5''0S 
Red.  (Tab.  9), 

G.  S.  T., 
Long., 

L.  S.  T., 

R.  A.  *  +  12h, 

R.  A.  *,          1"  33°' 

4"  31" 
+     0  18 

'12^ 
07 

4  49 
—         12 

19 
42 

G.  S.  T.,                             1 
R.  A.M.  S.  Gr.5'»0^-     8 

51 
54 

27.4 
39.8 

16  36 

+     8  54 
+           2 

37 

39. 

43, 

Sid.  int.,                           16 
Red.  (Tab.  8),           - 

56 
2 

47.6 
46.6 

,8 

,7 

G.  M.  T.,                          16 

C.  C.  (sign reversed ),+ 

54 

12 

01.0 
42 

1  34 

+  11  41 

00. 

48 

.5 

Chro.  time,                        5 
C-W,                         -     0 

06 

18 

43 
07 

13  15 
13  33 

48. 
15. 

,5 
,4 

Watch  time  transit,          4 
Watch  time  obs.,             4 

48 
31 

36 
12 

17 
15^4 

27 

,  fMean  time, 
\Sid.  time, 

Obs.  alt:  *,     26° 

17 
17 

52' 

24 

27 

00" 

L  C,           + 

4' 
1 

20" 

48" 
55 

Dec,                 57° 

50' 

■  28"  S. 

dip,             — 
ref.,             - 

p,                       32= 

■  09'  32" 

a  (Tab.  26), 
at^  (Tab.  27), 

0".6 
3'  03" 

- 

6 

43 

Corr. ,           — 

y 

2.3" 

/(,                       26° 
at\               - 

46' 
3 

37" 
03 

H,                      26 
P,                       32 

43 
09 

34 
32 

L,                       58 

53 

06  S. 

BY  A  SINGLE  ALTITUDE  AT  A  GIVEN  TIME. 


339.  This  observation  should  be  limited  to  conditions  where  the  body  is  within  three  hours  of 
meridian  passage  and  where  it  is  not  more  than  45°  from  the  meridian  in  azimuth.  On  the  prime 
vertical  the  solution  by  this  method  is  inexact,  and  when  the  hour  angle  is  6''  it  is  impracticable. 

The  problem  is:  Given  the  hour  angle,  declination,  and  altitude,  to  find  the  latitude.  The  solution 
is  accomplished  by  letting  fall,  in  the  usual  astronomical  triangle,  a  perpendicular  from  the  body  to  the 
meridian,  and  considering  separately  the  distances  on  the  meridian,  from  the  pole  and  zenith,  respec- 
tively, to  the  point  of  intersection  of  the  perpendicular;  the  sum  or  difference  of  these  distances  is  the 
co-latitude. 

Following  the  usual  designation  of  terms  and  introducing  the  auxiliaries  <?>'  and  <p",  the  formulae  are 
as  follows: 

tan  ^'=tan  d  sec  t; 

cos  (p'  =  sin  h  sin  <p"  cosec  d; 

The  terms  9)'  and  ^"  will  have  different  directions  of  application  according  to  the  position  of  the 
body  relatively  to  the  observer.  From  a  knowledge  of  the  approximate  latitude,  the  method  of  com- 
bining them  will  usually  be  apparent;  it  is  better,  however,  to  have  a  definite  plan  for  so  doing,  and 
this  may  be  based  upon  the  following  rule: 

Mark  ^"  north  or  south,  according  to  the  name  of  the  declination;  mark  ^'  north  or  south,  accord- 
ing to  the  name  of  the  zenith  distance,  it  being  north  if  the  body  bears  south  and  east  or  south  and  west, 
and  south  if  the  body  bears  north  and  east  or  north  and  west.  Then  combine  95"  and  <p^  according  to 
their  names;  the  result  will  be  the  latitude,  except  in  the  case  of  bodies  near  lower  transit,  when 
180°  — <p"  must  be  substituted  for  ^'  to  obtain  the  latitude. 

It  may  readily  be  noted  that  if  we  substitute  <p'^  for  declination  and  cp'  for  zenith  distance,  the 
problem  takes  the  form  of  a  meridian  altitude;  indeed,  the  method  resolves  itself  into  the  finding  of 
the  zenith  distance  and  declination  of  that  point  on  the  meridian  at  which  the  latter  is  intersected  by  a 
perpendicular  let  fall  from  the  observed  body. 

The  time  should  be  noted  at  the  instant  of  observation,  from  which  is  found  the  local  time,  and 
thence  the  hour  angle  of  the  celestial  object. 


100 


LATITUDE. 


If  the  sun  i.s  observed,  the  hour  angle  is  the  L.  A.  T.  in  the  case  of  a  p.  m.  sight,  or  12''  —  L.  A.  T. 
for  an  a.  m.  sight.     If  any  other  body,  the  hour  angle  may  be  found  as  hitherto  explained. 

Example:  June  7, 1879,  in  Lat.  30°  25'  N.,  Long.  81°  25'  30"  W.,  by  account;  chro.  time,  6"  22'"  52»; 
obs.  Q  75°  13',  bearing  south  and  east;  I.  C.  —  3'  00";  height  of  the  eye,  25  feet;  chro.  corr.  —  2"'  36». 
Find  the  latitude. 


Chro.t, 
C.C, 

G.  M.  T. 

Eq.t., 

G.A.T., 
Long. , 


6"  22"'  §2* 
2    36 


6   20 

+           1 

16 
26 

6  21 
-     5   25 

42 
42 

Obs.  alt.  Q,    75°  13'  00" 
Corr.,         +         7  40 


S.D., 


L.A 


■T.=r,    { 


dip, 

p.  &  r. , 


0''56"00^E.     I.e., 
14°  00'  00" 


Corr., 


75 

20 

40 

+ 

15' 

48" 

— 

4'  54" 

14 
3   00 

- 

8 

08 

Dec, 

H.D..       + 
G.M.T.,  + 


22°  45' 09".9  N.     Eq.t.,  1"' 28».85 


14".6 
6".3 


H.  D.,      - 
G.M.T.,+ 


0\46 
6".  3 


91".98 
1'32" 


2^85 


Corr.,      {j; 

Dec,  22°  46' 42"     N.     (^"(^d  to  mean  time.) 


Corr.,      — 

Eq.t.,         l'"26'.  0 


+ 


7' 40" 


t 
d 

14° 
22 

75 
23 

7 

00' 00" 
46  42 

20  40 
24  07  N. 

02  30  N. 

sec 
tan 

tan 

.01310 
9.62317 

cosec 

sin 
sin 

cos 

.41210 

h 

9.63627 

9.98563 
9.59898 

<f^ 

9.99671 

Lat. 

30 

26  37  N. 

Example:  May  28,  1879,  p.  m.,  in  Lat.  6°  20'  S.  by  account.  Long.  30°  21'  30"  W.;  chro.  time, 
7''  35""  10";  observed  altitude  of  moon's  upper  limb,  75°  33'  00",  bearing  north  and  east;  I.  C,  —3'  00"; 
height  of  eye,  26  feet;  chro.  fast  of  G.  M.  T.,  1""  37^5.     Eequired  the  latitude. 


Chro.  t., 
C.C, 

G.  M.  T., 
R.  A.  M.  S., 
Red.  (Tab.  9), 

G.  S.  T., 
R.  A.  C. 

H.  A.  from  Gr. 
Long., 


7h 

35- 

'10> 

- 

1 

37.5 

7 

33 

32.5 

+  4 

22 

37.3 

+ 

1 

14.5 

11 

57 

24.3 

-10 

22 

17 

1 

35 

07 

2 

01 

26 

Obs.  alt.'C. 

S.  D., 
Aug., 
dip, 
I.  C, 


75°  33'  00" 

15'  51" 
0  16 
5  00 
3  00 

24  07 


R.  A.  C, 

M.  D., 
No.  mill., 

Corr., 
R.  A., 


lOh 

21" 

,.  07» 

.78 

+ 

28 

.06 
.54 

-{ 

1' 

69«.09 
"09' 

Dec, 

M.  D., 
No.  mill., 

Corr., 
Dec, 


6°49'52".4  N. 

14".46 
33"'.54 

486" 
05" 
6°  41'  47" 


-I      ' 

I   8' I 


N. 


W. 
\V. 

Oh  26ni  19*    E.. 
6°  34'  4.5" 


Approx.  alt.,  75°  08'  ,53" 

p.  (t-r.(Tab.24),    +       14  37 

h.  75   23  80 


Hor.  Par.,        58'  03" 


t 
d 

h 
^" 

9,' 

Lat. 


6°  34'  45" 
6    41    47 

75    23    30 
6    44   26  N. 

13    05   40  S. 

6    21    14  S. 


sec 
tan 


.00286 
9.06973 


tan     9.07259 


sin 
sin 


.93324 

9.98573 
9.06959 


cos        9.98856 


Example:  August  6,  1879,  p.  m.,  in  Lat.  52°  47'  S.  by  D.  R.,  Long.  146°  32'  E.,  observed  altitude  of 
Achernar,  near  lower  transit,  24°  01'  20"  bearing  south  and  west;  watch  time,  6''  48"'  22";  C— AV,  9"  46" 
27';  chro.  corr.  on  G.  M.  T.,  +  1'"  57%  height  of  eve,  18  feet;  I.  C.  +  1'  00".     Find  the  latitude. 


Watch  time, 

c-w. 

6"  48"' 
+    9   46 

'22' 
27 

Obs.  alt.  y^, 
Corr.,       — 

I.  c,      + 

dip,          - 
ref.,         — 

Corr.,       — 

24° 

01'  20" 
5   19 

R.A.  *,    1"  33-"  15'.  3 
•Dec,       57°  50'  28"  S. 

Chro.  t., 
C.C, 

4 

+ 

34 
1 

49 
57 

23 

56  01 

— 

I'OO" 

4'  09" 
2   10 

G.  M.  T.,  5^ 
R.  A.  M.  S., 
Red.  (Tab.  9), 

16 

+    8 

36 

54 

2 

46 

39.8 

43.7 

G.  S.  T., 
R.  A.  *, 

1 
1 

34 
33 

09.5 
15.3 

6   19 

5' 19" 

H.  A.  from  Gr. 
Long., 

,,       0 
9 

00 
46 

54  W. 

.  08  E. 

H.  A., 

9 

47 

02  W. 

t, 

f    2" 
I  83° 

12"'  58' 
' 14'  30" 

t 
d 

33° 
57 

23 
-<f/'   117 

64 

14'  30^' 
50  28 

56  01 

44  18  S. 

54  15  N. 

LATITUDE. 

sec  .07760 
tan  .20153 

coeec 

sin 
sin 

cos 

. 07233 

h 
180°- 

tan  .27913 

9. 60818 
9.  94699 

'P' 

9. 62750 

Lat. 

52 

50  03  S. 

101 


BY  THE  POLE  STAR. 

340.  This  method,  confined  to  northern  latitudes,  is  available  when  the  star  Polaris  and  the  hori- 
zon are  distinctly  visible,  the  time  of  the  observation  being  noted  at  the  moment  the  altitude  is  measured. 

Two  methods  will  be  given.  The  first  is  sufficiently  precise  for  nautical  purposes,  involving  the 
computation  of  the  formula: 

L  =^h  —  p  cos  t, 
in  which, 

h  =  true  altitude,  deduced  from  the  observed  altitude; 

p  =  polar  distance  =  90°  —  d,  the  apparent  declination  being  taken  from  the  Nautical  Almanac 

for  the  date;  " 

t  =  star's  hour  angle. 

Find  the  right  ascension  and  declination  of  Polaris  from  the  Nautical  Almanac;  then  find  the  hour 
angle  in  the  usual  way. 

To  the  log  cosine  of  the  hour  angle  add  the  logarithm  of  the  polar  distance  in  minutes;  the  number 
corresponding  to  the  resulting  logarithm  will  be  a  correction  in  minutes  to  be  subtracted  from  the  star's 
true  altitude  to  find  the  latitude. 

Attention  must  be  paid  to  the  sign  of  the  correction  p  cos  t.  If  t  is  more  than  6*'  and  less  than  18'', 
the  sign  of  cos  /  is  — ;  hence  the  formula  becomes  arithmetically: 

L  =  /(  +  p  cos  t. 

Example:  June  11,  1879,  from  an  observed  altitude  of  Polaris  the  true  altitude  was  found  to  be 
29°  5' 55''.  The  time  noted  by  a  Greenwich  chronometer  was  13'' 41'"  26^^;  chro.  corr.  —  2"' 22';  Long. 
5h25.n42»  W. 

h,                    29°  05'  55"                   R.  A.  *,                  1"  14"'  04» 
p  cos  t,        +  1    19  54  

Dec,  88°  39'  47"  N. 


Chro.  time, 
C.  C, 

13"  41"  26' 
-     2  22 

G;  M.  T.,  ll^ 
R.A.M.S., 
Red.  (Tab.  9) , 

13 

+  5 

+ 

39  04 

17  49 

2  15 

G.S.T., 
R.  A.  *, 

18 
-  1 

69  08 
14  04 

H.  A.  from  Gr. 
Long., 

,   17 
5 

45  04  W. 
25  42  W. 

H.  A., 
t. 

^2  19  22  W. 

r  11"  40'"  38'  E. 
\175°09'  30" 

Lat.,  30    25  49    N. 


°  20'  13" 


^'  I  80'.  2 

p,  80'.  2  log  1. 90417 

t,  175°  m'  30"  cos  ( -)  9. 99845 

pcosr,      ^1019/54// 


341.  The  second  method  is  more  rigorous,  and  should  be  employed  when  greater  accuracy  is 
sought.     It  is  embodied  in  Table  28. 

Reduce  the  observed  altitude  of  the  star  to  the  true  altitude.  Find  from  the  Nautical  Almanac  the 
apparent  right  ascension  and  declination  of  the  star  at  the  time  of  observation.  Find  the  hour  angle  in 
the  usual  manner. 

With  the  hour  angle  take  out  the  first  correction,  A,  from  Table  28,  giving  to  it  the  sign  — when  the 
hour  angle  is  numerically  less  than  6";  the  sign  +  when  the  hour  angle  is  greater  than  6". 

With  the  hour  angle  and  altitude  take  out  the  second  correction,  B,  from  Table  28.  The  sign  of  this 
correction  is  always  -j-.  (If  the  altitude  is  greater  than  60°,  this  correction  may  be  found  by  taking 
that  for  45°  and  multiplying  it  by  the  tangent  of  the  altitude;  adding,  if  desirable,  the  second  term  in 
the  expression  for  B,  viz:  +  0".0076  sin*  t  tan'  /(. ) 

With  B  and  the  declination  take  out  the  third  correction,  C,  from  Table  28,  giving  it  the  sign  f 
when  the  declination  is  less  than  88°  48';  —  when  the  declination  is  greater  than  88°  48'. 

With  A  and  the  declination  take  out  the  fourth  correction,  D,  from  Table  28,  giving  it  the  same  sign 
as  that  of  A  when  the  declination  is  less  than  88°  48';  the  opposite  sign  when  the  declination  is  greater 
than  88°  48'. 

Combine  these  corrections  with  the  true  altitude  according  to  their  signs;  the  result  is  the  latitude 
of  the  place  of  observation. 

If,  when  several  sights  are  taken,  great  precision  is  required,  or  the  intervals  are  great,  it  will  be 
necessary  to  take  out  the  first  and  second  (corrections  for  each  observation  separately;  in  other  cases  the 


102  LATITUDE. 

mean  of  the  times  may  be  used.  The  means  of  these  two  corrections  may  always  he  used  for  finding 
the  third  and  fourth  corrections;  and  these  four  quantities  may  be  combined  with  the  mean  of  the 
altitudes. 

If  the  nearest  W^  suffices  for  each,  the  corrections  may  be  taken  out  for  the  nearest  arguments 
without  interpolation,  and  all  but  the  first  may  thus  be  taken  out  when  a  precision  of  ^''is  required.  If 
a  precision  of  V  is  sufljcient  for  each  correction,  as  is  ordinarily  the  case  at  sea,  an  hour  angle  within 
3™  will  suffice  for  A;  C  and  D  may  be  neglected,  and  B  used  only  when  the  altitude  exceeds  47°. 

Example:  January  1,  1903,  about  9  p.  m..  Longitude  79°  54''  07'^  W.,  observed  doul)le  altitude 
of  Polaris  with  artificial  horizon,  81°  57^  20^'';  chro.  time  1''  55"  12^  chro.  corr.  on  G.  M.  T.  + 1'"  07'; 
I.  C. —O'SO".  (The  necessary  quantities,  taken  from  the  Nautical  Almanac  for  1903,  are  given 
below.)     Required  the  latitude. 

Chro.  time,  li^  55™  12'  Obs.  2  alt.  *,         81°  57'  20"  R.  A.  *,    1"  24"' 33».3 

C.  C,  +  1    07 

Dec,        88°  47'  42'' N. 


G.  M.  T.,  13    56    19 

R.  A.  M.  S.,     +18    39    50.9 
Red.  (Tab.  9),  +  2    17.4 


G.  S.  T., 
R.  A.  *, 

8 
1 

38 
24 

27.3 
33.3 

H.  A.  froniGr., 
Long., 

7 
5 

13 
19 

54  W. 
37  W. 

H.  A.,  1     54     17  W. 


Obs.  2  alt. 

*, 

81° 

57' 

20" 

LC, 

— 

0 

50 

2)81 

56 

30 

40 

58 

15 

ref., 

— 

1 

07 

h, 

40 

57 

08 

A, 

—   1 

03 

13.9 

B, 

+ 

08.9 

0, 

00.0 

D, 

— 

15.7 

Lat, 

39 

53 

47  N. 

LONGITUDE.  103 


CHAPTER  XIII. 
LONGITUDE. 


342.  The  longitude  of  a  position  on  the  earth's  surface  is  measured  by  the  arc  of  the  equator 
intercepted  between  the  j^rime  meridian  and  the  meridian  passing  through  the  place,  or  by  the  angle 
at  the  pole  between  those  two  meridians. 

Meridians  are  great  circles  of  the  terrestrial  sphere  passing  through  the  poles. 

The  prhne  meridian  is  that  one  assumed  as  the  origin,  passing  through  the  location  of  some  principal 
observatory,  such  as  Greenwich,  Paris,  or  Washington.  That  of  Greenwich  is  the  prime  meridian  not 
only  for  English  but  also  for  American  navigators,  and  those  of  many  other  nations. 

Secondari/  meridians  are  those  connected  with  the  primary  meridian,  directly  or  indirectly,  by 
exchange  of  telegraphic  time  signals. 

Tertiary  meridians  are  those  connected  with  secondaries  by  carrying  time  in  the  most  careful  manner 
with  all  possible  corrections. 

Longitude  is  found  by  taking  the  ■difference  between  the  hour  angle  of  a  celestial  body  from  the 
prime  meridian  and  its  hour  angle,  at  the  same  instant,  from  the  local  meridian.  In  determinations 
ashore  the  hour  angle  from  the  prime  meridian  may  be  found  either  from  chronometers  or  from 
telegraphic  signals;  the  local  hour  angle  may  ])e  found  by  transit  instruments  or  by  sextant.  In 
determinations  at  sea  the  chronometer  and  sextant  give  the  only  means  available. 

DETERMINATION  ASHORE. 

343.  Telegraphic  Determination  of  Secondary  Meridians. — In  order  to  locate  with  accuracy 
the  positions  of  prominent  points  on  the  coasts,  it  is  necessary  to  refer  them,  by  chronometric  measure- 
ments, to  secondary  meridians  of  longitude  which  have  been  determined  with  the  utmost  degree  of  care. 

Before  the  establishment  of  telegraphic  cables,  this  was  attempted  principally  through  the  observa- 
tion of  moon  culminations,  which  seemed  always  to  carry  with  them  unavoidable  errors,  or  by  trans- 
porting to  and  fro  a  large  number  of  chronometers  between  the  principal  observatory  and  the  position 
to  be  located;  and  in  this  method  it  can  be  conceived  that  errors  would  be  involved,  no  matter  how 
thorough  the  theoretical  compensation  for  error  of  the  instruments. 

By  the  aid  of  the  electric  telegraph,  differences  of  longitude  are  determined  with  great  accuracy, 
and  an  ever-increasing  number  of  secondary  meridional  positions  are  thus  established  over  the  world; 
these  afford  the  necessary  bases  in  carrying  on  the  surveys  to  map  correctly  the  various  coast  lines,  and 
render  possible  the  publication  of  reliable  and  accurate  navigators'  charts. 

344.  To  determine  telegraphically  the  difference  of  longitude  between  two  points,  a  small  observa- 
tory containing  a  transit  instrument,  chronograph,  break-circuit  sidereal  chronometer,  and  a  set  of 
telegraph  instruments  is  established  at  each  of  the  two  points,  and,  being  connected  by  a  temporary 
wire  with  the  cable  or  land  line  at  each  place,  the  two  observatories  are  placed  in  telegraphic  com- 
munication with  each  other. 

By  means  of  transit  observations  of  stars,  the  error  of  the  chronometer  at  each  place  on  its  own  local 
sidereal  time  is  well  determined,  and  the  chronometers  are  then  accurately  compared  by  signals  sent 
first  one  way  and  then  the  other,  the  times  of  sending  and  receiving  being  very  exactly  noted  at  the 
respective  stations.  The  error  of  each  chronometer  on  local  sidereal  time  being  applied  to  its  reading, 
the  difference  between  the  local  times  of  the  two  places  may  be  found,  and  consequently  the  difference 
of  longitude.  The  time  of  transmission  over  the  telegraph  line  is  eliminated  by  sending  signals  both 
ways.  By  the  employment  of  chronometers  keeping  sidereal  time,  the  computation  is  simplified, 
though  mean-time  chronometers  may  be  used. 

345.  Establishment  of  Tertiary  Meridians. — Let  it  be  supposed  that  the  meridional  distance 
between  A  and  B  is  to  be  measured,  of  which  A  is  a  secondary  meridional  position  accurately  deter- 
mined, and  B  a  tertiary  meridional  position  to  be  determined. 

If  possible,  two  sets  of  observations  should  be  taken  at  A  to  ascertain  the  e'  irs  and  rates  of  the  chro- 
nometers. The  run  is  then  made  to  B,  and  observations  made  to  determine  i  time,  and  hence  the 
difference  of  longitude;  and  on  the  same  spot  altitudes  of  the  sun,  or  of  a  nu  ^r  of  pairs  of  stars,  or 
both,  should  be  taken  to  determine  the  latitude.  ~ 

Now,  if  chronometer  rates  could  be  relied  on  to  })e  uniform,  this  measurement  would  suffice,  but 
since  variations  may  always  arise,  the  run  Ijack  to  A  should  be  made,  or  to  another  secondary  meridio- 
nal position,  C,  and  new  rates  there  obtained.  Finally,  the  errors  of  the  chronometers  on  the  day  when 
the  observations  were  made  at  the  tertiary  position  should  be  corrected  for  the  loss  or  gain  in  rate,  and 
for  the  difference  of  the  errors  as  thus  determined. 

When  opportunity  does  not  permit  obtaining  a  rate  at  the  secondary  meridional  station  or  stations, 
both  before  and  after  the  observations  at  B,  the  navigator  may  obtain  the  errors  only,  and  assume  that 
the  rate  has  been  uniform  between  those  errors. 

A  modification  of  the  foregoing  method  that  may  sometimes  prove  convenient  is  to  make  the  first  and 
third  sets  of  observations  at  the  position  of  the  tertiary  meridian,  and  the  intermediate  one  at  the  second- 
ary meridian;  in  this  case  the  error  will  be  obtained  at  the  secondary  station,  and  the  rate  at  the  tertiary. 


104 


LONGITUDE. 


Example:  A  vessel  at  a  station  A,  of  known  longitude,  obtained  chronometer  eirors  as  follows: 

May  27,  noon,  ehro.  slow,  7'»  18^9, 
June  3,  noon,  chro.  slovv,  7    12  .7; 

then  proceeding  to  a  station  B  a  series  of  observations  for  longitude  was  taken  on  June  17:  after  which 
returning  to  A,  the  following  errors  were  obtained:  ' 

July    3,  noon,  chro.  slow,  7""  00\7, 
July  10,  noon,  chro.  slow,  6    59  .8. 
Required  the  correct  error  on  June  17. 

May  27,       -7»  18^9  July  3,         -7"' 00«.7 

June  3,         —7    12.7  July  10,       —6    59,8 


Change,   +        6.2  Change,  +        0  .9 


Daily  rate,  +        0'.89  Daily  rate,  +        0M3 

Therefore,  assuming  that  these  rates  were  correct  at  the  middle  of  the  periods  for  which  thev  were 
determmed,  we  have,  j        -^ 

May  30,  Midnight,  Rate,     +0\89 
July   6,  Midnight,  Rate,     -f  0  .13 


Change  of  rate,  37  days,  —0  .76 

Daily  change  of  rate,  — 0*.021 

Change  of  rate  for    3J  days,  — 0^07;  rate  June    3,  noon,  +0^89— 0\07=+0*  82 
Change  of  rate  for  17|  days,  —0^37;  rate  June  17,  noon,  +0  .89—0  .37=+0 .52 

Mean  daily  rate,  June  3  to  17,     '  -fO  .67 


Total  change  of  error,  June  3  to  17,  -f  0"'  09".38 

Error,  June  3,  _7    12.7 


Error,  June  17,  —7    03  .3 

346.  Single  Altitudes.— The  determination  of  longitudes  ashore  by  single  altitudes  of  a  celestial 
body  IS  identical  in  principle  with  the  determination  at  sea  by  that  method,  which  will  be  explained 
hereafter  (art.  349).     It  may  be  remarked,  however,  that  by 'taking  observations  on  opposite  sides  of 
the  meridian,  at  altitudes  as  nearly  equal  as  possible,  a  means  is  afforded,  which  is  not  available  at  sea 
of  eliminating  certain  constant  errors  of  observation.  ' 

34T.  Equal  Altitudes.— The  method  of  equal  altitudes,  explained  in  article  321,  Chapter  XI  is 
available  for  the  determination  of  longitudes  as  well  as  for  chronometer  error.  In  the  case  of  the  sun 
the  sight  ^ives  the  chronometer  time  of  L.  A.  noon  or  midnight;  applying  the  chronometer  correction 
and  equation  of  time  (the  latter  with  its  sign  for  mean  time),  we  obtain  the  G.  A.  T.,  which  equals  the 
longitude,  if  west,  or  24"  minus  the  longitude,  if  east.  For  any  other  body,  the  sight  gives  the  chro- 
nometer time  of  transit;  apply  the  chronometer  correctfon  and  there  results  G.  M.  T.,  which  may  be 
reduced  to  G.  S.  T.;  the  difference  between  the  latter  and  the  R.  A.  of  the  bodv  (this  being  L  8  T^ 
is  the  longitude.  j  \  ^     ■    •  '■•), 

Example:  April  20  p.  m.  and  April  21  a.  m.,  1879,  in  Lat.  30°  25'  N.,  Long,  (approx.)  81°  26'  \V 
chro.  corr.  ~3"'  U'A,  observed  times  and  equal  altitudes  of  the  sun  as  stated  below;  C  — W  for  p  m' 
sights,  5"  31™  58".5,  and  for  a.  m.  sights,  S"  32™  01'.     Required  the  longitude. 

Dec,  11°  29'  17".l  N.       H.  D.  (20th),     +5I".45 

H.  D.  (21st),     ,+50  .97 


WATCH, 

,  P.  M. 

ALTS. 

2>'51» 

>40» 

90°    0' 

52 

a5 

89    60 

52 

30 

40 

52 

55 

30 

53 

20 

20 

Mean,  W.  T.,  P.  M.,     2h  Si-" 

'30«.0 

Mean,  W.  T. 

C-W,-    ■                +5   31 

58  .5 

C  -  W, 

P.  M.  Chro.  T.,            8   24 

r 

A.M.  Chro.: 

V'ATCH 

,  A. 

M. 

8h  59" 

'00' 

58 

34 

.5 

58 

09 

.5 

57 

40 

.0 

57 

20 

.0 

H.D.atMid.,+  .51".10 

Long.  H-12h,  17'>.43  DiflF.  24^,  -0.48 


A.  M.  Chro.,  T. +12'',  26   30    1 


2)10   54    39  .5      Klapsed  Time, 


M.,     8h  58" 
+  5    32 

'10" 
01 

L21',   26 
8 

30 
24 

11  .0 

28  .5 

18 

05 

42  ,5 

1" 

04 '.9 

+ 

0'.54 
17''.43 

+ 

9».4 

Dec,  11°  44'  08"   N. 


f     890".7  Diflf.  Ih,  _  0".02 

114'  .51"  — — 

DiflF.  I'^AS,        -  0".a5 
H.  D.  at  Mid.,  +.51".10 


Mid.  Chro.  T.,  5   27    19  .75 

Eq.  eq.  alt.,  +  19.35    Eq.  t..  1"04».9      Tab.  37  log  A   (  +  )9.9364  logB(-)9.7912 

H.D.+51".101og        (+)1.7084  log    (  +  )1.7084 


Chro.t.L.A.Mid.,     6   27    39.1      H.  D.,  +  0'.54    Lat.    30°  25' ten       (  +  )9.7687    ri+ll°44'tan    (  +  )9.3175 

Eq.  t.,  +        1    14  .3      Long.  + 12!>, 


1st  Part  4-25'.911og(  +  )1.4135 


Chro. t.,L.M. Mid.,    6   28    53.4      Corr.,  +  9».4      2d  Part  -  6  .56  log    (-)0.8171 

C.  C. ,  -        3    11  .4  

Eq.t,  lml4.».3      *^%^^- }+19  .35 

Lop„    -yy  f  Sh  25"  42 '.0  {Plus  to  mean  time.) 

"  l81°25'  30" 


LONGITUDE. 


105 


348.  In  the  same  example  the  equation  of  equal  altitudes  may  be  found  by  the  less  exact  method 
heretofore  given  (art.  324),  as  follows: 

Change  in  declination  between  sights  =  H.  D.  X  Elapsed  time  =  51'''.10  X  IS*".!  =  925^''. 
Change  in  altitude  due  to  100'^  declination  (Tab.  25)  =  +  53^^ 


h'  =  + 

V  =  + 


53  X925, 
100  X  60 
2''53'"20«- 


=  +  8M9. 

2"  51"' 40^  ^  ^  100'  , 
90°  00^  -  -  89°  20^  '    40'' 

Eq.  eq.  alt.  =  +  8.19  X  2'.5  =  i  20'.5. 


:  +  2'.5. 


DETERMINATION  AT  SEA. 

349.  The  Time  Sight. — The  method  of  determining  longitude  at  sea  which  is  employed  almost  to 
the  exclusion  of  all  others  is  that  of  the  lime  sight,  sometimes  called  the  chronometer  method.  The  altitude 
of  the  body  above  the  sea  horizon  is  measured  with  a  sextant  and  the  chronometer  time  noted;  the 
hour  angle  of  the  body  is  then  found  by  the  process  described  in  article  316,  Chapter  XI. 

If  the  sun  is  observed,  the  hour  angle  is  equal  to  the  local  apparent  time;  the  Greenwich  apparent 
time  may  be  determined  by  applying  the  equation  of  time  to  the  Greenwich  mean  time  as  shown  by  the 
chronometer;  the  longitude  is  then  equal  to  the  difference  between  the  local  and  the  Greenwich  appar- 
ent times,  being  east  when  the  local  time  is  the  later,  and  west  when  it  is  the  earlier  of  the  two. 

If  any  other  celestial  body  is  employed,  the  hour  angle  from  the  local  meridian,  found  from  the 
sight,  is  compared  with  the  hour  angle  from  the  Greenwich  meridian  to  obtain  the  longitude;  the 
Greenwich  hour  angle  is  found  by  converting  the  Greenwich  mean  time  into  Greenwich  sidereal  time 
in  the  usual  manner,  and  then  taking  the  difference  between  the  latter  and  the  right  ascension  of  the 
body,  the  remainder  being  marked  east  or  west,  according  as  the  (xreenwich  sidereal  time  is  the  lesser 
or  greater  of  the  two  quantities;  and  as  the  local  hour  angle  may  be  marked  east  or  west  according  to 
the  side  of  the  meridian  upon  which  it  was  observed,  the  name  of  the  longitude  will  be  indicated  in 
combining  the  (juantities. 

350.  As  has  been  stated,  the  most  favorable  position  of  the  celestial  body  for  tinding  the  hour 
angle  from  its  altitude  is  when  nearest  the  prime  vertical,  provided  the  altitude  is  not  so  small  as  to  be 
seriously  affected  by  refraction. 

351.  In  determining  the  longitude  at  sea  by  this  method,  it  is  necessary  to  employ  the  latitude 
by  account.  This  is  seldom  exactly  correct,  and  a  chance  of  error  is  therefore  introduced  in  the  result- 
ing hour  angle;  the  magnitude  of  such  an  error  depends  upon  the  position  of  the  body  relatively  to  the 
observer.  The  employment  of  the  Sumner  line,  which  is  to  be  explained  in  a  later  chapter,  insures  the 
navigator  against  being  misled  from  this  cause,  and  its  importance  is  to  be  estimated  accordingly. 

Example:  At  sea,  May  18,  1879,  a.  m.;  Lat.  41°  33'  N.;  Long.  33°  30'  W.,  by  D.  K.,  the  following 
altitudes  of  the  sun's  lower  limb  were  observed,  and  times  noted  by  a  watch  compared  with  the  Green- 
wich chronometer.  Chro.  corr.,  -f  4'"  59''.2;  I.  C,  —  30^';  height  of  the  eye,  23  feet;  C-  W,  2"  17'"  06". 
Required  the  true  longitude. 

Eq.  t.,  3"'  47 -.68 


VV.  T., 

7" 

20^15' 

20  47 

21  14 

-h 

A. 
A. 

Obs.  alt.  0 

Mean, 

Corp., 

h, 

.S.  D., 

dip, 
p.  A  r., 

I.e., 

Corr., 

29° 

41 

70 

,     29°  35' 
41 
46 

30" 

20 

10 

Dec, 

H.  D 
G.  M. 

Corr., 

Dec, 

P, 

19°  32' 

01".S    X. 

+ 
T.,  - 

33".09 
2h.3 

Mean, 
C-W, 

7 
+    2 

20 
17 

4.5.3 
06 

29 

+ 

41 

9 

00 
05 

19°  30' 

76".  1 
16" 

46"       N. 

Ohro.  t., 
C.  C, 

9 

+ 

37 
4 

51.3 
59.2 

29 

50 

05 

+ 
+ 

50' 
33 
29 

1.5' 

51" 

G.  M.  T., 

Eq.  t., 

17'>,     21 

+ 

42 
3 

50.5 
47.9 

70°  29' 

sec 
cosec 

cos 
sin 

sin  i  t 

14" 

4' 
1 
0 

42" 
34 
30 

G.  A.  T., 

21 

46 

38.4 

h 
L 
P 

8 
S- 

G. 
L. 

6 

46 

9' 

05'' 
00 
14 

05" 

.12588 
.02569 

2)141 

70 
41 

52 

56 

06 

19 

09 
04 

9.51406 

9.81782 

T.         21^ 
T.         19 

46™ 
32 

38' 
07 

2)19.48345 
9.74172 

H.  D.,      -  0«.09 

G.  M.T.,  -  2';.3 


Corr.,       +       0".21 
Eq.  t.,  3">47».9 

{Plun  to  mean  time.) 


Long.      {32: 14;  ^i;}w. 


106  LONGITUDE. 

Example:  At  sea,  April  16,  1879,  p.  m.,  in  T.at.  11°  47'  S.,  Long.  0°  20'  E.,  by  D.  R.,  observed  au 
altitude  of  the  star  Aldebaran,  west  of  the  meridian,  23°  13'  20";  chronometer  time,  e*"  56'"  32";  chro- 
nometer fast  of  G.  M.  T.,  2"'  27";  I.  C.  —2'  00";  height  of  eye,  26  feet.     What  was  the  longitude? 

Chro.  t.,  6"  56'"  32" 

C.  C,  -        2    27 

« 


G.  M.  T.,  6    54    05 

R.  A.  M.  S.,    +1     37    01.9 
Red.  (Tab.  9),+        1    08.0 


G.  S.  T.,  8    32     14.9 

R.  A.  *,  4    28    59. 6 


Obs.alt.*, 

23°  13'  20" 

R.  A.  5+:,  4"  28°'  59^6 

Corr., 

-          9  16 

Dec,        16°  15'  59"  IS 

'', 

23    04  04 

p,           106°  15'  59" 

I.e., 

-          2'  00" 

dip. 

-          5  00 

ref., 

-          2   16 

H.A.fromGr.,   4    03     15    W. 


Corr.,  -  9   16 


/(  23°  04'  04" 

L  11    47  00  sec  .00925 

p  106    15  59  cosec       .01774 


2)141    07  03 


s  70    33  32  cos        9.52223 

s—h  Al    29  28  sin         9.86757 


2)19.41679 


Gr.H.A.  4''  03'"  15^  W. 

H.  A.        4    05    50  W.         sin  \  t    9.  70839 


rO"  02™  35n, 
.ong.      Iqo  38,  45,/|i 


Example:  At  sea,  April  17,  1879,  a.  m.,  in  Lat.  25°  12'  S.,  Long.  31°  32'  W.,  by  D.  R.,  observed  an 
altitude  of  the  planet  Jupiter,  east  of  the  meridian,  45°  40';  watch  time,  5*'  48""  02';  C  — W,  2"  05""  42'; 
C.  C,  +2'»  18^;  I.  C,  +1'  30";  height  of  eye,  18  feet.     Required  the  longitude. 

W.  T.,  5h  48°>  02-  Obs.  alt.  *, 

C— \V,  2   05    42  Corr., 


Chro.  t.,  7   53    44  /(, 

C.C,  +         2    18 


G.M.T.,16«,  19    56    02 

R.  A. M.S., OS    +1     37    01.9 
Red.  (Tab.  9),    +         3    16.5 


I.e., 

dip, 
ref., 


45° 

40' 
3 

00" 
36 

45 

36 

24 

+ 

1' 

30" 

- 

4' 
0 

09" 

57 

_ 

5 

06 

R.  A.  (17' 

10''), 

221' 27° 

>19».0 

Dec.  (mOk), 

H.D., 
G.M.T., 

Corr.. 

Dec, 

P, 

,    10°  36' 28".l  S. 

H.D., 
G.M.T., 

Corr.. 

+ 

1».8 
4t'.l 

7'. 4 

+ 

10".0 
4«'.l 

41". 

R.A., 

22h  27" 

'  11^6 

10°  37' 

■  09"     S. 

79°  22' 

51" 

G.S.T., 

21  36    20.4 

22  27    11.6 

Corr., 

h 
L 

P 

8 
8— 

Gr 
H. 

h 

.H 
A. 

-          3'  36" 

45°  36'  24" 
25    12  00 
79    22  51 

sec 
cosec 

cos 
sin 

sin  J  / 

H.A.fromGr., 

0    50    51 E. 

.  04343 
.00750 

2)150    11    15 

75    05  38 
29    29   14 

9.41032 
9.  69217 

\ 

.  A.  0"  50'"51'E. 
2    57  21  E. 

2)19.15342 
■      9. 57671 

T^.,„       /  2"06'"30nT^ 
Long.      |3io37,3o//|W. 


LONGITUDE.  107 

Exami'lk:  At  sea,  June  26,  1879,  p.  m.,  in  Lat.  49°  50' N.,  Long.  6°  16' W.,  by  account,  observed  an 
altitude  of  the  moon's  lower  limb  21°  18'  10",  the  body  bearing  east;  chronometer  time,  2"  26'"  58»; 
chronometer  slow  of  G.  M.  T.,  42*;  I.  C.,  — 1'  45";  height  "of  eye,  22  feet.     Find  the  longitude. 

Chro.  t,  2"  26-58  • 

C.  C,  +  42 


G. 

M 

.  T., 

2 

27 

40 

R. 

A. 

M.  S., 

+  6 

16 

57.5 

E< 

S. 

(Tab.  9), 
T., 

+ 

0 

24.3 

G. 

8 

45 

01.8 

R. 

A. 

^C- 

11 

38 

39.3 

H.  A.  from  Gr.,      2   53    37-    E. 


Ote.  alt, 

•i. 

,  alt 
rab. 

2)" 

1 

21°  18'  10" 

R.  A., 

M.  D.,        + 

No.  min., 

Corr.,        + 
R.  A., 

Hor.  par., 

sec 
cosec 

cos 
sin 

sin  i  t 

llh  37'°  41'.96 

Dec, 

M.  D., 

No.  min., 

Corr., 

Dec. , 
P. 

2°  35'  36".4  S. 

S.  D., 
Aug., 

+        15'  59" 
+               6 

2».07 
27'". 7 

15".  1 
27°'.  7 

+        16  05 

57'.34 

_f          419".3 
I      6'    59".3 

2°  42' 36"     S. 

dip, 

I.e., 

-  4'  36" 

-  1   45 

llh  38-"  39^.3 

58' 35" 

.19043 
.00049 

9.11923 
9.93799 

-         6  21 

92°  42'  36" 

1st  corr. 

+         9'  44" 

Approx, 

p.&r.  (1 

21°  27'  54" 
24),  +        52  06 

h 
L 

P 

22    20  00 

22°  20'  00" 
49    50  00 
92    42  36 

8 

s—h 

164    52  36 

82    26   18 
60    06   18 

Gr.  H.  . 
H.  A. 

2"  53™  37'  E. 
3  19    04    E. 

2)19.24814 
9.62407 

Long. 

0"  25-  27'-!^ 
6°  21' 45"/"^- 

352.  Equal  Altitudes. — The  method  of  finding  the  longitude  at  sea  by  observation  of  equal  alti- 
tude.'! of  a  heavenly  body  is  one  that  may  be  conveniently  employed  when  applicable,  though  the  limits 
of  apj)licability  are  narrow. 

If,  on  board  a  vessel  which  is  either  stationary  in  position  or  moving  at  a  uniform  rate  of  speed  in  a 
true  east  or  west  direction,  equal  altitudes  of  the  sun,  a  planet,  or  a  star  be  observed  before  and  after 
transit,  and  the  times  noted  by  chronometer  or  watch,  the  interval  from  meridian  being  not  greater  than 
ten  minutes  of  time  and  the  altitude  not  less  than  75°,  the  mean  of  the  times  will  be  the  time  (by  the 
chronometer  or  watch  used)  of  the  meridian  passage  of  the  body;  from  this  may  be  found  the  Green- 
wich mean  time  of  transit  and  thence  the  longitude. 

If  (the  limits  of  time  and  altitude  remaining  as  stated)  observations  be  taken  when  the  body  bears 
not  less  than  80°  from  the  meridian,  the  time  of  meridian  passage  may  with  accurracy  be  regarded  as 
equal  to  the  mean  of  the  times  of  observation,  no  matter  what  course  may  have  been  steered  by  tb< 
vessel  in  the  interval. 

But  if  the  azimuth  of  the  body  is  less  than  80°  from  the  north  or  south  point  of  the  horizon  the 
method  is  not  available  for  vessels  making  a  material  amount  of  northing  or  southing;  and  if  the  hour 
angle  is  greater  than  10™  or  the  altitude  less  than  75°,  it  can  not  be  accurately  employed  by  any  vessel, 
no  matter  what  course  is  steered.  The  navigator  .«hould  not  yield  to  the  temptation  offered  by  the 
simplicity  of  this  method  to  follow  it  beyond  the  limits  within  which  it  may  properly  be  considered 
to  apply. 

353.  To  deduce  the  longitude  by  this  method  take  the  mean  of  the  watch  times  before  and  after 
transit,  which  will  give  the  watch  time  of  transit;  correct  this  watch  time  in  the  usual  manner  for 
C— W  and  chronometer  correction,  from  which  is  derived  the  Greenwich  mean  time  of  transit. 

In  the  case  of  the  sun,  apply  to  the  Greenwich  mean  time  the  equation  of  time,  giving  it  its  sign  of 
application  to  mean  time;  the  result  is  the  Greenwich  apparent  time  of  transit,  which  is  equal  to  the 
longitude  if  the  latter  is  west,  or  to  24''  mhiii.^  the  longitude  if  east. 

For  other  bodies,  convert  Greenwich  mean  time  into  Greenwich  sidereal  time  by  the  usual  method; 
the  body  being  on  the  meridian,  the  local  sidereal  time  is  equal  to  the  body's  right  ascension;  the 
difference  between  Greenwich  and  local  sidereal  times  is  the  longitude — east  if  the  local  time  is  greater, 
and  west  if  it  is  less. 


108  LONGITUDE. 

Example:  April  2,  1879,  in  Lat.  3°  30'  X.,  Long.  86°  00'  E.,  by  D.  R.,  observed  equal  altitudes  of 
Q  before  and  afternoon,  using  same  sextant  and  same  height  of  eve.  Watch:  a.  m..  11'' 52°' 37";  p.m., 
12"  07""  22";  C  -  W,  6"  17"  48';  C.  C,  +  2™  32'.  Vessel  steering  west' between  sights.  Required  the  longi- 
tude at  noon. 

W.  T.,  A.  M.,  11"  52-"  37»  Eq.  t.,  3"'  42\5 

W.  T.,  P.  M.,  12    07    22  

«  H.  D.,       -        0^.75 

G.  M.T.,  -        5".7 

W.  T.,L.  A.,noon,  11    59    59.5  Corr.,        +        4».3 

C-W, 

Eq.  t.,  3'"  46^8 

Chro.  t.,  L.  A.,noon,  6    17    47.5  ( /S'u6<rad  from  mcaji  time.) 

c.  c,  ~  - 

G.  M.  T.,  L.  A.,  noon,  1  J, 
Eq.  t, 

G.  A.  T.,L.  A.,  noon, 

T         4.  A  f    5"  43-"  27"  )  r? 

Longitude,  |  g^o  ^y  45// 1 E. 

Example:  August  6,  1879,  p.  m.,  in  Lat.  25°  55'  S.,  by  obs.,  and  Long.  36°  58'  W.,  by  account, 
observed  equal  altitudes  of  the  star  Antares,  the  chronometer  times  before  and  after  passage  being 
gh  42m  38s  and  10*"  00'"  26',  and  the  true  azimuths  S.  81°  E.  and  S.  81°  W.,  respectively;  chro.  fast  of 
G,  M.  T.,  1'"  27".     The  ship  was  steaming  on  a  course  SSW.     What  was  the  longitude? 

Chro.  time  before,  9*'  42"'  38" 

Chro.  time  after,  10  00    26 


Chro.  time  passage, 
C.  C, 

G.  M.  T.  passage, 
R.  A.  M.  S., 
Red.  (Tab.  9), 


2)23 

59 

59 

11 

+  6 

59 
17 

59.5 

48 

6 

17 
2 

47.5 
32 

18 

20 
3 

19.5 
46.8 

18 

16 

33 

G.  S.  T.  passage, 

L.  8.  T.  passage  (R.  A 

Longitude,  {gfo  o|/'  ^^,/}w. 


2)19  43 

04 

9  51 

-    1 

32 

27 

9  50 

+  8  58 

+    1 

05 

36.3 

36.9 

18  50 
,  16  22 

18.2 
03.4 

AZIMUTH.  109 


chaptp:r  XIV. 

AZIMUTH. 


354.  The  azimuth  of  a  body  has  been  defined  (art.  223,  Chap.  VII)  as  the  arc  of  the  horizon 
interceptea  between  the  meridian  and  the  vertical  circle  passing  through  the  body;  and  the  amplitude 
(art.  224)  as  the  arc  measured  between  the  position  of  the  body  when  its  true  altitude  i.s  zero  and  the 
east  or  west  point  of  the  horizon.  The  amplitude  is  measured  from  the  east  point  at  rising  and  the  west 
point  at  setting,  and,  if  added  to  or  subtracted  from  90°,  will  agree  with  the  azimuth  of  the  body  when 
in  the  true  horizon.  The  azimuth  is  usually  measured  from  the  north  point  of  the  horizon  in  north 
latitude,  and  from  the  south  point  in  south  latitude,  through  180°  to  the  east  or  west;  thus,  if  a  body 
bore  N.  by  E.,  its  azimuth  would  l)e  named  N.  1^°  E.  in  north,  or  S.  168J°  PI  in  south  latitude. 

The  determination  of  the  azimuth  of  a  celestial  body  is  an  operation  of  frequent  necessity.  At 
sea,  the  comparison  of  the  true  bearing  with  a  bearing  by  compass  affords  the  only  means  of  ascertain- 
ing the  error  of  the  compass  due  to  variation  and  deviation;  on  shore,  the  azimuth  is  required  in  order 
to  furnish  a  knowledge  of  the  variation,  and  is  further  essential  in  all  surveying  operations,  the  true 
direction  of  the  base  line  being  thus  obtained. 

355.  There  are  various  methods  of  obtaining  the  true  azimuth  of  a  celestial  body,  which  will  be 
described  as  follows:  ('/)  Amplitudes,  (h)  Time  Azimuths,  (c)  Altitude  Azimuths,  (d)  Time  and  Altitude 
Azimidlis.  A  further  method,  by  means  of  the  Sumner  line,  will  be  explained  later  (Chap.  XV). 
Still  another  operation  jjertains  to  this  subject,  namely:  {e)  The  determination  of  the  Tme  Bearing  of  a 
Terrestrial  Object. 

AMPLITUDES. 

356.  The  method  of  obtaining  the  compass  error  by  amplitudes  consists  in  observing  the  compass 
bearing  of  the  sun  or  other  celestial  body  when  its  center  is  in  the  true  horizon,  the  true  bearing,  under 
such  conditions,  being  obtained  by  a  short  calculation.  Since  the  true  horizon  is  not  marked  by  any 
visible  line  (differing  as  it  does  from  the  visible  horizon  by  reason  of  the  effects  of  refraction,  parallax, 
and  dip),  allowance  may  be  made  for  the  difference  by  an  estimate  of  the  eye,  or  else  the  observation 
may  be  made  in  the  visible  horizon  and  a  correction  applied. 

357.  When  the  center  of  the  sun  is  at  a  distance  above  the  horizon  equal  to  its  own  diameter  it 
is  almost  exactly  in  the  true  horizon;  at  such  a  time,  note  its  bearing  by  compass,  and  also  note  (as  in 
all  observations  for  determining  compass  error)  the  ship's  head  by  compass,  and  the  angle  and  direction 
of  the  ship's  heel. 

Or,  note  the  bearing  at  the  instant  at  which  the  center  of  the  body  is  in  the  visible  horizon;  in  the 
case  of  the  sun  and  moon,  the  correct  bearing  at  that  time  mav  be  most  accurately  ascertained  by  taking 
the  mean  of  the  bearings  when  the  upper  and  the  lower  limbs  of  the  disk  are  just  appearing  or  disap- 
pearing. 

35§.  To  find  the  true  amplitude  hij  computation  there  are  given  the  latitude,  I^,  and  declination,  d. 
The  quantities  are  connected  by  the  fornuila, 

sin  Amp.  =sec  L  sin  d, 

from  a  solution  of  which  the  amplitude  is  obtained. 

To  find  the  true  amplitude  hy  inspection  enter  Table  39  with  the  declination  at  the  top  and  the  lati- 
tude in  the  side  column;  under  the  former  and  opposite  the  latter  will  be  given  the  true  amplitude. 
To  obtain  accurate  results,  interpolate  for  minutes  of  latitude  and  declination. 

To  reduce  tJte  observed  atnplitude  when  taken  in  the  visilile  horizon  to  what  it  would  have  been  if 
taken  in  the  true  horizon,  enter  Table  40  with  the  latitude  and  declination  to  the  nearest  degree  and 
apply  the  correction  there  found  to  the  observed  amplitude;  the  result  will  be  the  corrected  amplitude 
by  compass,  which,  l)y  comjiarison  with  the  true  amplitude,  gives  the  compass  error.  When  the  body 
observed  is  the  sun,  a  star,  or  a  ])lanet,  apply  the  correction,  at  rising  in  north  latitude  or  at  setting  in 
south  latitude,  to  the  right,  and  at  setting  in  north  latitude  or  at  rising  in  south  latitude,  to  the  left. 
For  the  moon,  apjjly  half  the  correction  in  a  contrary  direction. 

Example:  At  sea,  in  Lat.  11°  29'  N.,  the  observed  bearing  of  the  sun,  at  the  time  of  rising  when  its 
center  was  estimated  to  be  one  diameter  above  the  visible  horizon,  was  E.  31°  N. ;  corrected  declination 
22°  32'  N.     Required  the  compass  error. 

By  computation.  By  inspection  (  Table  S9). 


L      11°  29^                     sec            .00878  L,  11°.5N.1t,                 .,   ooo  a  at 

d      22    32                        sin           9. 58345  d,  22  . 5  N.}  Trueamp.  E.  23°.  0  N. 

Obsd.  amp.                     E.  31  .ON. 

True  amp.      E.  23°  01'  N.  sin  9. 59223  

Obsd.  amp.    E.  31    00  N.  Error,                                      8°.  0  E. 

Error,  7°  59'  E. 


110  AZIMUTH. 

Example:  At  sea,  in  Lat.  25°  03''  S.,  the  observed  bearing  of  Venus  when  in  the  visible  horizon  at 
rising  was  E.  18°  30^  N.,  its  declination  being  21°  44'  N.     Kequired  the  compass  error. 

By  compuiation.  By  inspection  ( Table  S9). 

L    25°  03'         sec      .04290  L,  25°.0S.lrp  v   o.o  i  xt 

d     2144.      sin    9.56854  d,  31  . 7  N.[  ^^^  ^"^1^-  >- 24°.  1  N. 

Obsd.  amp.  E.  18°.  5  N.    j  ^  v   1  q     c  xr 

True  amp.    E.  24°  08'  N.  sin    9.61144  Corr.  (Tab.  40)  0.  3  left.J  ''^'"P*  '^'"P-  ^^-  ^^  '  ^  ^• 


Comp.amp.E.  18    48  N. 
Error,  5°  20'  W. 


Error,  5°.  3  W. 


Example:  At  sea,  in  Lat.  40°  27'  N.,  the  mean  of  the  observed  bearings  of  the  upper  and  lower 
limbs  of  the  moon  when  in  contact  with  the  visible  horizon  at  setting  was  W.  17°  S. ;  declination, 
21°  12'  S.     What  was  the  error  of  the  compass? 

By  computation.  By  inspection  ( Table  39). 

L     40°  27'           sec    .11863  L,  "^"^"-^  ^-j  True  amn     W  28°  4  S 

d     21    12            sin  9.55826  d,  21  . 2  S.j    ^™^ '""P-     ^^•^^•'if'- 

Obsd.  amp.         AV.  17°.0S.        )  p  ait  i^    7  c 

True  amp.    W.  28°  22'   S.  sin  9.67689  Corr.  (Tab. 40)  0.3  right. f  <^omp.amp.  w.  lb  ./  b. 

Comp.  amp.W.  16    42     S.  

Error,  11°.  7  W. 

Error,  11°  40'  W. 

TIME  AZIMUTHS. 

359.  In  this  method  are  given  the  hour  angle  at  time  of  observation,  t,  the  polar  distance,  p,  and 
the  latitude,  L;  to  find  the  azimuth,  Z. 

Any  celestial  body  bright  enough  to  be  observed  with  the  azimuth  circle  may  be  employed  for 
observation;  the  conditions  are,  however,  most  favorable  for  solution  when  the  altitude  is  low. 

360.  Take  a  bearing  of  the  object,  bisecting  it  if  it  has  an  appreciable  disk,  and  note  the  time  with 
a  watch  of  known  error.  Record,  as  usual,  the  ship's  head  by  compass  and  the  amount  of  heel.  If 
preferred,  a  series  of  bearings  may  l)e  taken  with  their  corresponding  times,  and  the  means  taken. 

361.  First  prepare  the  data  as  follows: 

(a)  Find  the  Greenwich  time  corresponding  to  the  local  time  of  observation. 

{h)  Take  out  the  declination  of  the  body  from  the  Nautical  Almanac;  if  the  method  of  computation 
is  employed  the  polar  distance  and  the  co-latitude  should  be  noted. 

(c)  Find  the  hour  angle  of  the  body  by  rules  heretofore  given. 

This  having  been  done,  the  true  azimuth  may  be  determined  either  by  Time  Azimuth  Tables,  by  the 
graphic  method  of  an  Azimuth  Diagram,  or  by  Solution  of  the  Astronomical  Triangle.  Owing  to  the  pos- 
sibility of  more  expeditious  working,  either  of  the  first-named  two  is  to  be  considered  preferable  to  the 
last,  and  the  navigator  is  recommended  to  supply  himself  with  a  copy  of  a  book  of  Azimuth  Tables,  or 
with  an  Azimuth  Diagram ;  an  explanation  of  the  method  of  use  accompanies  each  of  these. 

362.  To  solve  the  triangle: 

Let  S  =  ^  sum  of  polar  distance  and  co-Lat. 

D  =  I  difference  of  polar  distance  and  co-Lat. 
ht  =  h  hour  angle. 
Z  =  true  azimuth. 

Then,  tan  X  =  sin  D  cosec  S  cot  ^  t; 
tan  Y  =  cos  D  sec  S  cot  ^  t; 
Z  =  X  +  Y,  or  X  ~  Y. 

First  Case. — If  the  half-sum  of  the  polar  distance  and  co-Lat.  is  less  than  90° :  take  the  sum  of  the 
angles  X  and  Y  if  the  polar  distance  is  greater  than  the  co-Lat. ;  take  the  difference  if  the  polar  distance 
is  less  than  the  co-Lat. 

Second  Ca^e. — If  the  half-sum  of  the  polar  distance  and  co-Lat.  is  greater  than  90°:  always  take  the 
difference  of  X  and  Y,  which  subtract  from  180°,  and  the  result  will  be  the  true  azimuth. 

In  either  case,  mark  the  true  azimuth  N.  or  S.  according  to  the  latitude,  and  E.  or  W.  according 
to  the  hour  angle.  It  may  sometimes  be  convenient  to  use  the  supplement  of  the  true*azimuth,  by 
subtracting  it  from  180°  and  reversing  the  prefix  N.  or  S.,  in  order  to  make  it  correspond  to  the  compass 
azimuth  when  the  latter  is  less  than  90°. 

The  cotangent  of  half  the  hour  angle  may  be  found  from  Tal)le  44  abreast  the  whole  hour  angle  in 
the  column  headed  "Hour  P.  M." 


AZIMUTH. 


Ill 


Examplk:  December  3,  1879,  a.  m.,  in  Lat.  30°  25'  X.,  Long.  5"  25™  42^  W.,  the  observed  bearing  of 
BUn's  center  was  N.  135°  30'  E.,  and  the  Greenwich  mean  time,  December  3,  2^  36'"  IP.  The  corrected 
decUnation  of  the  sun  was  22°  07'  S.;  the  equation  of  time  (additive  to  mean  time),  10™  03'.  Required 
the  error  of  the  compass. 


G.M.T.  (Dec.3), 
Long., 


2h  36m  lis 

5   25    42 


co-Lat.,       59°  35' 
p,  112    07 


L.M.T.  (Dec.2),     21   10   29 
Eq.t,  +       10   03 

L.A.T.,  21    20   32 

t,  2"  39"' 28" 


p+co-L,  171    42 

S,  85    51 

p-co-L,  52°  32'      X+Y  139   03 

D,  26    16 

True  azimuth,      N.  139°  03'  E. 
Comp.  azimuth,  N.  135    30  E. 


t 

s 

D 

2"  39"' 
85°  51' 
26    16 

50   44 
88    19 

28" 

cot  J(  .44051 
cosec    .00114 
sin     9.64596 

cot  it    .44051 
sec       1.14045 
cos       9.95267 

X 

Y 

tan       .08761 

tan  1.53363 

Compass  error, 


3    33  E. 


Example:  April  9,  1879,  in  Lat.  2°  16'  N.,  the  observed  bearing  of  the  sun's  center  was  N.  85°  15'  E; 
sun's  hour  angle,  3''  44"  16%  and  its  declination,  7°  38'  N.     Required  the  compass  error. 


co-Lat.,       87° 
p,                82 

44' 
22 

t 

S 
D 

X 
Y 

Y-X 

True  a; 
Comp. 

Com  pa 

3"  44"'  16" 
85°  03' 
2    41 

5    03 
87    22 

cot  it  .27372 
cosec    .00162 
sin      8. 67039 

cot  it 
sec 

cos 

tan 

. 27372 
1. 06406 
9. 99952 

p+co-L,  170 

06 

tan     8. 94573 

82°  19'  E. 
85    15   E. 

8,               .85 

03 

1.  33730 

co-L—p,      5° 

22' 

:82    19 

zimuth,      N. 
azimuth,  N. 

88  error, 

D,                  2 

41 

2    56  W. 

Example:  April  26,  1879,  Lat.  16°  32'  S.,  observed  bearing  of  Venus  56°  00'  W.,  its  hour  angle 
being  4''  27"'  31",  and  its  declination  23°  12'  N.     What  was  the  error  of  the  compass? 


co-Lat. , 
P, 

73°  28' 
113    12 

t 
S 
D 

X 

Y 

Y- 
Z 

-X 

4h  27n> 

93°  20' 
19   52 

27   16 

87  40 

31" 

cot  it   .  18022 
cosec     . 00074 
sin       9.53126 

cot  i  I 

sec 

cos 

tan 

:    .18022 
1.23549 
9.  97335 

p+co-L, 

186    40 

tan      9. 71222 

s, 

93    20 
.  39°  44' 

1. 38906 

p  —  co-L, 

(iO  24 
119°  36' 

D, 

19    52 

True  azimuth,    S.  119°  36'  W. 
Comp.  azimuth,  S.  124    00  W, 


4    24   W. 


ALTITUDE  AZIMUTHS. 

363.  This  method  is  employed  when  the  altitude  of  the  body  is  observed  at  the  same  time  as  tiie 
azimuth;  in  such  a  case  the  hour  angle  need  not  be  known,  though  the  time  of  observation  should  be 
recorded  with  sufficient  accuracy  for  the  correction  of  the  declination  of  the  sun,  moon,  or  a  planet. 

There  ace  given  the  altitude,  /(,  the  polar  distance,  p,  and  the  latitude,  L;  to  find  the  azimuth,  Z. 

364.  Take  a  bearing  of  the  body  by  compass,  bisecting  it  if  the  disk  is  of  appreciable  diameter,  and 
simultaneously  measure  the  altitude;  note  the  time  approximately.  Observe  also  the  ship's  heading 
(by  compass)  and  the  heel. 

Or  a  series  of  azimuths,  with  corresponding  altitudes,  may  be  observed,  and  the  mean  employed. 

365.  Calculate  the  true  altitude  and  declination  from  the  observed  altitude  and  the  time.  Then 
compute  the  true  azimuth  from  the  following  formula: 

cos  i  Z  =v/ooH  s  cos  (.s— />)  sec  L  sec  h, 

in  which  s  =  i  (/i  +  L  -fp)-     The  resulting  azimuth  is  to  be  reckoned  from  the  north  in  north  latitude 
and  from  the  south  in  south  latitude. 


112  AZIMUTH. 

It  may  occur  that  the  term  (s— ;  )  will  have  a  negative  value,  but  since  the  cosine  of  a  negative  angle 
less  than  90°  is  positive,  the  result  will  not  be  affected  thereby. 

Example:  December  3,  1879,  in  Lat.  30°  25'  N.,  the  observed  l)earing  of  the  sun's  center  was 
N.  135°  30'  E.,  and  its  corrected  altitude  24°  59';  the  approximate  G.  M.  T.  was  2''.6,  the  declination  at 
that  time  being  22°  07'  S.     Required  the  compass  error. 


h 

L 

P 

•24° 

30 

112 

59' 

25 

07 

sec 
sec 

. 04267 
. 06431 

2)167 

31 

s 

8-p 

83 
-28 

45 
22 

cos 
cos 

2 

9. 03690 
9. 94445 

) 19. 08833 

z 

69 
139 

30 

00 

cos 

9. 54416 

True  azimuth,     N.  139°  00'  E. 
Comp.  azimuth,  N.  135    30  E. 


Compass  error,  3    30  E. 


/   39°  52' 
(I       22  07 
/(   24  59 

sin  9.  80686 
cos  9.  96681 
sec  .04267 

Z  S.  40°  56'  E. 

sin  9.  81634 

TIME   AND   ALTITUDE    AZIMUTHS. 

366.  AVhen,  at  the  time  of  observing  the  compass  bearing  of  a  celestial  body,  the  altitude  is  meas- 
ured and  the  exact  time  noted,  the  true  azimuth  may  be  very  expeditiously  determined,  a  knowledge 
of  the  latitude  being  unnecessary. 

In  view  of  the  simplicity  of  the  computation  this  method  strongly  commends  itself  to  observers  not 
provided  with  an  azimuth  table  or  diagram. 

SeT.  The  observation  is  identical  with  that  of  the  altitude  azimuth  (art.  364),  with  the  exception 
that  the  times  of  observation  must  be  exactly  instead  of  approximately  noted. 

36§.  Ascertain  the  declination  of  the  body  at  time  of  sight,  and  correct  the  observed  altitude;  com- 
I^ute  the  hour  angle.     We  then  have : 

sin  Z=sin  t  cos  d  sec  h, 

from  which  the  azimuth  may  be  found. 

This  method  has  a  defect  in  that  there  is  nothing  to  indicate  whether  the  resulting  azimuth  is 
measured  from  the  north  or  the  south  point  of  the  horizon;  but  as  the  approximate  azimuth  is  always 
known,  cases  are  rare  when  the  solution  will  be  in  question. 

Example:  December  3,  1879,  in  Lat.  30°  25'  N.,  Long.  5*'  25™  42*  W.,  the  observed  bearing  of  the 
sun's  center  was  N.  135°  30' E. ;  its  altitude  at  the  time  was  24°  59';  hour  angle,  2"  39™  28»  (39°  52'),  and 
declination  22°  07'  S.  Find  the  compass  error.  (See  example  under  Altitude  Azimuths  and  first 
example  under  Time  Azimuths. ) 

True  azimuth,      N.  139°  04'  E. 
Comp.  azimuth,  N.  135    30  E. 

3    34  E. 

TRUE  BEARING  OF  A  TERRESTRIAL  OBJECT. 

369.  Thus  far,  sea  observations  for  combined  variation  and  deviation  have  been  discussed,  but  if  it 
becomes  necessary,  as  in  surveying,  to  ascertain  the  Tnie  Bearing  of  a  Terrestriid  Ofijed,  or  to  find  the 
variation  at  a  shore  station,  more  accurate  methods  than  the  foregoing  must  be  resorted  to. 

The  most  reliable  method  is  that  by  an  Asitronomical  Bearing.  This  consists  in  finding  the  true 
bearing  of  some  well-defined  object  by  taking  the  angle  between  it  and  the  sun  or  other  celestial  body 
with  a  sextant  or  a  theodolite,  and  simultaneously  noting  the  time  by  chronometer,  or  measuring  the 
altitude,  or  observing  both  time  and  altitude.  It  should  always  be  noted  whether  the  object  is  right 
or  left  of  the  sun. 

370.  By  Sexiant. — Measure  the  angular  distance  between  the  object  and  the  sun's  limb;  and  if  there 
is  a  second  observer,  measure  the  altitude  of  the  sun  at  the  same  moment  and  note  the  time.  In  the 
absence  of  an  as.sistant,  first  measure  the  altitude  of  the  sun;  next,  the  angular  distance  between  the 
sun  and  the  object;  then,  a  second  altitude  of  the  sun,  noting  the  time  of  each  observation.  Also 
measure  the  altitude  of  the  defined  point  above  the  sea  or  shore  horizon. 

By  Tlieodolite. — This  instrument  is  far  more  convenient  than  the  sextant,  for,  being  leveled,  the 
horizontal  angle  between  the  sun  and  the  object  is  at  once  given,  no  matter  what  may  be  the  altitudes  of 
the  oljjects.  In  case  the  altitude  of  the  sun  is  needed,  it  may  be  read  accurately  enough  from  the  vertical 
circle,  although  not  as  finely  graduated  as  the  limb  of  the  sextant.  The  error  in  altitude  nmst,  how- 
ever, be  found  by  the  level  attached  to  the  telescope,  since  it  will  usually  be  found  to  differ  from  the 
levels  of  the  horizontal  circle.  If,  in  directing  the  telescope  to  the  sun,  there  is  no  colored  eye-piece,  an 
image  of  the  sun  may  be  cast  on  a  piece  of  white  paper  held  at  a  little  distance  from  the  eye-piece,  and 
by  adjusting  the  focus  the  shadow  of  the  cross-wires  will  be  seen. 

It  should  be  understood  that  any  celestial  body  may  be  used  as  well  as  the  sun,  and  there  are,  in 
fact,  certain  advantages  in  the  use  of  the  stars;  the  sun  is  chosen  for  illustration,  because  it  will  usually 
be  found  most  convenient  to  emi)loy  that  body. 


AZIMUTH. 


113 


371.  Find  the  true  azimuth  of  the  celestial  body  by  any  one  of  the  methods  previously  explained 
in  this  chapter  and  applj'  to  it  the  azimuth  difference,  or  horizontal  angle  between  the  celestial  and  the 
terrestrial  body,  having  regard  to  the  direction  of  one  from  the  other. 

To  find  the  azimuth  difference  from  sextant  observations,  change  the  observed  altitudes  of  the 
bodies  into  apparent  altitudes  by  correcting  them  for  index  error  of  the  sextant,  dip,  and  semidiameter; 
change  the  observed  angular  distance  into  apparent  angular  distance,  by  correcting  for  index  error  and 
semidiameter.     Then  if  S  =  J  (App.  Dist.  +  App.  Alt.  Q  -f-  App.  Alt.  Object) ,  we  have: 


cos  I  Az.  Diff.  =  v/sec  App.  Alt.  0  sec  App.  Alt.  Object  cos  S  cos  (S  —  App.  Dist. ), 

whence  the  azimuth  difference  is  deduced. 

When  the  theodolite  is  used,  the  horizontal  angle  is  given  directly.  If  only  one  limb  of  the  sun  is 
observed,  it  will  be  necessary^  to  apply  the  semidiameter,  but  it  is  usual  to  eliminate  this  correction  by 
taking  the  mean  of  observations  of  both  limbs. 

Example:  Decemlier  10,  1879,  a.  m.,  in  Lat.  30°  25'  24''  N.,  Long.  81°  25'  24"  W.,  made  observa- 
tions with  a  sextant  and  obtained  the  following  data  for  finding  the  true  bearing  of  a  station: 


Watch  time,     11"  22-"  36'  Obs.  Ang.  Dist.  0,  117°  07'  Left. 

C-W,  5    21    18  Obs.  2Q,  71°  37' 20" 

Chro.  corr.,  +         2    16  Obs.  alt.  Station,  20' 

I.  C,  zero. 


Dec.  S.,     22°  56'  27" 
Eq.  t.,   +  7°' 00^ 

S.  D.,  16'  17" 


Required  the  true  bearing  of  the  object. 

2  0, 


W.  T., 
C-W, 

Chro.  t., 
C.  C, 

G.M.T.,Dec.  10, 
Eq.  t., 

G.  A.  T., 
Long., 

L.  A.  T., 


11"  22"'  36' 
5   21     18 


4   43 

+          2 

54 

16 

4   46 

-]-'          7 

10 

00 

4   53 
-    5  25 

10 
42 

23   27 

28 

S.  D. 


71°  37'  20" 

35    48   40 
16   17 


8°  08'  00" 
22    56  27 
36    03  37 


App.  Alt.,  36    04   57 
;).  &r.,  —  1    13 


,/  S.      9°  17'  E. 
IN.  170    43   E. 


sin  9.15069 
cos  9.96422 
sec    .09239 

sin  9.20730 


36    03   44 


t, 

fO"  32"' 

32" 

\8°08'  00" 

Obs.  Ang.  Dist., 

117°  07'  00" 

App.  Dist. 

117°  23' 

True  bearing  0,        N.  170°  43'  E. 

0'sS.  D., 

+           16  17 

App.  Alt.  0 

36    05 

sec  0.092.50 

Az.  Diff.,                           125    00  Left. 

App.  Alt.  Object 

20 
2)153    48 

sec  0.00001 

Api>.  Ang.  Dist., 

117    23   17 

True  bearing  object,  X.  45°  43'  E. 

S 

76    54 

cos  9.35536 

S  —  App.  Dist. 

-40    29 

cos  9.88115 

2)19.32902 

k  Az.  Diff. 

62°  30' 

cos  9.6&151 

Az.  Diflf. 

125    00 

Example:  Same  date  and  place  and  same  objects  as  in  the  preceding  example;  measurement  made 
with  a  theodolite,  angular  distance  C{),  123°  17';  object  left  of  sun.  AVatcli  time,  ll""  16""  34''.5;  watch  slow 
of  L.  A.  T.,  4"'  53^5.     Dec.  0,  22°  56'  S.     Required  the  true  bearing. 


W.T.,  ll''16"'34\5 

W.  slow,  +         4    53.5 


L.  A.  T.,      23   21    28  .0 
t,  0  38    32 


co-Lat.,       59°  .35' 
/>,  112    56 


p-i 

-  co-L, 

-  co-L, 

172 

31 

S, 

86 

15 

P- 

53 

21 

t 

S 
D 

0"  38"' 
86°  15' 
26    41 

79°  24' 
89    39 

32» 

cot  h  t  1.07435 
cosec      .00093 
sin        9.65230 

cot  J< 

sec 

cos 

tan 

1.07435 
1.18440 
9.95110 

X 

tan         .72758 

Y 

2.20985 

X  +  Y169    03 


D, 


26     41 


True  bearing  0, 
Az.  Diff., 


N.  169°  03'  E. 
123    17  Left. 


Trtie  bearing  object,  X.    45    46  E. 


22489—03- 


114 


THE    SUMNEE    LINE. 


CHAPTER   XV. 

THE  SUMNEE  LINE. 


DESCRIPTION  OF  THE  LINE. 

372.  The  method  of  navigation  involving  the  use  of  the  Sumner  Hue  takes  its  name  from  Capt. 
Thomas  H.  Sumner,  an  American  shipmaster,  who  discovered  it  and  published  it  to  the  world.  As  a 
proof  of  its  value,  the  incident  which  led  to  its  discovery  may  be  related: 

"  Having  sailed  from  Charleston,  S.  C,  25th  November,  1837,  bound  for  Greenock,  a  series  of  heavy 
gales  from  the  westward  promised  a  quick  passage;  after  pansing  the  Azores  the  wind  prevailed  from 
the  southward,  with  thick  weather;  after  passing  .longitude  21°  W.  no  observation  was  had  vmtil  near 
the  land,  but  soundings  were  had  not  far,  as  was  supposed,  from  the  bank.  The  weather  was  now  more 
boisterous,  and  very  thick,  and  the  wind  still  southerly;  arriving  about  midnight,  ITth  December, 
within  40  miles,  by  dead  reckoning,  of  Tuskar  light,  the  wind  hauled  SE.  true,  making  the  Irish  coast 
a  lee  shore;  the  ship  was  then  kept  close  to  the  wind  and  several  tacks  made  to  preserve  her  position 
as  nearly  as  possible  until  daylight,  when,  nothing  being  in  sight,  she  was  kept  on  ENE.  under  short 
sail  with  heavy  gales.  At  about  10  a.  m.  an  altitude  of  the  sun  was  observed,  and  the  chronometer  time 
noted;  but,  having  run  so  far  without  oliservation,  it  was  plain  the  latitude  by  dead  reckoning  was  liable 
to  error  and  could  not  be  entirely  relied  upon." 

The  longitude  by  chronometer  was  determined,  using  this  uncertain  latitude,  and  it  was  found  to 
be  15'  E.  of  the  position  by  dead  reckoning;  a  second  latitude  was  then  assumed  10'  north  of  that  l)y 
dead  reckoning,  and  toward  the  danger,  giving  a  position  27  miles  ENPl  of  the  former  position;  a  third 
latitude  was  assumed  10'  farther  north,  and  still  toward  the  danger,  giving  a  third  position  ENE.  of  the 
second  27  miles.  Upon  plotting  these  three  positions  on  the  chart,  they  were  seen  to  be  in  a  straight 
line,  and  this  line  passed  through  Smalls  light. 

"  It  then  at  once  appeared  that  the  observed  altitude  must  have  happened  at  all  the  three  i>oints 
and  at  Smalls  light  and  at  the  ship  at  the  same  instant." 

Then  followed  the  conclusion  that,  although  the  absolute  position  of  the  ship  was  uncertain,'  she 
must  be  somewhere  on  that  line.  The  ship  was  kept  on  the  course  EN?].,  and  in  less  than  an  hour 
Smalls  light  was  made,  bearing  ENE.  ^  E.  and  close  aboard. 

The  latitude  by  dead  reckoning  was  found  to  be  8'  in  error,  and  if  the  ]wsition  given  by  that  latitude 
had  been  assumed  "correct  the  error  Avould  have  been  8  miles  too  far  S.  and  81'  30"  of  longitude  too  far 
W.,  and  the  result  to  the  ship  might  have  been  disastrous  had  this  wrong  position  been  adopted.  This 
represents  one  of  the  ijractical  applications  of  the  Sumner  line. 

The  properf.es  of  the  line  thus  found  will  now  be  explained. 

373.  C'iRCLKs  OF  EQr.\L  Altitude. — In  figure  43,  if  EE'E"  represent  the  earth  projected  upon  the 
horizon  of  a  point  A,  and  if  it  be  assumed  that,  at  some  particular  instant  of  time,  a  celestial  body  is  in 

the  zenith  of  that  point,  then  the  true  altitude  of 
the  body  as  observed  at  A  will  be  90°.  In  such  a 
case  the  great  circle  EE'E",  which  forms  the  hori- 
zon of  A,  will  divide  the  earth  into  two  hemi- 
spheres, and  from  any  point  on  the  surface  of  one 
of  those  hemispheres  the  body  will  be  visible,  while 
over  the  whole  of  the  other  hemisphere  it  will  be 
invisible.  The  great  circle  EE'E",  from  the  fact 
of  its  marking  the  limit  of  illumination  of  the  botly, 
is  termed  the  circle  of  illniiiuuition,  and  from  any 
point  on  its  circumference  the  true  altitude  of  the 
center  of  the  body  will  be  zero.  If,  now,  we  con- 
sider any  si'nall  circle  of  the  sphere,  BB'B",  CC'C", 
DD'D",  whose  plane  is  parallel  to  the  plane  of  the 
circle  of  illumination  and  which  lies  within  the 
hemisphere  throughout  which  the  body  is  visible, 
it  will  be  apparent  that  the  true  altitude  of  the 
body  at  any  point  of  one  of  these  circles  is  equal 
to  its  true  altitude  at  any  otiier  point  of  the  same 
circle;  thus,  the  altitude  of  the  body  at  B  is  equal 
to  its  altitude  at  B'  or  B",  and  its  altitude  at  D  is 
the  same  as  at  D'  or  D". 

It  therefore  follows  that  at  any  instant  of  time 
there  is  a  series  of  positions  on  the  earth  at  wliich 
a  celestial  bodv  appears  at  the  same  given  altitude, 
and  these  positions  lie  in  the  circumference  of  a 
circle  described  upon  the  earth's  surface  whose 
center  is  at  that  position  which  has  the  body  in  the  zenith,  and  whose  radius  depends  upon  the  zenith 
distance,  or — what  is  the  same  thing — upon  the  altitude.     Such  circles  are  termed  circles  of  etjnal  altittuk. 


Fig.  43. 


THE    SUMNER    LINE.  115 

374.  The  data  for  an  astronomical  s-i^ht  comprise  merely  the  time,  declination,  and  altitude.  The 
first  two  fix  the  position  of  the  body  and  may  be  regarded  a^  giving  the  latitude  and  longitude  of  that 
point  on  the  earth  in  whose  zenith  thel)ody  is  found;  the  zenith  distance  (the  complement  of  the  altitude) 
indicates  the  distance  of  the  observer's  zenith  from  that  point;  but  there  is  nothing  to  show  at  which 
of  the  numerous  positions  fulfilling  the  required  conditions  the  observation  may  have  been  taken.  A 
number  of  navigators  may  measure  the  same  altitude  of  a  l)ody  at  the  same  instant  of  time,  at  places 
thousands  of  miles  apart;' and  each  proceeds  to  work  out  his  position  with  identical  data,  so  far  as  this 
eight  is  concerned.  It  is  therefore  clear  that  a  single  observation  is  not  enough,  in  itself,  to  locate  the 
point  occupied  by  the  observer,  and  it  becomes  necessary,  in  order  to  fix  the  position,  to  employ  a 
second  circle,  which  may  be  either  that  of  another  celestial  body  or  that  of  the  same  body  given  by  an 
observation  when  it  is  in  the  zenith  of  some  other  point  than  when  first  taken;  knowing  that  the  point 
of  observation  lies  upon  each  of  two  circles,  it  is  only  possible  that  it  can  be  at  one  of  their  two  points 
of  intersection ;  and  since  the  position  of  the  ship  is 
always  known  within  fairly  close  limits,  it  is  easy  to 
choose  the  proper  one  of  the  two.  Figure  44  shows 
the  plotting  of  observations  of  two  bodies  vertically 
over  the  points  A  and  A'  upon  the  earth,  the  zenith 
distances  corresponding  respectively  to  the  radii  A() 
and  A^O. 

375.  The  Sumxer  Line. — In  practice,  under 
the  conditions  existing  at  sea,  it  is  never  necessary 
to  determine  the  whole  of  a  circle  of  equal  altitude, 
as  a  very  small  portion  of  it  will  suffice  for  the  pur- 
poses of  navigation;  the  position  is  always  known 
within  a  distance  which  will  seldom  exceed  thirty 
miles  under  the  most  unfavorable  conditions,  and 
which  is  usually  very  much  less;  in  the  narrow  linuts 
thus  required,  the  arc  of  the  circle  will  practically 
coincide  with  the  tangent  at  its  middle  point,  and 
may  be  regarded  as  a  straight  line.  Such  a  line,  pj^.  44 
comprising  so  much  of  the  circle  of  etjual  altitude  as 

covers  the  probable  limits  of  po.«ition  of  the  ol)Ferver,  is  called  a  Sumner  line  or  Lii^e  of  position. 

376.  Since  the  direction  of  a  circle  at  any  point — that  is,  the  direction  of  the  tangent — must  be 
perpendicular  to  the  radius  at  tliat  point,  it  follows  that  the  Sumner  line  always  lies  in  a  direction  at 
right  angles  to  that  in  which  the  body  bears  from  the  oliserver.  Thus,  in  figure  44,  it  may  be  seen  that 
m  n/  an(l  n  1/,  the  extended  Sunmer  lines  corresponding  to  the  Ijodies  at  A  and  A^,  are  respectively 
perpendiculur  to  the  bearings  of  the  bodies  OA  and  OA''.  This  fact  has  a  most  important  application 
m  the  employment  of  the  Sumner  line. 

377.  I'sEs  OK  THE  SiMXER  LiNE. — The  Sumner  line  is  valuable  because  it  gives  to  the  navigator' 
a  knowledge  of  all  of  the  probable  positions  of  his  vessel,  while  a  sight  worked  with  a  single  assumed 
latitude  or  lorgitude  gives  but  one  of  tlie  probable  positions;  it  must  be  recognized  that,  in  the  nature 
of  things,  an  error  in  the  assumed  coordinate  will  almost  invariably  exist,  and  its  possible  effect  should 
betaken  into  consideration;  the  line  of  position  reveals  the  difference  of  longitude  due  to  an  error  in 
the  latitude,  or  the  reverse. 

Since  the  Sumner  line  is  at  right  angles  to  the  bearing,  it  may  be  seen  that  when  the  body  bears 
east  or  west — that  is,  when  it  is  on  the  prime  vertical — the  resulting  line  runs  north  and  south,  coincid- 
ing with  a  meridian;  if,  in  this  case,  two  latitudes  are  assumed,  the  deduced  longitudes  will  be  the  same. 
When  the  body  bears  north  or  south,  or  is  on  the  meridian,  the  line  runs  east  and  west  and  becomes 
identical  with  a  parallel  of  latitude;  in  such  a  case,  two  assumed  longitudes  will  give  the  same  latitude. 
Any  intermediate  bearing  gives  a  Sunnier  line  inclined  to  both  meridians  and  parallels;  if  the  line 
agrees  in  direction  more  nearly  with  the  meridian,  latitude  should  generally  be  assumed  and  the  longi- 
tude worked;  if  it  is  nearer  a  parallel,  the  reverse  course  is  usually  preferable.  The  values  of  the 
assumed  coordinates  may  vary  from  10'  to  1°,  according  to  circumstances. 

37S.  Tlie  greatest  l)enelit  to  be  derived  from  the  Sumner  method  is  when  two  lines  are  worked 
and  their  intersections  found.  The  two  lines  may  be  given  liy  different  bodies,  which  is  generally 
preferable,  or  two  different  lines  may  be  obtained  from  the  same  IkhIv  from  observations  taken  at 
different  times.  The  position  given  by  the  intersection  of  two  lines  is  more  accurate  the  more  nearly 
the  lines  are  at  right  angles  to  each  other,  as  an  error  in  one  line  thus  produces  less  effect  upon  the 
result.  When  two  observations  of  the  same  body  are  taken,  the  i)osition  of  the  ship  at  the  time  of  first 
eight  must  be  brought  forward  to  that  at  the  second  in  considering  the  intersection;  if,  for  example,  a 
certain  line  is  determined,  and  the  ship  then  runs  NW.  27  miles,  it  is  evident  that  her  new  position  is 
on  a  line  jiarallel  with  the  first  and  27  miles  to  the  NW.  of  it;  a  second  line  being  obtained,  the  inter- 
section of  this  with  the  first  line,  as  corrected  for  the  run,  gives  the  ship's  position. 

Besides  the  employment  of  two  lines  for  intersections  with  each  other,  a  single  line  may  be  made 
to  serve  various  useful  purposes  for  the  navigator.     These  are  described  in  article  400,  Chapter  XVI. 

METHODS  OF  DETERMINATION. 

379.  Any  line  may  be  defined  in  either  of  two  way^ — by  two  of  its  points,  or  by  one  point  and  the 
direction.     Tliere  are  thus  two  methods  by  which  a  Sumner  line  may  be  determined: 

(a)  Assume  two  values  of  one  coordinate  and  find  the  corresponding  values  of  the  other.  Two 
values  of  the  latitude  may  be  assumed  and  the  longitudes  determined,  as  was  done  by  Captain  Sumner 
on  the  occasion  that  led  to  the  discovery  of  the  method;  or  else  two  values  of  the  longitude  may  be 
assumed  and  the  latitudes  determined.  Two  points  are  fixed  in  this  way,  and  the  line  joining  them  is 
the  line  of  position. 

(6)  Assume  either  one  latitude  or  one  longitude  and  determine  the  corresponding  coordinate.  This 
gives  one  point  of  the  line.     The  azimuth  of  the  body  is  then  ascertained,  and  a  line  is  drawn  through 


116 


THE    SUMNER    LINE. 


the  determined  point  at  right  angles  to  the  direction  in  which  the  body  bore  at  the  time  of  sight.  This 
will  be  the  line  of  position. 

3§0.  It  follows  that  if  the  Sumner  line  be  located  by  the  first  method  and  its  direction  thus 
defined,  the  azimuth  of  the  observed  body  maybe  determined  by  finding  the  angle  made  by  the  line 
with  the  meridian  and  adding  or  substracting  90°. 

Example:  At  sea  April  17,  1879,  A.  M.,  in  Lat.  25°  12'  S.,  Long.  31°  32'  W.,  by  D.  R.,  observed  an 
altitude  of  the  planet  Jupiter,  east  of  the  meridian,  45°  40';  watch  time,  5"  48'°  02';  C  —  W,  2'>  05'"  42»; 
C.  C,  +  2™  18';  I.  C,  -t-  r  30";  height  of  eye,  18  feet.     Required  the  Sumner  line. 

From  a  solution  of  this  same  problem'for  a  single  longitude  (art.  351,  Chap.  XIII),  the  following 
were  found:  H.  A.  from  Gr.,  0"50'"  51'  E.;  /*,  45°  36'  24";  ]>,  79°  22'  51".  Assume  values  of  Lat.  25°  02' 
and  25°  22'  S. 


h 
P 


45' 
25 


36'  24" 
02   00 
22   51 


sec 
cosec 


.04278 
.00750 


Lj      25°  22'  00" 


sec 
cosec 


.04403 
.00750 


Gr.  H 


H.  A 


2)150 

01 

15 

cos         9.41282 
sin         9.69105 

82       75 
.tj— 7t  29 

10  38 
34   14 

«!         75 
81— /t29 

00 
24 

38 
14 

cos  9.40794 
sin         9.69328 

i.  A.      0" 

2 

50" 
57 

•  51'  E. 
30  E. 

2)19.15415 
sin  i  ^  9.57708 

Gr.  H.  A.    0" 

H.  A..,         2 

50"'  51' 
57   12 

2)19.15275 
sin  1 1,   9.57638 

Lony 


/  2"  06'"39'\ 
•1  \31°  39'  45"/ 


^W. 


,  r  2"  06™21'\„. 

Lon^-^  \31°  35' 15"r^ 


It  should  be  observed  that  s.^  and  s-^  —  h  can  be  obtained,  respectively,  from  ^-j  and  s^—h  by  adding 
half  the  difference  between  Lj  and  L,^;  also  that  log  cosec  p  is  the  same  for  both  hour  angles.  The 
determination  of  the  second  hour  angle  is  thus  considerably  simplified. 

A  comparison  of  these  results  with  those  obtained  by  the  solution  with  a  single  latitude  shows  that 
the  hour  angle,  and  consequently  the  longitude,  corresponding  to  the  latitude  25°  12'  S.  are  the  means 
of  those  corresponding  to  the  latitudes  here  used;  and  therefore  that  the  assumption  that  the  Sumner 
line  is  a  straight  line  is  accurate. 

The  line  of  the  same  sight  might  also  have  been  found  as  follows: 

Working  with  the  single  latitude  25°  12'  S.,  it  was  found  that  the  corresponding  longitude  was 
31°  37'  30"  \V.  Now  by  referring  to  an  azimuth  table  or  azimuth  diagram,  the  azimuth  corresponding 
to  Lat.,  25°. 2  8.,  Dec,  i0°.6  S.,  H.  A.,  2^  57'".  3  E.  is  S.  101°  24'  E.;  therefore  the  Sumner  line  extends 
S.  11°  24'  E. 

The  line  may  therefore  be  defined  in  either  of  two  ways,  thus: 


A 


Or, 


/25°  02'  00"    S. 
H31    39    45    W. 

25°  12'  00"    S. 
31    37    30    W. 


^{: 


.    /25°  22'  00"    S. 
^^  \31    35    15    W. 

Line  runs  S.  11°  24'  E. 


By  inspection  of  the  coordinates  of  Aj  and  A^  it  may  l)e  seen  that — 

+  20'  diff.  lat.  makes  — 4'.5  diff.  long.;  or, 

+  20  miles  diff.  lat.  makes  — 4.1  miles  departure. 

Therefore  by  reference  to  Table  2  it  appears  that  the  line  runs  about  S.  11^°  E.,  and  the  azimuth 
of  the  bodv  is  S.'  101^"  E. ;  thus  the  results  obtained  by  the  two  methods  agree. 

Example:  At  sea,  Mav  18,  1879,  A.  M.,  Lat.  41°  33'  N.,  Long.  33°  30'  W.,  by  D.  R.,  the  mean  of  a 
series  of  observed  altitudes  of  the  sun's  lower  limb  was  29°  35'  30";  the  mean  watch  time,  7"  20""  45'.3; 
C.  C.,  +  4'"  59'.2;  I.  C,  —  30";  height  of  the  eye,  23  feet;  C  —  AV,  2^  17'"  06'.     Required  the  Sumner  line. 

From  a  solution  of  this  same  problem  for  a  single  longitude  (art.  351,  Chap.  XIII)  the  following 
were  found:  G.  A.  T.,  21"  46'"  38';  h,  29°  50'  05";  p,  70°  29'  14".  Assume  values  of  the  latitude  41°  03' 
and  42°  03'  X. 


P 


29°  50'  05" 
41    03    00 
70    29    14 


sec 
cosec 


. 12255 
. 02569 


L, 


42°  03'  00" 


sec 
cosec: 


12927 
.  02569 


2)141    22    19 

70    41    09 
40    51    04 

cos            9. 51950 
sin            9. 81564 

s-i              71 
.*.,—/(         41 

11 
21 

09 
04 

cos 
sin 

sin 

9. 50852 
9.  81999 

21"  46™  38' 

2)19.48338 

■ 

sin  i  /i      9.  74169 

G.  A.T.  21" 
L.  A.T..,  19 

46" 
32 

'38'      , 
06 

2)19.48347 

19    32    08 

i  <j      9.  74174 

G.  A.  T. 

21"  46™  38' 

L.  A.  T., 

19    32    08 

Ix)ng.i| 

2"  14"  30»\^ 
33°  37' 30"/^- 

A.{ 

41°  03'  00"  N. 
33    37    30    W. 

J  r  2"  14"'  32'  \,,r 

l-ong.2  J33038/  00"/^^  • 


.  /42°  03'  00"  N. 
^i'\33    38  00    W. 


+  60'  diff.  lat.  makes  +  0'.5  long. 

+  60  miles  diff.  lat.  makes  +  0.4  mile  departure. 


Line  runs,  X.  ^  W.     Azimuth,  X.  89i°  E. 


THE    SUMNER    LINE. 


117 


The  same  sight  worked  with  a  single  latitude,  41°  33'  X.,  ais  was  <lone  in  tlie  original  example,  with 
azimuth  taken  from  tables  or  diagram,  gives: 


. /41°  33'  00"  N. 
^133 


133    37  45  W. 


Azimuth,    N.  89°  38'  E. 
Line  runs,  N.    0°  22'  W. 


This  example  illustrates  the  case  in  which  an  observation  is  taken  practically  on  the  prime  vertical; 
the  azimuth  shows  the  bearing  to  be  within  0°  22'  of  true  East,  and  the  Sumner  line  is  therefore  within 
U°  22'  of  the  meridian;  a  variation  of  30'  in  either  direction  from  the  dead  reckoning  latitude  makes  a 
difference  of  only  15"  in  the  longitude. 

Example:  May  28,  1879,  in  Lat.  6°  20'  S.  by  account,  Long.  30°  21'  30"  W.;  chro.  time,  7''  35'"  10"; 
observed  altitude  of  moon's  upper  limb,  75°  33'  00",  bearing  north  and  east;  I.  C.,  —  3'  00";  height  of 
eye,  26  feet;  chro.  fast  of  (1.  M.  T.,  1™  37^5.     Required  the  Sumner  line. 

From  a  solution  of  the  same  problem  with  a  single  longitude  (art.  339,  Chap.  XII),  the  following 
values  were  obtained:  H.  A.  from  Greenwich,  1"  35'"  07''  W.;  h,  75°  23'  30";  d,  6°  41'  47"  N.  Assume 
the  longitudes  30°  10'  and  30°  30'  W. 


Gr.  H.  A.  1"  35"'  07^  W. 
Long.,        2   00    40  W. 


Gr.  H.  A.  1"  35"'  07" 
lvong.2        2   02    00 


<1 

d 

6^ 
6 

75 

6 

13 

'  23'  15" 
41   47 

23   30 
44   17   N. 

11   20   S. 

,   JO"  25'"  33' 
^i\6°23'  15" 

sec      .00270 
tan  9.06973 

^2\6° 

cosec     .93324 

sin       9.98573 
sin       9.06942 

26'"  53' 
43'  15" 

'^  >  \.30 

A      /«° 

^^H30 

\ 

h 

tan   9.07243 

sec     .00299 
tan  9.06973 

27'  03"  S. 
10   00  W. 

9\ 

cos       9.98839 

cosec    .93324 

sin      9.98573 
sin      9.06972 

Lat., 
d 

1    fi 

6° 
6 

75 
6 

13 

27 

43' 
41 

23 
44 

01 

03   S. 

15" 
47 

30 
33 

00 

h 

tan  9.07272 

16'  27"  S. 
30   00   W. 

¥. 

cos      9.98869 

Lat.  J  6    16   27  S. 

Working  by  the  other  method,  and  finding  the  azimuth,  we  have: 

.  /  6°  21'  14"  S.  T  •  V-   ,.oo  Av 

130    21    30   W  Lnie  runs  >. .  b2°  W. 

It  might  be  shown  that  the  results  check  with  each  other,  as  in  previous  cases. 

Example:  At  sea,  July  12,  1879,  in  Lat.  50°  N.,  Long.  40°  W.,  observed  circum-meridian  altitude 
of  the  sun's  lower  limb,  the  time  by  a  chronometer  regulated  to  Greenwich  mean  time  being  ^  41'"  39"; 
chro.  corr.,  —  2'"  30^;  I.  C,  —  3'  0";  height  of  the  eye,  15  feet.     Find  the  Sumner  line. 

From  the  solution  of  the  same  problem  for  a  single  latitude  (art.  338,  Chap.  XII)  the  following 
values  were  obtained:  G.  A.  T.,  2"  33'"  50';  /;,  61°  57' 01";  d,  21°  59'  27"  N.;  a  (Tab.  26),  2"  .5. 
Assume  longitudes  39°  45'  and  40°  15'  W. 


Gr.  H.  A. 
Long.  1 


2"  33"  50' 
2   39    00 


k 

5    10 

h 

61° 

+  . 

57'  01" 
1   06 

Hx 

61 

58  07 

2l 

d 

28 
21 

01   53  N. 
59  27  N. 

Gr.  H. 
Long. . 

A.    2>'33'"50' 
i     -2    41    00 

h 

7    10 

h 
at./ 

61°  57'  01" 

+           2   08 

H, 

61    59   09 

22 
d 

28    00  51 
21    59   27 

Li  50    01   20  N. 

The  line  given  by  these  coordinates  is  then : 


.     r50°  01' 
'■^'\39    45 


20"  N. 
00    AV. 


■'{ 


50    00   18  N. 


50°  00'  18"  N. 
40    15  00   W. 


118  THE  sumnp:r  line. 

This  shows  that  the  Sumner  Hne  lies  so  nearly  in  a  due  east-and-west  direction  that  a  difference  of 
longitude  of  30'  makes  a  difference  of  latitude  of  only  1''. 

From  an  azimuth  table  or  diagram,  it  is  found  that  the  azimuth  of  the  sun  corresponding  to  Lat.  50° 
N.  Dec.  22°  N.  and  H.  A.  6"'  10'  E.,  is  N.  177°  E.  Therefore,  using  the  values  given  by  the  earlier 
solution,  the  line  is  defined  as  follows: 


50°  OO'  5V'  N.  T  •  XT     O-O   17 

40    00  00    N.  LmerunsN.  8/°E. 


The  direction  of  the  line  thus  given  and  the  one  found  from  the  double  coordinates  mav  )>e  shown 
to  agree  as  in  examples  before  given. 

FINDING  THE  INTERSECTION  OF  SUMNER  LINES. 

3§1.  The  intersection  of  Sumner  lines  may  be  found  either  graphically  or  by  computation. 

3S2.  Graphic  Methods. — Each  line  may  be  plotted  upon  the  chart  of  the  locality  in  which  the 
ship  is  being  navigated  and  the  intersection  thus  found.  The  details  of  the  plotting  will  be  obvious, 
whether  the  line  is  defined  by  two  of  its  points,  or  by  one  point  and  its  direction.  This  plan  will  com- 
mend itself  especially  when  the  vessel  is  near  shore,  as  the  chart  in  use  will  then  jn-obably  be  one  of 
conveniently  large  scale,  and  it  will  be  an  advantage  to  see  where  the  position  falls  with  reference  to 
soundings  and  landmarks. 

3§3.  When  clear  of  the  land  it  is  often  inconvenient  to  follow  this  plan;  a  large  scale  chart  may 
not  be  at  hand,  it  may  not  be  desired  to  deface  the  chart  with  numerous  lines,  or  the  necessary  space  for 
chart  work  may  not  be  available.  In  such  a  case,  the  following  method  «  is  recommended,  as  it  obviates 
the  disadvantages  of  the  other. 

To  understand  the  principle  of  this  method,  suppose  that  the  lines  are  defined  ])y  the  latitude  and 
longitude  of  two  points  of  each,  and  consider  that  they  are  plotted  on  a  chart  which  is  constructed  upon 
a  sheet  of  elastic  rubber.  It  i.s  evident  that  if,  while  holding  it  fast  in  the  direction  of  the  meridians, 
we  stretch  this  rubber  along  the  lines  of  the  parallels  in  a  uniform  manner  until  the  length  of  each 
minute  of  longitude  is  made  to  equal  a  minute  of  latitude,  the  chart,  while  losing  its  accuracy  as  por- 
traying actual  conditions  on  the  earth's  surface,  still  correctly  represents  the  jiositions  of  the  various 
points  in  terms  of  the  new  coordinates  which  have  been  created,  namely,  those  in  which  a  minute  of 
latitude  is  equal  to  a  minute  of  longitude.  Thus,  if  on  the  true  chart  a  point  is  m  minutes  north  and  n 
minutes  east  of  another,  on  the  stretched  one  it  will  still  be  vi  minutes  north  and  n  minutes  east,  the 
only  difference  being  that  the  minutes  of  longitude  will  now  be  of  a  different  length;  and  if  on  the  orig- 
inal chart  the  two  Summer  lines  intersect  at  a  point  ?«  minutes  north  and  7i  minutes  east  (on  the 
original  scale)  of  some  definite  point  of  one  of  the  lines,  the  intersection  on  the  stretched  chart  will  lie 
m  minutes  north  and  n  minutes  (of  the  new  scale)  to  the  east  of  the  same  point. 

A  stricter  mathematical  conception  of  the  stretched  chart  and  its  properties  may  perhaps  be 
obtained  by  considering  the  chart  of  the  locality  to  be  projected  (with  the  eye  at  the  zenith)  upon  a 
plane  Avhich  passes  through  one  of  the  meridians  and  makes  an  angle  with  tbe  plane  of  the  horizon 
which  is  equal  to  the  latitude;  each  minute  of  longitude  will  then  be  increased  by  multiplying  it  by  the 
secant  of  the  latitude,  and  thus  becomes  equal  to  a  minute  of  latitude. 

From  a  consideration  of  the  properties  of  this  hypothetical  chart  it  may  be  seen  that  the  following 
rule  may  be  laid  down:  If  two  or  more  Sumner  lines  be  plotted  by  their  latitude  and  longitude  upon 
any  sheet  of  paper,  using  a  scale  whereon  latitude  and  longitude  are  equal  regardless  of  the  latitude  of 
the  locality,  the  intersection  of  those  lines,  measured  by  coordinates  on  the  scale  employed,  correctly 
represents  the  intersection  of  the  lines  as  it  would  be  measured  upon  a  true  chart. 

It  follows  from  this  that  we  may  plot  Sumner  lines  upon  any  piece  of  paper,  measuring  the  coordi- 
nates with  an  ordinary  scale  ruler,  and  assigning  any  convenient  length  for  the  mile;  the  larger  the 
scale  the  more  accurate  will  be  the  determination.  Or,  what  is  even  more  convenient,  we  may  employ 
"profile  paper,"  whereon  lines  are  ruled  at  right  angles  to  each  other  and  at  equal  distances  apart,  in 
which  case  no  scale  ruler  is  needed. 

One  caution  must  be  observed  in  using  this  method;  all  longitudes  employed  on  the  paper  for  any 
purpose  must  be  those  of  the  scale,  namely,  one  minute  of  longitude  equals  one  minute  of  latitude. 
For  instance,  if  the  two  Sunmer  lines  be  taken  at  different  times,  in  bringing  the  first  up  to  the  iX)sition 
of  the  second  by  the  intermediate  run,  that  run  must  be  laid  down  to  scale;  that  is,  the  easting  or 
westing  must  appear  as  so  many  minutes  of  longitude,  not  so  many  miles.  To  do  this  enter  the  traverse 
table  with  course  and  distance  run,  and  pick  out  latitude  and  departure;  then,  by  means  of  the  middle 
latitude,  convert  departure  into  minutes  of  longitude  and  bring  the  first  line  to  the  second  by  laying  off 
so  many  minutes  of  latitude  north  or  south,  and  so  many  of  longitude  east  or  west. 

In  the  case  where  the  Sumner  is  defined  by  one  position  and  its  line  of  direction,  it  is  not  correct  to 
lay  down  the  angle  to  the  meridian  on  the  hypothetical  chart,  for  all  angles  are  distorted  thereon.  The 
best  way  is  to  find  another  position  on  the  line  by  assuming  a  second  latitude  ten  or  twenty  miles 
removed  from  that  of  the  point  given,  entering  the  traverse  tal)le  with  the  angle  that  the  line  makes  with 
the  meridian  as  a  course,  and  abreast  the  latitude  taking  out  the  departure;  (convert  departure  into  differ- 
ence of  longitude,  and  plot  the  second  point  by  its  coordinates  from  the  first. 

Example:  Let  it  be  required  to  find  the  intersection,  by  each  of  the  methods,  of  the  following  lines: 


.  /40°  00'  N.  .    f40°  20'  N. 

^1163    15    W.  ^463    07    W. 

T./40    05   N.  „r40    15  N. 

^i\63    03    W.  ^4^3    12   W. 


1  Suggested  by  Lieut.  G.  W.  Logan,  U.  8.  Navy. 


THE    SUMNER    LINE. 


119 


Figure  45  shows  the  intersection,  (1)  by  Mercator  chart,  (2)  by  scale,  and  (3)  on  profile  paper, 
as  follows: 


20' 


f^ 

/ 

/     : 

A, 
III'' 

LrrA 

1 1 1 1.|  1  III,  y 

20' 


J  40"'    >^ 

63°  L5'  12'  10'   err'     03'    63'<'" 

1  -prtilft  =  .06in.cK 

Fig.  45. 


Ai, 

y 

:     .:_     z      t 

:     ---JL.  -Z--    -  - 

23:__L 

\  ':  : 

__      S_                     - 

;.;_::L.:i 

: J        I " 

_   ::._  A   z  :^L-- 

:_::.::2  __  ...5, 

:l 5:_- 

"":::.:::::_;: 

-      -_          Z                      -          --*L 

:::  :i::  _.      .:     ' 

zz-.A ± 

^o' 


10' 


63' 


iH>* 


r40°  12'  8  N 
Intersection  :|g3-   09  ig  W . 

Suppose,  in  the  example  just  given,  the  first  line  had  been  defined  as  follows:  • 

A|g^°  15^  W  ^^"^  '■""^  ^'-  ^''°  ^• 

To  find  a  second  coordinate  bv  which  to  plot  it,  proceed  as  follows: 

In  Table  2,  for  17°:  Lat.  20'  X.,  Dep.  6.1  m.  E.     For  Mid.  Lat.:  40°,  Dep.'6.1  m.,  diff.  long.  8'.0  E. 
Hence,  as  jjreviously  given: 


/40°  00'  X. 
''iteS    15    W 


.  /40°  20^  N. 
^463    07    W. 


3§4.  Methods  by  Computation." — The  finding  of  the  intersection  of  two  Sumner  lines  by  compu- 
tation may  l)e  divided  into  two  cases: 

Case  I.  When  one  line  lies  in  a  XP].-S'\V.  direction,  and  the  other  in  a  XW.-SE.  direction. 

Case  II.  When  l)oth  lie  in  a  XE.-.S\V.,  or  both  in  a  XW.-SE.  direction. 

Suppose,  first,  that  the  lines  are  defined  by  the  latitude  and  longitude  of  two  points  of  each,  and  for 
the  simplification  of  the  problem  consider  the  lines  projected  on  a  plane  passing  through  one  of  the 
meridians  and  making  an  angle  with  the  i^lane  of  the  horizon  equal  to  the  latitude,  the  properties  of 
which  were  explained  under  the  graphic  method,  (art.  383);  this  saves  the  necessity  ot  converting 
minutes  of  longitude  into  miles  of  departure  before  the  solution  and  converting  them  back  again  after- 
wards; as  all  points  are  thus  projected  in  corresponding  relative 
J)08itions,  the  results  are  as  exact  as  if  the  longer  method  be 
oUowed  of  dealing  with  minutes  of  latitude  and  longitude  of 
unequal  length. 

3§5.  Cfw  I  One  line  NE.-SW.,  and  the  other  NW.-SE.— 
Suppose  the  two  lines,  projected  as  described,  are  as  shown  in 
figure  46,  Aj  A;^  and  Bj  Bj;  for  the  present  assume  that  the  two 

Soints,  Aj  and  B,,  have  a  common  latitude.  Drop  the  perpen- 
icular  PO  from  the  intersection;  then  the  latitude  of  the  inter- 
section will  be  a  distance  OP  above  the  conmion  latitude  of  Aj 
and  Bi,  and  its  longitude  will  be  a  distance  XyO  to  the  right  of 
Ai  and  BjO  to  the  left  of  Bi. 

Find  the  angles  <r  and  fi  from  the  traverse  table  (Table  2), 

they  being  taken  out  with  the  difference  of  latitude  between  the 

two  points  of  the  same  line  in  the  column  Lat.  and  the  differ-  A,' 

ence  of  longitude  in  the  column  Dep.     (Do  not  overlook  the 

fact  that  we  are  dealing  now  with  the  plane  of  projection  and  }!u.t.  46. ; 

that  a  and  (i  are  not  the  angles  made  by  the  Sumner  line  with 

meridians  on  the  earth's  surface. )    The  solution  may  now  be  accomplished  by  either  of  two  methods: 

(o)  Observe  that  the  case  is  the  same  as  if  a  ship  were  steaming  along  the  line  A^  Bj  and  took  the 
first  bearing  of  the  point  P  when  at  A,,  at  an  angle  from  the  course  equal  to  90°— n-,  and  the  second 
bearing  when  at  B,,  at  an  angle  from  the  course  equal  to  90°+/i,  with  an  intervening  run  equal  to  the 
difference  of  longitude  Aj  B,;  or,  she  may  be  considered  as  steaming  from  Bj  to  Aj,  in  which  case  the 
first  angle  is  90°—/?  and  the  second  90°-r«.  Picking  out  of  Table  5  B,  corresponding  to  the  angles 
given,  the  quantity  in  the  second  column,  we  shall  have  the  ratio  of  the  distance  of  passing  abeam,  OP, 
to  the  distance  Aj  B,;  multiply  the  difference  of  longitude  by  this  ratio,  and  we  shall  have  the  actual 
length  of  OP.  Then  entering  the  traverse  table  with  this  as  a  latitude  and  a  as  a  course,  we  find  in  the 
departure  column  the  distance  AjO  by  which  the  longitude  of  OP  is  defined;  it  is  recommended  also 
to  pick  out  BjO,  using  the  angle  fi,  which  affords  a  proof  of  the  correctness  of  all  work  done  after  the 
finding  of  a  and  f3. 

««Suj?jrested  by  Lieut.  G.  W.  Logan,  r.  S.  Navy. 


120 


THE    SUMNER    LINE. 


{b)  The  second  method  is  to  find  by  trial  and  error  some  latitude  such  that  its  departure  correspond- 
ing to  a,  plus  its  departure  corresponding  to  fi,  equals  the  difference  of  longitude  Aj  Bj;  then  the  point 
will  be  defined  by  the  latitude,  and  by  its  longitude  from  Aj  and  Bj,  the  agreement  of  the  longitude  as 
established  from  the  different  points  furnishing  a  check  upon  the  operation. 


Example:  Find  the  intersection  of  the  following  Sumner  lines: 


^^4  6    55.3  W. 


/SO 
L-A  7 


50°  0(K    N. 
20.0  W. 


+20^ 
+24.7 


lat. 
long. 


'.{ 


49 


40     N. 
32.5  W. 


B,{% 


00     N. 
11.3  W. 


+20     lat. 
—21.2  long. 


Line  runs  NW.-SE. 
(i-=51°. 

Line  runs  NE.-SW. 

/i=47°. 


Longitude  A^  B,=22 


Fig.  47. 
Hence,  intersection: 


First  draw  a  rough  sketch  (fig.  47)  to  illustrate  the  direction 
of  coordinates. 

Notice  that  A,  is  west  of  Bj.  The  line  through  Aj  runs 
NW.-SE.  That  through  B„  NE.-SW.  The  intersection  is 
therefore  south  of  both,  east  of  Aj,  and  west  of  Bj. 

(a)  To  solve  by  Table  5  B:  First  bearing  (90°— a)  =39°; 
second  bearing  (90° -^/J)  =  137°.  Corresponding  ratio,  0.43,  mul- 
tiplied by  22^8  =  9'. 8  lat.  (The  angles  90° - /i and  90°—  a  would 
have  given  the  same  ratio,  0.43. )  Then  (Table  2)  with  a  =  51°, 
lat.  =9'.8,  dep.  =12M;  and  with  /i  =  47°,  lat.  =9^8,  dep.  = 
10^5. 


9^8  S.  of  lat.  49°  40'  N.  =49= 
12  .1  E.  of  long.  6  55.3  W.  =  6' 
10  .5  W.  of  long.  6    32.5  W.  =   6' 


(b)  To  solve  by  Table  2: 

Assuming  lat y 

Dep.  for  51° 6.2 

Dep.  for  47° 5.3 


Hence,  intersection: 


Sum 


.11.5 


9.7 

8.5 


18.2 


30' 
;°  43 

;°  43. 

10' 

12.3 
10.7 

23.0 


,2N. 

0  YV.  n^^*^^' 


9'.9 

12.2 
10.6 

22.8 


9'.9  S. 
12  .2  E. 
10  .6  W. 


of  49°  40' 
of    6   55.3 
of    6  32.5 


=  49°  30'.  1. 
=  6  43  .11 
=   6    43  .1/ 


check. 


It  may  be  seen  that  the  results  by  the  two  methods  substantially  agree. 

396.  Case  II.  Both  lines  XE.-SW.,  or  both  XW.-SE. — Consider  the  lines  as  drawn  in  figure  48,  and 

continue  the  assumption  that  Aj  and  B,  have  a  common 
latitude.  The  differences  from  the  first  case  by  both 
methods  simply  involve  a  change  of  signs. 

(o)  If  the  ship  is  steaming  from  Aj  toward  B,,  the 
first  angle  from  the  keel  line  is  90°  —  a,  and  the  second, 
90°  —/i]  if  steaming  from  Bi  toward  A,,  the  first  angle  is 
90°  +  /i,  and  the  second  90°^  a;  in  other  words,  either 
add  both  angles  to  90°  or  subtract  both  from  90°  and 
enter  with  the  smaller  angle  as  the  first  bearing. 

{h )  It  may  be  seen  that  0  Aj  ~  OBj  =  Aj  Bj ;  in  other 
words,  to  solve  by  the  second  method,  the  values  must 
be  so  found  that  the  difference  of  the  corresponding  depar- 
tures equals  the  difference  of  longitude,  instead  of  their 
sums,  as  before. 


Fig.  48. 
Example:  Find  the  intersection  of  the  Sumner  lines  defined  V)elow; 


i   /  49°  30'    N.         .    f  49°  50' 
^U   5    24.8  W.       -^n    5    21.5 

T,  /49    30     N.        „   149    50 
■^H   5    25.8  W.       ^4   4    52.1 

Ai  Bi=l'.0. 


+20'    lat. 
—3.3    long. 

+20     lat. 
—33.7  long. 


Line  runs  NE.-SW. 

<r=9°. 

Line  runs  NE.-SW. 
/i=59°. 


In  this  case  (fig.  49)  B,  is  west  of  A,,  the  lines 
both  run  NE.-SW.,  and  fi  is  the  greater  angle;  there- 
fore intersection  lies  to  the  north  and  east  of  both  points. 

(a)  By  Table  5  B:  First  course  (90°  +  a)  =  99°; 
second  course  (90°  +  /3)=  149°;  ratio  0.67X^.0  = 
0'.7;  or,  first  course  (90°  — /if)  =  31°;  second  course 
(90°  — a)  =  81°;  ratio  =  0.67,  as  before. 


Fig.  49. 

=  9°,  lat.  =0'.7,  dep.  =0'.l;  and  (i-- 


:59°,  lat.  =0'.7,  dep.  =1'.2. 


THE    SUMNER   LINE. 


121 


Hence,  intersection: 


(b)  By  Table  2: 


.7  N.  of  49°  3(y      N.    =49°  30^7  N. 
.1  E.  of    5    24  .8  W.  =  5    24 
.2  E.  of    5    25  .8  AV.  =   5 


6  w!  }  check. 


Assuming  lat 2^.0 

Dep.  for    9° 0.3 

Dep.  for  59° 3  .3 

Difference 3.0 


24.6 


0^5         0^6 


0.1 
0.9 

0.8 


0.1 
1  .1 

1  .0 


Hence,  intersection: 


0^.6  N.  of  49°  30' 

0  .1  E.  of    5    24 

1  .1  E.  of    5    25 


=  49°  30^6 
;=  5    24.7 

1=  5    24 


-  j- check. 


387.  In  discussing  these  cases,  we  have  assumed  that  there  was  a  point  of  one  Une  which  had  a 
common  latitude  with  a  point  of  the  other  line;  this  would  be  the  case  if  two  lines  were  worked  from 
time  sights  taken  at  the  same  time.  It  may  occur,  however,  either  that  they  have  not  a  common  lati- 
tude, but  do  have  a  common  longitude,  as  in  the  case  of  two  lines 
worked  from  <p'  q/^  (latitude)  sights  taken  at  the  same  time;  or  that 
they  have  neither  a  common  latitude  nor  a  common  longitude,  as 

with  one  time  sight  and  one 
latitude  sight,  or  with  two 
sights  taken  at  different 
times. 

In  case  there  is  a  com- 
mon longitude  (fig.  50), 
which  will  be  rather  a  rare 
one,  the  problem  is  worked 
with  OP  as  a  longitude  co- 
ordinate; the  modification 
of  the  other  method  will 
B,  suggest  itself,  the  principal 

change  rendered  necessary  being  due  to  the  fact  that  the 
angles  from  the  course  in  Table  5  B  will  be  complementary 
to  what  they  were  before,  as  we  are  now  dealing  with  angles 
to  the  meridian  instead  of  angles  to  the  parallel. 

When  there  is  no  common  coordinate  of  either  latitude 
or  longitude,  the  simplest  way  of  solving  is  first  to  find  some 
point  on  one  line  which  corresponds  in  latitude  with  one  of 
the  points  on  the  other  line,  then  solve  as  before. 

Thus,  in  figure  51,  given  A,  A.^  and  Bj  B.^,  find  ix  and  p,  and 
thence  the  longitude  of  a  point  A3  corresponding  to  the  difference  of  latitude  between  Aj  and  By  on  the 
course  a;  then  find  intersection  of  A3  A.^  and  Bj  Bj  in  the  usual  way. 

Example:  Let  it  be  required  to  find  the  intersection  of  Sumner  lines  as  follows: 

/  25°  50^  S.         +20'  lat.  Line  runs  SE.-NW. 


• 

\ 

% 

\ 

<(" 

/A3 

0 

~^^/ 

a  / 

Fig.  51. 


.  /  25°  30^  S. 
^H115    22  E. 

T,  /  25    15    S. 
^M115    37   E. 


*\115    40   E.         +18   long.         a=42°. 


B, 


25    35    S. 
nil5    30  E. 


-20  lat. 
-  7   long. 


Line  runs  NE.-SW. 
/i=19° 


Find  where  Bj  B.^  crosses  parallel  25°  30'  S. 

/i=19°,  lat.  =  +15',  dep.  =  —  5'.1.     Hence,  the  line  B3  Bj,  becomes: 

f    25°  30'  S.        ^    c  _„,  o     Line  runs  NE.-SW. 

Ii=  19°. 


B. 


=9'.  9 


Ullo    31.9  E.     '"^1  ^=* 

The  directions  of  the  lines  (fig.  52)  require  us  to  follow  Case  I.    Aj  is  west  of  B3.    The  line  through 
,  runs  SE.-NW.,  and  that  through  Bg.SW.-NE.     Therefore,     A  o 


A,  runs  bh^.-.n  vv  .,  ana  tnat  tnrougn  Ug,  s vv  .->  Ji.     ineretore,    /\ 
the  intersection  is  south  of  Ai  and  B3,  east  of  Aj,  and  west 
ofBj. 

(o)  By  Table  5  B.  (90°-a)=48°,  (90°4-/i)=109°.  Ratio 
0.81X9'.9=8'.0  lat.;  a=42°,  lat.=8'.0,  dep.=7'.2.  /i=19°; 
lat.  =8'.0,  dep.=2'.7. 


Hence,  intersection: 


(6)  By  Table  2: 


8'    S.  of    25°  30'     S.  =  25°  38'    S. 

7.2  E.  of  115    22     E.=115  29.2  E.\  ,      , 

2.7W.ofll5    31.9E.=115  29.2  E.r^^^'^" 

Assuming  lat 6'  8' 

Dep.  for  42° 5.5        7.2 

Dep.  for  19° 2.1        2.7 

Sum 7.G        9.9 


122 


THE    SUMNEE    LINE. 


Intersection: 


8^    S.    of    25°  30'    =  25°  38' 

7.2  E.    of  115    22     =115    29.2\  ,      , 

2.7  W.  of  115    31.9=115    29.2r"^"^- 


3§§.  The  foUow^jpg  is  a  summary  of  the  method  when  lines  are  given  by  coordinates  of  two 
points  of  each: 


(a)  By  Tables  B. 

1.  Write  down  hnes;  find  a  and  /?. 

2.  If  there  are  no  points  which  have  a  common 
latitude,  reduce  one  point  of  one  line  to  latitude  of 
some  given  point  of  the  other. 

3.  Write  down  difference  of  longitude. 

4.  Draw  rough  sketch  to  illustrate  direction  of 
point  of  intersection. 

5.  Enter  Table  5  B: 

Case  I,  angles  (90°  -  a)  and  (90°  +  /3)  or  (90°  - 
fi)  and  (90°  + a). 

Case  II,  angles  (90°  +  a)  and  (90°  +  ft)  or  (90°  — 
fi)  and  (90° -a). 

Take  out  ratio  from  second  column,  and  multiply 
by  difference  of  longitude;  this  gives  difference  of 
latitude  of  intersection  from  the  common  latitude. 

6.  Find  departure  corresponding  respectively  to 
cc  and  ft  with  latitude;  this  gives  differences,  of 
longitude  to  the  point  of  intersection  from  the  re- 
spective points  or  common  latitude. 


(6)  By  Table  2. 

1.  Write  down  lines;  find  a  and  ft. 

2.  If  there  are  no  points  which  have  a  common 
latitude,  reduce  one  point  of  one  line  to  latitude  of 
some  given  point  of  the  other. 

3.  Write  down  difference  of  longitude. 

4.  Draw  rough  sketch  to  illustrate  direction  of 
point  of  intersection. 

5.  Enter  Table  2,  at  pages  a  and  ft;  find  by  trial 
some  latitude  at  which — 

Case  I,  the  sum  of  the  corresponding  departures 
equals  the  total  difference  of  longitude; 

Case  II,  the  difference  of  the  corresponding  de- 
partures equals  the  total  difference  of  longitude. 

These  give  differences  of  latitude  and  longitude 
to  the  point  of  intersection  from  the  respective 
points  of  common  latitude. 


3§9.  If  the  lines,  instead  of  being  defined  by  coordinates  of  two  points,  are  defined  by  the  coordi- 
nates of  one  point  of  each  with  its  direction  as  deduced  from  the  azimuth  of  the  body,  it  will  be  better 
not  to  consider  the  projection  on  the  fictitious  plane  through  the  meridian,  as  there  will  then  be  no 
advantage  in  so  doing.  In  this  case,  consider  the  angles  of  the  lines  with  the  meridian,  as  given,  a  and 
ft;  reduce  the  difference  of  longitude  Aj  Bi  to  departure,  and  use  this  in  miles  instead  of  the  Ai  B,  in 
minutes;  and  when  AjO  and  BjO  are  found,  being  in  miles  of  departure,  they  must  be  reduced  to  min- 
utes of  longitude  l)efore  being  applied  to  the  longitude  of  A,  and  Bj. 

Example:  The  Sumner  lines  of  the  last  example  being  expressed  by  a  single  point  and  the  direction, 
as  given  below,  find  the  intersection. 


f  25°  40^ 
1115    31 


B 


ill 


25    25      S. 


115    33.5   E. 


Line  runs  (a  =)  N.  39°  W. 
Line  runs  {ft  =)  N.  18°  E. 


First  bring  second  line  up  to  Lat.  25°  40^8.     ft  =  18°;   lat.  =  +  15';  dep.  =  —  4.9  m. ;  diff.  long.  = 
—  5^.4;  hence  we  have: 

40'    S. 


28.1  E. 


Line  runs  {ft  =  )  N.  18°  E. 


Fig.  53. 
Intersection: 


AB'  =  2'.9  =  2.6  miles. 

B'  Ijeing  west  of  A  ( fig.  53) ,  and  the  lines  through  the  two 
points  running  respectively  NE.  and  NW.,  the  intersection  is  north 
of  both,  east  of  B',  and  west  of  A. 

(a)  By  Table  5  B.  (90°  -  a)  =51°;  (90° +^)  =  108°.  Ratio 
0.88  X  2.6  =  2'.3  lat.  a  =  39°,  lat.  =  2'.3,  dep.  =  1.8 m., diff.  long.  = 
2.0.     ft  =  18°,  lat.  =  2'.3,  dep.  =  0.7  m.,  diff.  long.  =  0.8. 


2'.3N.    of    25°  40'    S.  =    25°  37'. 7  S. 

2  .0  W.  of  115    31     E.  =  115    29      K-Lheck. 


0  .8  E.    of  115    28.1  E.  =  115    28 


(ft)   By  Table  2: 


Assuminglat 1-4'  2'  2'.3 

Dep.  for  39° 3.2  1.6  1.9  =  2'.l 

Dep.forl8° 1.3  0.7  0.7=0.8 

Sum 4.5  2.3  2.6  =  2.9 


Intersection: 


=    25°  37'  7 
2  .IW.  of  115    31     =115    28:9|^heck. 


2'.3  N.  of     25°  40 

2  .1  W.  ol 

0.8E.  of  115    28.1  =  115    28 


THE    SUMNEE    LINE. 


123 


The  followinjj;  Hiimmary  gives  the  various  steps  when  the  lines  are  each  given  Ity  tlie  coordinates  of 
one  point  with  the  direction: 


(«)  By  Tables  B. 

1.  Write  down  lines  as  given. 

2.  If  the  points  have  not  a  common  latitude, 
reduce  one  point  to  latitude  of  the  other. 

3.  Write  down  difference  of  longitude  and  con- 
vert it  to  departure. 

4.  Draw  rough  sketch  to  illustrate  direction  of 
point  of  intersection. 

5.  Enter  Table  5  B: 

Case  I,  angles  (90°-a)  and  (90°!  /i)  or  (90° -/i) 
and  (90°+<:r). 

Vase  IT,  angles  (90°4-^0  and  (90°+/i)  or  (90°-/i) 
and  (90°— ct). 

Take  out  ratio  from  second  column,  and  multiply 
by  departure  between  the  two  points;  this  gives 
difference  of  latitude  of  intersection  from  common 
latitude. 

6.  Find  departure  corresponding  respectively  to 
a  and  fi  with  this  difierence  of  latitude,  and  con- 
vert to  difference  of  longitude;  this  gives  differences 
of  longitude  to  the  point  of  intersection  from  the 
respective  points  of  common  latitude. 


{b)  By  Tabled. 

1.  Write  down  lines  as  given. 

2.  If  the  points  have  not  a  common  latitude, 
reduce  one  jjoint  to  latitude  of  the  other. 

3.  Write  down  difference  of  longitude  and  con- 
vert it  to  departure. 

4.  Draw  rough  sketch  to  illustrate  direction  of 
point  of  intersection. 

5.  Enter  Table  2  at  pages  cc  and  fi;  find  ])y  trial 
some  latitude  at  which — 

Case  I,  the  sum  of  the  corresponding  departures 
equals  the  departure  between  the  two  points; 

Case  II,  the  difference  of  the  corresponding 
departures  equals  the  departure  between  the  two 
points. 

This  difference  of  latitude,  and  these  departures 
(converted  into  difference  of  longitude)  give  dis- 
tance of  point  of  intersection  in  latitude  and 
longitude  from  the  respective  points  of  common 
latitude. 


390.  The  modification  of  the  methods  for  finding  the  intersection  of  two  Sumner  lines,  where  there 
is  a  run  between  the  observations  from  which  they  are  deduced,  will  be  readily  apparent.  It  is  known 
that  at  the  time  of  taking  a  sight  the  vessel  is  at  one  of  the  points  of  the  Sumner  line,  but  which  of  the 
various  points  represents  her  precise  position  must  remain  in  doubt  until  further  data  are  acquired. 
Sujipose,  now,  that  after  an  observation  the  ves.«el  sails  a  given  distance  in  a  given  direction;  it  is  clear 
that  while  her  exact  position  is  still  undetermined  it  must  be  at  one  of  the  series  of  points  comprised  in 
a  line  parallel  to  the  Sumner  line  and  at  a  distance  and  direction  therefrom  corresponding  to  the  course 
and  distance  made  good;  hence,  if  a  second  sight  is  then  taken,  the  position  of  the  vessel  may  be  found 
from  the  intersection  of  two  lines — one,  the  Sumner  line  given  by  the  second  observation,  and  the  other 
a.  line  parallel  to  the  first  Sumner  but  removed  from  it  by  the  amount  of  the  intervening  run. 

Positions  may  be  brought  forward  graphically  on  a  chart  by  taking  the  course  from  the  compass 
rose  with  parallel  rulers,  and  the  distance  by  scale  with  dividers.  If  the  method  given  in  article  383  be 
employed,  runs  in  latitude  and  longitude  must  each  be  applied  on  their  own  scales,  as  explained  in  the 
description  of  the  method.  If  one  of  the  methods  by  computation  be  adopted,  the  point  or  points  of 
the  first  line  are  brought  forward  by  the  traverse  tables,  using  middle  latitude  sailing.  The  direction  of 
a  Sumner  line  as  determined  from  the  azimuth  of  the  body  always  remains  the  same,  whatever  shift 
may  be  made  in  the  position  of  the  point  by  which  the  line  is  further  defined. 


124  THE    PEACTICE    OF    NAVIGATION    AT    SEA. 


•  CHAPTER  XVI. 

THE  PEACTICE  OF  NAViaATION  AT  SEA. 


391.  Having  set  forth  in  previous  chapters  the  methods  of  working  dead  reckoning  and  of  solv- 
ing problems  to  find  the  latitude,  longitude,  chronometer  correction,  and  azinuith  from  astronomical 
observations,  it  will  be  the  aim  of  the  present  chapter  to  describe  the  conditions  which  govern  the 
choice  and  employment  of  the  various  problems,  together  with  certain  considerations  by  which  the 
navigator  may  be  guided  in  his  practical  work  at  sea. 

392.  Departire  and  Dead  Reckoning. — On  beginning  a  voyage,  a  good  departure  must  be  taken 
while  landmarks  are  still  in  view  and  favorably  located  for  the  purpose;  this  becomes  the  origin  of  the 
dead  reckoning,  which,  with  frequent  new  departures  from  positions  by  observation,  is  kept  up  to  the 
completion  of  the  voyage,  thus  enabling  the  mariner  to  know,  with  a  fair  degree  of  accuracy,  the  posi- 
tion of  his  vessel  at  any  instant. 

At  the  moment  of  taking  the  departure,  the  reading  of  the  patent  log  (which  should  have  been 
put  over  at  least  long  enough  previously  to  be  regularly  running)  must  be  recorded,  and  thereafter  at 
the  time  of  taking  each  sight  and  at  every  other  time  when  a  position  is  required  for  any  purpose,  the 
log  reading  must  also  be  noted.  It  is  likewise  well  to  read  the  log  each  hour,  for  general  information  as 
to  the  speed  of  the  vessel  as  well  as  to  observe  that  it  is  in  proper  running  order  and  that  the  rotator 
has  not  been  fouled  by  seaweed  or  by  refuse  thrown  overboard  froin  the  ship.  It  is  a  good  plan  to 
record  the  time  by  ship's  clock  on  each  occasion  that  the  log  is  read,  as  a  supplementary  means  of  arriv- 
ing at  the  distance  will  thus  be  available  in  case  of  doubt.  If  a  vessel  does  not  use  the  patent  log  but 
estimates  her  speed  by  the  number  of  revolutions  of  the  engines  or  the  indications  of  the  chip  log,  the 
noting  of  the  time  becomes  essential.  A  good  sight  is  of  no  value  unless  one  knows  the  point  in  the 
ship's  run  at  which  it  was  taken,  so  that  the  position  it  gave  may  be  brought  forward  with  accuracy  to 
any  later  time. 

393.  Routine  Day's  Work. — The  routine  of  a  day's  work  at  sea,  no  part  of  which  should  ever  be 
neglected  unless  cloudy  weather  renders  it  impossible  to  follow,  consists  in  working  the  dead  reckoning, 
an  a.  m.  time  sight  and  azimuth  taken  when  the  sun  is  in  its  most  favorable  position  for  the  purpose,  a 
meridian  altitude  of  the  sun  (or,  when  clouds  interfere  at  noon,  a  sight  for  latitude  as  near  the  meridian 
as  possible) ,  and  a  p.  m.  time  sight  and  azimuth.  This  represents  the  minimum  of  work,  and  it  may  be 
antplified  as  circumstances  render  expedient. 

394.  Morning  Sights. — The  morning  time  sight  and  azimuth  should  be  observed,  if  possible,  when 
the  sun  is  on  the  prime  vertical.  As  the  body  bears  east  at  that  time,  the  resulting  Sumner  line  is  due 
north  and  south,  and  the  longitude  will  thus  be  obtained  without  an  accurate  knowledge  of  the  latitude. 
Another  reason  for  so  choosing  the  time  is  that  near  this  point  of  the  sun's  apparent  path  the  body  is 
changing  most  slowly  in  azimuth,  and  an  error  in  noting  the  time  will  have  the  minimum  effect  in 
its  computed  bearing.  The  time  when  the  sun  will  be  on  the  prime  vertical — that  is,  when  its  azimuth 
is  90° — may  be  found  from  the  azinmth  tables  or  the  azimuth  diagram.  Speaking  generally,  during 
half  the  year  the  sun  does  not  rise  until  after  having  crossed  the  prime  vertical,  and  is  therefore  never 
visible  on  a  bearing  of  east.  In  this  case  it  is  best  to  take  the  observation  as  soon  as  it  has  risen  above 
the  altitude  of  uncertain  atmospheric  effects — between  10°  and  15°. 

A  series  of  several  altitudes  should  be  taken,  partly  because  the  mean  is  more  accurate  than  a  single 
sight,  and  partly  because  an  error  in  the  reading  of  the  watch  or  sextant  may  easily  occur  when  there 
is  no  repetition.  If  the  sextant  is  set  in  advance  of  the  altitude  on  even  five  or  ten  minute  divisions  of 
the  arc,  and  the  time  marked  at  contacts,  the  method  will  be  found  to  possess  various  advantages.  As 
the  sight  is  being  taken  the  patent  log  should  be  read  and  ship's  time  recorded.  It  is  well,  too,  to  make 
a  practice  of  noting  the  index  correction  of  the  sextant  each  time  that  the  sextant  is  used.  The  bearing 
of  the  sun  by  compass  should  immediately  afterward  be  observed,  and  the  heading  by  compass  noted, 
as  also  the  time  (by  the  same  watch  as  was  used  for  the  sight). 

Before  working  out  the  sight,  the  dead  reckoning  is  brought  up  to  the  time  of  observation,  and  the 
latitude  thus  found  used  as  the  approximate  latitude  at  sight.  It  is  strongly  recommended  that  every 
sight  be  worked  for  a  Sumner  line,  either  by  assuming  two  latitudes,  or  by  using  one  latitude  and  the  azi- 
muth, the  advantages  derived  therefrom  being  always  well  worth  the  small  additional  labor  expended. 

The  compass  error  is  next  obtained.  From  the  time  sight  the  navigator  learns  that  his  watch  is  a 
certain  amount  fast  or  slow  of  L.  A.  T.,  and  he  need  only  apply  this  correction  to  the  watch  time  of 
azimuth  to  obtain  the  L.  A.  T.  at  which  it  was  observed;  thence  he  ascertains  the  sun's  true  bearing 
from  the  azimuth  tables  or  azimuth  diagram,  compares  it  with  the  compass  bearing,  and  obtains  the 
compass  error;  he  should  subtract  the  variation  by  chart  and  note  if  the  remainder,  the  deviation,  agrees 
with  that  given  in  his  deviation  table;  but  in  working  the  next  dead  reckoning,  if  the  Ship's  course 
does  not  change,  the  total  compass  error  thus  found  may  be  used  without  separating  it  into  its  compo- 
nent parts.  It  should  be  increased  or  decreased,  however,  as  the  ship  proceeds,  by  the  amount  of  any 
change  of  the  variation  that  the  chart  may  show. 

395.  If  there  is  any  fear  of  the  weather  being  cloudy  at  noon,  the  navigator  should  take  the  pre- 
caution, when  the  sun  has  changed  about  30°  in  azimuth,  to  observe  a  second  altitude  and  to  record 
the  appropriate  data  for  another  sight,  though  this  need  not  actually  be  worked  unless  the  meridian 


THE    PRACTICE    OF    NAVIGATION    AT    SEA.  125 

observation  is  lost.  If  it  is  required,  it  may  be  worked  for  either  a  time  sight  or  cp'  cp"  sight,  according 
to  circumstances,  a  second  Sumner  line  obtained,  and  the  intersection  of  the  earlier  Sumner  with  it  will 
give  the  ship's  position. 

396.  Noox  SuiHTs. — Between  11  and  11.30  o'clock  (allowing  for  gain  or  loss  of  time  due  to  the 
day's  run)  the  ship's  clocks  should  be  set  for  the  L.  A.  T.  of  the  prospective  noon  position.  The  noon 
longitude  may  be  closely  estimated  from  the  morning  sight  and  the  probable  run.  The  navigator 
should  also  set  his  own  watch  for  that  time,  to  the  nearest  minute,  and  note  exactly  the  number  of 
seconds  that  it  is  in  error.  lie  may  now  compute  the  constant  (art.  333,  Chap.  XII)  for  the  meridian 
altitude.  The  daily  winding  of  the  chronometer  is  a  most  important  feature  of  the  day's  routine,  and 
may  well  be  pei'formed  at  this  hour.  At  a  convenient  time  before  noon,  the  observations  for  meridian 
altitude  are  commenced  and  continued  until  the  watch  shows  L.  A.  noon,  at  which  time  the  meridian 
altitude  is  measured  and  the  latitude  deduced. 

If  the  weather  is  cloudy  and  there  is  doubt  of  the  sun  being  visible  on  the  meridian,  an  altitude 
may  be  taken  at  any  time  Avithin  a  few  minutes  of  noon,  the  time  noted,  and  the  interval  from  L.  A. 
noon  found  from  the  known  error  of  the  watch.  It  is  then  the  work  of  less  than  a  minute  to  take  out 
the  a  from  Table  26,  the  of  from  Table  27,  and  apply  the  reduction  to  the  observed  altitude  to  obtain 
the  meridian  altitude.  Indeed,  the  method  is  so  simple  that  it  may  be  practiced  every  day  and  several 
values  of  the  meridian  altitude  thus  obtained,  instead  of  only  one. 

397.  It  now  becomes  necessary  to  find  the  longitude  at  noon.  This  may  be  done  graphically  by 
a  chart,  or  by  computation.  The  former  plan  needs  no  explanation.  There  are  a  number  of  variations  in 
the  methods  of  computation,  one  of  which  will  l)e  given  as  a  type. 

By  the  ship's  run,  work  1)ack  the  noon  latitude  to  the  latitude  at  a.  m.  time  sight.  If  the  Sumner 
line  was  found  from  two  assumed  latitudes  which  differed  +  '«  minutes,  while  the  corresponding  longi- 
tudes differed  zfc  n  minutes,  then  V  difference  of  latitude  causes  ±  —  minutes  difference  of  longitude.    If 

m 

the  true  latitude  at  sight  is  rf:  o-  minutes  from  one  of  the  assumed  latitudes,  then  i  .)-•  X  —  is  the  corre- 

m 

sponding  difference  of  longitude.     If  the  Sumner  line  was  found  from  one  assumed  latitude  and  an 

azimuth,  Z,  it  makes  an  angle  with  the  meridian  equal  to  90°  — Z.     Enter  the  traverse  table  with  this 

as  a  course  and  with  the  difference  between  the  true  and  assumed  latitudes  as  a  latitude,  and  the 

departure  will  be  found;  convert  this  into  difference  of  longitude  at  the  latitude  of  observation,  and 

apply  the  result  with  its  ])roper  sign  to  the  longitude  corresponding  to  the  assumed  latitude.     Having 

thus  the  longitude  at  sight,  the  longitude  at  noon  is  worked  forward  for  the  run.     If  the  sights  show  a 

considerable  current  it  should  be  allowed  for,  both  in  working  back  the  latitude  and  in  bringing  uji  the 

longitude  for  the  run  between  the  sight  and  noon. 

39§.  CiKRENT  AND  EuN. — The  current  may  be  found  by  comparing  the  noon  positions  as  obtained 
by  observation  and  by  dead  reckoning;  and  the  day's  run  is  calculated  from  the  difference  between  the 
day's  noon  position  by  observation  and  that  of  the  preceding  day.  To  "current"  is  usually  attributed 
all  discrepancies  between  the  dead  reckoning  and  observations;  but  it  is  evident  that  this  is  not  entirely 
due  to  motion  of  the  waters,  as  it  includes  errors  due  to  faulty  steering,  improper  allowance  for  the 
compass  error,  and  inaccurate  estimate  of  the  vessel's  speed  through  the  water. 

The  noon  position  by  observation  becomes  the  departure  for  the  dead  reckoning  that  follows. 

399.  Afterxoon  SiciHTS. — The  p.  m.  time  sight  and  azimuth  is  similar  to  the  morning  observation. 

400.  Sumner  Lines. — By  performing  the  work  that  has  just  been  described  a  good  position  is 
obtained  at  noon  each  day,  which,  in  a  slow-moving  vessel  with  plenty  of  sea  room,  may  be  considered 
sufficient;  but  conditions  are  such  at"  times  as  to  render  it  almost  imj)eratively  necessary  that  a  more 
frequent  determination  of  the  latitude  and  longitu<ie  be  made.  If  the  vessel  is  near  the  land  or  in  the 
vicinity  of  off-lying  dangers,  if  she  is  running  a  great  circle  course  requiring  frequent  changes,  if  she  is 
making  deep-sea  soundings,  if  she  has  just  come  through  a  period  of  foggy  or  cloudy  weather,  or  if  the 
indications  are  that  she  is  about  to  enter  upon  such  a  period,  it  is  obviously  inexpedient  to  await  the 
coming  of  the  next  noon  for  a  tix.  The  responsibilities  resting  upon  the  navigator  require  that  he  shall 
earlier  find  his  ship's  position;  and,  generally  speaking,  the  greater  the  speed  made  bj^  the  vessel  the 
more  absolute  is  this  recjuirement. 

The  key  to  all  such  determinations  will  lie  in  the  Sumner  line,  and  a  clear  understanding  of  the 
properties  of  such  a  line  will  greatly  facilitate  the  solutions.  The  mariner  must  keep  in  mind  two  facts: 
First,  that  a  single  observation  of  a  heavenly  body  can  never,  by  itself,  give  the  point  occupied  by  an 
observer  on  the  earth's  surface;  and  second,  that  whenever  any  celestial  body  is  visible,  together  with 
enough  of  the  horizon  to  permit  the  measuring  of  its  altitude,  an  observer  may  thereby  determine  a  Viue 
which  passes  through  his  own  position  on  the  earth's  surface  in  a  direction  at  right  angles  to  the  bearing 
of  the  body. 

It  may  readily  be  seen  that  if  two  Sumner  lines  are  determined  the  observer's  position  must  be  at 
their  intersection,  and  that  that  intersection  will  be  most  clearly  marked  when  the  angle  between  the 
lines  equals  90°;  hence,  if  two  heavenly  bodies  are  in  sight  at  the  same  time  the  position  may  be  found 
from  the  intersection  of  their  Sumner  lines,  the  angle  of  intersection  being  equal  to  the  horizontal 
angle  between  the  bodies.  If  only  one  body  is  in  sight,  as  is  generally  the  case  when  the  sun  is  shining, 
one  line  of  position  may  be  gotten  from  an  altitude  taken  at  one  time,  and  a  second  line  from  another 
altitude  takeii  when  it  has  changed  some  30°  in  azinmth — usually,  a  couple  of  hours  later.  Bringing 
forward  the  first  line  for  the  intervening  run,  the  intersection  may  be  found. 

With  the  general  principles  of  the  Sumner  line  clearly  before  him,  the  navigator  will  find  no  diffi- 
culty in  making  the  choice  of  available  bodies.  If  about  to  take  a  star  sight,  and  sky  and  horizon  are 
equally  good  in  all  iiuarters,  two  bodies  should  be  taken  whose  azimuths  differ  as  nearly  as  possible  by 
90°.  If  one  body  can  be  taken  on  or  near  the  meridian,  its  bearing  being  ])ractically  north  or  south, 
the  resulting  Sumner  line  will  be  east  and  west — that  is,  it  may  be  said  that  whatever  the  longitude 
(within  its  known  limits)  the  latitude  will  be  the  same;  the  other  sight  may  then  be  worked  as  a  time 
si^ht  with  this  single  latitude  and  time  will  thus  be  saved.  The  same  is  true  if  Polaris  is  observed,  and 
it  is  a  very  convenient  practice  to  take  an  altitude  of  that  star  at  dawn  and  obtain  a  latitude  for  working 


126  THE    PRACTICK    OF    NAVIGATION    AT    SEA. 

the  a.  m.  time  sijiht  of  the  sun.  A  similar  c:ise  arises  when  a  both-  is  observed  on  the  prime  vertical; 
its  Sumner  line  then  runs  north  and  south  and  coincides  with  a  meridian;  if  the  other  body  is  favorably 
located  for  a  ip'  (p''  sijrht,  it  niav  be  worked  with  a  single  longitude  and  the  latitude  thus  found  directlv. 

If  it  is  not  possible  to  obtain  two  lines  and  thus  exactly  locate  the  ship,  the  indications  of  a  single 
line  may  be  of  great  value  to  the  navigator.  A  Sumner  line  and  a  terrestrial  bearing  will  give  the  ship's 
position  by  their  intersection  in  the  same  manner  as  two  lines  of  position  or  two  l)earing.<;  or  the  posi- 
tion of  the  ship  on  a  line  may  be  shown  with  more  or  le.«s  accuracy  by  a  sounding  or  a  series  of 
soundings.  If  the  body  be  observed  when  it  bears  in  a  direction  at  right  angles  to  the  trend  of  a 
neighboring  shore  line,  the  resulting  line  will  be  parallel  with  the  coast  and  thus  show  the  mariner  his 
distance  from  the  land,  which  may  be?  of  great  importance  even  if  his  exact  position  on  the  line  remains 
in  doubt.  If  t'.ie  bearing  be  ]>arallel  to  the  coast  line,  then  the  Sumner  line  will  point  toward  shore; 
the  value  of  a  line  thafc*!eads  to  the  point  that  the  vessel  is  trying  to  pick  up  is  amply  demonstrated  by 
the  experience  of  Captain  Sumner  that  led  to  the  discovery  of  the  method  (art.  372,  Chan.  XV). 

For  especially  accurate  work  three  Sumner  lines  may  be  taken,  varying  in  azimuth  about  120°;  if 
they  do  not  intersect  in  a  point,  the  most  probable  position  of  the  ship'  is  at  the  center  of  the  triangle 
that  they  form. 

If  two  pairs  of  lines  be  determined,  each  pair  based  upon  observation  of  two  bodies  l^earing  in 
nearly  opposite  directions  and  at  about  the  same  altitude,  the  mean  positi(>n  that  results  from  the  inter- 
Bection  of  the  four  lines  will  be  as  nearly  as  possible  free  frf)m  those  errors  of  the  instrument,  of  refrac- 
tion, and  of  the  observer,  which  can  not  otherwise  be  eliminated.  This  is  fullv  explained  in  article  451, 
Chapter  XVII. 

401.  Use  of  Staks,  Planets,  and  Moox. — It  may  be  judged  that  the  employment  in  navigation 
of  other  heavenly  bodies  than  the  sun  is  considered  of  the  utmost  imi»ortance,  ancl  mariners  are  urged 
to  familiarize  themselves  with  the  methods  by  which  observations  fif  star.-;,  planets,  and  the  mofni  may 
be  utilized  to  reveal  to  them  the  position  of  their  vessels  at  frequent  intervals  throughout  the  twenty- 
four  hours. 

It  should  be  remembered,  however,  that  in  order  to  be  of  value  these  observations  must  be  accu- 
rate; and  to  measure  an  accurate  altitude  of  the  body  above  the  horizon  it  is  required  not  only  that  the 
body  be  visible  but  also  that  the  horizon  be  distinctly  in  view.  Care  should  therefore  be  taken  to  make 
the  observations,  if  possible,  at  the  time  when  the  horizon  is  plainest — that  is,  during  morning  and 
evening  twilight.  It  may  be  urgently  required  to  get  a  position  during  hours  of  darkness,  and  a  dim 
horizon  line  may  sometimes  be  seen  and  an  observation  taken,  using  the  star  telescope  of  the  sextant; 
if  the  moon  is  shining,  its  light  will  be  a  material  aid;  but  results  ol)tained  from  such  sights  should  be 
regarded  as  questionable  and  used  with  caution.  Altitudes  measured,  however,  just  before  sunrise  and 
just  after  sunset  are  open  to  no  such  criticism;  a  fairly  well-practiced  observer  who  takes  a  series  of  sights 
at  such  a  time,  setting  the  sextant  for  equal  intervals  of  altitude,  will  find  the  regularity  of  the  corre- 
sponding time  intervals" such  as  to  assure  him  of  accuracy. 

402.  Identification  of  Unknown  Bodies. — On  account  of  the  very  great  value  to  be  derived  from 
the  use  of  stars  and  planets  in  navigation,  it  is  stnjngly  recommendetl  that  all  navigators  familiarize 
themselves  with  the  names  and  positions  of  those  fixed  stars  whose  magnitude  renders  possible  their 
employment  for  observations,  and  also  with  the  general  characteristics — magnitude  and  color — of  the 
three  planets  (Venus,  Jupiter,  and  Mars)  which  are  most  frequently  used.  A  study  of  the  different 
portions  of  the  heavens,  with  the  aid  of  any  of  the  numerous  charts  and  books  which  bear  upon  the 
subject,  W'ill  enable  the  navigator  to  recognize  the  more  important  constellations  and  single  stars  by 
their  situation  with  relation  to  each  other,  and  to  the  pole  and  the  equator. 

It  may  occur,  however,  that  occa.«ion  will  arise  for  observing  a  body  Avhose  name  is  not  known, 
either  because  it  has  not  been  learned,  or  because  the  surrounding  stars  by  which  it  is  usually  identified 
are  obscured  by  clouds  or  rendered  invisible  by  moonlight  or  daylight.  In  such  a  case  the  observer 
may  estimate  the  hour  angle  and  declination  (the  hour  angle  applied  to  local  sidereal  time  giving  the 
right  ascension),  and  the  star  or  planet  may  thus  be  recognized  from  a  chart  or  from  an  inspection  of 
the  Nautical  Almanac.  This  rough  method  will  generally  suffice  when  the  body  is  the  only  one  of  its 
magnitude  within  an  extensive  region  of  the  heavens;  but  cases  often  arise  where  a  much  closer 
approximation  is  necessary,  and  more  exact  data  is  required  for  identification. 

403.  If  in  doubt  as  to  the  name  of  the  body  at  the  time  of  taking  the  sight,  it  should  be  made  an 
invariable  rule  to  observe  its  bearing  by  compass,  whence  the  true  azimuth  may  l)e  approximately 
deduced  by  applying  the  compass  error.  The  method  «  to  be  descril)ed  then  affords  a  convenient  n\eans 
of  identification.  The  quantities  given  are  the  corrected  altitude  of  observation,  /;,  the  (approximate) 
true  azimuth  of  the  body,  Z,  and  the  latitude  by  dead  reckoning,  L;  those  to  be  determined  are  the 
declination,  d,  and  the  hour  angle,  /.     From  the  astronomical  triangle  we  have: 

sin  Zsin  t 

~. r;  or,  sm  Z  cos  /i=.«in  t  cos  (/. 

sin  j)    cos  ft 

The  value  of  sin  Z  cos  h  (calculated  from  the  given  azimuth  and  altitude)  must  therefore  equal 
sin  t  cos  (I,  whatever  the  values  of  t  and  d  mav  prove  to  be. 

From  a  given  latitude,  azimuth  and  declination,  the  hour  angle  may  be  found  either  by  azimuth 
tables  or  an  azimuth  diagram;  or  from  a  given  latitude,  azimuth  and  hour  angle,  the  declination  may 
be  found  by  the  same  means.  If,  therefore,  some  probable  value  of  the  declination  be  assumed,  using 
the  known'latitude  and  azimuth,  we  may  ascertain  the  corresponding  hour  angle;  or,  if  the  hour  angle 
be  assumed,  the  corresponding  declination  is  obtained;  then  the  product  of  sin  t  cos  d  may  be  calculated, 
and  if  it  agrees  substantially  with  sin  Z  cos  /(,  the  trial  values  of  the  hour  angle  and  declination  are  the 
correct  ones;  if  not,  other  trials  mav  be  made  until  the  correct  ones  are  found.  It  may  be  remembered 
that  absolutely  exact  results  are  not  sought,  and  in  practice  the  operation  may  be  made  very  short;  the 

n  Suggested  by  Lieut.  G.  W.  Logan,  U.  8.  Navy. 


THE    PRACTICE    OF    NAVIGATIOlSr    AT    SEA. 


127 


values  of  the  quantities  may  be  taken  in  even  degrees  and  the  logarithms  need  not  be  carried  beyond 
the  third  place;  the  sum  of  the  logarithms  will  suffice  and  the  corresponding  numbers  do  not  have  to  be 
taken  out.  The  possibility  that  the  observed  body  may  have  been  a  planet  must  always  be  kept  in 
mind  in  looking  it  up  in  the  star  table  or  chart. 

Example:  May  16,  1879,  in  Lat.  5°  N.,  Long.  2'*  53""  W.  by  I).  R.,  a  star  is  observed  whose  corrected 
altitude  is  38°,  and  true  azimuth  N.  107°  E.  The  Greenwich  sidereal  time  (as  computed  for  use  in  the 
regular  working  of  the  sight)  is  12''  53'".     Let  it  be  required  to  identify  the  body. 

First  find  the  logarithm  of  sin  Z  cos  //. 

Z      107°     sin  9. 981 
h       38°     cos  9.  897 


sin  Z  cos  h  log  9.  878 

Now  suppose  the  observer  estimates  from  the  position  of  the  body  that  its  declination  is  3°  S.  Look 
in  the  azimuth  table  on  the  page  of  latitude  5°  (declination  contrary  name  to  latitude),  and  find  the  hour 
angle  (p.  m.)  corresponding  to  Dec.  3°  and  Az.  107°;  this  is  about  1''  40"';  then  with  fZ==3°,  ^=1''  40'", 
find  sin  t  cos  d.  (Sin  t  may  be  obtained  either  by  converting  time  into  arc  and  taking  from  the  table  in 
the  usual  way,  or  by  multiplying  by  2  and  finding  it  from  the  column  headed  "Hour  P.  M."  Thus  in 
the  present  case  find  the  sine  of  25°  00'  or  of  3''  20"'.  In  using  the  time  column  be  careful  to  take  the 
name  from  the  foot  of  the  page  when  the  double  angle  exceeds  6''. ) 


t   P 
d 


40" 
3° 


sin  9. 626 
cos  9. 999 


sin  t  cos  d  log  9.  625 

As  this  logarithm  should  equal  9.878,  it  is  seen  that  the  assumj)tion  is  incorrect.     Try  a  value  of  the 
declination  5°  farther  south — that  is,  8°  S.     The  corresponding  hour  angle  is  2''  50"'. 

t  2^  50"'     sin  9.  830 
d        8°     cos  9. 996 


sin  t  cos  '/  log  9.  826 

The  logarithm  is  not  yet  (juite  large  enough;  assume  <leclination  10°  S. ;  the  hour  angle  is  3''  20'". 

t  3"  20'"     sin  9.  884 
d       10°      cos  9. 993 


gin  t  cos  d  log  9.  877 

This  is  practically  identical  with  the  logarithm  of  sin  Z  cos  /*,  and  the  correct  values  are,  therefore, 
t=Z^  20"',  d=\Q°  S. 

We  now  have: 

G.  S.  T.  12"    oS-" 

Long.      J 53  W. 

L.  S.  T.  10      00 

H.  A.     _3 20  E. 

R.  A.      13      20 

From  the  Nautical  Almanac  it  is  found  that  the  right  ascension  of  Spica  is  13''  19""  and  the  decli- 
nation 10°  32''  S.     This  is  therefore  the  body  observed. 

Example:  March  18,  1879,  in  Lat.  26°  S..  Long.  5"  42"'  E.,  by  D.  R.,  the  altitude  of  a  body  is  41° 
and  its  azimuth  S.  84°  E. ,  the  Greenwich  sidereal  time  being  10"  52™.     Required  the  name  of  the  body. 

Z  84°  sin  9.998 
h  41°  cos  9^78 
sin  Z  cos  h  log  9.876 

Assume  first  an  hour  angle  of  3''  00'".  The  corresponding  declination  is  23°  (same  name  as  lati- 
tude). 

<  3"  00™  sin  9.849 
d  23°  cos  9.964 
sin  t  cos  d  log  9.813 


Next  assume  an  hour  angle  of  3"  30™.     The  declination  is  tiien  21°  S. 


t  3"  30"'  sin  9.899 
d  21°  cos  9.970 
sin  t  cos  d  log  9.869 


128  THE    PRACTICE    OF    NAVIGATION    AT    SEA. 

Assume  hour  angle  3''  35"'.     Declination  is  gtill  nearest  to  21°  S 

t  '6^  35'"  8in  9.907 
(/  21°  cos  9.970 
sin/  cos(/  log  9.877 

The  last  assumption,  is  therefore  correct. 
We  then  have: 

G.  8.  T.  10"    52"' 

Long.  5 42  E. 

•  L.  S^  T.  16     34 

H.  A.  _3 35  K 

R.  A.  20     09 

As  there  is  no  fixed  star  corresponding  to  these  coordinates  the  tables  for  the  planets  should  be 
consulted.  On  [March  18,  1879,  the  right  ascension  of  Mars  is  20"  09"',  and  the  declination  21°  06^  S. 
This  is  therefore  the  body  that  was  observed. 

404.  The  following  is  a  summary  of  the  method  employed: 

1.  Reduce  time  of  observation  to  Greenwich  sidereal  time  and  find  the  true  altitude  to  the  nearest 
degree.  (These  operations  must  be  performed  before  any  sight  can  be  worked;  they  are,  therefore,  not 
Btrictly  a  part  of  the  ]>rocess  of  identification.) 

2.  Correct  the  observed  azimuth  for  deviation  and  variation. 

3.  Find  the  logarithm  of  sin  Z  cos  h  to  the  third  place. 

4.  Assume  a  declination  and  find  the  corresponding  hour  angle  that  will  produce  the  given  azimuth 
at  the  given  latitude;  orassuine  an  hour  angle  and  find  the  corresponding  declination.  ( Use  an  azimuth 
table  or  diagram  for  the  purpose.) 

5.  Find  the  logarithm  of  sin  t  cos  (/  to  the  third  place. 

0.  Observe  whether  this  agrees  with  the  logarithm  of  sin  Z  cos  /;,  and  if  it  does  not,  repeat  trials 
until  an  agreement  is  found. 

7.  Having  found  the  hour  angle  and  declination,  convert  the  Greenwich  sidereal  time  into  local 
sidereal  time  and  subtract  the  hour  angle  if  west,  or  add  it  if  east;  the  result  is  the  ri^ht  ascension  of 
the  observed  l)ody,  by  which,  with  the  declination  and  magnitude,  the  identification  is  accomplished. 

405.  The  exactness  with  which  the  comparison  of  logarithms  is  carried  out  will  depend  upon  the 
possibility  of  errors  of  identification  in  the  region  of  the  heavens  involved.  It  will  not  usually  be 
necessary  to  find  the  correspondence  as  closely  as  has  been  done  in  the  examples  given,  and  the  cases 
will  be  rare  when,  with  a  fair  estimate  of  hour  angle  or  declination  at  beginning,  a  sufficiently  accurate 
knowle<lge  of  the  values  can  not  be  arrived  at  after  the  second  approximation;  and  frequently  the  first 
will  suffice  for  identificaton. 

406.  Value  of  the  Moon  in  Observations. — Next  to  the  sun,  the  most  conspicuous  body  in  the 
heavens  is  the  moon,  and  it  may  therefore  frequently  be  employed  by  the  mariner  with  advantage. 
Owing  to  its  nearness  to  the  earth  and  the  rapidity'with  which  it  changes  right  ascension  and  declina- 
tion, the  various  corrections  entailed  render  observations  of  this  body  somewhat  longer  to  work  out, 
with  consequent  increased  chances  of  error;  and  errors  in  certain  parts  of  the  work  will  have  more 
serious  results  than  with  other  bodies;  the  navigator  will  therefore  usually  pass  the  moon  by  if  a  choice 
of  celestial  bodies  is  offered  for  a  determination  of  position;  but  so  many  occasions  present  themselves 
when  there  is  no  available  substitute  for  the  moon  that  the  extra  time  and  care  necessary  to  devote  to 
it  are  well  repaid.  During  hours  of  daylight  it  is  often  clearly  visible,  and  its  line  of  position  may  cut 
with  that  of  the  sun  at  a  favorable  angle,  giving  a  good  fix  from  two  observations  taken  at  the  same 
time,  when  the  only  other  method  of  finding  the  position  would  be  to  take  two  sights  of  the  sun  sepa- 
rated by  a  time  interval  in  which  an  imperfect  allowance  for  the  true  run  intervening  would  affect  the 
accuracy  of  the  result,  or  a  clouding-over  of  the  heavens  would  prevent  any  definite  result  whatever  being 
reached;  and  during  the  night,  the  gleam  upon  the  water  directly  below  the  moon  may  define  the 
horizon  and  give  opportunity  for  an  altitude  of  that  body  when  it  is  impossible  to  take  an  observation 
of  any  other.  Navigators  are  therefore  recommended  to  make  use  of  the  moon  with  complete  confidence 
whenever  it  will  serve  their  purposes.  It  has  been  the  purpose  of  this  work  to  point  out  the  features  of 
the  various  sights  wherein  the  practice  with  the  moon  differs  from  that  of  the  sun,  stars,  or  planets; 
care  and  intelligent  consideration  will  render  these  quite  clear. 

Besides  its  availability  for  determining  Sumner  lines  of  position,  which  it  shares  with  other  bodies, 
the  moon  affords  a  means  for  ascertaining  the  Greenwich  meantime  independently  of  the  chronometer, 
thus  rendering  it  possible  to  deduce  the  longitude  and  chronometer  error.  This  is  accomplished  by  the 
method  of  lunar  distances,  which  is  fully  explained  in  Appendix  V.  If  the  Greenwich  time  given  by 
an  observation  of  lunar  distance  could  be  relied  upon  for  accuracy,  the  methoti  would  be  a  great  boon 
to  the  navigator;  but  this  is  not  the  case.  The  jnost  practiced  observer  can  not  be  sure  of  obtaining 
results  as  close  as  modern  navigation  demands,  and  the  errors  to  which  the  method  is  subject  are  larger 
than  the  errors  that  may  be  expected  in  the  chronometer,  even  when  the  instrument  is  only  a  moder- 
ately good  one  and  its  rate  is  carried  forward  from  a  long  voyage.  The  method  is  not,  therefore,  recom- 
mended for  use  except  Avhere  the  chronometer  is  disabled  or  where  it  is  known  to  have  acquired  some 
extraordinary  error;  and  when  lunar  distances  are  resorted  to  care  must  be  taken  to  navigate  with  due 
allowance  for  possible  inaccuracy  of  the  results.  In  this  connection  it  is  appropriate  to  say  that  the 
best  safeguard  against  the  dire  consequences  that  may  result  from  a  disabled  or  unreliable  chronometer 
is  for  every  vessel  to  carry  two — or,  far  better,  three — of  those  instruments,  the  advantages  of  which 
plan  are  stated  in  article  265,  Chapter  VIII. 

40T.  Employment  of  Bodies  nKPEXOEXT  upon  their  Po.sition. — The  practical  navigator  will  soon 
observe  that  there  are  certain  conditions  in  which  bodies  are  especially  well  adapted  for  the  finding  of 
latitude,  and  others  where  the  longitude  is  obtained  most  readily. 


THE    PRACTICE    OF    NAVIGATION    AT    SEA.  129 

Taking  the  sun  for  an  example,  when  a  vessel  is  on  the  equator  and  the  declination  is  zero,  that 
body  will  rise  due  east  of  the  observer  and  continue  on  the  same  bearing  until  noon,  when  for  an  instant 
it  will  be  directly  overhead,  with  a  true  altitude  of  90°,  and  will  then  change  to  a  bearing  of  west,  which  it 
will  maintain  until  its  setting.  In  such  a  case  any  observation  taken  throughout  the  day  -will  give  a  true 
north-and-south  Sumner  line,  defining  longitude  perfectly,  but  giving  no  determination  of  the  latitude, 
excepting  for  a  moment  only  when  the  body  is  on  the  meridian.     With  the  exception  noted,  all  efforts 

to  determine  the  latitude  will  fail.  The  reduction  to  the  meridian  takes  the  form  ^ ,  becoming  inde- 
terminate, and  in  the  q/  q/'  sight  the  cosine  of  cf/  will  assume  a  value  that  corresponds  alike  to  any 
angle  within  certain  wide  limits — the  limits  within  which  the  circle  of  equal  altitude  has  practically  a 
north-and-south  direction.  In  conditions  approximating  to  this  we  may  obtain  a  longitude  position 
more  easily  than  one  for  latitude,  even  within  a  few  minutes  of  noon. 

As  the  latitude  and  declination  separate,  conditions  become  more  favorable  for  finding  latitude  and 
less  so  for  longitude;  the  intermediate  cases  cover  a  wide  range,  wherein  longitude  may  be  well  determined 
by  observations  three  to  five  hours  from  the  meridian,  and  latitude  by  those  within  two  hours  of 
meridian  passage.  As  extreme  conditions  are  approached  the  accuracy  of  longitude  determinations  con- 
tinues to  decrease;  at  a  point  in  60°  north  latitude,  when  the  sim  is  near  the  southern  solstice,  its  bear- 
ing differs  only  39°  from  the  meridian  at  rising;  or,  in  other  words,  even  if  observed  at  the  most 
favorable  position,  the  resulting  Sumner  line  is  such  that  V  in  latitude  makes  a  difference  of  1.3  miles  of 
departure,  or  2^.6  of  longitude,  and  is  far  better  for  a  latitude  determination  than  for  longitude.  And  in 
higher  latitudes  still  this  condition  is  even  more  marked. 

Having  grasped  these  general  facts,  the  navigator  must  adapt  his  time  for  taking  sights  to  the  cir- 
cumstances that  prevail,  and  when  the  sun  does  not  serve  for  an  accurate  determination  of  either 
latitude  or  longitude  the  ability  to  utilize  the  stars,  planets,  and  moon  as  a  substitute  will  be  of  the 
greatest  advantage. 

40§.  Use  of  Various  Sights. — Having  taken  a  sight,  the  navigator  may  sometimes  be  in  doubt  as 
to  the  best  method. of  working  it.  No  rigorous  rules  can  be  laid  down,  and  experience  alone  must  be 
his  guide.  In  a  general  way  it  may  be  well,  when  the  body  is  nearer  to  the  prime  vertical  than  to  the 
meridian,  to  work  it  for  longitude,  assuming  latitude,  and  using  the  time  sight;  and  when  nearer  the 
meridian  to  work  it  for  latitude,  assuming  longitude,  by  the  q/  q/'  method.  The  time  sight  is  more 
generally  used  than  the  other,  it  has  wider  limits  of  accurate  application  and  is  probably  a  little  quicker; 
but  as  the  meridian  is  approached  and  the  hour  angle  decreases  small  errors  in  the  terms  make  large 
ones  in  the  results.  The  q/  q/'  or  latitude  method  should  not  ordinarily  be  employed  beyond  three 
hours  from  the  meridian,  and  only  then  when  the  body  is  within  45°  or  azimuth  from  the  meridian; 
when  the  hour  angle  is  six  hours  (90°)  its  secant  becomes  infinity  and  the  method  is  not  available;  nor, 
as  has  been  noted  (art.  339,  Chap.  XII),  does  it  give  definite  results  when  the  azimuth  is  90°  or  there- 
abouts. 

When  the  body  is  close  enough  to  the  meridian  for  the  method  of  reduction  to  the  meridian  to  be 
applicable,  that  method  is  to  be  preferred  because  of  its  quickness  and  facility.  It  should  be  noted, 
however,  that,  though  close  enough  to  employ  the  reduction,  it  may  not  be  suflSciently  correct  to 
assume  that  the  body  bears  due  north  or  south,  and  the  sight  should  be  worked  with  two  longitudes, 
or  the  Sumner  line  determined  by  the  azimuth,  unless  the  bearing  nearly  coincides  with  the  direction 
of  the  meridian. 

In  cases  where  a  body  transits  near  the  zenith,  a  good  fix  both  in  latitude  and  longitude  may  be 
obtained  by  sights,  a  few  minutes  apart,  near  its  meridian  passage.  Various  special  methods  have 
been  devised  for  doing  this,  but  it  seems  simpler  to  treat  the  problem  as  an  ordinary  one  for  Sumner 
lines,  except  where  it  falls  within  the  narrow  limits  of  application  of  the  equal  altitude  method  (art. 
352,  Chap.  XIII).  The  solution  is  possible,  because  in  the  condition  where  it  is  available  (that  of  a  high 
transit)  the  body  makes  a  very  rapid  change  of  azimuth  (from  nearly  east  to  nearly  west)  in  a  short 
space  of  time,  and  two  observations  separated  by  a  short  interval  give  Sumntr  lines  that  cut  sPt  a 
favorable  angle.  The  time  sight  or  latitude  sight  may  be  used  according  as  the  body's  bearing  is 
greater  or  less  than  45°  from  the  meridian.  If  one  observation  be  taken  when  the  bearing  is  about  SE. 
and  the  other  when  it  is  about  SW.,  the  intersection,  allowing  for  intervening  run,  will  not  only  give 
the  longitude,  but  will  also  afford  a  good  check  upon  the  meridian  observation  for  latitude,  which,  in 
the  case  of  high  transits,  it  is  difficult  to  make  with  perfect  accuracy. 

409.  Working  to  Seconds  and  Accuracy  op  Determinations. — The  beginner  who  seeks  counsel 
from  the  more  experienced  in  matters  pertaining  to  navigation  will  find  that  he  receives  conflicting 
advice  as  to  whether  it  is  more  expedient  to  carry  out  the  terms  to  seconds  of  arc,  or  to  disregard  seconds 
and  work  with  the  nearest  whole  minute. 

It  is  a  well -recognized  fact  that  exact  results  are  not  attainable  in  navigation  at  sea;  the  chro- 
nometer error,  sextant  error,  error  of  refraction,  and  error  of  observation  are  all  uncertain;  it  is  impos- 
sible to  make  absolutely  correct  allowance  for  them,  and  the  uncertainty  increases  if  the  position  is 
obtained  by  two  observations  taken  at  different  times,  in  which  case  an  exactly  correct  allowance  for 
the  intervening  run  of  the  ship  is  an  essential  to  the  correctness  of  the  determination.  "No  navigator 
should  ever  assume  that  his  position  is  not  liable  to  be  in  error  to  some  extent,  the  precise  amount 
depending  upon  various  factors,  such  as  the  age  of  the  chronometer  rate,  the  quality  of  the  various 
instruments,  the  reliability  of  the  observer,  and  the  conditions  at  the  time  the  sight  was  taken;  perhaps 
a  fair  allowance  for  this  possible  error,  under  favorable  circumstances,  will  be  2  miles;  therefore, 
instead  of  plotting  a  position  upon  the  chart,  and  proceeding  with  absolute  confidence  in  the  belief  that 
the  ship's  position  is  on  the  exact  point,  one  may  describe,  around  the  point  as  a  center,  a  circle  whose 
radius  is  2  miles — if  we  accept  that  as  the  value  of  the  possible  error — and  shape  the  future  courses 
with  the  knowledge  that  the  ship's  position  may  be  anywhere  within  the  circle. 

It  is  on  account  of  this  recognized  inexactness  of  the  determination  of  position  that  some  navigators 
assume  that  the  odd  seconds  may  be  neglected  in  dealing  with  the  different  terms  of  a  sight;  the  average 
possible  error  due  to  this  course  is  probably  about  one  minute,  though  under  certain  conditions  it  may 

22489—03 9 


180  THE    PRACTICE    OF   NAVIGATION    AT    SEA. 

be  considerably  more.  It  is  possible  that,  in  a  particular  case,  the  error  thus  introduced  through  one 
term  would  be  offset  by  that  from  others,  and  the  result  would  be  the  same  as  if  the  seconds  had  been 
taken  into  account;  but  that  does  not  affect  the  general  fact  that  the  neglect  of  seconds  as  a  regular 
thing  renders  any  determination  liable  to  be  in  error  about  one  minute.  Those  that  omit  the  seconds 
argue,  however,  that  since,  in  the  nature  of  things,  any  sight  may  be  in  error  two  minutes,  it  is  imma- 
terial if  we  introduce  an  additional  possibihty  of  error  of  one  minute,  because  the  new  error  is  as  liable 
to  decrease  the  old  one  as  to  increase  it;  but  the  fallacy  of  the  argument  will  be  apparent  when  w'e  return 
to  the  circle  drawn  around  our  plotted  point.  The  eccentricity  of  the  sextant  may  exactly  offset  the 
improper  allowance  for  refraction,  and  the  mistake  in  the  chronometer  error  may  offset  the  observer's 

J)ersonal  error,  but  unless  we  know  that  such  is  the  case — which  we  never  can — we  have  no  justification 
or  doing  otherwise  than  assume  that  the  ship  may  be  any  place  within  the  2-mile  circle.  If,  now, 
we  increase  the  possible  trror  by  1  mile,  our  radius  of  uncertainty  must  be  increased  to  3  miles,  and  the 
diameter  of  the  circle,  representing  the  range  of  uncertainty  in  any  given  direction,  is  thereby  increased 
from  4  to  6  miles. 

It  is  deemed  to  be  the  duty  of  the  navigator  to  put  forth  every  effort  to  obtain  the  mod  probable 
position  of  the  shiji,  which  requires  that  he  shall  eliminate  possible  errors  as  completely  as  it  lies 
within  his  power  to  do.  By  neglecting  seconds  he  introduces  a  source  of  error  that  might  with  small , 
trouble  be  avoided.  This  becomes  of  still  more  importance  since  modern  instruments  and  modern 
methods  constantly  tend  to  decrease  the  probability  of  error  in  the  observation,  and  to  place  it  within 
the  power  of  the  navigator  to  determine  his  ship's  position  with  greater  accuracy. 

410.  There  is  a  more  exact  way  of  defining  the  area  of  the  ship's  possible  position  than  that  of 
describing  a  circle  around  the  most  probable  point,  as  mentioned  irt  the  preceding  article,  and  that  is  to 
draw  a  line  on  each  side  of  each  of  the  Sumner  lines  by  which  the  position  is  defined,  and  at  a  uniform 
distance  therefrom  equal  to  the  po.ssible  error  that  the  navigator  believes  it  most  reasonable  to  assume 
under  existing  conditions;  the  parallelogram  f(  rmed  by  these  four  auxiliary  lines  marks  the  limit  to  be 
a.«signed  for  the  shiji's  position;  this  method  takes  account  of  the  errors  due  to  poor  intersections,  and 
warns  the  navigator  of  the  direction  in  which  his  position  is  lea.«t  clearly  fixed  and  in  which  he  must 
therefore  make  extra  allowance  for  the  uncertainty  of  his  determination. 

It  must  be  remembered  in  this  connection  that  no  position  can  ever  be  obtained  except  from  the 
intersection  of  two  Sumner  lines,  whether  or  not  the  lines  are  actually  plotted;  thus,  a  meridian  altitude 
gives  a  Sumner  line  that  extends  due  east  and  west,  and  a  sight  on  the  prime  vertical  a  line  that  extends 
north  and  south,  though  it  may  not  have  been  considered  necessary  to  work  the  former  with  two 
longitudes  or  the  latter  with  two  latitudes. 

411.  The  "Work  Book  and.Fobms  for  Sights. — The  navigation- work  book,  or  sight  book,  being 
the  official  record  of  all  that  pertains  to  the  navigation  of  the  ship  when  not  running  by  bearings  of  the 
land,  should  be  neatly  and  legibly  kept,  so  that  it  will  be  intelligible  not  only  to  the  person  who  per- 
formed the  work,  but  also  to  any  other  who  may  have  reason  to  refer  to  it. 

Each  day's  work  should  be  begun  on  a  new  page,  the  date  set  forth  clearly  at  the  top,  and  prefer- 
ably, also,  a  brief  statement  of  the  voyage  upon  which  the  ship  is  engaged.  It  is  a  good  plan  to  have 
the  dead  reckoning  begin  the  space  allotted  for  the  day,  and  then  have  the  sights  follow  in  the  order  in 
which  taken.  The  page  should  be  large  enough  to  permit  the  whole  of  any  one  sight  to  be  contained 
thereon  without  the  necessity  of  carrying  it  forward  to  a  second  page.  No  work  should  be  commenced 
at  the  bottom  of  a  page  if  there  is  not  room  to  complete  it.  Every  operation  pertaining  to  the  working 
of  the  sights  shoula  appear  in  the  book,  and  all  irrelevant  matter  should  be  excluded. 

It  is  well  to  observe  a  systematic  form  of  work  for  each  sight,  always  writing  the  different  terms  in 
the  same  position  on  the  page;  this  practice  will  conduce  to  rapidity  and  lessen  the  chances  of  error. 
In  order  to  facilitate  the  adoption  of  such  a  method,  there  are  appended  to  this  work  (Appendix  II) 
a  series  of  forms  that  are  recommended  for  dead  reckoning,  and  for  time  sights,  meridian  altitudes,  and 
latitude  sights  (both  by  cp'  q^'  formula  and  method  of  reduction  to  the  meridian),  for  the  sun,  stars, 
planets,  and  moon,  respectively.  For  beginners,  these  are  deemed  of  especial  importance,  and  it  is 
recommended  that,  until  perfect  familiarity  with  the  different  sights  is  acquired,  the  first  step  in  work- 
ing out  an  observation  be  to  Avrite  down  a  copy  of  the  appropriate  blank  form,  indicating  the  proper 
sign  of  application  of  each  quantity  (for  which  the  notes  will  be  a  guide),  and  not  to  put  in  any  figures 
until  the  scheme  has  been  completely  outlined;  then  the  reinainder  of  the  work  will  consist  m  writing 
down  the  various  quantities  in  their  proper  places  and  performing  the  operations  indicated. 


MARINE    SURVEYING. 


131 


CHAPTER  XVII. 

MAEINE  SUEVEYING. 


412.  Definitions. — Surveying  is  the  art  of  representing  upon  paper  the  .surface  of  the  earth,  giving 
its  characteristic  features,  such  as,  on  land,  the  position  of  prominent  objects,  heights,  and  depressions, 
and  on  water,  the  depth,  character  of  bottom,  and  position  of  shoals. 

Topographical  Surrrgiiig  delineates  the  land,  and  Ifi/c/rographlc  Surveying,  the  water. 

GmdeKy  is  a  higher  kind  of  surveying,  which  takes  into  account  the  curvature  of  the  earth.  To 
points  determined  by  a  geodetic  survey  other  surveys  are  referred. 

It  is  not  deemed  appropriate  to  include  in  this  Avork  a  complete  treatise  on  Marine  Surveying.  The 
scope  of  this  chapter  will  be  to  set  forth  such  general  information  regarding  the  principles  of  surveying 
and  the  instruments  therein  employed  as  will  give  the  navigator  an  intelligent  understanding  of  the 
subject  sufficient  to  enable  him  to  comprehend  the  methods  by  which  marine  charts  are  made,  and,  if 
occasion  should  arise,  to  conduct  a  survey  with  such  accuracy  as  the  instruments  ordinarily  at  hand  on 
shipboard  may  permit.  For  a  more  detailed  discussion  of  Marine  Surveying,  the  student  is  referred  to 
the  various  publications  which  treat  the  subject  exhaustively. 

INSTRUMENTS   EMPLOYED    IN   MARINE    SURVEYING. 

413.  The  Theodolite 
AND  Transit. — The  Theodo- 
lite (fig.  54)  is  an  instrument 
for  the  accurate  measure- 
ment of  horizontal  and  ver- 
tical angles.  While  these 
instruments  vary  in  detail 
as  to  methods  of  construc- 
tion, the  essential  principles 
are  always  identical. 

A  telescope  carrying  cross- 
hairs in  the  common  focus 
of  the  object-glass  and  eye- 
piece is  so  mounted  as  to 
have  motion  about  two  axes 
at  right  angles  to  one  an- 
other; graduated  circles  and 
verniers  are  provided  by 
which  angular  motion  in 
azimuth  and  (usually)  in 
altitude  may  be  measured; 
and  the  instrument  is  capa- 
ble of  such  adjustment  by 
levels  that  the  planes  of  mo- 
tion about  the  respective 
axes  will  (iorrespond  exactly 
with  the  horizontal  and  the 
vertical. 

The  telescope  is  carried 
in  appropriate  supports 
upon  a  horizontal  plate 
which  lias,  immovably  at- 
tached to  it,  one  or  more 
verniers,  and  which  revolves 
just  over  a  graduated  circle 
that  is  marked  upon  the 
periphery  of  a  second  hori- 
zontal i)late,  a  means  of 
measuring  the  motion  of 
the  upper  plate  relatively  to 
the  lower  one  being  thus 
provided.  Thumb- screws 
are  fitted  by  which  the  up- 
per plate  may  be  clamped 
to  the  lower,  and  (except- 
ing in  some  simpler  forms  of 
the  instrument)  others  by 
which  the  lower  plate  may 
be  made  immovable  in  azi- 
muth, or  allowed  free  mo- 

tion,  at  will;  all  clamping  ^^^'-  ^'*- 

arrangements  include  slow-motion  tangent-screws  for  finer  control. 


132  MARINE    SURVEYING. 

A  vertical  graduated  circle,  or  arc,  with  a  vernier,  clamps,  and  tangent-screws,  is  fitted  to  most 
theodolites,  for  the  measurement  of  the  angular  motion  of  the  telescope  iii  altitude. 

The  theodolite  usually  carries  a  magnetic  needle,  with  a  graduated  circle  an(l  vernier  for  compass 
bearings.  The  instrument  is  mounted  upon  a  tripod,  and  levels  and  leveling-screws  afford  a  means  of 
bringing  the  instrument  to  a  truly  horizontal  position. 

The  Transit  used  in  surveying  is  a  modified  form  of  the  theodolite,  and  is  generally  employed  where 
less  accuracy  is  required;  it  takes  its  name  from  the  fact  that  the  telescope  may  be  turned  completely 
about  its  horizontal  axis,  or  transited,  without  removal  from  its  supports. 

414.  The  line  of  collimation  of  a  telescope  is  an  imaginary  line  passing  through  the  optical  center  of 
the  object-glass  in  a  direction  at  right  angles  to  that  of  its  axis  of  rotation.  This  is  also  called  the  axis 
of  collimation.  The  line  of  sight  i?,  sm  imaginarv  line  passing  through  the  optical  center  of  the  object- 
glass  and  the  point  of  intersection  of  the  cross-hairs. 

A  theodolite  or  transit,  before  it  can  be  used  for  the  accurate  measurement  of  angles,  must  be  in 
adjustment  in  the  following  respects:  (a)  The  vertical  axes  of  revolution  of  the  upper  and  lower  hori- 
zontal plates  must  be  coincident;  (h)  the  axis  must  be  vertical  and  the  plates  horizontal  when  the 
bubbles  of  the  levels  are  in  their  central  positions;  (c)  the  vertical  cross  hair  must  be  perpenclicular 
to  the  horizontal  axis  of  the  telescope;  {d)  the  line  of  collimation  must  coincide  with  the  line  of  sight; 
(e)  the  horizontal  axis  of  the  telescope  must  be  perpendicular  to  the  vertical  axis  of  the  instrument; 
(/)  the  bubble  of  the  telescope  level  must  stand  at  the  middle  of  its  scale,  and  the  vertical  circle  must 
read  zero,  when  the  line  of  collimation  is  horizontal. 

The  last-named  condition  may  be  disregarded  if  vertical  angles  are  not  to  be  measured. 

415.  The  instrument  being  in  adjustment,  to  observe  angles  it  should  be  set  up,  leveled,  and 
focused.  This  involves  placing  the  tripod  so  that  a  plumb  bob  from  the  center  of  the  instrument  shall 
hang  directly  over  the  spot  at  which  the  measurement  is  to  be  made.  The  legs  of  the  tripod  should  be 
firmly  placed  in  Such  manner  that  the  height  shall  be  convenient  for  the  observer  and  the  instrument 
shall  be  nearly  level.  Then  the  horizontal  plates  are  brought  to  a  true  level  by  means  of  the  leveling 
screws  and  bubbles.  The  telescope  should  next  be  focused  by  moving  the  object  glass  and  eyepiece  in 
such  manner  that  the  object  sighted  and  the  cross  hairs  may  be  plainly  seen  and  that  the  object  will 
not  appear  to  have  motion  relatively  to  the  cross  hairs  as  the  eye  is  moved  to  the  right  or  left  in  front 
of  the  eyepiece.  This  last  condition  insures  the  cross  hairs  being  at  the  common  focus  of  the  eyepiece 
and  objective. 

To  observe  a  horizontal  angle  with  a  theodolite  or  transit,  clamp  the  upper  plate  to  the  lower  at  zero, 
leaving  the  lower  plate  undamped;  swing  the  telescope  so  that  its  vertical  cross  hair  bisects  one  of  the 
objects,  and  clamp  the  lower  plate;  unclamp  the  upper  plate  and  bring  the  telescope  to  bisect  the  other 
object,  and  the  reading  of  the  vernier  on  the  scale  will  give  the  required  angle.  (The  final  nice  motion 
by  which  the  cross-hair  is  brought  exactly  upon  a  point  is  always  given  by  the  tangent  screw. ) 

In  taking  a  round  of  angles,  this  operation  is  repeated  successively  upon  each  object  to  be  observed 
about  the  horizon,  the  upper  plate  being  always  swung,  while  the  lower  is  kept  where  set  upon  the 
first  object,  or  origin.  The  result  will  give  the  angular  distance  of  each  object  from  the  origin,  and,  if 
the  observations  have  been  accurately  made,  upon  finally  sighting  back  to  the  origin,  the  reading 
should  be  zero. 

To  repeat  an  angle,  having  made  the  first  measurement  of  it  in  the  usual  way,  unclamp  the  lower 
circle  and  swing  back  the  telescope  until  it  again  points  to  the  first  object,  and  clamp  it;  then  unclamp 
the  upper  circle,  swing  to  the  second  object,  and  clamp.  The  scale-reading  should  now  be  double  that 
of  the  first  angle.  Kepeat  as  often  as  the  importance  of  the  angle  requires,  and  the  accepted  value  will 
be  the  final  reading  divided  by  the  number  of  measurements.  All  angles  of  the  main  triangulation, 
and  others  of  importance  in  the  survey,  are  repeated. 

Defects  in  adjustment  of  the  instrument  may  be  eliminated  by  taking  one  series  of  angles  with 
the  telescope  direct  and  another  with  the  telescope  reversed.  To  reverse  the  telescope,  revolve  it  about  its 
horizontal  axis  through  180°,  then  swing  it  about  its  vertical  axis  through  180° — in  other  words, 
invert  it. 

Vertical  angles  are  measured  on  the  same  principle  as  that  described  for  horizontal  ones. 

The  process  of  setting  up  the  instrument  at  a  station  and  observing  the  angles  between  the  various 
objects  that  are  visible  is  called  occupying  the  station. 

416.  The  Plane  Table. — This  is  an  instrument  by  which  positions  are  plotted  in  the  field  directly 
upon  a  working  sheet.  It  consists  (fig.  55)  of  a  drawing  board  mounted  upon  a  tripod  in  such  manner 
as  to  be  capable  of  motion  in  azimuth,  and  with  facilities  for  being  brought  to  a  perfect  level;  in  con- 
nection with  it  is  employed  an  alidade,  consisting  of  a  straightedge  ruler,  upon  which  is  mounted  a 
telescope  with  cross-hairs  whose  line  of  sight  is  exactly  parallel  to  the  vertical  plane  through  the  edge 
of  the  rule.  It  is  evident  that  if  a  sheet  representing  a  chart  be  placed  upon  such  a  board  and  turned 
so  that  the  true  meridians,  as  portrayed  thereon,  lie  in  the  direction  of  the  earth's  meridian  at  that 
place,  then  all  lines  of  bearings  on  the  chart  will  coincide  with  the  corresponding  lines  on  the  earth's 
surface;  from  which  it  follows  that  if  the  alidade  be  so  placed  that  its  rule  passes  through  the  spot 
on  the  chart  representing  the  position  of  the  observer,  while  the  telescope  is  directed  to  some  visible 
object,  the  position  of  that  object  on  the  chart  lies  somewhere  upon  the  line  drawn  along  the  edge  of 
the  rule.     Upon  this  general  principle  depend  the  various  applications  of  the  plane  table. 

The  drawing  board  is  usually  made  of  several  pieces  of  well-seasoned  wood,  tongued  and  grooved 
together,  with  the  grain  running  in  different  directions  to  prevent  warping;  about  its  edge  are  several 
metal  clips  for  securing  the  paper  in  place.  It  is  supported  upon  three  strong  brass  arms,  to  which  it  is 
attached  by  screws,  thus  permitting  its  removal  at  will.  The  arms  are  attached  to  a  horizontal  plate 
which  revolves  upon  a  second  horizontal  plate  lying  immediately  below  it;  a  clamp  and  tangent  screw 
are  fitted,  by  which  the  upper  plate,  and  with  it  the  drawing  board,  may  be  secured  to  the  lower  plate, 
or  may  be  given  a  fine  motion  in  azimuth.  Three  equidistant  lugs  of  brass,  grooved  on  the  under  side, 
project  down  from  the  lower  plate,  resting  on  screws  in  the  top  of  the  tripod,  by  which  the  instrument 
IS  leveled;  when  adjusted  in  this  respect  it  is  firmly  clamped  in  position,  and,  aa  the  tripod  is  made 
unusually  large,  the  adjustment  is  not  easily  deranged. 


MARINE    SURVEYING. 


133 


The  alidade  is  a  metal  straightedge  with  a  vertical  column  at  its  center,  at  the  top  of  which  are  the 
supports  which  carry  the  telescope;  a  vertical  arc  and  vernier  are  provided  for  measuring  the  motion  of 
the  telescope  in  altitude.  The  telescope  is  usually  so  fitted  that  it  may  he  revolved  in  azimuth  through 
an  arc  of  exactly  180°,  for  the  purpose  of  adjusting  the  line  of  collimation.  On  top  of  the  rule  near  its 
center  is  the  level — sometimes  replaced  by  two  levels  at  right  angles — by  means  of  which  it  may  be  seen 
when  the  table  is  in  a  true  horizontal  position. 

A  magnetic  needle  mounted  in  a  rectangular  metal  box,  whose  outer  straightedge  is  parallel  to  the 
zero  line  of  a  graduated  scale  over  which  the  needle  swings,  is  provided  for  drawing  the  north-and-south 
line  on  the  chart;  this  is  called  a  dedinatoire. 


417.  To  be  in  correct  adju.«tment,  a  plane  table  must  comply  with  the  following  conditions: 

(«)  The  fiducial  edge  of  the  rule  must  be  perfectly  straight,  {b)  The  level  must  have  the  bubble  in 
its  central  position  when  the  table  is  truly  horizontal,  (c)  The  vertical  cross  hair  must  be  perpendic- 
ular to  the  horizontal  axis  of  the  telescope,  (d)  The  line  of  collimation  must  coincide  with  the  line  of 
sight,  {e)  The  horizontal  axis  of  the  telescope  must  be  parallel  to  the  plane  of  the  table.  (/)  The 
vertical  circle  should  read  zero  when  the  line  of  collimation  is  horizontal. 

418.  The  results  derived  from  the  use  of  the  plane  table,  like  all  others  dependent  upon  graphic 
methods,  must  be  regarded  as  less  accurate  than  those  deduced  by  computation,  and  even  less  accurate 
than  those  derived  from  the  careful  plotting  of  theodolite  angles.  Hence  it  is  that,  in  a  careful  marine 
survey,  this  instrument  would  be  employed  only  for  the  topography  and  shore  line. 

For  whatever  purpose  used,  the  plane  table  would  not  ordinarily  be  called  into  requisition  until  the 
survey  had  so  far  progressed  that  a  chart  could  be  furnished  the  observer  showing  certain  stations 
whose  positions  were  already  established;  with  this  chart,  the  first  step  would  be  to  occupy  one  of  the 
determined  points.  The  table  must  be  set  up  with  the  point  on  the  chart  directly  over  the  center  of  the 
station;  it  must  then  be  leveled  and  the  telescope  focused  as  described  for  the  theodolite  or  transit;  and 
finally  it  must  be  oriented,  that  is,  so  turned  in  azimuth  that  all  lines  of  the  chart  are  parallel  to  similar 
lines  of  the  earth's  surface.  To  orient,  unclamp  the  table  and  swing  it  until  the  north-and-south  lineof  the 
chart  is  approximately  parallel  to  that  of  the  earth,  one  means  of  doing  which  is  afforded  by  the  decli- 
natoire;  place  the  alidade  so  that  the  edge  of  the  rule  passes  through  the  points  on  the  chart  representing 
the  station  occupied  and  some  second  station  which  is  clearly  in  view;  then,  sighting  through  the  tele- 
scope, per/ect  the  adjustment  of  the  table  by  swinging  it  until  the  second  station  is  exactly  bisected  by 
the  vertical  cross  hair,  the  final  slow  motion  being  obtained  by  clamping  the  table  and  working  the 
tangent  screw.  If  the  adjustment  has  been  correctly  made,  the  rule  may  be  laid  along  the  line  joming 
the  station  occupied  and  any  other  on  the  chart,  and  the  telescope  will  point  exactly  to  that  other  station. 

Being  properly  oriented,  if  the  alidade  be  so  placed  that  the  edge  of  the  rule  pass  through  the  station 
occupied,  and  the  telescope  point  directly  to  some  unknown  object  whose  position  is  to  be  determined. 


134  MARINE    SURVEYING. 

then  a  line  drawn  along  the  rule  will  contain  the  ])oint  which  represents  the  position  of  that  object. 
If,  now,  the  plane  table  l)e  set  np  at  a  second  station,  oriented  for  its  new  position,  and  a  line  be  simi- 
larly drawn  from  that  station  toward  the  one  to  be  established,  it  will  intersect  the  first  line  in  the 
required  point.  This  is  the  method  of  determining  positions  by  prosection.  Actually,  the  surveyor  does 
not  regard  the  point  as  well  established  until  the  intersection  is  checked  by  a  line  from  a  third  station. 

In  practical  work,  of  course,  each  station  is  not  occupied  separately  for  the  determination  of  each 
point;  tlie  instrument  is  set  up  at  a  station,  lines  are  drawn  to  all  required  points  in  view,  and  each  line 
is  a]>proi)riately  marked;  then  a  second  station  is  occupied,  and  the  operation  repeateii,  and  so  on,  the 
various  intei-sections  being  marked  as  the  work  proceeds. 

A  second  method  of  establishing  positions  is  that  of  resection;  in  this  the  first  line  is  drawn  from 
some  known  station,  as  in  the  preceding  method,  and  the  observer  next  proceeds  to  the  place  whose 
position  is  required  ana  occupies  it;  the  plane  table  is  there  oriented  by  means  of  the  line  already 
drawn,  placing  the  edge  of  the  rule  along  the  line,  sighting  back  toward  the  first  station,  and  swinging 
the  table  until  that  station  is  in  the  line  of  sight  of  the  telescope;  then  choose  some  other  established 
station  as  nearly  as  possible  at  right  angles  to  the  direction  of  the  first;  i:>lace  the  edge  of  the  rule  upon, 
the  plotted  position  of  this  station  and  swing  the  alidade  (the  rule  always  being  kept  on  the  plotted 
point)  until  the  object  is  bisected  by  the  telescope  cross-hairs;  draw  this  line,  and  its  interse(!tion  with 
the  first  will  give  the  required  point,  the  accuracy  of  which  can  be  checked  from  some  other  plotted 
station. 

A  third  method  of  locating  a  point  is  by  means  of  a  single  bearing  from  a  known  station,  with  the 
distance  from  the  occupied  station  to  the  required  one,  the  process  of  plotting  being  self-evident. 

A  fourth  method  is  given  by  occupying  an  luidetermined  position  from  which  three  established 
stations  are  in  view;  the  point  occupied  by  the  observer  is  then  plotted  by  an  application  of  the  "three- 
point  problem." 

419.  It  may  be  seen  that  where  the  greatest  accuracy  is  not  essential  the  plane  table  may  be 
employed  for  plotting  all  the  points  of  a  survey.  In  such  a  case  it  would  only  be  necessary  to  begin 
with  the  two  base  stations,  plotted  on  the  sheet  on  any  relative  bearing  whatsoever  and  at  a  distance 
apart  eijual  to  the  length  of  the  base  line  (reduced  t )  scale),  as  measured  by  the  most  accurate  means 
available.  The  work  of  plotting  might  even  proceed  before  the  base  line  had  been  measured,  the  two 
stations  being  laid  off  at  any  convenient  distance  apart;  when,  later,  the  base  line  wa^  measured,  the 
scale  of  the  chart  would  be  determined,  being  eciual  to  the  distance  on  the  chart  between  base  stations 
divided  by  the  length  of  the  base  line. 

420.  A  plane  table  could  be  improvised  on  shipboard  which  would  greatly  facilitate  the  operation  of 
any,  surveying  work  that  a  vessel  not  equipped  with  instruments  might  be  called  upon  to  perform.  A 
drawing  board  could  be  mounted  upon  a  tripod  (as,  for  example,  the  tripod  supplied  for  compass  work 
on  shore)  in  such  manner  as  to  be  capable  of  motion  in  azimuth;  it  could  be  brought  nearly  to  the 
horizontal,  if  no  better  means  offered,  by  moving  the  tripod  legs,  and  this  adjustment  could  be  proved 
by  any  small  spirit  level;  sight  vanes  could  be  erected  upon  an  ordinary  ruler  to  take  the  place  of  the 
alidade;  in  case  there  was  difficulty  in  observing  any  object  with  such  an  alidade,  because  of  its  altitude 
or  for  other  reasons,  a  horizontal  angle  might  be  observed  with  a  sextant  and  plotted  with  a  pro- 
tractor. By  this  means  work  could  be  done  which,  even  if  it  should  lack  complete  accuracy,  might  be 
of  great  value. 

421.  The  Telemeter  and  Stadia. — Any  telescope  fitted  with  a  pair  of  horizontal  cross-hairs  at 
the  focus  may  be  used  as  a  telemeter,  and  v/hen  accompanied  by  a  graduated  staff,  called  a  stadia,  affords 
a  means  of  measuring  distance  (up  to  certain  limits)  with  a  close  degree  of  accuracy;  the  method  con- 
sists in  observing  the  number  of  divisions  of  the  scale  subtended  by  the  hairs  when  the  stadia  is  held 
up  vertically  and  perpendicular  to  the  line  of  sight  of  the  teles -ope,  it  being  evident  that  the  closer  the 
distance  the  fewer  divisions  will  appear  between  them.  The  facility  with  whicli  distances  can  be 
measured  by  this  method  makes  it  most  important  that  all  telescopes  of  theodolites,  transits,  and  plane 
tables  be  fitted  as  telen^eters,  and  that  stadia  rods  be  provided  for  all  surveying  work. 

Speaking  api)roximately,  it  may  be  .said  that  the  number  of  divisions  intercepted  between  the  cross- 
hairs will  vary  directly  as  the  distance  of  the  stadia  rod.  This  would  be  exactly  true  if  we  looked  at  the 
object  through  an  empty  tube,  directly  between  the  hairs.  Since,  however,  the  rays  from  the  stadia  are 
refracted  by  the  object  glass  before  they  are  intercepted  by  the  wires,  the  statement,  to  be  absolutely 
exact,  must  be  slightly  modified;  but  for  j^ractical  surveying  work  it  may  be  accepted  as  given. 

422.  There  are  two  methods  of  installing  the  telemeter  cross-hairs — the  first,  in  which  they  are 
immovably  secured  in  the  telescope  and  always  remain  at  the  same  distance  apart,  and  the  second,  in 
which  the  distance  of  the  cross  hairs  is  made  variable,  being  under  the  control  of  the  observer.  The 
former  is  generally  regarded  as  the  preferable  method,  and  when  it  is  employed  it  is  evident  that  the 
subtended  height  of  the  stadia  bear3  a  constant  ratio  to  the  distance  of  the  staff  from  the  telescope.  It 
proves  mf)st  convenient  in  i)ractice  to  space  the  hairs  so  that  this  constant  ratio  is  some  even  multiple 
of  10,  for  facility  in  converting  scale  readings  into  distance;  it  is  also  advantageous  to  mark  the  stadia 

.  in  the  unit  of  the  chart  scale  and  decimals  thereof;  for  example,  if  the  ratio  of  stadia  height  to  distance 
were  100,  and  the  stadia  were  marked  in  meters  and  decimals,  a  reading  of  2.07  would  at  once  be  con- 
verted into  a  distance  of  207  meters.  Any  units  and  any  ratio  may,  however,  be  employed,  and  for  any 
given  setting  of  cross-hairs  it  is  very  easy  to  graduate  a  stadia,  by  experiment,  for  any  desired  units;  for 
example,  if  it  is  required  to  mark  the  stadia  in  feet,  set  up  and  level  the  telescope,  measure  off  a  distance 
of  exactly  100  feet  from  it,  hold  up  an  unmarked  staff  and  mark  upon  it  the  points  intersected  by  the 
cross  hairs;  the  interval  between  these  marks  will  represent  100  feet  of  the  scale;  divide  this  length  into 
100  parts,  each  of  which  will  represent  a  distance  of  one  foot,  and  mark  the  whole  staff  on  the  same  scale; 
then  if  the  stadia  be  held  up  at  any  distance,  the  cross-hairs  will  intercept  a  number  of  divisions  corre- 
sponding to  the  r. umber  of  feet  of  distance. 


MARINE    SUEVEYING.  135 

When  the  cross-hairs  are  movable  the  ratio  becomes  variable,  but  the  principle  of  measuring 
remains  the  same — namely,  the  distance  of  the  staff  from  the  telescope  is  equal  to  the  existing  ratio 
multiplied  by  the  distance  intercepted  on  the  scale. 

4S3.  The  stadia  is  made  of  a  light,  narrow  piece  of  wood  and  is  usually  hinged  for  convenience  in 
transporting.  Ordinarily  the  background  of  the  scale  is  painted  white,  while  the  main  divisions  are 
marked  in  red,  with  minor  divisions  in  black,  and  geometrical  figures  are  employed  to  facilitate  the 
reading  of  fractional  parts  of  the  scale.  Devices  are  furnished  by  which  the  man  holding  the  stadia 
may  know  when  it  is  at  right  angles  to  the  line  of  sight  of  the  telescope — an  essential  condition  for 
accuracy  of  measurements. 

424.  Tlie  use  of  the  telemeter  and  stadia  for  measuring  distances  is  limited  to  the  distance  at 
which  the  scale  divisions  can  be  accurately  read  through  the  telescope.  For  fairly  close  work  and  with 
the  class  of  telescope  usually  supplied  with  surveying  instruments,  400  meters  represents  about  the 
greatest  distance  at  which  it  can  be  employed.  With  this  limitation,  the  character  of  the  survey 
determines  the  nature  of  its  employment.  In  a  careful  survey  its  greatest  use  would  be  in  connection 
with  the  theodolite  or  plane  table  in  putting  in  shore  lines,  contour  lines,  and  topography  generally. 
In  a  survey  where  only  approximate  results  are  sought  it  might  afford  the  best  means  for  the  measure- 
ment of  the  base. 

425.  If  the  telemeter  be  applied  to  a  theodolite,  transit,  or  plane  table  which  is  fitted  with  a 
graduated  vertical  arc  or  circle,  it  is  possible  to  measure  the  distance  to  the  stadia  not  only  in  a  horizontal 
but  also  in  a  vertical  direction.  In  this  case  the  vertical  angle  must  be  observed  as  well  as  the  stadia 
reading.     Tables  are  computed  giving  the  solution  of  the  triangles  involved. 

426.  In  making  a  survey  with  the  ordinary  resources  of  a  ship,  the  principle  of  the  telemeter  and 
stadia  may  be  profitably  employed,  using  a  sextant  and  improvised  staff.  In  this  case  it  is  usual  to  have 
the  stadia  of  some  convenient  flxed  length,  as,  for  example,  10  feet,  and  of  slight  width  and  thickness; 
this  is  held  at  right  angles  to  the  line  of  sight  from  the  observer,  who  notes  the  angle  subtended  by  the 
total  length;  tables  are  prepared  by  which  the  distance  corresponding  to  each  angle  is  given. 

427.  TiiK  Skxtant. — This  instrument  is  of  the  greatest  value  in  hydrographic  surveying.  It  is 
fully  described  elsewhere  in  this  work  and  its  adjustment  explained  (Chap.  VIII). 

Sextants  are  manufactured  of  a  form  especially  adapted  to  surveying  work;  they  are  smaller  and 
lighter  than  those  usually  employed  in  astronomical  observations,  but  have  a  longer  limb,  by  which 
angles  may  be  measured  up  to  135° ;  the  vernier  is  marked  for  quick  reading  and  has  no  finer  graduation 
than  half  minutes;  the  telescope  has  a  large  field. 

This  instrument  is  principally  employed  in  measuring  the  horizontal  angles  by  means  of  which 
soundings  are  plotted.  It  may,  however,  be  put  to  various  uses  when  making  an  approximate  survey, 
as  has  already  been  explained.  It  should  be  remembered,  in  measuring  terrestrial  angles  with  a  sextant, 
that  rigorous  methods  require  a  reduction  to  the  horizontal  if  either  of  the  objects  has  material  altitude 
above  the  horizon. 

42S.  The  Level. — This  is  an  instrument  for  the  accurate  measure  of  differences  of  elevation.  It 
consists  of  a  telescoi)e,  carried  in  a  Y-shaped  rest,  which  is  mounted  upon  a  tripod  and  leveled  in  a  man- 
ner similar  to  a  theodolite;  but  it  differs  from  that  instrument  in  that  the  telescope  is  not  capable  of 
motion  about  a  horizontal  axis,  and  in  having  no  graduated  circle  for '  measurements  of  altitude  and 
azimuth.  The  principle  of  its  use  contemplates  placing  the  line  of  collimation  of  the  telescope  in  a  truly 
horizontal  plane  and  keeping  it  so  fixed. 

429.  It  is  principally  employed  in  marine  surveying  to  determine  heights  and  contour  lines — the 
latter  being  lines  of  equal  elevation  above  the  sea  level — and  for  locating  bench  marks  for  tidal  ob.serva- 
tions  (Chap.  XX).  In  connection  with  it  is  used  a  graduated  staff  called  a  leveling  rod,  carrying  a  con- 
spicuous mark,  adjustable  in  height,  called  a  target.  To  ascertain  the  difference  of  level  between  any 
two  points,  set  up  the  level  with  the  telescope  horizontal  at  some  place  between  them;  let  an  assistant 
take  the  leveling  rod  to  one  of  the  jioints,  and,  while  holding  it  on  the  ground  in  a  truly  vertical  posi- 
tion, move  the  target,  under  the  dire(!tion  of  the  observer  at  the  telescope,  to  a  point  where  it  is  exactly 
bisected  by  the  horizontal  cross-hair;  the  height  of  the  target  on  the  staff — that  is,  the  height  of  the  cross- 
hair above  the  level  of  tlie  first  point — is  then  accurately  read  with  a  vernier;  now,  without  moving  the 
level,  shift  the  rod  to  the  second  point  and  again  adjust  the  target  and  read  it.  It  is  evident  that  a  com- 
parison of  the  reading  at  the  first  position  with  that  at  the  second  will  give  the  difference  of  height  at 
the  two  points.  The  difference  that  can  be  read  from  one  location  of  the  instrument  is  limited  by  the 
length  of  the  rod;  but  by  making  a  sufficient  luimber  of  shifts  any  difference  may  be  mea.sured. 

The  work  of  the  level  may  be  performed  equally  well  by  a  theodolite  whose  telescope  is  adjusted 
to  the  true  horizontal. 

430.  Heliotrope  and  HELioGRAPn.-^These  are  instruments  sometimes  employed  in  surveying,  by 
means  of  which  the  sun's  rays  may  be  reflected  in  any  given  direction;  the  object  of  their  use  is  to 
render  conspicuous  a  station  which  is  to  be  observed  at  a  distance  and  which  would  not  otherwise  jje 
distinguishable.  The  instruments  vary  widely  in  form  of  construction  and,  in  the  absence  of  those 
made  for  the  purpose,  substitutes  may  easily  be  devised. 

4tJl.  Astro xoMicAL  Transit  Ixhtrumexts. — Various  instruments  are  employed  for  the  astronom- 
ical determinations  necessary  in  a  marine  survey.  Among  these  are  the  zenith  telescope  and  portable 
transit.  While  differing  in  detail  they  consist  essentially  of  a  telescope  mounted  upon  a  horizontal 
axis  that  is  placed  truly  in  the  prime  vertical,  thus  insuring  the  revolution  of  the  line  of  collimation  in 
the  meridian;  a  vertical  graduated  circle  and  vernier  are  supplied,  affording  a  measure  of  altitude;  in 
the  focus  are  a  number  of  equidistant  vertical  cross-hairs  or  lines;  a  small  lamp  is  so  placed  that  its 
rays  illuminate  the  cross-hairs  and  render  possible  observations  at  night.  Latitude  is  obtained  by 
observing  the  meridian  altitude  of  stars;  hour  angle  (and  thence  longitude)  by  observing  the  times  of 
their  meridian  transit,  which  is  taken  from  the  mean  of  the  times  of  passing  all  of  the  vertical  cross-hairs. 

Excepting  in  surveys  of  a  most  accurate  nature,  the  astronomical  determination  of  position  by  the 
sextant  and  artificial  horizon  is  regarded  as  satisfactory. 


136 


MARINE    SURVEYING. 


432.  The  Three- Armed  Protractor,  or  Station'  Pointer. — This  is  an  instrument  whereby  posi- 
tions are  plotted  on  the  principle  of  the  "three-point  problem,"  of  which  an  explanation  is  given  in 
article  152,  Chapter  IV.  It  consists  (tig. 
56)  of  a  graduated  circle  with  three  arms 
pivoted  at  the  center;  each  arm  has  one 
edge  that  is  a  true  rule,  the  direction  of 
which  always  passes  through  the  center 
of  the  circle.  The  middle  arm  is  immov- 
ably fixed  at  the  zero  of  the  scale;  the 
right  and  left  arms  each  revolve  about  the 
center  on  their  own  side^  and  are  ])ro- 
vided  with  verniers  giving  the  angular 
distance  from  the  middle  arm.  The  pro- 
tractor being  set  for  the  right  and  left 
angles,  it  is  so  moved  that  the  three  arms 
pass  through  the  respective  stations,  when 
the  center  marks  the  position  of  the  ob- 
server. Center  pieces  of  vari-jus  forms 
are  provided,  being  cylindrical  plugs 
made  to  fit  into  a  socket  at  the  pivot,  and 
by  employing  one  or  the  other  of  them 
the  true  center  may  be  pricked  with  a 
needle,  dotted  with  a  pencil,  or  its  position 
indicated  by  cross-hairs.  Adjustable  arms 
are  provided  which  can  be  fitted  to  the 
ends  of  the  ordinary  arms  when  working 
with  distant  signals. 

The  most  valuable  use  of  the  three- 
armed  protractor  is  in  plotting  the  posi- 
tions of  soundings  taken  in  boats,  where 
sextant  angles  between  signals  are  ob- 
served. It  may  occur,  however,  that 
certain  shore  stations  will  be  located  by 
its  use. 

433.  In  default  of  a  three-armed 
protractor,  a  piece  of  tracing  paper  may 
be  made  to  answer  its  purpose.  To  use 
the  tracing  paper,  draw  a  line,  making  a 
dot  on  it  to  represent  the  center  station, 
and  with  the  center  of  an  ordinary  pro- 
tractor on  the  dot,  lay  off  the  two  observed 
angles  right  and  left  of  the  line;  then, 
laying  this  on  the  plan,  move  it  about  till 
the  three  lines  pass  exactly  through  the 
three  stations  observed.  The  dot  from 
which  thev  were  laid  off  will  be  on  the 


Fu;.  56. 


position  of  the  observer,  and  must  be  pricked  lightly  through  or  marked  underneath  in  pencil. 

434.  The  Beam  Compass. — This  instrument  (fig.  57)  is  employed  in  chart  drafting  and  performs 

the  functions  of  compasses  and  dividers  when  the  dis- 
tance that  must  be  spanned  is  beyond  the  limits  of 
those  instruments  in  their  ordinary  form.  It  consists 
of  an  angular  bar  of  wood  or  metal  upon  which  two 
instruments  termed  beam  heads  are  fitted  in  such  a 
manner  that  the  bar  may  slide  easily  through  them. 
A  clamping  screw  attached  to  one  side  of  the  beam 
head  will  fix  it  in  any  jmrt  of  its  course  along  the 
beam.  Upon  each  head  a  socket  is  constructed  to 
carry  a  plain  point,  exchangeable  for  an  ink  or  a 
pencil  point.  For  exact  purposes  the  beam  head 
placed  at  the  end  of  the  beam  has  a  fine  adjustment, 
which  moves  the  point  a  short  distance  to  correct 
any  error  in  the  first  rough  setting  of  the  instrument. 
This  adjustment  generally  consists  of  a  milled-head 
screw,  which  jjasses  through  a  nut  fixed  upon  the 
end  of  the  beam  head,  which  it  carries  with  its 
motion. 

435.  Proportional  Dividers. — These  are  prin- 
cipally employed  for  reducing  or  enlarging  drawings 
in  any  given  proportion.  They  consist  (fig.  58)  of 
two  narrow  flat  pieces  of  metal  called  legs^,  which 
turn  upon  a  pivot  whose  position  is  movable  in  the 

direction  of  their  length.     The  ends  of  both  legs  are  shaped  into  points  like  those  of  ordinary  dividers. 

When  the  pivot  is  fixed  at  the  middle  of  the  legs,  any  distance  measured  by  the  points  at  one  end  is 

just  equal  to  that  measured  by  those  at  the  other;  for  any  other  location  of  the  pivot,  however,  the 


Fig.  57 


MARINE    SURVEYING. 


137 


distances  thus  measured  will  not  be  equal,  but  with  a  given  setting  of  the  pivot  any  distance  measured 
by  one  end  bears  a  fixed  ratio  to  that  measured  by  the  other.  The  path  of  travel  of  the  pivot  is  gradu- 
ated so  that  the  ratio  may  he  given  any  desired  value.  Being  adjusted  in  this  respect,  if  a  distance  is 
taken  off  a  chart  with  the  legs  at  one  end  of  the  instrument,  then  those  at  the  other 
end  will  show  the  same  distance  on  the  scale  of  a  chart  enlarged  or  reduced  in  the  pro- 
portion represented  by  the  ratio  for  which  the  pivot  was  set. 


METHODS   EMPLOYED   IN   A   HYDROGRAPHIC    SURVEY. 

436.  A  geodetic  survey  has  for  its  object  the  determination,  with  the  greatest 
attainable  accuracy,  of  points  on  the  surface  of  the  earth,  by  the  employment  of  a  pro- 
cess of  triangulation,  all  positions  being  located  either  trigonometrically  or  astronomic- 
ally, and  the  curvature  of  the  earth  being  taken  into  account. 

Before  commencing  a  survey  a  general  inspection  of  the  field  is  made;  a  base  line 
is  located  and  its  extremities  marked  by  Klgnah;  certain  other  positions,  known  as  inahi 
tricmgvlatlon  points,  are  selected  and  also  marked  with  signals,  being  so  chosen  that, 
starting  with  the  base  and  proceeding  thence  from  one  to  another  of  these  points,  a 
series  of  well-conditioned  triangles  or  quadrilaterals  may  cover  the  field  of  survey.  The 
base  line  is  measured  with  the  greatest  degree  of  accuracy  which  the  resources  of  the 
survey  render  possible.  Each  extremity  of  the  base  line  and  each  other  main  tri- 
angulation point  is  occupied  by  an  observer  with  a  theodolite,  who  measures  the  angles 
at  each  station  between  all  the  other  stations  which  are  in  sight.  An  astronomical 
determination  is  made  of  the  latitude  and  longitude  of  some  point  of  the  survey  (fre- 
quently one  of  the  extremities  of  the  base)  and  of  the  true  azimuth  of  some  known  line 
(frequently  the  base  line) .  Data  is  now  at  hand  for  the  location  upon  the  chart  of  the 
base  line  and  main  triangulation  points. 

If  the  survey  is  one  of  considerable  extent  it  is  expedient  to  measure  a  check  haM' 
near  the  end  of  the  triangulatif)n,  a  comparison  between  the  measured  and  the  computed 
distance  between  any  two  stations  showing  the  accuracy  of  the  work  and  affording  a 
means  of  reconciling  discrepancies.  The  position  of  a  second  observation  spot  may  be 
determined  for  a  similar  purpose. 

The  primary  triangulation  gives  a  skeleton  of  the  field,  but  the  points  thus  deter- 
mined are  not  usually  close  enough  together  to  afford  a  basis  for  all  the  detail  work 
that  must  be  done.  A  second  system  of  points  is  therefore  selected  and  signals  erected 
thereon,  and  the  position  of  these  points  is  determined  by  a  series  of  angles  from  the 
main  triangulation  points  and  from  each  other.  This  is  known  as  the  secondary  tri- 
angulation. The  yjoints  thus  located  are  used  in  the  plotting  of  the  topography  and  hydro- 
graphy. It  is  not  essential  that  their  determination  be  as  accurate  as  that  of  main 
triangulation  points. 

The  topography  is  put  in,  and  includes  the  delineation  of  the  features  of  the  land — 
shore  line,  light-houses,  beacons,  contour  lines,  peaks,  buildings,  and,  in  short,  every- 
thing that  may  be  recognized  by  the  navigator  and  utilized  by  him  in  locating  the  ship's         pxG.  58. 
position. 

The  hydrographic  work  is  taken  up  and  the  depth  of  water  and  character  of  bottom  determined  as 
accurately  as  possible  for  the  complete  water  area,  especial  care  being  taken  to  develop  all  shoals  and 
dangers  to  navigation  and  to  locate  all  aids  to  navigation,  such  as  buoys,  light-ships,  and  beacons. 

One  or  more  tidal  .'Stations  are  established  where  observations  are  taken,  continually  and  at  frequent 
intervals,  of  the  height  of  the  tide  and  direction  and  velocity  of  the  tidal  and  other  currents,  whence 
data  is  derived  for  the  reduction  of  all  soundings  to  the  plane  of  reference  and  for  the  information  aVjout 
tides  and  currents  which  is  to  appear  upon  the  chart. 

Observations  are  made  to  determine  the  magnetic  A'ariation  and  dip,  and  the  intensity  of  the  earth's 
magnetic  force. 

437.  The  foregoing  represent,  in  outline,  the  various  steps  that  must  be  taken  in  the  accumulation 
of  the  data  necessary  for  the  construction  of  a  complete  hydrograpliic  chart.  In  the  following  para- 
graphs the  details  of  the  various  operations  will  be  more  fully  set  forth. 

The  navigator  who  is  called  upon  to  conduct  a  marine  survey  without  having  available  the  time, 
instruments,  and  general  facilities  necessary  for  the  most  thorough  performance  of  the  work  must 
exercise  his  discretion  as  to  the  modifications  of  method  that  he  will  make,  and  call  upon  his  ingenuity 
to  adapt  his  means  to  the  particular  work  in  hand,     x 

'838.  The  Base  Line. — As  the  base  line  is  the  foundation  for  all  distances  on  the  chart,  the  cor- 
rectness of  the  results  of  the  survey  will  depend  largely  upon  the  degree  of  accuracy  with  which  it  is 
measured.  The  triangulation  merely  affords  a  measure  of  the  various  distances  as  compared  with  the 
distances  between  the  two  initial  points  from  which  it  began;  if  that  initial  distance  is  1,000  feet,  we 
have  certain  values  for  the  sides  of  the  various  triangles;  if  the  same  base  line  is  2,000  feet,  th^  value 
of  each  side  becomes  twice  as  great  as  it  was  before;  with  the  same  triangulation,  therefore,  distances 
vary  directly  with  the  length  of  the  base  line;  it  may  thus  be  seen  that  if  an  error  exists  in  measurement 
which  is  only  a  small  fraction  of  the  total  length,  the  error  will  become  much  more  material  as  the 
more  distant  points  of  the  survey  are  reached.  In  a  base  line  1,000  feet  long,  if  a  mistake  of  10  feet  be 
made,  all  distances  measured  upon  the  chart  will  be  in  error  1  per  cent,  And  a  point  plotted  by  trian- 
gulation 10  miles  from  the  observation  spot  (the  point  at  which  plotting  begins),  would  be  out  of  its 
correct  position  one-tenth  of  a  mile. 

It  is  important  that  the  base  line  should  be  as  long  as  possible,  as  an  error  in  measurement  will 
thus  constitute  a  smaller  percentage  of  the  total  length  and  will  not  accumulate  so  rapidly  as  the  work 
proceeds.     The  position  of  the  line  must  be  such  as  to  afford  favorably  conditioned  triangles  and  quadri- 


138  MARINE    SURVEYING. 

laterals  with  adjoining  main  triangulation  points,  and  its  extremities  must  be  visible  from  those  points 
and  from  each  other.  The  character  of  the  ground  and  the  facility  for  measuring  will  of  course  form  an 
important  consideration  in  the  choice. 

.439.  In  measuring  a  base  by  tape,  chain,  or  similar  means,  a  number  of  successive  fleets  are  made 
with  the  measure,  wliatever  its  nature,  the  distance  traversed  l^eing  appropriately  marked  after  each 
fleet,  while  an  observer,  with  a  theodolite  or  transit,  insures  the  measurement  b?nig  made  accurately 
along  the  line. 

440.  The  most  careful  measurements  are  made  by  a  steel  tape  100  feet  long,  stretched  along  a  series 
of  battens  which  are  supported  by  metal  crutches  and  made  exactly  horizontal  by  a  level.  The  tape  is 
stretched  to  a  uniform  tens^ion  by  a  spring  balance;  its  exact  length  at  that  tension  is  known  from  compar- 
ison with  some  standard;  a  correction  for  temperature  is  applied.  The  ends  of  the  fleets  are  marked  by 
driving  into  the  grouncfa  peg  carrying  in  its  top  a  tack;  the  exact  end  of  the  tape  is  marked  by  a  score 
filed  on  the  head  of  the  tack  at  a  point  marked  by  a  plumb  bob  from  the  tape,  and  this  score  becomes  the 
origin  for  the  next  fleet.  An  assistant  precedes  the  measuring  party  before  each  shift  of  the  battens,  and 
is  accurately  aligned  by  the  theodolite  to  mark  the  true  direction  of  the  base  line.  The  result  of  this 
method  of  measurement  gives  the  horizontal  distance  between  the  points.  It  can  be  depended  upon  for 
the  greatest  degree  of  accuracy  of  any  method,  excepting  that  with  a  special  hasc-measurmg  apparatus, 
which  is  seldom  employed  in  marine  surveys. 

441.  A  second  method  of  })ase  measurement  is  with  the  surveyor's  chain.  This  depends  for  accu- 
racy upon  the  surface  traversed  being  plane  and  level,  a  condition  that  is  well  fulfilled  on  a  sandy 
beach,  where  the  chain  is  nearly  as  accurate  as  the  tape  and  much  more  rapid.  A  surveyor's  chain  is 
usiially  100  feet  long;  the  exact  value  of  its  length  must  be  obtained  by  comparison  with  a  standard, 
and  a  correction  applied  for  expansion  or  contraction  due  to  temperature.  The  ends  of  the  fleets  are 
marked  by  steel  pnis  driven  into  the  ground;  the  alignment  is  kept  by  the  theodolite. 

442.  Where  neither  chain  nor  ttipe  is  available  substitutes  may  be  improvised  from  sounding 
wire  taken  from  the  deep-sea  sounding  machine,  or,  failing  this,  from  well-stretched  cod  line. 

443.  Measurements  made  by  the  telemeter  and  stadia  afford  a  close  approximation  to  the  true 
result,  and  if  these  instruments  are  not  at  hand  the  sextant  angle  of  a  rod  of  fixed  length  can  be  employed. 
The  masthead  height  of  the  vessel  may  be  used  in  determining  the  length  of  base  line  on  this  principle, 
either  by  making  the  ship  itself  mark  one  of  the  extremities  and  observing  the  masthead  angle  from 
the  other  extremity,  or  by  simultaneously  observing  the  masthead  angle  from  both  ends  of  a  shore 
base,  and  also  the  three  horizontal  angles  of  the  triangle  formed  by  the  ship  and  the  two  base  stations. 
The  latter  plan  is  far  preferable  where  accuracy  is  sought,  as,  if  the  angles  are  all  taken  by  different 
observers  at  the  same  instant  (which  can  be  marked  by  the  hauling  down  of  a  flag),  the  error  arising 
from  the  motion  of  the  ship  about  her  anchor  is  eliminated,  and,  moreover,  the  data  furnished  offers  a 
double  solution  of  the  triangle  and  the  mean  may  be  taken  as  giving  a  closer  result. 

444.  A  crude  method  of  measuring  a  base  is  by  means  of  the  velocity  of  sound,  though  this  would 
never  be  used  where  close  results  are  expected.  Fire  a  gun  at  one  end  of  the  base  and  at  the  other 
note  by  the  most  accurate  means  available  the  time  between  seeing  the  flash  and  hearing  the  report. 
Eepeat  several  times  in  each  direction.  The  mean  number  of  seconds  and  tenths  of  a  second  multiplied 
by  the  velocity  of  sound  per  second  at  the  temperature  of  observation  (art.  314,  Chap.  XI)  gives  the 
approximate  length  of  base  line. 

445.  When  for  any  reason  the  existing  conditions  do  not  permit  of  a  direct  measurement  being 
made  along  the  line  between  the  two  base  stations,  recourse  must  be  had  to  a  broken  base,  that  is,  one 
in  which  the  length  of  the  base  is  obtained  by  reduction  from  the  measured  length  of  two  or  more 
auxiliary  lines.  Necessity  for  resorting  to  a  broken  base  arises  frequently  when  the  two  stations  are 
situated  on  a  curving  shore  line  and  the  straight  line  between  them  passes  across  water,  or  where  wooded 
or  unfavorable  country  intervenes,  or  where  a  stream  must  be  crossed.  The  most  common  form  of 
broken  base  is  that  in  which  the  auxiliary  lines  run  from  each  extremity  of  the  base  at  an  acute  angle 
and  intersect;  in  addition  to  measuring  each  of  these  lines,  the  angles  of  the  triangle  formed  by  them 
with  the  base  line  must  be  observed  and  the  true  length  of  the  base  deduced  by  solution  of  the  triangle. 
The  form  that  is  most  frequently  used  where  only  a  short  section  of  the  base  is  incapable  of  measure- 
ment (as  is  the  case  where  a  deep  stream  flows  across)  is  that  of  an  auxiliary  right  triangle  whose  base 
is  the  required  distance  along  the  base  line  and  altitude  a  distance  measured  along  a  line  perpendicular 
thereto  to  some  convenient  point;  by  this  measured  distance  and  the  angles  which  are  observed,  the 
triangle  is  solved  and  the  length  of  the  unmeasured  section  determined. 

446.  In  a  survey  of  considerable  extent,  where  good  means  are  at  hand  for  the  correct  determina- 
tion of  latitude  and  longitude,  a  base  line  actually  measured  upon  the  earth  may  be  dispensed  with, 
and,  instead  of  that,  the  jtositions  of  the  two  stations  which  are  most  widely  separated  may  be  deter- 
mined astronomically  and  plotted;  the  triangulation  is  then  plotted  upon  any  assumed  scale,  and  when 
it  has  been  brought  up  to  connect  the  two  stations  the  true  value  of  the  scale  is  ascertained.  This  is 
called  the  method  of  an  astronomical  base. 

447.  Signals. — All  points  in  the  survey  whose  positions  are  to  be  located  from  other  stations,' or 
from  which  other  ])ositions  are  to  be  located,  must  be  marked  by  signals  of  such  character  as  will  render 
them  distinguishable  at  the  distance  from  which  they  are  observed.  The  methods  of  constructing  signals 
are  of  a  wi(le  variety.  " 

A  vessel  regularly  fitted  out  for  surveying  would  carry  scantlings,  lumber,  bolts,  nuts,  nails,  white- 
wash, and  sheeting  for  the  erection  of  signals;  however  meager  the  equipment,  the  whitewash  and 
sheeting  (or  some  substitute  for  sheeting,  preferably  half  of  it  white  and  half  dark  in  color, )  should  he 
provided,  if  possible,  before  l)eginning  any  surveying  work.  Regular  tripod  signals,  which  are  quickly 
erected  and  are  visible,  under  favorable  circumstances,  for  many  miles,  are  almost  invariably  employed 
to  mark  the  main  triangulation  stations;  among  other  advantages  the  tripod  form  permits  the  occupation 
with  the  theodolite  of  the  exact  center  of  the  station,  and  avoids  the  necessity  for  the  reduction  which  must 
otherwise  be  applied.     Signals  on  secondary  stations  take  an  innumerable  variety  of  forms,  the  require- 


MARINE    SURVEYING.  139 

ment  being  only  that  they  shall  be  seen  throughout  the  area  over  which  they  are  to  be  made  use  of; 
a  whitewashed  spot  on  a  rock,  a  whitewashed  trunk  of  a  tree,  a  whitewashed  cairn  of  stones,  a  sheeting 
flag,  a  piece  of  sheeting  wrapped  about  a  bush  or  hung,  with  stones  attached,  over  a  cliff,  or  a  white- 
washed barrel  or  box  filled  with  rocks  or  earth  and  surmounted  by  a  flag,  suggest  some  of  the  secondary 
signals  that  may  be  employed;  sometimes  objects  are  found  that  are  sufiiciently  distinct  in  themselves 
to  be  used  as  signals  without  further  marking,  as  a  cupola  or  tower,  a  hut,  a  lone  tree,  or  a  bowlder;  but 
it  is  seldom  that  an  object  is  not  rendered  more  conspicuous  by  the  flutter  of  a  flag  above  it,  or  by  the 
dead-white  ray  reflected  from  a  daub  of  whitewash. 

For  convenience,  each  signal  is  given  some  short  name  by  which  it  is  designated  in  the  records. 

448.  The  Main  Triangulatiox. — ^The  points  selected  as  stations  for  the  main  triangulation  mark 
in  outline  the  whole  area  to  be  surveyed;  they  are  close  enough  together  to  afford  an  accurate  means 
of  plotting  all  intermediate  stations  of  the  secondary  triangulation;  and  they  are  so  placed  with  relation 
to  one  another  that  the  triangles  or  quadrilaterals  derived  from  them  are  well  conditioned.  The  points 
are  generally  so  chosen  that  small  angles  will  be  avoided.  In  order  to  fulfill  the  other  conditions,  it 
frequently  becomes  necessary  to  carry  forward  the  triangulation  by  means  of  stations  located  on  points 
a  considerable  distance  inland,  suclii  as  mountain  peaks,  which  would  not  otherwise  be  regarded  as 
properly  within  the  limits  of  the  surv^ey. 

Great  care  should  be  taken  in  observing  all  angles  upon  which  the  main  triangulation  is  based;  the 
best  available  instrument  should  be  employed;  angles  taken  with  a  theodolite  or  transit  should  be 
repeated,  and  observed  with  telescope  direct  and  reversed,  and  the  mean  result  taken;  if  the  sextant  is 
used,  a  number  of  separate  observations  of  each  angle  should  be  taken  and  averaged  for  the  most  prob- 
able value.  It  must  be  remembered  that  while,  in  any  other  part  of  the  work,  an  error  in  an  angle 
affects  only  the  results  in  its  immediate  vicinity,  a  mistake  in  the  main  triangulation  goes  forward 
through  all  the  plotting  that  comes  after  it. 

It  frequently  occurs  that  the  purposes  of  the  survey  are  sufficiently  well  fulfilled  by  a  graphic  plot- 
ting of  the  main  triangulation,  but  where  more  rigorous  methods  prevail,  the  results  are  obtained  by 
calculation.  The  sum  of  the  angles  of  each  triangle  is  taken,  and  if  it  does  not  exactly  equal  180°  the 
values  are  adjusted  to  make  them  comply  with  this  condition.  The  lengths  of  the  various  sides  are 
then  computed,  regarding  the  stations,  usually,  as  forming  a  series  of  quadrilaterals,  and  allowing  for 
the  curvature  of  the  earth  where  the  sides  are  sufficiently  long  to  render  it  expedient  to  do  so. 

449.  The  Secondary  Triangulation. — The  points  of  the  secondary  triangulation  are  located,  as 
far  as  possible,  by  angles  from  the  main  triangulation  stations;  these  angles,  having  less  dependent  upon 
them,  need  not  be  repeated.     A  graphic  plotting  of  these  stations,  without  calculation,  will  suffice. 

450.  Astronomical  Work. — This  comprises  the  determination  of  the  correct  latitude  and  longitude 
of  some  point  of  the  survey,  which  is  the  first  position  plotted,  and  of  the  true  direction  of  some  other 
point  from  the  observation  spot,  which  is  the  first  line  to  be  laid  down  on  the  chart;  it  is  evident  that 
these  determinations  form  the  origin  of  all  positions  and  of  all  directions,  without  which  the  chart 
could  not  be  constructed. 

The  methods  of  finding  latitude,  longitude,  and  the  true  bearing  of  a  terrestrial  object  are  fully  set 
forth  in  previous  chapters.  The  feature  that  distinguishes  such  work  in  surveying  from  that  of  deter- 
mining the  position  of  a  ship  at  sea  lies  in  the  greater  care  that  is  taken  to  eliminate  possible  errors. 
At  sea,  results  of  absolute  exactness  are  recognized  as  unattainable  and  are  not  required;  but  in  a  careful 
survey  no  step  which  will  contribute  to  accuracy  should  be  neglected. 

Tlie  results  should  therefore  be  based  upon  a  very  large  number  of  observations,  employing  the 
best  instruments  that  are  available,  and  the  various  sights  being  so  taken  that  probable  errors  are  offset 
in  reckoning  the  mean. 

4.51.  By  taking  a  number  of  sights  the  observer  arrives  at  the  most  probable  result  of  which  his 
instruments  and  his  own  faculties  render  him  capable;  but  this  result  is  liable  to  an  error  whose  amount 
is  indeterminate  and  which  is  etiual  to  the  algebraic  sum  of  a  number  of  small  errors  due,  respectively, 
to  his  instruments  (which  must  always  lack  perfection  in  some  details),  to  an  improper  allowance  for 
refraction  under  existing  atmospheric  conditions,  and  to  his  own  personal  error.  Assuming,  as  we 
may,  that  the  personal  error  is  approximately  constant,  these  three  causes  give  rise  to  an  error  by  which 
all  altitudes  appear  too  great  or  too  small  by  a  uniform  but  unknown  amount.  Let  us  assume',  for  an 
illustration,  that  this  error  has  the  effect  of  making  all  altitudes  appear  30'^  too  great;  if  an  observer 
attempted  to  work  his  latitude  from  the  meridian  altitude  of  a  star  bearing  south,  the  result  of  this 
unknown  error  would  give  a  latitude  30'''  south  of  the  true  latitude;  if  another  star  to  the  southward 
were  observed,  this  mistake  would  be  repeated;  but  if  a  star  to  the  north  were  taken,  the  resulting 
latitude  would  be  30'^  to  the  north.  It  is  evident,  therefore,  that  the  true  latitude  will  be  the  mean  of 
the  results  of  observation  of  the  northern  and  the  southern  star,  or  the  mean  of  the  average  of  several 
northern  stars  and  the  average  of  several  southern  stars.  A  similar  process  of  reasoning  will  show  that 
errors  in  the  determination  of  hour  angle  are  offset  by  taking  the  mean  of  altitudes  of  objects  respectively 
east  and  west  of  the  meridian. 

452.  It  must  be  remembered  that  the  uniformity  of  the  unknown  error  only  exists  where  the 
altitude  remains  approximately  the  same,  as  instrumental  and  refraction  errors  may  vary  with  the 
altitude;  another  condition  of  uniformity  requires  that  the  instrument  and  the  observer  remain  the  same, 
and  that  all  observations  be  taken  about  the  same  time,  in  order  that  atmospheric  conditions  remain 
unchanged;  to  preserve  uniformity,  if  the  artificial  horizon  is  used,  the  same  end  of  the  roof  should 
always  be  the  near  one  to  the  observer;  in  taking  the  sun,  however,  as  the  personal  error  may  not  be 
the  same  for  approaching  as  for  separating  limbs,  every  series  of  obsers^ations  should  be  made  up  of  an 
equal  number  of  sights  taken  under  each  condition. 

453.  With  all  of  this  in  mind,  we  arrive  at  the  general  rule  that  astronomical  determinations 
shall  be  based  upon  the  mean  of  observations,  under  similar  conditions,  of  l)odies  whose  respective  dis- 
tances from  the  zenith  are  nearly  equal,  and  which  bear  in  opposite  directions  therefrom. 


140  MARINE    SURVEYING. 

454.  This  condition  eliminates  the  sun  from  availability  for  observations  for  latitude,  though  it 
properly  admits  the  use  of  that  body  for  longitude  where  equal  altitudes  or  single  a.  m.  and  p.  m.  sights 
are  taken.  Opposite  stars  of  approximately  equal  zenith  distance  should  always  be  used  for  latitude, 
circum-meridian  altitudes  being  observed  during  a  few  minutes  before  and  after  transit;  excellent  results 
are  also  obtained  from  stellar  observations  for  longitude;  but  very  low  stars  should  be  avoided,  on 
account  of  the  uncertainty  of  refraction,  and  likewise  very  high  ones,  as  the  reflection  from  the  index 
mirror  of  the  sextant  may  not  be  perfectly  distinct  when  tne  ray  strikes  at  an  acute  angle. 

455.  If  there  is  telegraphic  communication,  an  endeavor  should  be  made  to  obtain  a  time  signal 
from  a  reliable  source,  instead  of  depending  upon  the  chronometers. 

456.  Topography. — The  plane-table,  with  telemeter  and  stadia,  affords  the  most  expeditious  means 
of  plotting  the  topograijhy,  and  should  be  employed  when  available.  Points  on  shore  may  also  be 
plotted  by  sextant  angled,  using  the  three-point  problem,  or  by  any  other  reliable  method. 

457.  Hydrography. — The  correct  delineation  of  the  hydrographic  features  being  one  of  the  most 
important  objects  of  the  survey,  great  care  should  be  devoted  to  this  part  of  the  work.  Soundings  are 
run  in  one  or  more  series  of  parallel  lines,  the  direction  and  spacing  oi  which  depend  upon  the  scope  of 
the  survey.  It  is  usual  for  one  series  of  lines  to  extend  in  a  direction  normal  to  the  general  trend  of  the 
shore  line.  In  most  cases  a  second  series  runs  perpendicular  to  the  first,  and  in  surveys  of  important 
bodies  of  water  still  other  series  of  lines  cross  the  system  diagonally.  In  developing  rocks,  shoals,  or 
dangers  the  direction  of  the  lines  is  so  chosen  as  will  best  illustrate  the  features  of  the  bottom.  When 
lines  cross,  the  agreement  of  the  reduced  soundings  at  their  intersection  affords  a  test  of  the  accuracy  of 
the  work. 

As  the  depth  of  water  increases,  if  there  is  no  reason  to  suspect  dangers,  the  interval  between  lines 
may  be  increased. 

Lines  are  run  by  the  ship  or  boat  in  such  manner  as  to  follow  as  closely  as  possible  the  scheme  of 
sounding  that  has  been  laid  out.  The  position  is  located  by  angles  at  the  beginning  of  each  line,  at  each 
change  of  course,  at  frequent  intervals  along  the  line,  and  at  the  point  where  each  line  is  finished. 
Soundings  taken  between  positions  are  plotted  by  the  time  interval  or  patent-log  distances. 

458.  There  are  a  number  of  methods  for  determining  positions  while  sounding,  which  may  be 
described  briefly  as  follows: 

By  tico  sextant  angles. — Two  observers  with  sextants  measure  simultaneously  the  angles  between 
three  objects  of  known  position,  and  the  position  is  located  by  the  three-point  problem.  This  is  the 
method  most  commonly  employed  in  boat  work,  and  has  the  great  advantage  that  the  results  may  be 
plotted  at  once  on  the  working  sheet  in  the  boat  and  the  lines  as  run  thus  kept  nearly  in  coincidence 
with  those  laid  out  in  the  scheme.  A  study  of  the  three-point  problem  (art.  153,  Chap.  IV)  will  give 
the  considerations  that  must  govern  in  the  selection  of  objects. 

By  two  theodolite  angles. — Two  stations  on  shore  are  occupied  by  observers  with  theodolites,  and  at 
certain  instants,  indicated  by  a  signal  from  the  ship  or  boat,  they  observe  the  angular  distance  thereof 
from  some  known  point.  The  intersection  of  the  direction  lines  thus  given  is  at  the  required  position. 
This  method  is  expeditious  where  the  signals  are  small  or  not  numerous.  Its  disadvantage  is  that  the 
plotting  can  not  be  kept  up  as  the  work  proceeds. 

By  one  sextant  and  one  theodolite  angle. — An  observer  ashore  occupies  a  station  with  a  theodolite  and 
cuts  in  the  ship  or  boat,  while  one  on  board  takes  a  sextant  angle  between  two  objects,  of  which  one 
should  preferably  be  the  occupied  station.  It  is  plotted  by  laying  off  the  direction  line  from  the  theodo- 
lite and  finding  with  a  three-armed  protractor  or  piece  of  tracing  paper  what  point  of  that  line  subtends 
the  observed  angle  between  the  objects.  Its  advantages  and  disadvantages  are  the  same  as  those  of  the 
preceding  method. 

In  running  lines  of  soundings  offshore,  where  signals  are  lost  sight  of,  the  best  method  is  to  get  an 
accurate  departure,  before  dropping  the  land,  by  the  best  means  that  offers,  keeping  careful  note  of  the 
the  dead  reckoning,  and  on  running  in  again,  to  get  a  position  as  soon  as  possible,  note  the  drift  and 
reconcile  the  plotting  of  intermediate  soundings  accordingly.  Where  circumstances  require,  the  position 
may  be  located  by  astronomical  observations  as  usually  taken  at  sea. 

459.  A  careful  record  of  soundings  must  be  kept,  showing  the  time  of  each  (so  that  proper  tidal 
correction  may  be  applied),  the  depth,  the  character  of  bottom,  and  such  data  as  may  be  required  to 
locate  the  position. 

460.  Tidal  Observations. — These  should  begin  as  early  as  practicable  and  continue  throughout 
the  survey,  it  being  most  important  that  they  shall,  if  possible,  cover  the  period  of  a  lunar  month.  In 
the  chapter  on  Tides  (Chap.  XX)  the  nature  of  the  data  to  be  obtained  is  explained. 

461.  Magnetic  Observations. — The  feature  of  the  earth's  magnetism  with  which  the  navigator  is 
most  concerned  is  the  variation,  which  is  set  forth  on  the  chart,  and  upon  the  determination  of  which 
will  depend  the  correctness  of  all  courses  and  bearings  on  shipboard.  It  is  usually  obtained  by  noting 
the  compass  direction  from  the  observation  spot  of  the  object  whose  true  bearing  is  known  by  calcula- 
tion, and  comparing  the  true  and  compass  bearings;  or  it  may  be  observed  by  mounting  the  ship's  com- 
pass in  a  place  on  shore  free  from  foreign  magnetic  influence,  and  finding  the  compass  error  as  it  is  found 
on  board.     Observations  for  dip  and  intensity  are  also  made  when  the  proper  instruments  are  at  hand. 

462.  Running  Survey. — Where  time  and  opportunity  permit  only  a  superficial  examination  of  a 
coast  line  or  water  area,  or  where  the  interests  of  navigation  require  no  more,  recourse  is  had  to  a  Run- 
ning Surrey,  in  which  shore  positions  are  determined  and  soundings  are  made  while  the  ship  steams 
along  the  coast  stopping  only  occasionally  to  fix  her  position,  and  in  which  the  assistance  of  boat  or 
shore  parties  may  or  may  not  be  employed. 

In  this  method  the  ship  starts  at  one  end  of  the  field  from  a  known  position,  fixed  either  by  astro- 
nomical observations  or  by  angles  or  bearings  of  terrestrial  objects  having  a  determined  location.  Care- 
ful compass  bearings  or  sextant  angles  are  taken  from  this  position  to  all  objects  ashore  which  can  be 
recognized,  and  a  series  of  direction  lines  is  thus  obtained.  The  ship  then  steams  along  the  coast,  at  a 
convenient  distance  therefrom,  keeping  accurate  account  of  her  run  by  compass  courses  and  patent  log. 


MARINE    SURVEYING.  141 

From  time  to  time  other  series  of  bearings  or  angles  are  taken  upon  those  objects  ashore  which  are  to  be 
located,  the  direction  lines  plotted  from  the  estimated  position  of  the  ship,  and  the  various  objects  located 
by  the  intersections  with  their  other  direction  lines.  During  all  the  time  that  the  ship  is  under  way, 
soundings  are  taken  at  regular  intervals  and  plotted  from  the  dead  reckoning.  As  frequently  as  circum- 
stances permit,  the  ship  is  stopped  and  her  position  located  by  the  best  available  means,  and  the  inter- 
vening dead  reckoning  reconciled  for  any  current  that  may  be  found. 

If  a  steam  launch  can  be  employed  in  connection  with  a  running  survey,  it  is  usually  sent  to  run  a 
second  line  inshore  of  the  ship.  The  boat's  position  is  obtained  by  bearings  of  objects  ashore  which  are 
located  by  the  ship,  or  by  bearings  and  mast-head  angles  of  the  ship,  or  by  such  other  means  as  offer. 
The  duty  of  the  boat  is  to  take  a  series  of  soundings,  and  to  collect  data  for  shore  line  and  topography. 

If  circumstances  allow  the  landing  of  a  shore  party,  its  most  important  duty  is  to  mark  the  various 
objects  on  shore  by  some  sort  of  signals  which  will  render  them  unmistakable.  Beyond  this,  it  can 
perform  such  of  the  duties  assigned  to  shore  parties  in  a  regular  survey  as  opportunity  permits. 


142  WINDS. 


CHAPTER  XVIIL 

WINDS. 


463.  Wind  is  air  in  approximately  horizontal  motion.  Observations  of  the  wind  should  include 
its  true  direction,  and  its  force  or  velocity.  The  direction  of  the  wind  is  designated  by  the  point  of  the 
compass  from  which  it  proceeds.  The  force  of  the  wind  is  at  sea  ordinarily  expressed  in  terms  of 
the  Beaufort  Scale,  each  degree  of  this  scale  corresponding  to  a  certain  velocity  in  miles  per  hour,  as 
explained  in  article  67,  Chapter  II. 

464.  The  Caise  of  the  Wind. — Winds  are  produced  by  differences  of  atmospheric  pressure,  which 
are  themselves  ultimately,  and  in  the  main,  attributable  to  differences  of  temperature. 

To  undei-stand  how  the  air  can  be  set  in  motion  by  these  differences  of  pressure  it  is  necessary  to 
have  a  clear  conception  of  the  nature  of  the  air  itself. 

The  atmosphere  which  completely  envelops  the  earth  may  be  considered  as  a  fluid  sea  at  the 
bottom  of  which  we  live,  and  which  extends  upward  to  a  considerable  height,  probably  200  miles, 
constantly  diminishing  in  density  as  the  altitude  increases. 

The  air,  or  material  of  which  this  atmosphere  is  composed,  is  a  transparent  gas,  which,  like  all 
other  gases,  is  perfectly  elastic  and  highly  compressible.  Although  extremely  light,  it  has  a  perfectly 
definite  weight,  a  cubic  foot  of  air  at  ordinary  pressure  and  temperature  weighing  1.22  ouncres,  or  about 
one  seven  hundred  and  seventieth  part  of  the  weight  of  an  equal  volume  of  water.  In  consequence  of 
this  weight  it  exerts  a  certain  pressure  upon  the  surface  of  the  earth,  amounting  on  the  average  to  15 
pounds  for  each  square  inch.  To  accurately  measure  this  pressure,  which  is  constantly  undergoing  ■ 
slight  changes,  we  ordinarily  employ  a  mercurial  barometer  (art.  48,  Chap.  II),  an  instrument  in  which 
the  weight  of  a  column  of  air  of  given  cross  section  is  balanced  against  that  of  a  column  of  mercury 
having  an  equal  cross  section;  and  instead  of  saying  that  the  pressure  of  the  atmosphere  is  a  certain 
number  of  pounds  on  each  square  inch,  we  say  that  it  is  a  certain  number  of  inches  of  mercury,  meaning 
thereby  that  it  is  equivalent  to  the  pressure  of  a  column  of  mercury  that  many  inches  in  height,  and 
one  square  inch  in  cross  section. 

All  gases,  air  included,  are  highly  sensitive  to  the  action  of  heat,  expanding  or  increasing  in  volume 
as  the  temperature  rises,  contracting  or  diminishing  in  volume  as  the  temperature  falls.  Suppose 
now  that  the  atmosphere  over  any  considerable  region  of  the  earth's  surface  is  maintained  at  a 
higher  temperature  than  that  of  its  surroundings.  The  warmed  air  will  expand,  and  its  upper  layers 
will  flow  off  to  the  surrounding  regions,  cooling  as  they  go.  The  atmospheric  pressure  at  sea  level 
throughout  the  heated  areas  Mill  thus  be  diminished,  while  that  over  the  circumjacent  cooler  areas  will 
be  correspondingly  increased.  As  the  result  of  this  difference  of  pressure,  there  will  be  movement  of 
the  surface  air  away  from  the  region  of  high  pressure  and  towards  the  region  of  low,  somewhat  similar 
to  the  flow  of  water  which  takes  place  through  the  connecting  bottom  sluice  as  soon  as  we  attempt  to 
fill  one  compartment  of  a  divided  vessel  to  a  slightly  higher  level  than  that  found  in  the  other. 

A  difference  of  atmospheric  pressure  at  sea  level  is  thus  immediatelj'  followed  by  a  movement  of 
the  surface  air,  or  by  winds;  and  these  differences  of  pressure  have  their  origin  in  differences  of  tempera- 
ture. If  the  atmosphere  were  everywhere  of  uniform  temperature  it  would  lie  at  rest  on  the  earth's 
surface — sluggish,  torpid  and  oppressive — and  there  would  be  no  winds.  This,  however,  is  fortunately 
not  the  case.  The  temperature  of  the  atmosphere  is  continually  or  periodically  higher  in  one  region 
than  in  another,  and  the  chief  variations  in  the  distribution  of  temperature  are  systematically  repeated 
year  after  year,  giving  rise  to  like  systematic  variations  in  the  distribution  of  pressure. 

465.  The  Normal  Distkibittion  of  Pressure. — The  winds,  while  thus  due  primarily  to  differences 
of  temperature,  stand  in  more  direct  relation  to  differences  of  pressure,  and  it  is  from  this  point  of  view 
that  they  are  ordinarily  studied. 

In  order  to  furnish  a  comprehensive  view  of  the  distribution  of  atmospheric  pressure  over  the 
earth's  surface,  charts  have  been  prepared  showing  the  average  reading  of  the  barometer  for  any  given 
period,  whether  a  month,  a  season,  or  a  year,  and  covering  as  far  as  possible  the  entire  globe.  These 
are  known  as  isobaric  charts,  from  the  fact  that  all  points  at  which  the  barometer  has  the  same  reading 
are  joined  by  a  continuous  line  or  isobar. 

The  isobaric  chart  for  the  year  (fig.  59)  shows  in  each  hemisphere  a  well-defined  belt  of  high 
pressure  (30.20  inches)  completely  encircling  the  globe,  that  in  the  northern  hemisphere  having  its 
middle  line  about  in  latitude  35°  North,  that  in  the  southern  hemisphere  about  in  latitude  30°  South, 
these  constituting  the  so-called  meteorological  tropics.  From  the  summit  or  ridge  of  each  of  these  belts 
the  pressure  fails  off  alike  toward  the  equator  and  toward  the  pole,  although  much  less  rapidly  in  the 
former  direction  than  in  the  latter.  The  equator  itself  is  encircled  by  a  belt  of  somewhat  diminished 
pressure  (29.90  inches),  the  middle  line  of  which  is  ordinarily  found  in  northern  latitudes.  In  the 
northern  hemisphere  the  diminution  of  pressure  on  the  poleward  slope  is  much  less  marked  and  much 
less  regular  than  in  the  southern  hemisphere,  minima  (29.70  inches)  occurring  in  the  North  Atlantic 
Ocean  near  Iceland,  and  in  the  North  Pacific  Ocean  near  the  Aleutian  Islands,  beyond  which  the 
pressure  increases.  In  the  southern  hemisphere  no  such  minima  are  apparent,  the  pressure  continuing 
to  diminish  uninterruptedly  as  higher  and  higher  latitudes  are  attained.  Along  the  sixtieth  parallel  of 
south  latitude  the  average  barometric  reading  is  29.30  inches. 


WIlN'DS. 


143 


Fig.  59. 


144  WINDS. 

466.  Seasoxal  Variatioks  of  Pressurk. — As  might  be  expected  from  its  close  relation  to  the 
temperature,  the  whole  system  of  pressure  distribution  exhibits  a  tendency  to  follow  the  sun's  motion 
in  declination,  the  barometric  equator  occupying  in  July  a  position  slightly  to  the  northward  of  its 
position  in  January.  In  either  hemisphere,  moreover,  the  pressure  over  the  land  during  the  winter 
season  is  decidedly  above  the  annual  average,  during  the  summer  season  decidedly  below  it;  the 
extreme  variations  occurring  in  the  case  of  continental  Asia,  where  the  mean  monthly  pressure  ranges 
from  30.50  inches  during  January  to  29.50  inches  during  July.  Over  the  northern  ocean,  on  the  other 
hand,  conditions  are  reversed,  the  summer  pressures  being  here  somewhat  the  higher.  Thus,  in  January 
the  Icelandic  and  the  Aleutian  minima  increase  in  depth  to  29.50  inches,  while  in  July  these  minima 
fill  up  and  are  well-nigh  obliterated,  a  fact  which  has  much  to  do  with  the  strength  and  frequency  of 
the  winter  gales  in  high  northern  latitudes  and  the  absence  of  these  gales  during  the  summer.  Over 
the  southern  ocean,  m  keeping  with  its  slight  contrast  between  winter  and  summer  temperatures, 
similar  variations  of  pressure  do  not  exist. 

467.  The  Prevailing  Winds. — As  a  result  of  the  distribution  of  pressure  just  described,  there  is 
in  either  hemisphere  a  continual  motion  of  the  surface  air  away  from  the  meteorological  tropic — on  one 
side  towards  the  equator,  on  the  other  side  towards  the  pole,  the  first  constituting  in  each  case  the 
trade  winds,  the  second  the  prevailing  winds  of  higher  latitudes.  Upon  a  stationary  earth  the  direction 
of  this  motion  would  be  immediately  from  the  region  of  high  towards  the  region  of  low  barometer,  the 
moving  air  steadily  following  the  barometric  slope  or  gradient,  increasing  in  force  to  a  gale  where  these 
gradients  are  steep,  decreasing  to  a  light  breeze  where  they  are  gentle,  sinking  to  a  calm  where  they 
are  absent.  The  earth,  however,  is  in  rapid  rotation,  and  this  rotation  gives  rise  to  a  force  which 
exercises  a  material  influence  over  all  horizontal  motions  upon  its  surface,  whatever  their  direction, 
serving  constantly  to  divert  them  to  the  right  in  the  northern  hemisphere,  to  the  left  in  the  southern. 
The  air  set  in  motion  by  the  difference  of  pressure  is  thus  constantly  turned  aside  from  its  natural 
course  down  the  barometric  gradient  or  slope,  and  the  direction  of  the  wind  at  any  point,  instead  of 
being  identical  with  that  of  the  gradient  at  that  point,  is  deflected  by  a  certain  amount,  crossing  the 
latter  at  an  angle  which  in  practice  varies  between  45°  and  90°  (4  to  8  compass  points),  the  wind  in 
the  latter  case  blowing  parallel  to  the  isobars.  As  a  consequence  of  this  deflection  the  northerly  winds 
which  one  would  naturally  expect  to  find  on  the  equatorial  slope  of  the  belt  of  high  pressure  in  the 
northern  hemisphere  become  northeasterly, — the  NE.  trade;  the  southerly  winds  of  the  polar  slope 
become  southwesterly, — the  prevailing  westerly  winds  of  northern  latitudes.  So,  too,  for  the  southern 
hemisphere,  the  southerly  winds  of  the  equatorial  slope  here  becoming  southeasterly, — the  SE.  trades; 
the  northerly  winds  of  the  polar  slope  northwesterly, — the  prevailing  westerly  winds  ti  southern 
latitudes. 

46§.  The  relation  here  described  as  existing  between  the  distribution  of  atmospheric  pressure  and 
the  direction  of  the  wind  is  of  the  greatest  importance.     It  may  be  briefly. stated  as  follows: 

In  the  northern  hemisphere  stand  with  the  back  to  the  wind;  in  this  position  the  region  of  high 
barometer  lies  on  your  right  hand  and  somewhat  behind  you;  the  region  of  low  barometer  on  your  left 
hand  and  somewhat  in  front  of  you. 

In  the  southern  hemisphere  stand  with  the  back  to  the  wind;  in  this  position  the  region  of  high 
barometer  lies  on  your  left  hand  and  somewhat  behind  you;  the  region  of  low  barometer  on  your  right 
hand  and  somewhat  in  front  of  you. 

This  relation  holds  absolutely,  not  only  in  the  case  of  the  general  distribution  of  pressure  and  cir- 
culation of  the  atmosphere,  but  also  in  the  case  of  the  special  conditions  of  high  and  low  pressure  which 
usually  accompany  severe  gales. 

469.  The  Trade  Winds. — The  Trade  Winds  blow  from  the  tropical  belts  of  high  pressure  towards 
the  equatorial  belt  of  low  pressure — in  the  northern  hemisphere  from  the  northeast,  in  the  southern 
hemisphere  from  the  southeast.  Over  the  eastern  half  of  each  of  the  great  oceans  they  extend  consid- 
erably farther  from  the  line  and  their  original  direction  inclines  more  towards  the  pole  than  in  mid- 
ocean,  where  the  latter  is  almost  easterly.  They  are  ordinarily  looked  upon  as  the  most  constant  of 
winds,  but  while  they  may  blow  for  days  or  even  for  weeks  with  slight  variation  in  direction  or 
strength,  their  uniformity  should  not  be  exaggerated.  There  are  times  when  the  trade  winds  weaken 
or  shift.  There  are  regions  where  their  steady  course  is  deformed,  notably  among  the  island  groups  of 
the  South  Pacific,  where  the  trades  during  January  and  February  are  practically  nonexistent.  They 
attain  their  highest  development  in  the  South  Atlantic  and  in  the  South  Indian  Ocean,  and  are  every- 
where fresher  during  the  winter  than  during  the  summer  season.  They  are  rarely  disturbed  by  cyclonic 
storms,  the  occurrence  of  the  latter  within  the  limits  of  the  trade  wind  region  being  furthermore  con- 
fined in  point  of  time  to  the  late  summer  and  autumn  months  of  the  resijective  hemispheres,  and  in 
scene  of  action  to  the  western  portion  of  the  several  oceans.  The  South  Atlantic  Ocean  alone,  however, 
enjoys  complete  immunity  from  tropical  cyclonic  storms. 

470.  The  Doldrums. — The  equatorial  girdle  of  low  pressure  occupies  a  position  between  the  high- 
pressure  belt  of  the  northern  and  the  similar  belt  of  the  southern  hemisphere.  Throughout  the  extent 
of  this  barometric  trough  the  pressure,  save  for  the  slight  diurnal  oscillation,  is  practically  uniform,  and 
decided  barometric  gradients  do  not  exist.  Here,  accordingly,  the  winds  sink  to  stagnation,  or  rise  at 
most  only  to  the  strength  of  fitful  breezes,  coming  first  from  one  point  of  the  compass,  then  from  another, 
with  cloudy,  rainy  sky  and  frequent  thunderstorms.  The  region 'throughout  which  these  conditions 
prevail  consists  of  a  wedge-shaped  area,  the  base  of  the  wedge  resting  in  the  case  of  the  Atlantic  Ocean 
on  the  coast  of  Africa,  and  in  the  case  of  the  Pacific  Ocean  on  the  coast  of  America,  the  axis  extending 
westward.  The  position  and  extent  of  the  belt  vary  somewhat  with  the  season.  Throughout  February 
and  March  it  is  found  immediately  north  of  the  equator  and  is  of  inappreciable  width,  vessels  following 
the  usual  sailing  routes  frequently  passing  from  trade  to  trade  without  interruption  in  both  the  Atlantic 
and  the  Pacific  Oceans.  In  July  and  August  it  has  migrated  to  the  northward,  the  axis  extending  east 
and  west  along  the  parallel  of  7°  north,  and  the  belt  itself  covering  several  degrees  of  latitude,  even  at 
its  narrowest  point.  At  this  season  of  the  year,  also,  the  southeast  trades  blow  with  diminished  fresh- 
ness across  the  equator  and  well  into  the  northern  hemisphere,  being  here  diverted,  however,  by  the 
effect  of  the  earth's  rotation,  into  southerly  and  southwesterly  winds,  the  so-called  southwest  monsoon 
of  the  African  and  Central  American  coasts. 


WINDS.  145 

471.  The  Horse  jlatitudes. — On  the  outer  margin  of  the  trades,  corresponding  vaguely  with  the 
summit  of  the  tropical  ridge  of  high  pressure  in  either  hemisphere,  is  a  second  region  throughout  which 
the  barometric  gradients  are  faint  and  undecided,  and  the  prevailing  winds  correspondingly  light  and 
variable,  the  so-called  hor^e  latitudes,  or  calms  of  Cancer  and  of  Capricorn.  Unlike  the  doldrums,  how- 
ever, the  weather  is  here  clear  and  fresh,  and  the  periods  of  stagnation  are  intermittent  rather  than 
continuous,  showing  none  of  the  persistency  which  is  so  characteristic  of  the  equatorial  region.  The 
explanation  of  this  difference  will  Ijecome  obvious  as  soon  as  we  come  to  study  the  nature  of  the  daily 
barometric  changes  of  pressure  in  the  respective  regions,  these  in  the  one  case  being  marked  by  the 
uniformity  of  the  torrid  zone,  in  the  other  sharing  to  a  limited  extent  in  the  wide  and  rapid  variations 
of  the  temperate. 

472.  The  Prevailing  Westerly  Winds. — On  the  exterior  or  polar  side  of  the  tropical  maxima 
the  pressure  again  diminishes,  the  barometric  gradients  being  now  directed  towards  the  pole;  and  the 
currents  of  air  set  in  motion  along  these  gradients,  diverted  to  the  right  and  left  of  their  natural  course 
by  the  earth's  rotation,  appear  in  the  northern  hemisphere  as  southwesterly  winds,  in  the  southern 
hemisphere  as  northwesterly — the  prevailing  westerly  winds  of  the  temperate  zone. 

Only  in  the  southern  hemisphere  do  these  winds  exhibit  anything  approaching  the  persistency  of 
the  trades,  their  course  in  the  northern  hemisphere  being  subject  to  frequent  local  interruption  by 
periods  of  winds  from  the  eastern  semicircle.  Thus  the  tabulated  results  show  that  throughout  the 
portion  of  the  North  Atlantic  included  between  the  parallels  40°-50°  North,  and  the  meridians  10°-50° 
West,  the  winds  from  the  western  semicircle  (South — NNW.)  comprise  about  74  per  cent  of  the  whole 
number  of  observations,  the  relative  frequency  being  somewhat  higher  in  winter,  somewhat  lower  in 
summer.  The  average  force,  on  the  other  hand,  decreases  from  force  6  to  force  4  Beaufort  scale,  with 
the  change  of  season.  Over  the  sea  in  the  southern  hemisphere  such  variations  are  not  apparent;  here 
the  westerlies  blow  through  the  entire  year  with  a  steadiness  little  less  than  that  of  the  trades  them- 
selves, and  with  a  force  which,  though  fitful,  is  very  much  greater,  their  boisterous  nature  giving  the 
name  of  the  "  Roaring  Forties"  to  the  latitudes  in  which  they  are  most  frequently  observed. 

The  exi)lanation  of  this  striking  difference  in  the  extra-tropical  winds  of  the  two  halves  of  the  globe 
is  found  in  the  distribution  of  atmospheric  pressure,  and  in  the  variations  which  this  latter  undergoes  in 
different  parts  of  the  world.  In  the  landless  southern  hemisphere  the  atmospheric  pressure  after  cross- 
ing the  parallel  of  30°  South  diminishes  almost  uniformly  towards  the  pole,  and  is  rarely  disturbed  by 
those  large  and  irregular  fluctuations  which  form  so  important  a  factor  in  the  daily  weather  of  the 
northern  hemisphere.  Here,  accordingly,  a  system  of  polar  gradients  exists  quite  comparable  in 
stability  with  the  equatorial  gradients  which  give  rise  to  the  trades;  and  the  poleward  movement  of  the 
air  in  obedience  to  these  gradients,  constantly  diverted  to  the  left  by  the  effect  of  the  earth's  rotation, 
constitutes  the  steady  westerly  winds  of  the  south  temperate  zone. 

473.  The  Monsoon  Winds. — Theairover  the  land  is  warmer  in  summer  and  colder  in  winter  than 
that  over  the  adjacent  oceans.  During  the  former  season  the  continents  thus  become  the  seat  of  areas 
of  relatively  low  pressure;  during  the  latter  of  relatively  high.  Pressure  gradients,  directed  outward 
during  the  winter,  inward  during  the  summer,  are  thus  established  between  the  land  and  the  sea,  which 
exercise  the  greatest  influence  over  the  winds  prevailing  in  the  region  adjacent  to  the  coast.  Thus,  off 
the  Atlantic  seaboard  of  the  United  States  southwesterly  winds  are  most  frequent  in  summer,  north- 
westerly winds  in  winter;  while  on  the  Pacific  coast  the  reverse  is  true,  the  wind  here  changing  from 
northwest  to  southwest  with  the  advance  of  the  colder  season. 

The  most  striking  illustration  of  winds  of  this  class  is  presented  by  the  monsoons  {Mausum,  season) 
of  the  China  Sea  and  of  the  Indian  Ocean.  In  January  abnormally  low  temperatures  and  high  pressure 
obtain  over  the  Asiatic  plateau,  high  temperatures  and  low  pressure  over  Australia  and  the  nearby 
portion  of  the  Indian  Ocean.  As  a  result  of  the  baric  gradients  thus  established,  the  southern  and 
eastern  coast  of  the  vast  Asiatic  continent  and  the  seas  adjacent  thereto  are  swept  by  an  outflowing 
current  of  air,  which,  diverted  to  the  right  of  the  gradient  by  the  earth's  rotation,  appears  as  a  north- 
east Avind,  covering  the  China  Sea  and  the  northern  Indian  Ocean.  Upon  entering  the  southern 
hemisphere,  however,  the  same  force  which  hitherto  deflected  the  moving  air  to  the  right  of  the 
gradient  now  serves  to  deflect  it  to  the  left;  and  here,  accordingly,  we  have  the  monsoon  appearing  as 
a  northwest  wind,  covering  the  Indian  Ocean  as  far  south  as  10°,  the  Arafura  Sea,  and  the  northern 
coast  of  Australia. 

In  July  these  conditions  are  precisely  reversed.  Asia  is  now  the  seat  of  high  temperature  and 
correspondingly  low  pressure,  Australia  of  low  temperature  and  high  pressure,  although  the  departure 
from  the  annual  average  is  by  no  means  so  pronounced  in  the  case  of  the  latter  as  in  that  of  the  former. 
The  baric  gradients  thus  lead  across  the  equator  and  are  addressed  toward  the  interior  of  the  greater 
continent,  giving  rise  to  a  system  of  winds  whose  direction  is  southeast  in  the  southern  hemisphere, 
southwest  in  the  northern. 

The  mtrtheast  (winter)  monsoon  blows  in  the  China  Sea  from  October  to  April,  the  southwest 
(summer)  monsoon  from  May  to  September.  The  former  is  marked  by  all  the  steadiness  of  the  trades, 
often  attaining  the  force  of  a  moderate  gale;  the  latter  appears  as  a  light  breeze,  unsteady  in  direction, 
and  often  sinking  to  a  calm.  Its  prevalence  is  frequently  interrupted  by  tropical  cyclonic  storms, 
locally  known  as  t;/phoons,  although  the  occurrence  of  these  latter  may  extend  well  into  the  season  of 
the  winter  monsoon. 

474.  Land  and  Sea  Breezes. — Corresponding  with  the  seasonal  contrast  of  temperature  and 
pressure  overland  and  water,  there  is  likewise  a  diurnal  contrast  which  exercises  a  similar  though  more 
local  effect.  In  summer  particularly,  the  land  over  its  whole  area  is  warmer  than  the  sea  by  day,  colder 
than  the  sea  by  night,  the  variations  of  pressure  thus  established,  although  insignificant,  sufficing  to 
evoke  a  system  of  littoral  breezes  directed  landward  during  the  daytime,  seaward  during  the  night, 
which,  in  general,  do  not  penetrate  to  a  distance  greater  than  30  miles  on  and  off  shore,  and  extend  but 
a  few  hundred  feet  into  the  depths  of  the  atmosphere. 

The  sea  breeze  begins  in  the  morning  hours — from  9  to  11  o'clock — as  the  land  warms.  In  the  late 
afternoon  it  dies  away.     In  the  evening  the  land  breeze  springs  up,  and  blows  gently  out  to  sea  until 

22489—03 10 


1 46  WINDS. 

morning.      In  the  tropics  this  process  is  repeated  day  after  day  with  great  regularity.     In  our  own 
latitudes,  the  land  and  sea  breezes  are  often  masked  by  winds  of  cyclonic  origin. 

475.  A  single  important  effect  of  the  seasonal  variation  of  temperature  and  pressure  over  the  land 
remains  to  be  described.  If  there  were  no  land  areas  to  break  the  even  water  surface  of  the  globe,  the 
trades  and  westerlies  of  the  terrestrial  circulation  would  be  developed  in  the  fullest  simplicity,  with 
linear  divisions  along  latitude  circles  between  the  several  members — a  condition  nearly  approached  in 
the  land-barren  southern  hemisphere  during  the  entire  year,  and  in  the  northern  hemisphere  during  the 
winter  season.  In  the  summer  season,  however,  the  tropical  belt  of  high  pressure  is  broken  where  it 
crosses  the  warm  land,  and  the  air  shouldered  off  from  the  continents  accumulates  over  the  adjacent 
oceans,  particularly  in  the  northern  or  land  hemisphere.  This  tends  to  create  over  each  of  the  oceans  a 
circular  or  elliptical  area  St  high  pressure,  from  the  center  of  which  the  baric  gradients  radiate  in  all 
directions,  giving  rise  to  an  outflowing  system  of  winds,  which  by  the  effect  of  the  earth's  rotation  is 
converted  into  an  outflowing  spiral  eddy  or  aniicydonic  whirl.  The  sharp  lines  of  demarcation  which 
would  otherwise  exist  between  the  several  members  of  the  general  circulation  are  thus  obliterated, 
the  southwesterly  winds  of  the  middle  northern  latitudes  becoming  successively  northwesterly,  northerly, 
and  northeasterly,  as  we  approach  the  equator  and  round  the  area  of  high  pressure  by  the  east;  the 
northeast  trade  becoming  successively  southeasterly,  southerly,  and  southwesterly,  as  we  recede  from  the 
equator  and  round  this  area  by  the  west;  similarly  for  the  other  hemisphere. 


147 


chaptp:r  XIX. 

OYCLONIO  STOEMS. 


476.  Variations  of  the  Atmospheric  Pressure. — The  distribution  of  the  atmospheric  pressure 
previously  described  (Chap.  XV^III)  and  the  attendant  circulation  of  the  winds  are  those  which  become 
evident  after  the  effects  of  many  disturbing  causes  have  been  eliminated  by  the  process  of  averaging,  or 
embracing  in  the  summation  observations  covering  an  extended  period  of  time.  The  distribution  of 
pressure  and  the  system  of  winds  which  actually  exist  at  a  given  instant  will  in  general  agree  with 
these  in  its  main  features,  but  may  differ  from  them  materially  in  detail. 

Confining  our  attention  for  the  time  being  to  the  subject  of  atmospheric  pressure,  it  may  be  said 
that  this,  at  any  given  point  on  the  earth's  surface,  is  in  a  constant  state  of  change,  the  mercury  rarely 
becoming  stationarv,  and  then  only  for  a  few  hours  in  succession.  The  variations  which  the  pressure 
undergoes  may  be  divided  into  two  classes;  viz,  periodic,  or  those  which  are  continuously  in  operation, 
repeating  themselves  within  fixed  intervals  of  time,  long  or  short;  and  non-periodic  or  accidental,  which 
occur  irregularly,  and  are  of  varying  duration  and  extent. 

477.  Periodic  Variations. — Of  the  former  class  of  changes  the  most  important  are  the  seasonal, 
which  have  been  already  to  some  extent  described,  and  the  diurnal.  The  latter  consists  of  the  daily 
occurrence  of  two  barometric  maxima,  or  points  of  highest  pressure,  with  two  intervening  minima. 
Under  ordinary  circumstances,  with  the  atmosphere  free  from  disturbances,  the  barometer  each  day 
attains  its  first  minimum  about  4  a.  ra.  As  the  day  advances  the  pressure  increases,  and  a  maximum, 
or  point  of  greatest  pressure,  is  reached  about  10  a.  m.  From  this  time  the  pressure  diminishes,  and 
a  second  minimum  is  reached  about  4  p.  m.,  after  which  the  mercury  again  rises,  reaching  its  second 
maximum  about  10  p.  m.  The  range  of  this  diurnal  oscillation  is  greatest  at  the  equator,  where  it 
amounts  to  ten  hundredths  (0.10)  of  an  inch.  It  diminishes  with  increased  latitude,  and  near  the  poles 
it  seems  to  vanish  entirely.     In  middle  latitudes  it  is  much  more  apparent  in  summer  than  in  winter. 

478.  Non-periodic  Variations. — The  equatorial  slope  of  the  tropical  belt  of  high  pressure  which 
encircles  the  globe  in  either  hemisphere  is  characterized  by  the  marked  uniformity  of  its  meteorological 
conditions,  the  temperature,  wind,  and  weather  changes  proper  to  any  given  season  repeating  them- 
selves as  day  succeeds  day  with  almost  monotonous  regularity.  Here  the  diurnal  oscillation  of  the 
barometer  constitutes  the  main  variation  to  which  the  atmospheric  pressure  is  subjected.  On  the  polar 
slope  of  these  belts  conditions  the  reverse  of  these  obtain,  the  elements  which  go  to  make  up  the  daily 
weather  here  passing  from  phase  to  phase  without  regularity,  with  the  result  that  no  two  days  are  pre- 
cisely alike;  and  as  regards  atmospheric  pressure,  it  may  be  said  that  in  marked  contrast  with  the 
uniformity  of  the  torrid  zone,  the  barometer  in  the  temperate  zone  is  constantly  subjected  to  non-periodic 
or  accidental  fluctuations  of  such  extent  that  the  periodic  diurnal  variation  is  scarcely  apparent,  the 
mercury  at  a  given  station  frequently  rising  or  falling  several  tenths  of  an  inch  in  twenty-four  hours. 

479.  Progressive  Areas  of  High  and  Low  Pressure. — The  explanation  of  this  rapid  change  of 
conditions  is  found  in  the  approach  and  passage  of  extensive  areas  of  alternately  high  and  low  pressure, 
which  affect  alike,  although  to  a  different  degree,  all  the  barometers  coming  within  their  scope.  The 
general  direction  of  motion  of  these  areas  is  that  of  the  prevailing  winds;  eastward,  therefore,  in  the 
latitudes  which  are  under  consideration. 

Taken  in  conjunction,  these  areas  of  high  and  low  pressure  exercise  a  controlling  influence  over  the 
weather  changes  of  the  temperate  zones.  As  the  low  area  draws  near,  the  sky  becomes  overclouded, 
the  prevailing  westerly  wind  falls  away,  and  is  succeeded  by  a  wind  from  some  easterly  direction,  faint 
at  first,  but  increasing  as  the  pressure  continues  to  diminish;  the  lowest  pressure  having  been  reached, 
the  wind  again  goes  to  the  westward,  the  glass  starts  to  rise,  and  the  weather  clears;  all  marking  the 
eastward  recession  of  the  low  area  and  the  approach  of  the  subsequent  high. 

The  first  stage  in  the  development  of  the  low  is  a  slight  diminution  of  the  atmospheric  pressure, 
amounting  in  general  to  not  more  than  one  or  two  hundredths  of  an  inch,  throughout  an  area  covering 
a  more  or  less  extensive  portion  of  the  earth's  surface,  either  land  or  water,  but  far  more  frequently 
over  the  former  than  over  the  latter.  Shortly  after  the  advent  of  this  initiatory  fall  the  decrease  of  pres- 
sure throughout  some  small  region  within  the  larger  area  assumes  a  more  decided  character,  the  mercury 
here  standing  at  a  lower  level  than  elsewhere  and  reading  successively  higher  as  we  go  outward,  the 
region  thus  becoming,  as  it  were,  the  center  of  the  whole  barometric  depression.  A  system  of  baro- 
metric gradients  is  by  this  means  established,  all  directed  radially  inward,  and  in  obedience  to  these 
gradients  there  is  a  movement  of  the  surface  air  towards  the  center  or  point  of  lowest  barometer.  The 
air  once  in  motion,  however,  the  effect  of  the  earth's  rotation  is  brought  into  play  precisely  as  in  the 
case  of  the  larger  movements  of  the  atmosphere,  with  the  result  that  the  several  currents,  instead  of 
following  the  natural  course  along  these  gradients,  are  deflected  from  them,  in  the  northern  hemisphere 
to  the  right  hand,  in  the  southern  hemisphere  to  the  left,  the  extent  of  the  deflection  being  from  4  to  8 
compass  points. 

4§0.  Cyclones  and  Cyclonic  Circulations. — A  central  area  of  low  barometer  will  thus  be  sur- 
rounded by  a  system  of  winds  which  constantly  draw  in  towards  the  center  but  at  the  same  time  circulate 
about  it,  the  whole  forming  an  inflowing  spiral;  the  direction  of  this  circulation  being  in  the  southern 
hemisphere  with  the  motion  of  the  hands  of  a  watch,  in  the  northern  hemisphere  opposed  to  this 


1.48 


CYCLONIC    STORMS. 


motion.  Where  the  barometric  gradients  are  steep,  these  winds  are  apt  to  be  strong;  where  they  are 
gentle,  the  winds  are  apt  to  be  weak;  where  they  are  absent,  as  is  the  case  at  the  center  or  bottom  of 
the  depression,  cahns  are  apt  to  prevail. 

Around  the  center  of  the  area  of  high  pressure  a  similar  system  of  wind  will  be  found,  but  l)lowmg 
in  a  contrary  direction.  Here  the  barometric  gradients  are  directed  radially  outward,  with  the  result 
that  in  place  of  the  inflowing,  we  have  an  outflowing  spiral,  the  circulatory  motion  being  right  handed 
or  with  the  hands  of  a  watch  in  the  northern  hemisphere,  left  handed  or  against  the  hands  of  a  watch 
in  the  southern. 

All  of  these  features  are  shown  in  the  accompanying  diagrams  (fig.  60),  which  exhibit  the  general 
character  of  cyclonic  (around  the  low)  and  anticy clonic  (around  the  high)  circulations  in  the  northern 
An'icyclonic.  northern  hemisphekk.  Otielnnir. 


Aiiticyclonic. 


Cyclonic. 


SOl'THERN  HEMISPHERE. 

Fig.  60. 

The  light  arrows  .show  the  direction  of  the  gradients;  the  heavy  arrows  the  direction  of  the  winds. 

and  the  southern  hemisphere,  respectively.  The  closed  curves  represent  the  isobars,  or  lines  along 
Avhich  the  barometric  pressure  is  the  same;  the  short  arrows  show  the  direction  of  the  gradients,  which 
are  everywhere  at  right  angles  to  the  isobars;  the  long  arrows  give  the  direction  of  the  winds,  deflected 
by  the  earth's  rotation  to  the  right  of  the  gradients  in  the  northern  hemisphere,  to  the  left  in  the 
southern. 

4§1.  Features  op  Cyclonic  and  Anticyclonic  Regions. — Certain  features  of  the  two  areas  may 
here  be  contrasted.  In  the  anticyclonic,  the  successive  isobars  are  as  a  rule  far  apart,  showing  weak 
gradients  and  consequently  light  winds;  the  areas  themselves  are  of  relatively  great  extent,  and  their 
rate  of  progression  is  sIoav.  During  the  summer  they  originate  as  extensions  into  higher  latitudes  of 
the  margins  of  the  tropical  belts  of  high  pressure;  during  the  winter,  as  offshoots  of  the  strong  anticy- 
clone which  covers  the  land  throughout  that  season.  Their  approach  and  presence  is  accompanied  by 
polar  or  westerly  winds,  temperature  below  the  seasonal  average,  fair  weather,  and  clear  skies.  In  the 
cyclonic  area  the  successive  isobars  are  crowded  together,  showing  steep  gradients  and  strong  winds; 
they  may  appear  either  as  trough-like  extensions  into  the  temperate  zone  of  the  polar  belt  of  low  pres- 
sure, in  which  case  the  easterly  winds  proper  to  their  polar  side  are  nonexistent,  or  (in  lower  latitudes) 
as  independent  areas,  sometimes,  indeed,  as  detached  portions  of  the  equatorial  low-pressure  belt,  which 
move  eastward  and  poleward  across  the  temperate  zone,  and  are  ultimately  merged  into  the  great 
cyclonic  area  surrounding  the  pole.  The  progress  of  these  independent  areas  is  invariably  attended  by 
the  strong  and  steadily  shifting  winds,  foul  weather,  and  other  features  which  make  up  the  ordinary 
storm  at  sea.  In  the  trough-like  depressions  of  higher  latitudes  these  features  may  or  may  not  be 
observed,  their  presence  depending  upon  the  depths  of  the  barometric  trough  and  the  steepness  of  its 
slopes.  In  these,  moreover,  the  cyclonic  circulation  is  never  completely  developed,  the  storm  winds 
having  rather  the  character  of  right  line  gales,  blowing  from  an  equatorial  or  easterly  direction  until  the 
axis  of  the  trough  is  at  hand,  and  as  this  passes  shifting  by  the  west  at  one  bound  to  a  polar  direction. 

482.  Cyclonic  Storms. — Strong  winds  are  the  result  of  steep  barometric  gradients.  These  may 
occur  with  cyclonic  or  with  anticyclonic  areas,  the  latter  being  exemplified  in  the  case  of  the  northers 
in  the  Gulf  of  Mexico  and  the  northwesterly  winter  gales  along  the  Atlantic  coast  of  the  United  States, 
which  are  almost  invariably  accompanied  by  barometers  above  the  average.  They  are,  however,  so 
much  more  frequent  in  the  case  of  areas  of  low  pressure  and  consequent  cyclonic  circulations,  wnth  their 
attendant  foul  weather  characteristics,  that  the  latter  are  generally  known  as  cyclonic  storms,  i.  e., 
storms  in  which  the  wind  circulation  is  cyclonic. 

Cyclonic  storms  may  with  convenience  be  divided  into  two  classes;  viz,  tropical,  or  those  which 
originate  near  but  not  on  the  equator;  and  extra-tropical,  or  those  which  first  appear  in  higher 
latitudes. 

4§3.  Tropical  Cyclonic  Storms. — The  occurrence  of  tropical  cyclonic  storms  is  confined  to  the 
summer  and  autumn  months  of  the  respective  hemispheres,  and  to  the  w^estern  part  of  the  several 
oceans,  the  North  Atlantic,  the  North  Pacific,  the  South  Pacific,  and  the  Indian  Ocean.  They  are 
unknown  in  the  South  Atlantic  Ocean. 

The  Arabian  Sea  and  the  Bay  of  Bengal  are  also  visited  by  cyclonic  storms,  the  season  of  their 
occurrence  extending  from  May  to  October. 

4§4.  Motion  of  the  Storm  Center. — In  the  case  of  tropical  cyclonic  storms  there  is  always  a 
tendency  for  the  barometric  depression,  impelled  by  the  general  motion  of  the  atmosphere  in  the 


CYCLONIC    STORMS. 


149 


trade  wind  region,  to  follow  a  path  which  tends  at  once  westward  and  away  from  the  equator.  This 
motion  conthmes  until  the  limits  of  the  trades  are  reached,  where  the  path  ordinarily  recurves,  and 
the  subsequent  motion  of  the  depression  is  eastward  and  towards  the  pole,  the  disturbance  at  the  same 
time  assuming  the  features  of  the  extra-tropical  cyclonic  storm. 

4§5.  Rate  of  Progress  op  the  Stor.^i  Center. — Within  the  tropics  (in  the  northern  hemisphere) 
the  average  velocity  of  the  storm  center  along  the  track  is  about  17  miles  per  hour;  in  the  latitudes  of 
recurvature  this  drops  to  8  miles  per  hour,  the  center  at  the  time  frequently  becoming  stationary;  in 
higher  latitudes  it  again  increases,  rising  to  20  or  even  to  30  miles  per  hour. 

In  the  southern  hemisphere  the  average  velocity  of  progress  as  far  as  determined  is  somewhat  less 
than  in  the  northern,  but  shows  about  the  same  relation  in  different  parts  of  the  track. 

The  general  path  of  the  tropical  cj-clonic  storm  in  either  hemisphere  and  the  cyclonic  circulation  of 
the  wind  about  the  storm  center  are  given  in  figures  61  and  62;  that  for  the  northern  hemisphere 
applying  to  the  West  India  hurricane;  that  for  ^ 

the  southern  hemisphere  to  the  hurricanes  of  ,„ ,,  ^P°      ^      .,.,.■.     .     ,'i     i— i     >""^    hi/iiT 

the  South  Pacific  Ocean.  ■'    '     '     '^  '^^  ^        .     .     ,     .     .     .    i         ^^^ 

486.  Character  of  Tropical  Cycloxic 
Storms. — Within  the  tropics  the  storm  area  is 
small,  the  region  covered  by  violent  winds  ex- 
tending in  general  not  more  than  150  miles  from 
the  center.  The  barometric  gradients  are,  how- 
ever, exceedingly  steep,  instances  having  been 
recorded  in  which  the  difference  of  pressure  for 
this  distance  amounted  to  2  inches.  In  the 
typhoons  of  the  North  Pacific  Ocean  gradients 
of  one  inch  in  60  miles  are  not  infrequent.  The 
successive  isobars  are  almost  circular.  As  a 
consequence  of  this  distribution  of  pressure  the 
winds  on  the  slopes  of  the  depression  are  fre- 
quently of  great  violence,  and  in  the  matter  of 
direction  they  are  more  symmetrically  disposed 
about  the  center  than  is  the  case  with  the  larger 
and  less  regularly  shaped  depressions  of  higher 
latitudes.  In  these  low  latitudes  the  average 
values  of  the  deflection  of  the  wind  from  the 
barometric  gradient  is  in  the  neighborhood  of 
six  compass  points, — to  the  right  in  the  northern 
hemisphere,  to  the  left  in  the  southern. 

4§7.  To  Fix  the  Bearing  of  the  Storm 
Center  from  the  Vessel. — On  this  assumption, 
the  following  rules  will  enable  an  observer  to 
fix  the  bearing  of  the  storm  center  from  his 
vessel : — 

In  the  northern  hemisphere,  stand  with  the 
back  to  the  wind;  the  storm  center  will  bear  six 
points  to  the  observer's  left. 

In  the  southern  hemisphere,  stand  with  the 
back  to  the  wind;  the  storm  center  will  bear  six 
points  to  the  observer's  right. 

On  the  basis  of  these  rules  the  tables  here- 
after given  (art.  492)  show  the  bearing  of  the 
center  corresponding  to  a  wind  of  any  direction. 

488.  To  Fix  the  Distance  of  the  Storm  Center  from  the  Vessel. — The  following  table,  taken 
from  Piddington's  "Sailor's  Horn  Book,"  may  prove  of  some  assistance  in  estimating  the  distance  of  the 
storm  center  from  the  vessel: 


Fig.  61. 


Average  fall  of  the  barometer 
per  hour. 

From  0.02  to  0.06  in. 
From  0.06  to  0.08  in. 
From  0.08  to  0.12  in. 
From  0.12  to  0.15  in. 


Distance  from  the  storm  center. 

From  250  to  150  miles. 
From  150  to  100  miles. 
From  100  to  80  miles. 
From    80  to    50  miles. 


The  table  assumes  that  the  vessel  is  hove-to  in  front  of  the  storm,  and  that  the  latter  is  advancing 
directly  toward  it. 

489.  To  Avoid  the  Center  of  the  Storm. — In  the  immediate  neighborhood  of  the  center  itself 
the  winds  attain  full  hurricane  force,  the  sea  is  exceedingly  turbulent,  and  there  is  danger  of  being 
struck  aback.  Every  effort  should  therefore  be  made  to  avoid  this  region,'  either  by  running  or  by 
heaving-to;  and  if  recourse  is  had  to  the  latter  maneuver,  much  depends  upon  the  selection  of  the 
proper  tack;  this  being  in  every  case  the  tack  which  will  cause  the  wind  to  draw  aft  with  each  successive 
shift. 

A  vessel  hovo-to  in  advance  of  a  tropical  cyclonic  storm  will  experience  a  long  heavj'  swell,  a  falling 
barometer  with  torrents  of  rain,  and  winds  of  steadily  increasing  force.  The  shifts  of  wind  will  depend 
upon  the  position  of  the  vessel  with  respect  to  the  path  followed  by  the  storm  center.  Immediately  upon 
the  path,  the  wind  will  hold  steady  in  direction  until  the  passage  of  the  central  calm,  the  ''eye  of 
the  storm,"  after  which  the  gale  will  renew  itself,  but  from  a  direction  opposite  to  that  which  it  previ- 


150 


CYCLONIC    STOEMS. 


ously  had.  To  the  right  of  the  path,  or  in  the  right-hand  semicircle  of  the  stomi  (the  observer  being 
supposed  to  face  along  the  track ),  the  wind,  as  the  center  advances  and  i)asses  the  vessel,  will  constantly 
shift  to  the  right,  the  rate  at  which  the  successive  shifts  follow  each  other  increasing  with  the  prox- 
imity to  the  center;  in  this  semicircle,  then,  in  order  that  the  wind  shall  draw  aft  with  each  shift,  the 
vessel  must  be  hove-to  on  the  starboard  tack;  similarly,  in  the  left-hand  semicircle,  the  wind  will  con- 
stantly shift  to  the  left,  and  here  the  vessel  must  l)e  hove-to  on  the  port  tack. 

These  rules  hold  alike  for  both  hemispheres  and  for  cyclonic  sti)rms  in  all  latitudes. 
The  above  shifts  of  the  wind  are  based  upon  the  supposition  that  the  vessel  is  lying-to.     A  vessel  in 
rapid  westerly  motion  may,  in  low  latitudes,  readily  overtake  the  storm  center,  in  which  case  the 
observed  shifts  will  be  just  the  reverse  of  those  here  described. 

490.  Dangerois  and  Navigable  Semicircles. — Prior  to  recurving,  the  winds  in  that  semicircle 
of  the  storm  which  is  more  remote  from  the  equator  (the  right-hand  semicircle  in  the  northern  hemi- 
sphere,   the    left-hand   semicircle   in   the 
180°  170°  southern )  are  liable  to  be  more  severe  than 

those  of  the  opposite  semicircle.  A  vessel 
hove-to  in  the  semicircle  adjacent  to  the 
equator  has  also  the  advantage  of  immu- 
nity from  bec(jming  involved  in  the  actual 
center  itself,  inasmuch  as  there  is  a  distinct 
tendency  on  tiie  part  of  the  latter  to  move 
away  from  the  equator.  For  these  reasons 
the  more  remote  semicircle  has  been  called 
the  dangerouK;  the  less  remote,  ihenavigable. 
491.  Maneuvering. — A  vessel  sus- 
l^ecting  the  dangerous  proximity  of  a  trop- 
ical cyclonic  storm  should  lie-to  for  a  time 
on  the  starboard  tack  to  locate  the  center 
by  observing  shifts  of  the  wind  and  the 
behavior  of  the  barometer.  If  the  former 
holds  steady  and  increases  in  force,  while 
the  latter  falls  rapidly,  say  at  a  greater  rate 
than  0.03  of  an  inch  per  liour,  the  vessel 
is  probably  on  the  track  of  the  storm  and 
in  advance  of  the  center.  In  this  position 
the  proper  step  (providing,  of  course,  that 
sea  room  permits)  is  to  run,  keeping  the 
wind,  in  the  northern  hemisphere,  at  all 
times  well  on  the  starboard  quarter;  in  the 
1^  southern  hemisphere,  well  on  the  port;  and 
thus  constantly  increasing  the  distance  to 
the  storm  center.  The  same  rule  holds  good 
if  the  observation  places  the  vessel  at  but 
a  scant  distance  within  the  forward  quad- 
rant of  the  dangerous  semicircle.  Here, 
too,  the  natural  course  will  be  to  seek  the 
navigable  semicircle  of  the  storm,  even 
though  such  a  course  involves  crossing  the 
track  in  advance  of  the  center,  always  ex- 
ercising due  caution  to  keep  the  wind  frotn 
drawing  too  far  aft. 

The  critical  case  is  that  of  a  vessel 
—  which  finds  herself  in  the  forward  quad- 
rant of  the  dangerous  semicircle  and  at  a 
considerable  distance  from  the  track,  for 
here  the  shifts  of  the  wind  are  sluggish  and 
the  indications  of  the  barometer  are  unde- 
cided, both  causes  conspiring  to  render  the 
bearing  of  the  center  doubtful.  If,  upon 
heaving-to,  the  barometer  becomes  station- 
ary, the  position  should  be  maintained 
until  indications  of  a  rise  are  apparent,  upon  which  the  course  may  be  resumed  with  safety  and  held  as 
long  as  the  rise  continues.  If,  however,  the  barometer  falls,  a  steamer  should  make  a  run  to  the  NNE. 
or  NE.  (southern  hemisphere,  SSE.  orSE. ),  keeping  the  wind  and  sea  a  little  on  the.port  (southern 
hemisphere,  starboard)  bow,  and  using  such  speed  as  will  at  least  keep  the  mercury  stationary.  Such 
a  step  will  in  general  be  attended  with  the  assurance  that  the  present  weather  conditions  will  in  any 
case  grow  no  worse.  For  a  sailing  vessel,  unable  to  stand  closer  to  the  wind  than  six  points,  the  last 
maneuver  will  be  impossible,  and  driven  to  leeward  bj'^  wind,  sea,  and  current,  she  may  be  compelled 
to  cross  the  track  immediately  in  advance  of  the  center,  or  may  even  become  involved  in  the  center 
itself.  In  this  extremity  the  path  of  the  storm  center  during  the  past  twenty-four  hours  should  be  laid 
down  on  a  diagram  as  accurately  as  the  observations  permit,  and  the  line  prolonged  for  some  distance 
beyond  the  present  position  of  the  center.  Having  assumed  an  average  rate  of  progress  for  the  center, 
its  probable  position  on  the  line  should  be  frequently  and  carefully  plotted,  and  the  handling  of  the 
vessel  should  be  in  accordance  with  the  diagram. 

492.  Summary  of  Rules. — The  following  summary  comprises  the  rules  for  maneuvering  in  the 
Northern  Hemisphere,  so  far  as  they  may  be  made  general: — 


Fig.  62. 


CYCLONIC    STORMS. 


151 


In  the  Right  Semicircle:  Haul  by  the  wind  on  the  starboard  tack  and  carry  sail  as  long  as  possible; 
if  obliged  to  heave-to,  do  so  on  starboard  tack. 

In  the  Left  Semicircle:  Bring  the  wind  on  the  starboard  quarter,  note  course  and  keep  it;  if  obliged 
to  heave-to,  do  so  on  port  tack. 

In  Front  of  Center:  Bring  wind  two  points  on  starboard  quarter,  note  course  and  keep  it;  if  obliged 
to  heave-to,  do  so  on  port  tack. 

In  Rear  of  Center:  Run  out  with  wind  on  starboard  quarter;  if  obliged  to  heave-to,  do  so  on  star- 
board tack. 

The  application  of  these  rules  for  the  various  directions  of  the  wind  is  shown  in  the  following 
table: — 

Storm  Table,  Northern  Hemisphere. 


If  wind 

1 

Direcyon 

Direction 

shifts  to- 

If wind  shifts  towards  the 

If  wind  steady  with  falling 

If  wind  steady  with  rising 

of  wind. 

of  center. 

wards  the 

left. 

barometer. 

barometer. 

right. 

North. 

ESE. 

a 

Run  SSW. 

K  ■ 

Run  SSW. 

K 

Run  SSW. 

a 

NNE. 
NE. 
ENE. 

SE. 

SSE. 

South. 

aul  b> 
and  cs 
ble;  il 
on  sta 

Run  SW. 
Run  WSW. 
Run  West. 

old  CO 
if  obli 
port  ti 

Run  SW. 
Run  AVSW. 
Run  West. 

old  course 
obliged  to 
port  tack. 

Run  SW. 
RunAVSW. 
Run  West. 

old  coi 
if  obli 
starbo 

East. 
ESE. 

SSW. 
SW. 

'  wind 

irry  sa 

oblige 

rboard 

RunWNW. 
Run  NW. 

arse 
ged 
ick. 

RunWNW. 
Run  NW. 

RunWNW. 
Run  NW. 

P5  ||I^    ^ 

"1  ^  7i 

SE. 

WSW. 

Run  NNW. 

f-i-  a 

Run  NNW. 

fo 
_^ao 

Run  NNW. 

1^: 

SSE. 

West. 

on  SI 
il  as  1 
dtoh 

tack. 

Run  North. 

Run  North. 

ffi  O 

Run  North. 

r  ET  ^ 

South. 

WNW. 

Run  NNE. 

2  o 

Run  NNE. 

^1 

Run  NNE. 

^o- 

ssw. 

NW. 

Run  NE. 

<  D 

Run  NE. 

Run  NE. 

<  D 

SW. 

NNW. 

1%^ 

Run  ENE. 

Run  ENE. 

Run  ENE. 

WSW. 

North. 

t^  g 

Run  East. 

p  m 

Run  East. 

t3 
ClO 

Run  East. 

P  § 

West. 

NNE. 

?^S  S 

Run  ESE. 

S'o 

Run  ESE. 

ogg 

Run  ESE. 

Cu^c 

WNW. 

NE. 

d  ta 

pos 

),  do 

Run  SE. 

Run  SE. 

g  E 

Run  SE. 

CD     00 

NW. 

ENE. 

Run  SSE. 

°  5-' 

Run  SSE. 

°  a 

Run  SSE. 

o  :f 

NNW. 

East. 

00  ^^  rt 

Run  South. 

2Jf 

Run  South. 

o 

Run  South. 

Dif 

a  Courses  given  are  for  wind  two  points  on  starboard  quarter,  but  it  is  preferable  to  take  wind  broad  on  quarter  if  possible. 

Similarly,  the  following  rules  and  table  apply  for  the  Southern  Hemisphere: — 

In  the  Right  Semicircle:  Bring  the  wind  on  the  port  quarter,  note  course  and  keep  it;  if  obliged  to 
heave-to,  do  so  on  starboard  tack. 

In  the  Left  Semicircle:  Haul  by  the  wind  on  the  port  tack  and  carry  sail  as  long  as  possible;  if 
obliged  to  heave-to,  do  so  on  port  tack. 

In  Front  of  Center:  Bring  wind  two  points  on  port  quarter,  note  course  and  keep  it;  if  obliged  to 
heave-to,  do  so  on  starboard  tack. 

In  Rear  of  Center:  Run  out  with  wind  on  port  quarter;  if  obliged  to  heave-to,  do  so  on  port  tack. 

Storm  Table,  Southern  Hemisphere. 


If  wind 

1 

Direction 

Direction 

If  wind  shifts  towards  the 

shifts  to- 

If wind  steady  with  falling 

If  wind  steady  with  rising 

of  wind. 

of  center. 

right. 

wards  the 
left. 

barometer. 

barometer. 

North. 

WSW. 

Run  SSE. 

a 

a 

Run  SSE. 

W 

Run  SSE. 

a 

NNE. 
NE. 

West. 
WNW. 

Run  South. 
Run  SSW. 

old  CO 
if  obli 
starbo 

aul 
carr 
obli 
port 

Run  South. 
Run  SSW. 

old 

obli 

star 

Run  South. 

Run  SSW. 

old  cour 
if  oblige 
port  tacl 

ENE. 

NW. 

Run  SW. 

te  2  -».  "^ 

Run  SW. 

o  rti  o 

Run  SW. 

East. 

NNW. 

Run  WSW. 

S5  aq  — 

5  2?^ 

O   03   D- 

Run  WSW. 

iirse 
d  to 
ard 

Run  WSAV. 

ESE. 

North. 

Run  West. 

CLP.^ 

Run  West. 

Run  West. 

Kl    p^  CO 

SE. 
SSE. 

NNE. 
NE. 

Run  WNW. 
Run  NW. 

fS  o  o 

Run  WNW. 
Run  NW. 

1^^ 

Run  WNW. 
RunNW. 

o   a 
p-i 

South. 

ENE. 

Run  NNW. 

S  o 

<S.  § 

Run  NNW. 

%  § 

Run  NNW\ 

S  o' 

SSW. 

East. 

Run  North. 

?^ 

por 
t  as 
e-tb. 

Run  North. 

OGR 

Run  North. 

II 

SW. 

ESE. 

Run  NNE. 

k 

Run  NNE. 

o  S 

Run  NNE. 

#1 

WSW. 

SE. 

Run  NE. 

°  g 

Run  NE. 

a^ 

Run  NE. 

West. 

SSE. 

Run  ENE. 

o  g 

o  ^  f 

Run  ENE. 

o  gg 

Run  ENE. 

%^ 

WNW. 

South. 

Run  East. 

!»    §0 

00   O"?^ 

Run  East. 

OD    O' 

Run  East. 

m  gg 

NW. 

SSW. 

Run  ESE. 

C 

Run  ESE. 

Run  ESE. 

Z  e! 

NNW. 

SV7. 

Run  SE. 

gir 

O  „  D 

Run  SE. 

o 

Run  SE. 

pif 

a  Courses  given  are  for  wind  two  points  on  port  quarter,  but  it  is  preferable  to  take  wind  broad  on  quarter,  if  possible. 

/ 


152 


CYCLONIC    STORMS. 


493.  Extra-Tropical  Cyclonic  Storms. — On  turning  to  the  cyclones  oi  temperate  latitudes,  we 
find  many  features  in  which  they  resemble  those  of  the  torrid  zone,  but  certain  other  features  in  which 
they  differ.  Their  fundamental  resemblance  to  tropical  cyclones  is  seen  in  their  incurving  winds,  form- 
ing an  inflowing  left-handed  spiral  about  the  center  of  low  pressure  in  the  northern  hemisphere,  an 
inflowing  right-handed  spiral  in  the  southern.  The  intensity  of  these  winds  varies  with  the  depth  of 
the  barometric  depression.  The  depression  itself,  however,  in  place  of  covering  a  few  miles,  as  is  the 
case  in  the  tropics,  will  frequently  have  a  diameter  of  several  hundred  or  even  a  thousand  miles,  and  for 
some  distance  around  the  center  the  gradients  will  have  a  tolerably  strong  value.  For  this  reason  there 
is  less  concentration  of  violence  close  to  the  center,  and  the  calm  and  clear  central  space,  or  "eye,"  is 
seldom  sharply  develop^l,  although  it  is  not  uncommon  to  discover  a  gradual  weakening  or  failing  of 
the  winds,  and  sometimes  even  an  imperfect  breaking  away  of  the  clouds  as  the  central  area  passes  over 
the  observer.  The  form  of  tropical  cyclones  as  defined  by  their  isobaric  lines  is  nearly  circular. 
Extra-tropical  cyclones  are  as  a  rule  less  symmetrical,  and  their  isobars  are  often  elongated  into  an  oval 
form,  the  longer  axis  of  the  oval  trending  (in  the  northern  hemisphere)  between  north  and  east — 
about,  therefore,  in  the  direction  of  progression.  The  steepest  gradients,  and  consequently  the  s'trongest 
winds,  are  apt  to  be  found  on  the  equatorial  and  westerly  sides  of  the  depression. 

Extra-tropical  cyclones  generally  follow^  an  easterly  course,  inclining  somewhat  towards  the  pole; 
but  they  occasionally  turn  to  one  side  or  the  other,  become  stationary,  or  even  move  backward.  The 
velocity  of  progression  varies  from  15  to  40  miles  an  hour.  If  they  exist  as  independent  barometric 
depressions,  with  strong  upward  gradients  on  all  sides  of  the  center,  the  cyclonic  circulation  will  be 
complete,  the  wind  shifting  with  the  sun  for  an  observer  situated  in  the  equatorial  semicircle  of  the 
storm,  against  the  sun  for  an  observer  situated  in  the  polar  semicircle. 

494.  Storms  Along  the  Transatlantic  Steamship  Koutes. — The  storms  which  are  so  frequently 
met  during  the  winter  season  along  the  steamshii:)  routes  between  America  and  Europe  are  not,  as  a 

rule,  due  to  central  barometric  depressions,  but 
to  depressions  having  a  trough  or  V  shape,  which 
extend  southerly  from  the  extensive  permanent 
area  of  low  pressure  having  its  center  in  the 
vicinity  of  Iceland.  They  are  not  attended  by 
complete  cyclonic  circulations,  inasmucn  Jis  the 
polar  gradients  which  would  otherwise  give  rise 
to  easterly  winds  on  this  polar  side  are  lacking. 
Their  approach  is  heralded  by  a  gradual  hauling 
of  the  wind  to  southward,  which  is  later  fol- 
lowed (at  the  time  of  passage  of  the  central  line 
of  the  trough )  by  a  change  to  NW. ,  accompanied 
by  heavy  rain  squalls  and  a  rapid  increase  in 
force.  The  general  distribution  of  pressure  and 
the  surrounding  winds  are  showii  m  figure  63. 
The  changes  in  wind  and  pressure  ensue  much  more  rapidly  in  the  case  of  a  westward-bound  vessel  than 
in  that  of  one  eastward  bound,  the  rate  at  which  the  observer  and  the  depression  approach  each  other 
being  in  the  former  case  the  sum  of  his  own  westward  velocity  and  the  eastward  velocity  of  the  trough, 
in  the  latter  case,  the  difference  of  these  velocities. 


TIDES.  153 


CPIAPTER  XX. 
TIDES. 


495.  Definitions. — Tidal  phenomena  present  themselves  to  the  observer  nnder  two  aspects — as 
alternate  elevations  and  depressions  of  the  sea,  and  as  recurrent  inflows  and  outflows  of  streams.  The 
word  tidr,  in  common  and  general  usage,  is  made  to  refer  without  distinction  to  both  the  vertical  and 
horizontal  motions  of  the  sea,  and  confusion  has  sometimes  arisen  from  this  double  application  of  the 
term;  in  its  strict  sense,  this  word  may  be  used  only  with  reference  to  the  changes  of  elevation,  while 
the  recurrent  streams  are  jjroperly  distinguished  as  tidal  cumnds. 

The  tide  rises  until  it  reaches  a  maximum  height  called  high  water  or  high  tide,  and  then  falls  to  a 
minimum  level  called  low  imter  or  low  tide;  that  period  at  high  or  low  water  marking  the  transition 
between  the  tides,  during  which  no  vertical  change  can  be  detected,  is  called  Hland. 

Of  the  tidal  currents,  that  which  arises  from  a  movement  of  the  water  in  a  direction,  generally 
speaking,  from  the  sea  toward  the  land,  is  called  Jlood,  and  that  arising  from  an  opposite  movement, 
ebb;  the  intermediate  period  between  the  currents,  during  which  there  is  no  horizontal  motion,  is  dis- 
tinguished as  slack-.  Set  and  drift  are  terms  applicable  to  the  tidal  currents,  the  first  referring  to  the 
direction  and  the  second  to  the  velocity. 

Care  should  be  taken  to  avoid  confusing  the  terms  relating  to  tides  with  those  which  relate  to  tidal 
currents. 

496.  Causk. — The  cause  of  the  tides  is  the  unequal  attraction  of  the  sun  and  moon  upon  different 
parts  of  the  earth.  These  bodies  attract  the  parts  of  the  earth's  surface  which  are  nearer  to  them  with 
greater  force  than  they  do  its  center,  and  attract  its  center  more  than  they  do  its  opposite  surface;  to 
restore  equilibrium  the  waters  take  a  spheroidal  figure,  whose  longer  axis  lies  in  the  direction  of  the 
attracting  body.  The  mean  force  of  the  moon  in  raising  the  tides  is  two  and  a  half  times  as  great  as 
that  of  the  sun,  for  though  the  mass  of  the  sun  is  vastlj-  greater  than  the  mass  of  the  moon,  the  sun's 
distance  is  so  great  that  it  attracts  the  different  parts  of  tlie  earth  with  nearly  equal  force.  Theory  is 
not  sufficiently  advanced  to  render  possible  a  prediction  of  tides  or  tidal  changes  from  a  mere  knowledge 
of  the  positions  of  the  sun  and  moon,  but  by  theory,  supplemented  by  observation  of  actual  tidal  condi- 
tions during  a  certain  period  of  time,  very  accurate  predictions  may  be  arrived  at. 

497.  EsT.VBLisHMKNT. — High  and  low  water  occur,  on  the  average  of  the  twenty-eight  days  com- 
prising a  lunar  month,  at  about  the  same  intervals  after  the  transit  of  the  moon  over  the  meridian. 
These  nearly  constant  intervals,  expressed  in  hours  and  minutes,  are  known  respectively  as  the  Jiigh 
water  litrritidal  interval  and  low  water  lunitidal  interval. 

The  interval  between  the  moon's  meridian  passage  at  any  place  and  the  time  of  the  next  succeeding 
high  water,  as  observed  on  the  days  when  the  moon  is  at  full  or  change,  is  called  the  vvlgar  (or  common) 
establi.'ilnnent  of  that  place,  or,  sometimes,  simply  the  establislmient.  This  interval  is  frequently  spoken 
of  as  the  time  of  Jiigh  water  on  full  and  cliange  days  (abbreviated  "H.  W.  F.  &  C.");  for  since,  on  such  days, 
the  moon's  two  transits  (upper  and  lower)  over  the  meridian  occur  about  noon  and  midnight,  the  vul- 
gar estaV^lishment  then  corresponds  closely  with  the  local  times  of  high  water.  When  more  extended 
observations  have  been  made,  the  average  of  all  the  high  water  lunitidal  intervals  for  at  least  a  lunar 
month  is  taken  to  obtain  what  is  termed,  in  distinction  to  the  vulgar  establishment,  the  corrected  estab- 
lishmeiit  of  the  port,  or  mean  high  water  lunitidal  interval.  In  defining  the  tidal  characteristics  of  a  place 
some  authorities  give  the  corrected  establishment,  and  others  the  vulgar  establishment,  or  "high  water, 
full  and  change;"  calculations  based  upon  the  former  will  more  accurately  represent  average  conditions, 
though  the  two  intervals  seldom  differ  ])v  a  large  amount. 

Having  determined  the  time  of  high  water  by  applying  the  establishment  to  the  time  of  moon's  transit, 
the  navigator  may  ol.)tain  the  time  of  low  water  with  a  fair  degree  of  apjiroximation  by  adding  or 
subtractings''  13'"  (one-fourth  of  a  mean  lunar  day);  but  a  closer  result  will  be  given  by  applying  to 
the  time  of  transit  the  mean  low  leater  lunitidal  interval,  which  occupies  the  same  relation  to  the  time  of 
low  water  as  the  mean  high  water  lunitidal  interval,  or  corrected  establishment,  does  to  the  time  of 
high  water. 

498.  Range. — The  range  of  the  tide  is  the  difference  in  height  between  low  water  and  high  water. 
This  term  is  often  applied  to  the  difference  existing  under  average  conditions,  and  may  in  such  a  case 
be  designated  as  the  mean  range  or  mean  rise  and  fall  to  distinguish  it  from  the  spring  range  or  neap  range, 
which  are  the  ranges  at  spring  and  neap  tides,  respectively. 

499.  Spring  and  Neap  Tides. — At  the  times  of  new  and  full  moon  the  relative  positions  of  sun 
and  moon  are  such  that  the  high  water  produced  by  one  of  those  bodies  occurs  at  the  same  time  as  that 
produced  by  the  other,  and  so  also  with  the  low  waters;  the  tides  then  occurring,  called  spring  tides, 
have  a  greater  range  than  any  others  of  the  lunar  month,  and  at  such  times  the  highest  high  tides  as 
well  as  the  lowest  low  tides  are  experienced,  the  tidal  range  being  then  at  its  maximum.  At  the  first 
and  third  cjuarters  of  the  moon  the  positions  are  such  that  the  high  tide  due  to  one  body  occurs  at  the 
time  of  the  low  tide  due  to  the  other,  so  that  the  two  actions  are  opposed;  this  causes  the  neap  tides, 
which  are  those  of  minimum  range,  the  high  waters  being  lower  and  the  low  waters  higher  than  at 
other  periods  of  the  month. 


154 


TIDES. 


Since  the  horizontal  motion  of  the  water  depends  directly  upon  the  rise  and  fall  of  the  tides,  it  follows 
that  the  currents  will  be  greatest  at  springs  and  least  at  neaps. 

The  effect  of  the  moon's  being  at  full  or  change  is  not  felt  at  once  in  all  parts  of  the  world,  and  the 
greatest  range  of  tides  does  not  generallj'  occur  until  one  or  two  days  thereafter;  thus,  on  the  Atlantic 
coast  of  North  America,  the  highest  tides  are  experienced  one  day,  and  on  the  AtJantic  coast  of  Europe, 
two  days  afterwar4,  though  on  the  Pacific  coast  of  North  America  they  occur  nearly  at  full  and  change. 

500.  The  nearer  the  moon  is  to  the  earth  the  stronger  is  its  attraction,  and  as  it  is  nearest  in  perigee, 
the  tides  will  be  larger  then  on  that  account,  and  consequently  less  in  apogee.  For  a  like  reason,  the 
tides  will  be  increased  by  the  sun's  action  when  the  earth  is  near  its  perihelion,  about  the  1st  of  January, 
and  decreased  when  near  its  aphelion,  about  the  1st  of  July. 

501 .  The  height  ^f  the  tides  at  any  place  .may  undergo  modification  on  account  of  strong  prevailing 
winds  or  abnormal  barometric  conditions,  a  wind  blowing  off  the  shore  or  a  high  barometer  tending  to 
reduce  the  tides,  and  the  reverse.  The  effect  of  atmospheric  jiressure  is  to  create  a  difference  of  about 
2  inches  in  the  height  of  tide  for  every  tenth  of  an  inch  of  difference  in  the  barometer. 

502.  Priming  and  Lagging. — The  tidal  day  is  the  varial)le  interval,  averaging  24''  50"',  between  two 
alternate  high  or  low  waters.  The  amount  by  which  corresponding  tides  grow  later  day  by  day — that 
is,  the  amount  by  which  the  tidal  day  exceeds  24'' — is  called  the  daily  retardation.  When  the  sun's  tidal 
effect  is  such  as  to  shorten  the  lunitidal  intervals,  thus  reducing  the  length  of  the  tidal  day  and  causing 
the  tides  to  occur  earlier  than  usual,  there  is  said  to  be  a  jyriming  of  the  tide;  when,  from  similar  causes, 
the  interval  is  lengthened,  there  is  said  to  be  a  lagging. 

503.  Types  of  Tidks. — The  observed  tide  is  not  a  simple  wave;  it  is  a  compound  of  several  elemen- 
tarj^  undulations,  rising  and  falling  from  the  same  conmion  plane,  of  which  two  can  be  distinguished  and 
separated  by  a  simple  grouping  of  the  data.  These  two  waves  are  known  as  the  semi-diurnal  and  the 
diurnal  tides,  because  the  first,  if  alone,  would  give  two  high  and  two  low  waters  in  a  day,  while  the 
second  would  give  but  one  high  and  one  low  water  in  an  equivalent  period  of  time.  In  nearly  all  ports 
these  two  tides  coexist,  but  the  proportion  between  them  varies  remarkably  for  different  seas.  The 
effect  of  the  coml)ination  of  these  two  types  of  tide  is  to  produce  a  diurnal  inequality,  both  in  the  height 
of  two  consecutive  high  or  low  waters,  and  in  the  intervals  of  time  between  their  occurrence.  The 
height  of  the  diurnal  wave  may  be  regarded  as  reaching  a  maximum  fortnightly,  soon  after  the  moon 
attains  its  extreme  declination  and  is  therefore  near  one  of  the  tropics.  The  tides  that  then  occur  are 
denominated  tropic  tides. 

In  undertaking  to  investigate  the  tides  of  a  port  it  is  important  to  ascertain  as  early  as  possible  the 
form  of  the  tide;  that  is,  whether  it  resembles  the  semi-diurnal,  the  diurnal,  or  the  mixed  type;  because 
not  only  may  this  information  be  of  scientific  value,  but  the  knowledge  thus  gained  at  the  outset  will 
enable  the  observer  to  fix  upon  the  best  method  of  keeping  his  record. 

304.  The  type  forms  referred  to  are 
illustrated  in  the  diagram  in  figure  64, 
where  the  waves  are  plotted  in  curves, 
using  the  times  as  abscissa?  and  the 
heights  as  ordinates.  In  this  diagram, 
the  curve  traced  in  the  full  line  is  a  tide- 
wave  of  the  semi-diurnal  type;  that 
traced  by  the  dotted  line  one  of  the  di- 
urnal; while  the  broken  line  is  one  of  the 
mixed  type,  in  this  case  the  compound 
of  the  two  others.  _ 

In  order  to  determine  the  type  to 
which  the  tide  of  any  port  belongs,  it  is 
usually  only  necessary  to  make  hourly 
observations  for  a  day  or  two  at  the  date 
of  the  moon's  maximum  declination,  and 
to  repeat  the  series  about  a  week  later, 
when  the  moon  crosses  the  equator. 
The  reported  irregularities  of  the  rise 
and  fall  at  any  place  should  not  deter 
persons  from  careful  investigation. 
When  analyzed,  even  the  most  compli- 
cated of  tides  are  found  to  follow  some 
general  law'. 

505.  Tidal,  Currents. — It  should 
be  clearly  borne  in  mind  by  the  naviga- 
tor that  the  jieriods  of  flood  and  ebb  currents  do  not  necessarily  coincide  with  those  of  rising  and  falling 
tides,  and  that,  paradoxical  though  it  may  seem  at  first  thought,  the  inward  set  of  the  surface  current 
does  not  always  cease  when  the  water  has  attained  its  maximum  height,  nor  the  outward  set  when  a 
minimum  height  has  been  reached.  Tinder  some  circumstances  it  may  occur  that  stand  and  slack  will 
be  simultaneous,  while  other  conditions  may  produce  a  maximum  current  at  stand,  with  a  maximum 
rate  of  rise  or  fall  at  slack  water. 

The  varying  effects  which  will  be  produced  according  to  local  conditions  may  be  considered  by  the 
comparison  of  two  tidal  basins,  to  one  of  which  the  tide-wave  has  access  from  the  sea  by  a  channel  of 
ample  capacity,  while  the  other  has  an  entrance  that  is  narrow  and  constricted.  In  the  first  case,  the 
process  of  filling  or  emptying  the  basin  keeps  pace  with  the  change  of  level  in  the  sea  and  is  practically 
completed  as  soon  as  the  height  without  becomes  stationary;  in  this  case  slack  and  stand  occur  nearly 
at  the  same  time,  as  do  flood  and  rise  and  ebb  and  fall.  In  the  second  case,  the  limited  capacity  of  the 
entrance  will  not  permit  the  basin  to  fill  or  empty  as  rapidly  as  the  tide  changes  its  level  without; 


( 

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Ff 

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3 
2 
1 
D 

1. 
2 
S 

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s 

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V 

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/ 

v 

/ 

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'  - 

-.^ 

^ 

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/' 

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''\ 

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^^^ 

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''' 

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r i7 

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— 

V 

L  U'1 

■  Semi-diurnal. 


diurnal. 

Fig.  64. 


•  mixed. 


TIDES.  155 

hence  there  is  still  a  difference  of  level  to  produce  a  current  when  the  vertical  motion  in  either  direction 
has  ceased  on  the  outside,  and  for  a  considerable  time  after  motion  in  the  reverse  direction  has  been  in 
progress;  under  extreme  conditions  it  may  even  occur  that  a  common  level  will  not  be  established 
until  mid-tide,  and  therefore  the  surface  current  at  some  places  will  ebb  until  three  hours  after  low 
water  and  flow  until  three  hours  after  high  water. 

Localities  that  partake  of  the  nature  of  the  first  case  are  those  upon  open  coasts  and  wide-mouthed 
bights.     Examples  of  the  latter  class  will  be  found  in  narrow  bays  and  long  channels. 

TIMES    OF  HIGH   AND   LOW   WATER. 

506.  Tide  Tablks. — The  most  expeditious,  as  well  as  most  exact,  method  of  ascertaining  the  times 
of  high  and  low  water  and  other  features  of  the  tides  will  be  by  reference  to  a  Tide  Table,  and  every 
navigator  is  recommended  to  provide  himself  with  such  a  publication.  The  United  States  Coast  and 
Geodetic  Survey  pubUshes  annually,  in  advance,  tables  giving,  for  every  day  in  the  year,  the  predicted 
time  and  height  of  the  tides  at  certain  principal  porta  of  the  world,  and  from  these,  by  a  simple  reduc- 
tion, the  times  and  heights  at  a  multitude  of  other  ports  may  readily  be  obtained;  data  for  ascertaining 
the  tidal  currents  in  certain  important  regions  are  also  provided.  General  tide  tables  are  also  published 
by  the  governments  of  other  maritime  nations,  and  special  tables  are  to  be  had  for  many  particular 
localities. 

507.  Where  no  tide  tables  are  available,  the  method  of  calculation  by  applying  the  lunitidal  inter- 
val to  the  time  of  the  moon's  meridian  passage  must  be  resorted  to. 

To  do  this,  find  first  the  time  of  the  moon's  meridian  passage,  upper  or  lower,  as  may  be  required. 
The  Greenwich  mean  time  of  upper  transit  at  Greenwich  is  given  in  the  Nautical  Almanac  (page  IV  of 
the  month) ;  the  corresponding  time  of  lower  transit  is  most  easily  found  by  taking  the  mean  of  the  two 
adjacent  upper  transits;  to  the  Greenwich  time  of  Greenwich  transit  apply  the  correction  for  longitude 
given  in  Table  11  (using  the  daily  variation  of  the  moon's  meridian  passage  shown  in  the  Almanac), 
adding  in  west  and  subtracting  in  east  longitude;  the  result  is  the  local  mean  time  of  local  transit. 
Add  to  this  the  high-water  or  low-water  lunitidal  interval  of  the  port  from  Appendix  IV,  according  as 
the  time  of  high  or  low  water  may  be  required.     The  result  is  the  time  sought. 

•  The  astronomical  date  must  be  strictly  adhered  to,  and  in  so  doing  it  may  be  found  necessary  to 
employ  the  time  of  a  lower  transit,  or  the  transit  of  a  preceding  day,  to  find  the  time  of  the  tide  in 
question. 

Appendix  IV  contains,  besides  the  geographical  positions  of  all  the  more  important  positions  in  the 
world,  a  series  of  tidal  data  relating  to  many  of  those  places.  In  such  data  are  comprised  the  mean 
lunitidal  intervals  for  high  and  low  water;  also,  for  places  where  the  semi-diurnal  type  of  tide  prevails, 
the  tidal  range  at  spring  and  at  neap  tides,  and  for  those  where  the  tide  is  of  the  diurnal  type,  the  tropic 
range.     An  alphabetical  index  is  appended  to  this  table. 

The  corrected  establishment  taken  from  the  charts  may  be  substituted  for  the  high-water  lunitidal 
interval  of  the  table;  or,  with  only  slight  variation  in  the  results,  the  vulgar  establishment  (H.  W.  F. 
&  C. )  may  be  employed. 

Example:  Find  the  times  of  the  high  and  low  waters  at  the  New  York  navy  yard,  occurring  next 
after  noon  on  April  22,  1879. 

G.  M.  T.  of  Gr.  transit,  22'»  0"  32™. 2 

Corr.  for  +  74°  Long.  (Tab.  11) ,  +  10 


L.  M.  T.  of  local  transit,  22    0    42 

Transit,  22'i  O"-  42'"  Transit,  22^  O**  42'" 

H.W.Lun.  Int.  (App.  IV),         8    44  L.  W.  Lun.  Int.  (App.  IV),  2    49 


L.M.T.,H.W.,  {iyi22!9.26p.m.  L.  M.  T.,  L.  W.,       •  {'^J,2f,3.Sl^.  rn. 

Example:  Find  the  time  of  high  water  at  the  Presidio,  San  Francisco,  Cal.,  on  the  afternoon  of 
May  7,  1879. 

G.  M.  T.  of  Gr.  transit,  6''  12"  Se^.G 

Corr.  for  + 122°  Long.  (Tab.  11),  -f-  22 


L.  M.  T.  of  local  transit,  6    12    59 

H.  W.  Lun.  Int.  (App.  IV),  +        11    43 


L.  M.  T.,  H.  W.,  I  L    ^T  ^-Fo  Ao 

'  '  \  May  7,  12.42  p.  m. 

Example:  Find  the  time  of  low  water  at  Singapore  on  the  night  of  May  28,  1879. 

G.  M.  T.  of  Gr.  transit,  28^  5'>  55™.  3 

Corr.  for  —104°  Long.  (Tab.  11),    —  13 


G.  M.  T.  of  local  transit,  28    5  42 

L.  W.  Lxm.  Int.  (App.  IV),  -f        4  02 


L.  M.  T.,  L.  W.,  j?J    ^oQ"^n^. 

'  '  \  May  28,  9.44  p.  m. 


156  TIDES. 

Example:  Find  the  time  of  morning  high  water  and  afternoon  low  water  at  GibraUar  on  June  26, 


1879. 


G.  INI.  T.  of  Gr.  upper  transit,        25''    4"  40'».l 
G.  M.  T.  of  Gr.  upper  transit,        26     5  27   .0 


2)51    10  07   .1 


G.  M.  T.  of  Gr.  lower  transit,         25   ]  7   04 
Corr.  for  -f  5°  Long.  (Tab.  11 ),  -[-  01 


L.  M.  T.  of  local  lower  trans.,        25   17  05 

Transit,  25'M7''05""  Transit,  25'^!  7**  05™ 

H.W.Lun.Int.  (App.  TV),  185  L.  W.  Lun.  Int.  (App.  IV),  7  55 

L   AI   T     H   W  P^   ^^   ^^  I    M   T     T    W  f  26     1    00 

L.  31.  i.,  n.  W.,  I  j^^^  26,  6.40  a.  m.  ^-  ^^-  ^^  ^-  ^^  -  {  June  26,  1  p.  m. 

TIDAL  OBSERVATIONS. 

508.  Since  navigators  will  frequently  have  opportunity  to  observe  tidal  conditions,  either  in  con- 
nection with  a  hydrographic  survey  or  otherwise,  at  places  where  existing  knowledge  of  the  tides  is 
incomplete,  an  understanding  of  the  methods  employed  in  tidal  observations  may  be  important. 

_509.  Tides. — For  the  proper  study  of  tides,  frequent  and  continuous  observations  are  necessary; 
it  will  not  suffice  to  observe  the  heights  of  the  high  and  low  waters  only,  even  if  they  present  them- 
selves as  distinct  phases,  but  the  whole  tidal  curve  for  each  day  should  be  develoi^ed  by  recording  the 
height  of  water  at  intervals,  which,  preferably,  should  not  exceed  thirty  minutes.  Observations,  to  be 
complete,  must  cover  a  whole  lunar  month ;  or,  if  it  be  impracticable  to  observe  the  tides  at  night,  the 
day  tides  of  two  lunar  months  may  be  substituted. 

510.  When  made  for  the  purposes  of  a  hydrographic  survey  the  tidal  observations  are  used  to 
correct  the  soundings,  and  care  must  be  taken  to  make  sure  that  the  gauge  is  placed  in  a  situation  visited 
by  the  same  form  of  tide  as  that  which  occurs  at  the  place  where  soundings  are  being  made.  It  will  not 
answer,  for  instance,  to  correct  the  soundings  upon  an  inlet-bar  liy  tidal  observations  made  within  the 
lagoon  with  which  this  inlet  communicates,  because  the  range  of  the  tide  within  the  lagoon  is  less  than 
upon  the  outside  coast.  A  partial  obstruction,  like  a  bridge,  or  a  natural  contraction  of  the  channel 
section,  while  it  may  not  reduce  the  total  range  of  the  tide  or  materially  affect  the  time  of  high  or  low 
tides,  will  alter  the  relative  heights  above  and  below  at  intermediate  stages,  so  that  the  hydrographer 
must  be  careful  to  see  that  no  such  obstruction  intervenes  between  his  field  of  work  and  the  gauge. 

511.  Tidal  Currents. — Observations  for  tidal  currents  should  be  made  with  the  same  regularity 
as  for  tides;  the  intervals  need  not  ordinarily  be  more  frequent  than  once  in  every  half  hour.  They 
should  always  be  made  at  the  same  point  or  points,  which  should  be  far  enough  from  shore  to  be  repre- 
sentative of  the  conditions  prevailing  in  the  navigable  waters.  The  ordinary  log  may  be  employed  for 
measuring  the  current,  but  it  is  better  to  replace  the  chip  by  a  pole  weighted  to  float  upright  at  a  depth 
of  about  fifteen  feet;  the  line  should  be  a  very  light  one,  and  buoyed  at  intervals  by  cork  floats  to  keep  it 
from  sinking;  the  set  of  the  current  should  be  noted  by  a  compass  bearing  of  the  direction  of  the  pole 
at  the  end  of  the  observation. 

512.  Record. — The  record  of  observations  should  be  kept  clearly  and  in  complete  form.  It  should 
include  a  description  of  the  locality  of  observation,  the  nature  of  gauge  and  of  instruments  used  for 
measuring  currents,  and  the  exact  position  of  both  tidal  and  current  stations,  together  with  situation 
and  height  of  bench  mark.  The  time  of  making  each  observation  should  be  shown,  and  data  given  for 
reduction  to  some  standard  time.  In  extended  tidal  observations  the  meteorological  conditions  should 
be  carefully  recorded,  the  instruments  used  for  the  observations  being  properly  compared  with  standards. 

51 3.  There  are  freciuently  remarkable  facts  in  reference  to  tides  and  currents  to  be  obtained  from 
persons  having  local  knowledge;  these  should  be  examined  and  recorded.  The  date  and  circumstances 
of  the  highest  and  lowest  tides  ever  known  form  important  items  of  information. 

514.  Planes  of  Keference. — The  plane  of  reference  is  the  plane  to  which  soundings  and  tidal  data 
are  referred.  One  of  the  principal  objects  of  observing  tides  when  making  a  survey  is  to  furnish  the 
means  for  reducing  the  soundings  to  this  plane.  Four  planes  of  reference  are  used;  namely,  mean  low 
water,  mean  low  water  springs,  mean  lower  low  waters,  and  the  harmonic  or  Indian  tide  plane. 

Mean  low  water  is  a  plane  whose  depression  below  mean  sea  level  corresponds  with  half  the  mean 
semi-diurnal  range,  while  the  depression  of  mean  low-water  springs  corresponds  with  half  tlie  mean  range 
of  spring  tide;  mean  lower  loiv  water  depends  upon  the  diurnal  inequality  in  high  and  low  water;  the 
harmonic  or  Indian  tide  plane  was  adopted  as  a  convenient  means  of  expressing  something  of  an  approxi- 
mation to  the  level  of  low  water  of  ordinary  spring  tides,  but  where  there  is  a  large  diurnal  inequality 
in  low  waters  it  falls  considerably  below  the  true  mean  of  such  tides. 

As  these  planes  may  differ  considerably,  it  is  important  to  ascertain  which  plane  of  reference  is 
adopted  before  making  use  of  any  chart  or  considering  data  concerning  the  tides. 

515.  The  tides  are  subject  to  so  many  variations  dependent  upon  the  movements  of  the  sun  and 
moon,  and  to  so  many  irregularities  due  to  the  action  of  winds  and  river  outflows,  that  a  very  long  series 
of  observations  would  be  necessary  to  fix  any  natural  plane.  In  consideration  of  this,  and  keeping  in 
view  the  possibilities  of  repetitions  of  the  surveys  or  subsequent  discoveries  within  the  field  of  work,  it 
is  necessary  to  define  the  position  of  the  plane  of  reference  which  has  resulted  from  any  series  of  obser- 
vations. This  is  done  by  leveling  from  the  tide  gauge  to  a  permanent  bench,  precisely  as  if  the  adopted 
plane  were  arbitrary. 

516.  Bench  ]\!ark. — The  plinth  of  a  light-house,  the  water  table  of  a  substantial  building,  the 
base  of  a  monument,  and  the  like,  are  proper  l^enches;  and  when  these  are  not  within  reach,  a  mark 


TIDES.  157 

may  be  made  on  a  rock  not  likely  to  be  moved  or  started  by  the  frost,  or,  if  no  rock  naturally  exists  in 
the  neighborhood,  a  block  of  stone  buried  l)elow  the  reach  of  frost  and  plowshare  should  be  the  resort. 
When  a  bench  is  made  on  shore,  it  should  be  marked  by  a  circle  of  2  or  3  inches  diameter  with  a  cross 
in  the  center,  iudicating  the  reference  point.  The  levelings  between  this  point  and  the  gauge  should  be 
be  run  over  twice  and  the  details  recorded.  A  bench  made  upon  a  wharf  or  other  perishable  structure 
is  of  little  value,  but  in  the  absence  of-  permanent  objects  it  is  better  than  nothing.  The  marks  should 
be  cut  in,  if  on  stone,  and  if  on  wood,  copper  nails  should  be  used.  The  bench  must  be  sketched  and 
carefully  described,  and  its  location  marked  on  the  hydrographic  sheet,  with  a  statement  of  the  relative 
position  of  the  plane  of  reference. 

517.  The  leveling  from  the  bench  mark  to  the  tide  gauge  may  be  done,  when  a  leveling  instrument 
is  not  available,  by  measuring  the  difference  of  height  of  a  number  of  intermediate  points'  by  means  of 
a  long  straight-edged  board,  held  horizontal  by  the  aid  of  a  carpenter's  spirit  level,  or  even  a  plummet 
square,  taking  care  to  repeat  each  step  with  the  level  inverted  end  for  end.  A  line  of  sight  to  the  sea 
horizon,  when  it  can  be  seen  from  the  bench  acrot^s  the  tide  staff,  will  afford  a  level  line  of  sufficient 
accuracy,  especially  when  observed  with  the  telescope.  It  may  often  be  convenient  to  combine  these 
methods. 

518.  Tide  Gauges. — The  Staff  Gauge  is  the  simplest  device  for  measuring  the  heights  of  tides,  and 
in  perfectly  sheltered  localities  it  is  the  best.  It  consists  of  a  vertical  staff  graduated  upward  in  feet  and 
tenths,  and  so  placed  that  its  zero  shall  lie  below  the  lowest  tides.  The  same  gauge  may  also  be  used 
where  the  surface  is  rough,  if  a  glass  tube  with  a  float  inside  is  secured  alongside  of  the  staff,  care  being 
taken  to  practically  close  the  lower  end  of  the  tube  so  as  to  exclude  undulations;  readings  may  also  be 
made  by  noting  the  point  midway  between  the  crest  and  trough  of  the  waves. 

A  staff  gauge  should  always  be  erected  for  careful  tidal  observations,  even  where  other  classes  of 
gauge  are  to  be  employed,  as  it  furnishes  a  standard  for  comparison  of  absolute  heights,  and  also  serves 
to  detect  any  defects  in  the  mechanical  details  upon  which  all  other  gauges  are  to  a  greater  or  less  extent 
dependent. 

519.  Where  there  is  considerable  swell,  and  where,  from  the  situation  of  the  gauge  or  the  great 
range  of  the  tide  (makiBg  it  inconvenient  for  the  observer  to  see  the  figures  in  certain  positions)  the 
staff  gauge  can  not  be  used,  recourse  must  be  had  to  the  Box  Gauge.  This  gauge  consists  of  a  vertical 
box,  closed  at  the  bottom,  with  a  few  small  holes  in  the  lower  part  which  admit  sufficient  water  to  keep 
the  level  within  equal  to  the  mean  level  without,  but  which  do  not  permit  the  admission  of  water  with 
sufficient  rapidity  to  be  affected  by  the  waves.  Within  the  box  is  a  copper  float;  in  some  cases  this 
float  carries  a  graduated  vertical  rod  whose  position  with  reference  to  a  fixed  point,of  the  box  affords  a 
measure  for  the  height  of  the  water;  in  other  gauges  of  this  class  the  float  is  attaclied  to  a  wire  or  cord 
which  passes  over  ])ulleys  and  terminates  in  a  counterpoise  whose  position  on  a  vertical  graduated  scale 
shows  the  height  of  tide. 

520.  An  Automatic  Gauge  requires  a  box  and  float  such  as  has  just  been  described.  The  motion  of 
the  float  in  rising  and  falling  with  the  tide  is  communicated  to  a  pencil  which  rests  upon  a  moving 
sheet  of  paper;  uniform  motion  is  imparted  to  the  paper  by  the  revolution  of  a  cylinder  driven  by  clock- 
work; the  motion  of  the  pencil  due  to  the  tide  is  in  a  direction  perpendicular  to  the  direction  of  motion 
of  the  paper,  and  a  curve  is  thus  traced,  of  which  one  coordinate  is  time,  and  the  other  height.  The 
paper,  which  is  usually  of  sufficient  length  to  contain  a  month's  record,  is  paid  out  from  one  cylinder, 
passes  over  a  second  whereon  it  receives  the  record,  and  is  rolled  upon  a  third  cylinder,  which  thus 
contains  the  completed  tidal  sheet. 

This  gauge,  besides  giving  a  perfectly  continuous  record,  has  the  further  merit  of  requiring  but 
little  of  the  observer's  time.  But  its  indications,  both  of  time  and  heights,  should  be  checked  by 
occasional  comparisons  with  the  standard  clock  and  tlie  staff  gauge,  the  readings  of  which  should  be 
noted  by  hand  at  api^ropriate  jioints  of  the  graphic  record. 


158  OCEAN    CURRENTS. 


CHAPTER  XXL 

OCEAN  OUKRENTS. 


521.  An  ocenn  current  is  a  progressive  horizontal  motion  of  the  water  occurring  throughout  a 
region  of  the  ocean,  as  a  result  of  which  all  bodies  floating  therein  are  carried  with  the  stream. 

The  set  of  a  current  is  the  direction  toward  which  it  flows,  and  its  drift,  the  velocity  of  the  flow. 

522.  Cause. — The  principal  cause  of  ocean  currents  is  the  wind.  Every  breeze  sets  in  motion,  by 
its  friction,  the  surface  particles  of  the  water  over  which  it  blows;  this  motion  of  the  upper  stratum  is 
imparted  to  the  stratum  next  beneath,  and  thus  the  general  movement  is  communicated,  each  layer  of 
particles  acting  upon  the  one  below  it,  until  a  current  is  established.  The  direction,  depth,  strength, 
and  permanence  of  such  a  current  will  depend  upon  the  direction,  steadiness,  and  force  of  the  wind; 
all,  however,  subject  to  modification  on  account  of  extraneous  causes,  such  as  the  intervention  of  land 
or  shoals  and  the  meeting  of  conflicting  currents. 

A  minor  cause  in  the  generation  of  ocean  currents  is  the  difference  in  density  of  the  sea  water  in 
different  regions,  as  a  result  of  which  a  set  is  produced  from  the  more  dense  toward  the  less  dense,  in 
the  effort  to  establish  equilibrium  of  pressure;  the  difference  of  density  may  be  due  to  temperature,  the 
warmer  water  near  the  equator  being  less  dense  than  the  colder  water  of  higher  latitudes;  or  it  may  be 
created  by  a  difference  in  the  amount  of  contained  saline  matter,  resulting  from  evaporation,  freezing, 
or  other  causes.  Another  minor  factor  that  may  have  influence  upon  ocean  currents  is  the  difference  of 
pressure  exerted  by  the  atmosphere  upon  the  water  in  different  regions.  But  neither  of  the  last- 
mentioned  causes  may  be  regarded  as  of  great  importance  when  compared  with  the  influence,  direct 
and  indirect,  of  the  wind. 

523.  Drift  and  Stream  Currents. — Ocean  currents  may  be  divided  into  two  classes:  Ihnfl  and 
Stream  Currents. 

A  Drift  Current  is  one  which  arises  from  the  effect  of  wind  upon  the  surface  water,  impelling  the 
particles  to  leeward.  Such  currents  reach  only  to  shallow  depths,  except  in  regions  where  caused  by 
winds  whose  prevalence  is  almost  unbroken,  and  where,  in  consequence,  motion  is  communicated  stratum 
by  stratum,  during  a  long  series  of  years,  until  the  influence  is  felt  at  great  depths. 

A  Stream  Current  is  one  which  arises  when  the  water  carried  forward  by  a  drift  current  encounters 
an  obstacle  which  prevents  a  further  flow  in  the  direction  which  it  has  been  following,  and  the  particles 
are  forced  to  acquire  a  new  motion  which  takes  such  direction  as  may  be  imposed  by  the  conditions 
existing  in  the  locality. 

Some  currents  are  compounded  of  both  drift  and  stream ;  for  a  stream  already  formed  may  pass 
through  the  region  of  a  prevalent  wind  in  such  direction  that  it  will  receive  an  accelerating  effect  due  to 
the  wmd. 

524.  Submarine  Currents. — In  any  scientific  investigation  of  the  circulation  of  ocean  waters  it  is 
necessary  to  take  account  of  the  submarine  currents  as  well  as  those  encountered  upon  the  surface;  but 
for  the  practical  purposes  of  the  navigator  the  surface  currents  alone  are  of  interest. 

525.  Methods  of  Determination. — The  methods  of  determining  the  existence  of  a  current,  with 
its  set  and  drift,  may  be  divided  into  three  classes;  namely,  (a)  by  observations  from  a  vessel  occupying 
a  stationary  position  not  affected  by  the  current;  (6)  by  comparison  of  the  position  of  avessel  under  way 
as  given  by  observation  with  that  given  by  dead  reckoning;  and  (c)  by  the  drift  of  objects  abandoned 
to  the  current  in  one  locality  and  reappearing  in  another. 

526.  Of  these  methods,  the  first  named,  by  observations  from  a  vessel  at  anchor,  is  by  far  the  most 
accurate  and  reliable,  but  being  possible  only  under  special  circumstances  is  not  often  available.  The 
most  valuable  information  about  ocean  currents  being  that  which  pertains  to  conditions  in  the  open  sea, 
the  great  depths  there  existing  usually  preclude  the  possibility  of  anchoring  a  vessel;  ships  especially 
fitted  for  the  purpose  have  at  times,  however,  carried  out  current  observations  with  excellent  results; 
the  most  notable  achievements  in  this  direction  are  those  of  the  survey  of  the  Gulf  Stream,  made  by 
United  States  naval  officers  acting  under  the  Coast  and  Geodetic  Survey,  during  which  the  vessel  was 
anchored  and  observations  were  made  in  positions  where  the  depth  reached  to  upward  of  2,000  fathoms. 

527.  The  method  of  determining  current  from  a  comparison  of  positions  obtained,  respectively, 
by  observation  and  by  dead  reckoning  is  the  one  upon  which  our  knowledge  must  largely  depend. 
This  method  is,  however,  always  subject  to  some  inaccuracy,  and  the  results  are  frequently  quite 
erroneous,  for  the  so-called  current  is  thus  made  to  embrace  not  only  the  real  set  and  drift,  but  also 
the  errors  of  observation  and  dead  reckoning.  In  the  case  of  a  modern  steamer  accurately  steered  and 
equipped  with  good  instruments  for  determining  the  speed  through  the  water  as  well  as  the  position  by 
astronomical  observations,  the  current  may  be  arrived  at  by  this  method  with  a  fairly  close  degree  of 
accuracy.  It  is  not  always  possible,  however,  to  keep  an  exact  reckoning,  and  this  is  especially  true 
in  sailing  vessels,  where  the  conditions  render  it  difficult  to  determine  correctly  the  position  by  account; 
this  source  of  error  may  be  combined  with  faulty  instrumental  determinations,  giving  apparent  currents 
differing  widely  from  those  that  really  exist. 

528.  Much  useful  knowledge  regarding  ocean  currents  has  been  derived  from  the  observed  drift 
of  objects  from  one  to  another  locality.  This  is  true  not  only  of  the  bottles  thrown  overboard  from  vessels 
with  the  particular  object  of  determining  the  currents,  but  also  of  derelicts,  drifting  buoys,  and  pieces 


OCEAN    CURRENTS.  159 

of  wreckage,  which  fulfill  a  similar  mission.  The  deductions  to  be  drawn  from  such  drift  are  of  a 
general  nature  only.  The  point  of  departure,  point  of  arrival,  and  elapsed  time  are  all  that  are  posi- 
tively known.  The  route  followed  and  the  set  and  drift  of  current  at  different  points  are  not  indicated, 
and  in  the  case  of  objects  floating  otherwise  than  in  a  completely  submerged  condition  account  must 
be  taken  of  the  fact  that  the  drift  is  influenced  l)y  the  wind.  But  even  this  general  information  is  of 
great  value  in  researches  as  to  ocean  currents,  and  navigators  who  desire  to  aid  in  the  work  of  investi- 
gation may  do  so  by  throwing  overboard,  from  time  to  time,  sealed  bottles  containing  a  statement  of 
date  and  position  at  which  they  are  launched. 

529.  Currents  of  the  Atlantic  Ocean. — A  consideration  of  the  currents  of  the  Atlantic  most 
conveniently  begins  with  a  description  of  the  Equatorial  Currents.  The  effect  of  the  northeast  and 
southeast  trade  winds  is  to  form  two  great  drift  currents,  setting  in  a  westerly  direction  across  the 
Atlantic  from  Africa  toward  the  American  continent,  whose  combined  width  covers  at  times  upward 
of  fifty  degrees  of  latitude.  These  are  distinguished  as  the  Northern  or  Southern  Equatorial  Currents, 
according  as  they  arise  from  the  trade  winds  of  the  northern  or  southern  hemisphere. 

Of  the  two,  the  Southern  Equatorial  Current  is  the  more  extensive.  It  has  its  origin  off  the  conti- 
nent of  Africa  south  of  the  Guinea  coast,  and  begins  its  flow  with  a  daily  velocity  that  averages  about 
15  miles;  it  maintains  a  general  set  of  west,  the  portion  near  the  equator  acquiring  later,  however,  a 
northerly  component,  while  the  drift  steadily  increases  until,  on  arriving  off  the  South  American  coast, 
a  rate  of  60  miles  is  not  uncommon.  AttCape  San  Roque  the  current  bifurcates,  the  main  or  equatorial 
branch  flowing  along  the  Guiana  coast,  while  the  other  branch  is  deflected  to  the  southward. 

The  Northern  Equatorial  Current  originates  to  the  northward  of  the  Cape  Verde  Islands  and  sets 
across  the  ocean  in  a  direction  that  averages  due  west;  though  parallel  to  the  corresponding  southern 
drift,  its  velocity  is  not  so  high. 

330.  Between  the  Northern  and  Southern  Equatorial  Currents  is  found  the  Equatorial  Counter 
Current,  which  sets  to  the  eastward,  being  apparently  a  flowing  back,  in  the  region  of  equatorial  calms, 
of  water  carried  westward  by  the  trade  drifts.  The  extent  and  strength  of  this  current  varies  with  the 
season,  a  maximum  being  attained  in  July  or  August,  when  its  effect  is  apparent  to  ths  westward  of 
the  flftieth  meridian  of  west  longitude,  while  at  its  minimum,  in  November  or  December,  its  influence  is 
but  slight  and  prevails  over  a  limited  area  only. 

531.  To  the  westward  of  the  region  of  the  Equatorial  Counter  Current  the  North  and  the  South 
Equatorial  Currents  unite.  A  large  part  of  the  combmed  stream  flows  into  the  Caribbean  Sea  through 
the  various  passages  between  the  Windward  Islands,  takes  up  a  course  first  to  the  westward  and  then 
to  the  northward  and  westward,  finally  arriving  off  the  extremity  of  the  peninsula  of  Yucatan;  from 
here  some  of  the  water  follows  the  shore  line  of  the  Gulf  of  Mexico,  while  another  portion  passes 
directly  toward  the  north  Cuban  coast;  by  the  reuniting  of  these  two  branches  in  the  Sti-aitsof  Florida 
there  is  formed  the  most  remarkable  of  all  ocean  currents — the  Gulf  Stream. 

From  that  portion  of  the  combined  equatorial  currents  which  fails  to  find  entrance  to  the  Caribbean 
Sea  a  current  of  moderate  strength  and  volume  takes  its  course  along  the  north  coasts  of  Porto  Rico, 
Haiti,  and  Cuba,  flows  between  the  last-named  island  and  the  Bahamas,  and  enters  the  Gulf  Stream  off 
the  Florida  coast,  thus  adding  its  waters  to  those  of  the  main  branch  of  the  equatorial  current  which 
have  arrived  at  the  same  point  by  way  of  the  Caribbean,  the  Yucatan  Passage,  and  the  Gulf. 

532.  The  Gulf  Stream,  which  has  its  origin,  as  has  been  described,  in  the  Straits  of  Florida,  and 
receives  an  accession  from  a  branch  of  the  Equatorial  Current  off  the  Bahamas,  flows  in  a  direction  that 
averages  true  north  as  far  as  the  parallel  of  31°,  then  curves  sharply  to  ENE.  until  reaching  the  latitude 
of  32°,  when  a  direction  a  little  to  the  north  of  NE.  is  assumed  and  maintained  as  far  as  Cape  Hatteras; 
at  this  point  its  axis  is  about  40  miles,  while  its  inner  edge  is  in  the  neighborhood  of  20  miles  off  the 
shore.  Thus  far  in  its  flow  the  average  position  of  the  maximum  current  is  from  11  to  20  miles  outside 
the  100-fathom  curve,  disregarding  the  irregularities  of  the  latter,  and  the  width  of  the  stream — about 
40  miles — is  nearly  uniform.  From  off  Hatteras  the  stream  broadens  rapidly  and  curves  more  to  the 
eastw^ard,  seeking  deeper  water;  its  northern  limit  may  be  stated  to  be  60  to  80  miles  off  Nantucket 
Shoals  and  120  to  150  miles  to  the  southward  of  Nova  Scotia,  in  which  latter  place  it  has  expanded  to 
a  width  of  about  250  miles.  Further  on,  its  identity  as  the  Gulf  Stream  is  lost,  but  its  general  direction 
is  preserved  in  a  current  to  be  described  later. 

The  water  of  the  Gulf  Stream  is  of  a  deep  indigo-blue  color,  and  its  junction  with  ordinary  sea 
water  may  be  plainly  recognized;  in  moderate  weather  the  edges  of  the  stream  are  marked  by  ripples; 
in  cool  regions  the  evaporation  from  its  surface,  due  to  difference  of  temperature  between  air  and  water, 
is  apparent  to  the  eye;  the  stream  carries  with  it  a  quantity  of  weed  known  as  "gulf  weed,"  which  is 
familiar  to  all  who  have  navigated  its  waters. 

In  its  progress  from  the  tropics  to  higher  latitudes  the  transit  is  so  rapid  that  time  is  not  given  for 
more  than  a  partial  cooling  of  the  water,  and  it  is  therefore  found  that  the  Gulf  Stream  is  very  much 
warmer  than  the  neighboring  waters  of  the  seas  through  which  it  flows.  This  warm  water  is,  however, 
divided  by  bands  of  markedly  cooler  water  which  extend  in  a  direction  parallel  to  the  axis  and  are 
usually  found  near  the  edges  of  the  stream  of  warm  water.  The  most  abrupt  change  from  warm  to  cold 
water  occurs  on  the  inshore  side,  where  the  name  of  the  Cold  Wall  has  been  given  to  that  band  which 
has  appeared  to  some  oceanographers  to  form  the  northern  and  western  boundary  of  the  stream. 

The  investigations  of  Pillsbury  tend  to  prove  that  the  thermometer  is  only  an  approximate  guide  to 
the  direction  and  velocity  of  the  current.  Though  it  indicates  the  limits  of  the  stream  in  a  general  way, 
it  must  not  be  assumed  that  the  greatest  velocity  of  flow  coincides  with  the  highest  temperature,  nor 
that  the  northeasterly  set  will  be  lost  when  the  thermometer  shows  a  region  of  cold  sea  water. 

The  same  authority  has  also  demonstrated  that  in  the  vicinity  of  the  land  there  is  a  marked  varia- 
tion in  the  velocity  of  current  at  different  hours  of  the  day,  which  may  amount  to  upward  of  2  knots, 
and  which  is  due  to  the  elevation  and  depression  of  the  sea  as  a  result  of  tidal  influences,  the  maximum 
current  being  encountered  at  a  period  which  averages  about  three  hours  after  the  moon's  transit.  Another 
effect  noted  is  that  at  those  times  when  the  moon  is  near  the  equator  the  current  presents  a  narrow 
front  with  very  hi^h  vel  >city  in  the  axis  of  maximum  strength,  while  at  periods  of  great  northerly  or 


160  OCEAN    CUREENTS. 

southerly  declination  the  front  broadens,  the  current  decreasing  at  the  axis  and  increasing  at  the  edges. 
These  tidal  effects  are  not,  however,  obi-erved  in  the  open  sea. 

The  velocity  of  the  Gulf  Stream  varits  with  the  seasons,  following  the  variation  in  the  intensity  of 
the  trade  winds,  to  which  it  largely  owes  its  origin.  The  drift  of  the  current  under  average  conditions 
may  be  stated  as  follows: 

'  Between  Key  West  and  Habana:  Mean  surface  velocity  in  axis  of  maximum  current,  2\  knots; 
allowance  to  be  made  by  a  vessel  crossing  the  entire  width  of  the  stream,  1.1  knots  per  hour. 

Off  Fowey  Rocks:  Mean  surface  velocity  in  axis,  3.5  knots;  allowance  in  crossing,  2}  knots  per  hour. 

Off  Cape  Hatteras:  Mean  surface  velocity  in  axis,  upward  of  2  knots;  allowance  in  crossing  the 
stream,  IJ  knot,s  jser  hour  between  the  lOC-fathora  curve  and  a  point  40  miles  outside  that  curve. 

533.  After  passin|:  beyond  the  longitude  of  the  easternmost  portions  of  North  America,  it  is  gen- 
erally regarded  that  the  Gulf  Stream,  as  such,  ceases  to  exist;  but  by  reason  of  the  prevalence  of  westerly 
winds  the  direction  of  the  set  toward  Europe  is  continued  until  the  continental  shores  are  approached, 
when  the  current  divides,  one  branch  going  to  the  northeastward  and  entering  the  Arctic  regions  and 
the  other  running  off  toward  the  south  and  east  in  the  direction  of  the  African  coa.st.  These  currents 
have  received,  respectively,  the  designations  of  the  Easterly,  Nortiwasf,  and  Southeast  Drift  Currents. 

534.  The  effect  of  the  currents  thus  far  described  is  to  create  a  general  circulation  of  the  surface 
waters  of  the  North  Atlantic,  in  a  direction  coinciding  with  that  of  the  hands  of  a  Avatch,  about  the 
periphery  of  a  huge  ellipse,  whose  limits  of  latitude  maybe  considered  as  10°  N.  and  45°  N.,  and  which 
IS  bounded  in  longitude  by  the  P^astern  and  Western  continents.  The  central  space  thus  inclosed,  in 
which  no  av ell-marked  currents  are  observed,  and  in  the  waters  of  which  great  quantities  of  the  Sargasso 
or  gulf  weed  are  encountered,  is  known  as  the  Sargasso  Sea. 

535.  The  Southeast  Drift  Current  carries  its  waters  to  the  northwest  coast  of  Africa,  whence  they 
follow  the  general  trend  of  the  land  from  Cape  Spartel  to  Cape  ^"erde.  From  this  point  a  large  part  of 
the  current  is  deflected  to  the  eastward  close  along  the  upper  Guinea  coast.  The  steam  thus  formed, 
greatly  augmented  at  certain  seasons  by  the  prevailing  monsoon  and  by  the  waters  carried  eastward 
with  the  Equatorial  Counter  Current,  is  called  the  Guinea  Current.  A  remarkable  characteristic  of  this 
current  is  the  fact  that  its  southern  limit  is  only  slightly  removed  from  the  northern  edge  of  the  west- 
moving  Equatorial  Current,  the  effect  being  that  the  two  currents  flow  side  by  side  in  close  proximity, 
but  in  diametrically  opposite  directions. 

536.  The  Arctic  or  Labrador  Current  sets  out  of  Davis  Strait,  flows  southward  down  the  coasts  of 
Labrador  and  Newfoundland,  and  thence  south  westward  past  Nova  Scotia  and  the  coast  of  the  United 
States,  being  found  inshore  of  the  Gulf  Stream.  It  brings  with  it  the  ice  so  frequently  met  at  certain 
seasons  off  Newfoundland. 

537.  RennelVs  Current  is  a  temporary  but  extensive  stream,  which  sets  at  times  from  the  Bay  of 
Biscay  toward  the  west  and  northwest,  across  the  entrance  to  the  English  Channel  and  to  the  westward 
of  Cape  Clear. 

538.  Of  the  two  branches  of  the  Southern  Equatorial  Current  which  are  formed  by  its  bifurcation 
off  Cape  San  Roque,  the  northern  one,  setting  along  the  coasts  of  northeastern  Brazil  and  of  Guiana  and 
contributing  to  the  formation  of  the  Gulf  Stream,  has  already  been  described;  the  other,  known  as  the 
Brazil  Current,  flows  to  south  and  west,  along  the  southeastern  coast  of  Brazil,  as  far  as  the  neighborhood 
of  the  island  of  Trinidad;  here  it  divides,  one  part  continuing  down  the  coast  and  having  some  slight 
influence  as  far  as  the  latitude  of  45°  S.,  and  the  other  curving  around  toward  east. 

539.  The  last-mentioned  branch  of  the  Brazil  Current  is  called  the  Soutlieryi  Connecting  Cm-rent  and 
flows  toward  the  African  coast  in  about  the  latitude  of  Tristan  d'Acunha.  It  then  joins  its  waters  with 
these  of  the  general  northerly  current  that  sets  out  of  the  Antarctic  region,  forming  a  current  which 
flows  to  the  northward  along  the  southwest  African  coast  and  eventually  connects  with  the  Southern 
Equatorial  Current,  thus  completing  the  surface  circulation  of  the  South  Atlantic. 

540.  There  are  two  other  currents  whose  effects  are  felt  in  the  Atlantic,  one  originating  in  the 
Indian  Ocean  and  flowing  around  the  Cape  of  Good  Hope,  the  other  originating  in  the  Pacific  and  flow- 
ing around  Cape  Horn.  They  will  be  described  under  the  currents  of  the  oceans  in  which  they  first 
appear. 

541.  Currents  of  the  Pacific  Ocean. — As  in  the  Atlantic,  the  waters  of  the  Pacific  Ocean,  in 
the  region  between  the  tropics,  have  a  general  drift  toward  the  westward,  due  to  the  effect  of  the  trade 
Avinds,  the  currents  produced  in  the  two  hemispheres  being  denominated,  respectively,  the  Nortltern  and 
the  Southern  Equatorial  Currents.  These  are  separated,  as  also  in  the  case  of  the  Atlantic,  by  an  ea.st- 
setting  stream,  about  300  miles  wide,  whose  mean  position  is  a  few  degrees  north  of  the  equator,  and 
which  receives  the  name  of  the  Equatorial  Counter  Current. 

542.  The  major  portion  of  the  Northern  Equatorial  Current,  after  having  passed  the  Mariana 
Islands,  flows  toward  the  eastern  coast  of  Formosa  in  a  WNW.  direction,  whence  it  is  deflected  north- 
ward, forming  a  current  which  is  sometimes  called  the  Jajmn  Stream,  but  which  more  frequently 
receives  its  Japanese  name  of  A'ttro  >S'm'o,  or  "black  stream."  This  current,  the  waters  of  which  are 
dark  in  color  and  contain  a  variety  of  seaweed  similar  to  "gulf  Aveed,"  carries  the  Avarm  tropical  water 
at  a  rapid  rate  to  the  northward  and  eastward  along  the  coasts  of  Asia  and  its  offlying  islands,  presenting 
many  analogies  to  the  Gulf  Stream  of  the  Atlantic. 

The  limits  and  volume  of  the  Kuro  Siwo  A'ary  according  to  the  monsoon,  being  augmented  during 
the  season  of  southwesterly  Avinds  and  diminished  during  the  prevalence  of  those  from  northeast.  The 
current  sets  to  the  north  along  the  east  coast  of  Formosa,  and  in  about  latitude  26°  N.  changes  its  course 
to  northeast,  arriving  at  the  extreme  south Avestern  point  of  Japan  by  a  route  to  westward  of  the  Meiaco- 
sima  and  Loo-choo  islands.  A  branch  makes  off  from  the  main  stream  to  follow  northAvard  along  the 
west  coast  of  Japan,  entering  the  Sea  of  Japan  by  the  Korea  Channel;  but  the  principal  current  bends 
toward  the  east,  floAvs  through  Van  Diemen  Strait  and  the  passages  betAveen  the  Linschoten  Isles,  and 
runs  parallel  to  the  general  trend  of  the  south  shores  of  the  Japanese  islands  of  Kiushu,  Sikok,  and 
Nipon,  attaining  its  greatest  velocity  l>etween  Bungo  and  Kii  channels,  where  its  average  drift  is 
between  2  and  3  knots  per  hour.     Continuing  beyond  the  southeastern  extremity  of  Nipon,  the  direction 


^  .  I 

OCEAN    CURRENTS.  161 

of  the  stream  ))ecomes  somewhat  more  northerlj-,  and  its  width  increases,  with  consequent  loss  of 
velocity.  In  the  Knro  Siwo,  as  in  the  Gulf  Stream,  the  temperature  of  the  sea  water  is  an  approximate, 
though  not  an  exact,  guide  as  to  the  existence  of  the  current. 

543.  Near  146°  or  147°  E.  and  north  of  the  fortieth  parallel  the  Kuro  Siwo  divides  into  two  parts. 
One  of  these,  called  the  Kamchatka  Current,  flows  to  the  northeast  in  the  direction  of  the  Aleutian 
Islands,  and  its  influence  is  felt  to  a  high  latitude.  The  second  branch  continues  as  the  main  stream, 
and  maintains  a  general  easterly  direction  to  the  180th  meridian,  where  it  is  merged  into  the  north  and 
northeast  drift  currents  which  are  generally  encountered  in  this  region. 

544.  A  cold  counter  current  to  the  Kamchatka  Current  sets  out  of  Bering  Sea  and  flows  to  the 
south  and  west  close  to  the  shores  of  the  Kuril  Islands,  Yezo  and  Nipon,  sometimes,  like  the  Labrador 
Current  in  the  Atlantic,  bringing  with  it  quantities  of  Arctic  ice.  This  is  often  called  by  its  Japanese 
name  of  0//a  Sivo. 

545.  On  the  Pacific  coast  of  North  America,  from  about  50°  N.  to  the  mouth  of  the  Gulf  of 
California,  23°  N.,  a  cold  current,  200  or  300  miles  wide,  flows  with  a  mean  speed  of  three-quarters  of  a 
knot,  being  generally  stronger  near  the  land  than  at  sea.  It  follows  the  trend  of  the  land  (nearly  SSE. ) 
as  far  as  Point  Concepcion  (south  of  Monterey),  Avhen  it  begins  to  bend  toward  SSW.,  and  then  to  WSW,, 
off  Capes  San  Bias  and  San  Lucas,  ultimately  joining  the  great  northern  equatorial  drift. 

On  the  coast  of  Mexico,  from  Cape  Corrientes  (20°  N.)  to  Cape  Blanco  (Gulf  of  Nicoya),  there  are 
alternate  currents  extending  over  a  space  of  more  than  300  miles  in  width,  whicli  appear  to  be  produced 
by  the  prevailing  winds.  During  the  dry  season — January,  February,  and  ^larch — the  currents  generally 
set  toward  southeast;  during  the  rainy  season — from  ]\Iay  to  October — especially  in  July,  August,  and 
September,  the  currents  set  to  northwest,  particularly  from  Cosas  Island  and  the  Gulf  of  Nicova  to  the 
parallel  of  15°. 

546.  The  Southern  Equatorial  Current  prevails  between  limits  of  latitude  that  may  be  approxi- 
mately given  as  4°  N.  and  10°  S.,  in  a  broad  region  extending  from  the  American  continent  almost  to 
the  one  hundred  and  eightieth  meridian,  setting  always  to  the  west  and  with  slowly  increasing  velocity. 
In  the  neighborhood  of  the  Fiji  Islands  this  current  divides;  one  part,  known  as  the  Ronsel  Cwn-enf,  con- 
tinues to  the  westward,  following  a  route  marked  by  the  various  passages  between  the  islands,  and  later 
acquiring  a  northerly  component  and  setting  through  Torres  Strait  and  along  the  north  coast  of  New 
Guinea;  the  other  part,  called  the  Australia  Cui-revt,  sets  toward  south  and  west,  arriving  off  the  east 
coast  of  Australia,  along  Avhich  it  flows  southward  to  about  latitude  35°  S.,  whence  it  bends  toward 
southeast  and  east  and  is  soon  after  lost  in  the  currents  due  to  the  prevailing  wind. 

547.  The  general  drift  current  that  sets  to  the  north  out  of  the  Antarctic  regions  is  deflected  until, 
upon  gaining  the  regions  to  the  southwest  of  Patagonia,  it  has  acquired  a  nearly  easterly  set;  in  striking 
the  shores  of  the  South  American  continent  it  is  divided  into  two  branches. 

The  first,  known  as  the  Cape  Horn  Cnrrcnt,  maintains  the  general  easterly  direction,  and  its  influence 
is  felt,  where  not  modified  by  winds  and  tidal  currents,  throughout  the  vicinity  of  Cape  Horn,  and,  in 
the  Atlantic  Ocean,  off  the  Falkland  Islands  and  eastern  Patagonia. 

The  second  branch  flows  northeast  in  the  direction  of  Valdivia  and  Valparaiso,  follows  generailj' 
the  direction  of  the  coast  lines  of  Chile  and  Peru  (though  at  times  setting  directly  toward  the  shore  iia 
such  manner  as  to  constitute  a  great  danger  to  the  navigator),  and  forms  the  important  current  which 
has  been  called  variously  the  Peruvian,  Chilean,  or  Humboldt  Current,  the  last  name  having  been  given 
for  the  distinguished  scientist  who  first  noted  its  existence.  The  principal  characteristic  of  the  Peru- 
vian Current  is  its  relatively  low  temperature.  The  direction  of  the  waters  between  Pisco  and  Payta  is 
between  north  and  northwest;  near  Cape  Blanco  the  current  leaves  the  coast  of  America  and  bears 
toward  the  Galapagos  Islands,  passing  them  on  both  the  northern  and  southern  sides;  here  it  sets  toward 
AVNW.  and  west;  beyond  the  meridian  of  the  Galapagos  it  widens  rapidly,  and  thecuiTent  is  lost  in  the 
equatorial  current,  near  108°  W.  As  often  happens  in  similar  cases,  the  existence  of  a  counter-current 
has  been  proved  on  different  occasions;  this  sets  toward  the  south,  is  very  irregular,  and  extends  only  a 
little  distance  from  shore. 

54§.  CiRRENTs  OF  THE  IxDiAN  OcEAN. — In  this  occau  the  currents  to  the  north  of  the  equator 
are-very  irregular;  the  periodical  winds,  the  alternating  breezes,  and  the  changes  of  monsoon  produce 
currents  of  a  variable  nature,  their  direction  depending  upon  that  of  the  wind  which  produces  them, 
upon  the  form  of  neighboring  coasts,  or,  at  times,  upon  causes  which  can  not  be  satisfactorily  explained. 

549.  There  is,  in  the  Indian  Ocean  south  of  the  equator,  a  regular  Equatorial  Current  which,  by 
reason  of  owing  its  source  to  the  southeast  trade  winds,  corresponds  with  the  Southern  Equatorial  Currents 
of  the  Atlantic  and  Pacific.  The  limits  of  this  west-moving  current  vary  with  the  longitude  as  well  as 
with  the  season.  Ui)on  reaching  about  the  meridian  of  Rodriguez  Island,  a  l)ranch  makes  off  toward 
the  south  and  west,  flowing  past  Mauritius,  then  to  the  south  of  Madagascar  (on  the  meridian  of  which 
it  is  480  miles  broad) ,  and  thereafter,  rapidly  diminishing  its  breadth,  forming  jiart  of  the  Agulhas  Cur- 
rent a  little  to  the  south  of  Port  Natal. 

The  main  equatorial  current  continues  westward  until  passing  the  north  end  of  Madagascar,  where, 
encountering  the  obstruction  presented  by  the  African  continent,  it  divides,  one  branch  following  the 
coast  in  a  northerly,  the  other  in  a  southerly,  direction.  The  former,  in  the  season  of  the  south-nest 
monsoon,  is  merged  into  the  general  easterly  and  northeasterly  drift  that  prevails  throughout  the 
ocean  from  the  northern  limit  of  the  Equatorial  Current  on  the  .'■'outh,  as  far  as  India  and  the  adjacent 
Asiatic  shores  on  the  north;  but  during  the  northeast  monsoon,  when  there  exists  in  the  northern 
regions  of  the  Indian  Ocean  a  westerly  drift  current  analogous  to  the  Northern  Equatorial  Currents 
produced  in  the  Atlantic  and  Pacific  by' the  northeast  trades,  there  is  formed  an  east-setting  Equatorial 
Counter  Current,  which  occupies  a  narrow  area  near  the  equator  and  is  made  up  of  the  waters  accumu- 
lated at  the  Avestern  continental  boundary  of  the  ocean  by  the  drift  currents  of  both  hemispheres. 

550.  The  southern  branch  of  the  Equatorial  Current  flows  to  the  south  and  west  down  the 
Mozambique  channel,  and,  being  joined  in  the  neighborhood  of  Port  Natal  by  the  stream  which 
arrives  from  the  open  ocean,  there  is  formed  the  warm  Agulhas  Current,  which  possesses  many  of  the 
characteristics  of  the  Gulf  and  Japan  streams.     This  current  skirts  the  east  coast  of  South  Africa  and 

22489—03 11 


162  OCEAN    CUERENTS. 

attains  considerable  velocity  over  that  part  between  Port  Xatal  and  Algoa  Bay.  During  the  summer 
months  its  effects  are  felt  farther  to  the  westward;  during  the  winter  it  diminishes  in  force  and  extent. 
The  meeting  of  the  Agulhas  Current  with  the  cold  water  of  higher  latitudes  is  frequently  denoted  by  a 
broken  and  confused  sea. 

Upon  arriving  at  the  southern  side  of  the  Agulhas  Bank,  the  major  part  of  the  current  is  deflected 
to  the  south,  and  then  curves  toward  east,  flowing  back  into  the  Indian  Ocean  with  diminished  strength 
and  temperature,  on  about  the  fortieth  parallel  of  south  latitude,  where  its  influence  is  felt  as  far  as  the 
eightieth  meridian.  A  small  part  of  the  stream  which  reaches  Agulhas  Bank  continues  across  the 
southern  edge  of  that  bank,  then  turns  to  the  northwest  along  the  west  coast  of  the  continent  until  it 
is  united  with  the  waters  of  the  Southern  Connecting  Current  of  the  Atlantic. 

551.  Along  the  fortieth  parallel  of  south  latitude,  between  Africa  and  Australia,  there  is  a  general 
easterly  set,  due  to  the  branch  of  the  Agulhas  current  already  described,  to  the  continuation  of  the  drift 
current  from  the  Atlantic  which  passes  to  southward  of  the  Cape  of  Good  Hope,  and  to  the  westerly 
winds  which  largely  prevail  in  this  region.  At  Cape  Leeuwin,  the  southwestern  extremity  of  Australia, 
this  east-setting  current  is  divided  into  two  branches;  one,  going  north  along  the  west  coast  of  Australia, 
blends  with  the  Equatorial  current  nearly  in  the  latitude  of  the  Tropic  of  Capricorn;  the  other  preserves 
the  direction  of  the  original  current  and  has  the  effect  of  producing  an  easterly  set  along  the  south  coast 
of  Australia. 

552.  As  in  the  other  oceans,  a  general  northerly  current  is  observed  to  set  into  the  Indian  Ocean 
from  the  Antarctic  regions. 


EXTRACTS    FROM   NAUTICAL    ALMANAC. 


163 


APPENDIX  I. 

EXTEAOTS  FEOM  THE  AMEKIOAN  EPHEMEEIS  AND  NAUTICAL  ALMA- 
NAC, FOE  THE  YEAE  1879,  WHICH  HAVE  EEFEEENCE  TO  THE 
EXAMPLES  FOE  THAT  YEAE  GIVEN  IN  THIS  WOEK. 


[Extracts:  Page  I.] 
AT  GREENWICH  APPARENT  NOON. 


THE  sun's 


Apparent 
Right  Ascension. 


Diff.  for 
1  hour. 


Apparent 
Dewination. 


Diff.  for 
1  hour. 


Semi- 
diameter. 


Sidereal 
Time  of 
the  Semi- 
diameter 
passing 
the 
Meridian 


Equation  of 

Time,  to  be 

added  to 


suhtraxied 

from  Appar- 

ent  Time. 


Diff.  for 
1  hour. 


JANUARY. 


Sun. 

19 

Mon. 

20 

Tues. 

21 

20    4  60. 17 

10. 626 

20    9  14.84 

10.595 

20  13  28.  75 

10.564 

20  21    9. 0 

+31.54 

20    8  20.4 

32.49 

19  55    9. 1 

-1-33.43 

16   17.58 

16  17.48 
16  17.38 

69.72 
69.61 
69. 51 

10  56.  68 

11  14.  74 
11  32.05 

0.769 
0.738 
0.706 


APRIL. 


Tues. 

1 

Wed. 

2 

Thur. 

3 

Sun. 

13 

Mon. 

14 

Tues. 

15 

Wed. 

16 

Thur. 

17 

Frid. 

18 

Sat. 

19 

Sun. 

20 

Mon. 

21 

0  41 
0  45 

0  49 

1  25 
1  29 
1  33 


54.87 

9.096 

33.24 

9.100 

11.70 

9.106 

47.34 

9.206 

28.45 

9.219 

9.91 

9.234 

51.74 

9.250 

33.95 

9.268 

16.56 

9.285 

59.58 

9.302 

43.01 

9.320 

26.87 

9.337 

N. 


N. 


4  30  43.  2 

+57.85  ' 

4  53  49. 1 

57.64  t 

5  16  49.  8 

.57.41 

9    0  54. 1 

.54.40 

9  22  35.4 

M.03  ; 

9  44     7.5 

53.64 

10    5  29.9 

53.23 

10  26  42.  3 

52.80 

10  47  44.  7 

62.37 

11     8  36.4 

61.92 

11  29  17.1 

.51. 46 

11  49  46.4 

+50.97 

16     2.16 

64.51 

16    1. 89 

64.53 

16     1.61 

64.55 

15  58.  86 

64.89 

15  58. 59 

64.94 

15  58.  31 

64.99 
65.04 

15  58. 04 

15  57.  77 

65.09 

15  57. 50 

65.15 

15  57.  24 

65.21 

15  56. 98 

65.  27 

15  56.  72 

65.  33 

4  0. 

3  42. 

3  24. 

0  35. 

0  19. 

0  4. 


0  10. 
0  24. 
0  38. 

0  51. 

1  4. 
1  17. 


0.758 
0.754 
0.748 
0.649 
0.635 
0.620 
0.604 
0.587 
0.570 
0.553 
0.536 
0.518 


MAY. 


Mon. 

5 

Tues. 

6 

Sat. 

10 

Sun. 

11 

Thur. 

15 

Frid. 

16 

Sat. 

17 

Sun. 

18 

48  30.  72 

9.626 

52  22.  03 

9.650 

7  53.  03 

9.747 

11  47.27 

9.771 

27  30.  07 

9.871 

31  27.  26 

9.895 

35  25.  03 

9.919 

39  23.  37 

9.942 

N.  16  13  40.  4 

16  30  40. 4 

17  35  53.  8 

17  51  29. 1 

18  50  48.  5 

19  4  51.6 
19  18  35.5 

N.  19  31  59.  8 


+42.86 
42.17 
39.33 
38.59 
35.52 
34.72 
33.91 

+33.06 


15  53.  36 

66.37 

15  53. 14 

66.45 

15  52. 25 

66.78 

15  52.  03 

66.86 

15  51.  20 

67.19 

15  51.00 

67.27 

15  50. 80 

67.35 

15  50.61 

67. 43 

3  25. 18 
3  30.  40 
3  45.58 
3  47.90 
3  51.32 
3  50.68 
3  49.  47 
3  47.69 


0.229 
0.206 
0.109 
0.084 
0.014 
0.039 
0.062 
0.086 


Note.— Mean  Time  of  the  Semidiameter  i)assing  may  be  found  by  substracting  0".18  from  the  Sidereal  Time. 

+  prefixed  to  the  hourly  change  of  declination  indicates  that  north  declinations  are  increasing  and  south 
declinations  are  decreasing;  —  indicates  that  north  declinations  are  decreasing  and  south  declinations 
increasing. 


164 


EXTRACTS    FROM    NAUTICAL    ALMANAC. 

[Extracts:  Page  I.] 
AT  GREENWICH  APPARENT  NOON— Continued. 


THE  SUN'S 


Apparent 
Right  Ascension. 


Diff.  for 
1  hour. 


Apparent 
Declination. 


DifE.  for 
1  hour. 


Semi- 
diameter. 


Sidereal 
Time  of 
the  Semi- 
dinmeter 
passing 

^he 
Meridian. 


Erjuation  of 

Time,  to  be  \ 

subtracted 

from 


atlfled  to 

Apparent 

Time. 


Diff.  for 
1  hour. 


JUNE. 


Sat. 

7 

Tues. 

10 

Wed. 

11 

Frid. 

13 

Sat. 

14 

Frid. 

20 

Sat. 

21 

Wed. 

25 

Thur. 

26 

Frid. 

27 

0 
12 
17 
25 
29 
54 
58 
15 
6  19 
6  23 


33.74 

10. 312 

57.61 

10. 348 

6.09 

10. 3.^8 

23.73 

10. 376 

32.  85 

10.383 

30.  05 

10. 402 

39.75 

10. 402 

18.00 

10. 389 

27.29 

10.383 

36.42 

10.376 

22  45     9.5 

+  14.64 

23     0  55. 9 

11.63 

23     5  22.9 

10.62 

23  13     3.8 

8.58 

23  16  17.4 

7.55 

23  27    0.  3 

1.36 

23  27  20.5 

-f  0.32 

23  24  33. 1 

-  3.78 

23  22  49.  5 

4.81 

23  20  41. 3 

-  5.84 

15 
15 
15 
15 
15 
15 
15 
15 
15 
15 


47.63 
47.30 
47.20 
47.00 
46.91 
46.48 
46.43 
46.27 
46.24 
46.22 


68.  70 
68.  81 
68.84 
68.90 
68.92 
68.98 
68.98 
68.94 
68.93 
68.91 


1  28.86 
0  54.  76 
0  42.  87 
0  18.42 
0  5.89 


1  11.75 

1  24.86 

2  16.72 
2  29.42 
2  41.97 


0. 4-V) 
0.490 
0.500 
0. 518 
0. 525 
0.  .546 
0.546 
0.532 
0.526 
0. 519 


JULY. 


Frid. 

11 

Sat. 

12 

Tues. 

22 

Wed. 

23 

Thur. 

24 

7 

21  16.72 

10.197 

7 

25  21.  24 

10. 179 

8 

^  39.  82 

9.%4 

8 

9  38.  68 

9.939 

8 

13  36.  94 

9.914 

N.  22  8  29.  2 
22  0  23.  2 
20  19  8.9 
20     7     5.2 

X.  19  54  41.3 


-19. 76 
20.71 
29. 72 
30.57 

-31.41 


15  46.  30 

68.30 

15  46.33 

68.24 

15  46.  94 

67.51 

15  47.  03 

67.43 

15  47.  13 

67.35 

5  10.04 

5  17.99 

6  10.  85 
6  13. 15 
6  14.84 


0.  339 
0.321 
0.108 
0.083 
0.059 


SEPTEMBER. 


Tobesubtract- 
edfrom  A])- 
2Mrent  Time. 


Wed. 
Thur. 


11  13  33.93 
11  17    9.68 


8.993 

8.988 


4  59  24.2 

-56.90 

15  55. 81 

4  36  36.  2 

-57.10 

15  56.06 

64.12 
64.10 


3     1.29 
3  22.03 


0.862 
0.867 


DECEMBER. 


Mon. 
Tues. 


18 
18 


1  24. 12 
5  50.  72 


11. 108 
11.107 


S.  23  27  17.  3 
S.  23  26  54.  3 


+  0.37 

16  18. 13 

71.  30 

+  1.55 

16  18. 18 

71.30 

1  16.61 
0  46.  64 


1.248 
1.246 


Note. — Mean  Time  of  the  Semidiameter  pas.sing  may  be  found  by  subtracting  0'.18  from  the  Sidereal  Time. 

-(-  prefixed  to  the  hourly  change  of  declination  indicates  that  north  declinations  are  increasing  and  south 
declinations  are  decreasing ;  —  indicates  that  north  declinations  are  decreasing  and  south  declinations 
increasing. 


EXTRACTS    FROM    KAUTICAL    ALMANAC. 


165 


[Extracts:  Page  II.J 
AT   GREEN^A^ICH    MEAN    NOON. 


Day  of 

the 
Week. 


Day  of 

the 
Month. 


THE  sun's 


Apparent 
Right  Ascension. 


h.    m.       s. 


Diff.  for 
1  hour. 


Apparc7it 
Declination. 


Diff.  for 
1  hour. 


E(^uation  of 

Time,  to  be 

sitbtractal  from     Diff.  for 

..   ,,    '■-  1  hour. 

added  to  Mean 

Time. 


JANUARY. 


Sidereal  Time 
or  Right  As- 
cension of 
Mean  Sun. 


//.     m. 


Frid. 

10 

Rat. 

11 

Mon. 

20 

Tues. 

21 

19  26  16.08 

10.866 

19  30  36.59 

10.842 

20    9  12.84 

10.593 

20  13  26.  71 

10.562 

S.21  58  32.0 

21  49  22. 7 

20    8  26.  6 

S.  19  55  15. 6 


+  22. 35 
23.41 
32. 48 

+  33.42 


7 

43.  42 

1.010  [ 

8 

7.37 

0. 986  1 

11 

14.60 

0.738  1 

11 

31.91 

0. 706  1 

19  18  32.  66 
19  22  29.  22 

19  57  58.  24 

20  1  54.80 


APRIL. 


Tues. 

1 

Wed. 

9 

Tues. 

8 

Wed. 

9 

Tues. 

15 

Wed. 

16 

Thur. 

17 

Sun. 

20 

Mon. 

21 

Tues. 

22 

Wed. 

23 

Thur. 

24 

Frid. 

25 

Tues. 

29 

Wed. 

30 

0  41 

0  45 

1  7 


11 
33 
36 
40 
51 
55 
59 
2  2 
2  6 
2  10 
2  25 
2  29 


54.27 

9.098 

32.68 

9.102 

26.22 

9.146 

5.87 

9. 1.57 

9.91 

9.236 

51.77 

9.252 

34.02 

9.269 

43.19 

9.321 

27.08 

9.338 

11.41 

9.356 

56.19 

9.375 

41.42 

9.394 

27.11 

9.414 

34.67 

9.494 

22.79 

9.515 

.  4  30 
4  53 
7  10 
7  32 
9  44 

10  5 

10  26 

11  29 

11  49 

12  10 
12  30 

12  50 

13  9 

14  26 
14  44 


39.4 

+  57.86 

45.6 

57.65 

20.3 

66.08 

42.8 

55.77 

7.4 

53.65 
63.24 

30.1 

42.8 

62.81 

18.1 

61.46 

47.6 

50.98 

5.4 

50.48 

11.2 

49.97 

4.7 

49.46 

45.4 

48.92 

14.5 

46.65 

46.7 

+  46.04 

4    0.65 

0.758 

3  42. 50 

0.754 

1  56.  74 

0.709 

1  39.83 

0.698 

0    4.54 

0.620 
0.604 

0  10. 15 

0  24. 46 

0.587 

1     4.94 

0.536 

1  17.61 

0.518 

1  29.83 

0.600 

1  41.  61 

0.481 

1  52.93 

0.462 

2    3.80 

0.442 

2  42.  46 

0.361 

2  50.  89 

0.340 

0  37 
0  41 


2  32 


53.62 
50.16 
29.48 
26.04 
5.  37 
1.92 
58.48 
48.13 
44.69 
41.24 
37.  80 
34.  35 
30.91 
17.13 
13.68 


MAY. 


Frid. 

9 

Sat. 

10 

Sun. 

11 

Mon. 

12 

Frid. 

16 

Sat. 

17 

Sun. 

18 

Wed. 

28 

Thur. 

29 

Frid. 

30 

Sat. 

31 

Sat. 

7 

Sun. 

8 

Wed. 

11 

Sat. 

14 

Sun. 

15 

Wed. 

25 

Thur. 

26 

Frid. 

27 

0.01 

9. 723 

53.65 

9.747 

47.89 

9.771 

42.71 

9.7% 

27.90 

9.895 

25.67 

9.919 

24.01 

9.942 

36.81 

10.155 

40.75 

10. 173 

45.12 

10.190 

49.91 

10.207 

17 
17 
17 
18 
19 


N.17  20  3.5 
35  56.  3 
51  31.6 
6  48.9 
4  53.8 
19  18  37.6 
19  32  1.  8 
21  27  5.9 
21  36  37. 4 
21  45  46. 5 
N. 21  54  33. 0 


JUNE. 


5    0  34.  GO 

10. 311 

5    4  41.  64 

10. 324 

5  17    6.22 

10.357 

5  29  32.  87 

10.382 

5  33  42. 11 

10.388 

6  15  17.60 

10.888 

6  19  26.  86 

10.382 

6  23  35. 96 

10. 375 

N.  22  45  9.  9 

22  50  49.  3 

23  5  23.0 
23  16  17.4 
23  19  6.4 
23  24  33.  2 
23  22  49.  7 

N.23  20  41.6 


+  40.06 
39.33 
38.69 
37.84 
34. 72 
33.91 
33.09 
24.28 
23.34 
22.40 

+  21. 45 


+  14. 64 

13.64 

10.62 

7. 55 

+  6.52 

-3.78 

4.81 

-5.84 


3  42. 68 
3  45. 59 
3  47.  91 
3  49.64 
3  50.  68 
3  49.  47 
3  47.  68 
3  0.46 
2  53.08 
2  4,5.26 
2  37.03 


To  be  added  to 


wbtrarted  from 
Mean  Time. 


1  28.85 
1  17.77 
0  42.  86 
0  5.89 


0  6.80 
2  16.  70 
2  29. 40 
2  41. 95 


0.134 
0.109 
0.084 
0. 060 
0.U39 
0.062 
0.086 
0.297 
0.315 
0.334 
0.3.51 


3  7  42.69 
3  11  39.24 
3  15  35.  80 
3  19  32.  35 
3  35  18.58 
3  39  15. 14 

3  43  11.69 

4  22  37.  27 
4  26  33.  83 
4  30  30.  38 
4  34  26.94 


0.456 
0. 467 
0.500 
0.  .525 
0.532 
0.532 
0. 526 
0.519 


Note. — The  Semidiameter  for  Mean  Noon  may  be  assumed  the  same  as  that  for  Apparent  Noon. 

+  prefixed  to  the  hourly  change  of  declination  indicates  that  north  declinations  are 
increasing  and  south  declinations  are  decreasing;  —  indicates  that  noMh  declinations  are 
decreasing  and  south  declinations  increasing. 


5  2  2. 85 
5  5  59. 41 
5  17  49.  08 
5  29  38.  76 

5  33  35.  31 

6  13  0.90 
6  16  57. 46 
6  20  54.  01 


Diff.  for  1  hour. 
-^9».8565. 


166 


EXTRACTS    FROM   NAUTICAL    ALMANAC. 


[Extracts:  I'age  II.] 
AT  GREENWICH  MEAN  NOON— Continued. 


Day  of 

the 
Week. 


Dav  of 

the 
Month. 


THE  sun's 


Apparent 
Right  Ascension. 


h.  m. 


Difif.  for 
1  hour. 


Appareiit 
Declination. 


Diff.  for 
1  hour. 


Equation  of 

Time,  to  be 

subtracted  frovi 

Mean  Time. 


Diff.  for 
1  hour. 


Sidereal  Time 
or  Ri^ht  As- 
cension of 
Mean  Sun. 


AUGUST. 


Tiies. 
Wed. 


0  27.45 
4  17.82 


9.610 
9.586 


N.  17     1  29. 2 
N.  16  45    8. 6 


-40.62 
-41.20 


SEPTEMBER. 


Wed. 

10 

Thur. 

11 

11 

13 

3-1. 

39 

8. 995 

11 

17 

10. 

19 

8.990 

N.  4  59  21.3      -56.91 
N.  4  36  32.9  i    -57.12 


5  47. 69 
5  41.51 


To  be  added  to 
Mean  Time. 


3     1.33 
3  22.07 


0.246 
0.270 


0. 862 
0.867 


8  54  39.  76 
8  58  36.  31 


11  16  35.72 
11  20  32.  26 


OCTOBER. 


Wed. 

15 

Thur. 

16 

Frid. 

17 

Tues. 

28 

Wed. 

29 

13  20  28.07 

9.309 

13  24  11.  75 

9.333 

13  27  56. 01 

9.357 

14    9  44.78 

9.662 

14  13  37.03 

9.693 

S.    8  29  16.  2 

8  51  28. 1 

9  13  32.4 
13  6    2.6 

S.  13  26    4. 6 


55.65 
55.34 
55.02 
50.34 
49. 82 


14     7. 02 

0.548 

14  19.89 

0. 524 

14  32. 18 

0..T00 

16    5.51 

0.195 

16     9.82 

0. 164 

13  34  35.08 
13  38  31.  64 

13  42  28.  19 

14  25  50.  29 
14  29  46.  84 


NOVEMBER. 


Wed. 
Thur. 


12 
13 


15    9  14.01 
15  13  18.  76 


10.180 
10.216 


s.  i; 
s.i; 


41  18.4 
57  27.6 


-  40. 77 
-39.99 


15  44. 60 
15  36.41 


0.323 
0. 359 


15  24  58.  61 
15  28  55. 17 


DECEMBER. 


Wed. 

3 

Thur. 

4 

Mon. 

8 

Tues. 

9 

Wed. 

10 

Thur. 

11 

Mon. 

22 

Tues. 

23 

Wed. 

24 

16  37  40.  65 

10.844 

16  42    1. 22 

10. 869 

16  59  29. 19 

10. 960 

17    3  52.48 

10. 979 

17     8  16.23 

10.998 

17  12  40. 41 

11.015 

18     1  24.34 

11.104 

18    5  50. 85 

11. 103 

18  10  17.33 

11. 101 

S.  22  6  24.  6 
22  14  43.  0 
22  43  35. 6 
22  49  42. 3 

22  55  21.9 

23  0  34. 3 
23  27  17.  3 
23  26  54.  3 

S.  23  26     2.  9 


-  21. 30 
20. 23 
15.83 
14.71 
13.58 

-  12.45 
0.37 
1.55 
2.73 


+ 


+ 


5.66 
41.65 
59.91 
33.18 
5.99 
6  38.  37 
1  16.58 
0  46.  63 
0  16.  71 


10 
9 
7 

7 
7 


0.987 
1.013 
1.104 
1.123 
1.142 
1.159 
1.248 
1.246 
1.244 


16  47  46, 31 

16  51  42.  87 

17  7  29. 10 
17  11  25.66 
17  15  22.22 

17  19  18.  78 

18  2  40.  92 
18  6  37. 48 
18  10  34.03 


Note. — The  Semidiameter  for  Mean  Noon  may  be  a.<«umed  the  same  a.s  that  for  Apparent  Noon. 

+  prefixed  to  the  hourly  change  of  declination  indicates  that  north  declinations  are 
increasing  and  south  declinations  are  decreasing:  —  indicates  that  north  declinations  are 
decreasing  and  south  declinations  increasing. 


Difl.  for  1  hour. 
+  9».a565 


EXTRACTS    FROM    NAUTICAL    ALMANAC. 


167 


[Extracts:  Page  III.] 
AT  GREENWICH  MEAN  NOON. 


Day  of 

the 
Month. 

Day  of 
the 
Year. 

THE  SUN'S 

Logarithm  of 

the  Radius 

Vector  of  the 

Earth. 

Diff.  for 
1  hour. 

Mean    time     of 
Sidereal  Oh. 

Tvue  LONGITUDE. 

Diff.  for 
1  hour. 

LATITUDE. 

A. 

A' 

0           '             II                                         1              II 

" 

II 

h.    m.      s. 

APRIL. 

21 
22 

Ill 
112 

30  60  16. 5 

31  58  46. 1 

59  47. 4 
58  16.9 

146.27 
146. 19 

+0.52 
+0.52 

0.  0023923 
0. 0025087 

+48.8 
+48.3 

21  59  38.53 
21  55  42.62 

[Extracts:  Page  IV.] 
GREEN\VICH  MEAN  TIME, 


THE  MOON 


SEMIDIAMETER. 


Noon. 


Midnight. 


HORIZONTAL  PARALLAX. 


Noon. 


Diff.  for 
1  hour. 


Midnight.         Diff.J- 


MERIDIAN  PASSAGE. 


Diff.  for 
1  hour. 


Noon. 


APRIL. 


16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 


15  4.7 
14  57.0 
14  51.1 
14  47.0 
14  44.  5 
14  43.  4 
14  43.  8 
14  45.  7 
14  49.2 

14  54.5 

15  1. 6 


15     0.6 

14  53. 

8 

14  48.  9  1 

14  45. 

6 

14  43. 

t 

14  43. 

4 

14  44. 

6 

14  47. 

2 

14  51. 

6 

14  57. 

8 

15     5. 

9 

55  13.6 

-1.34 

54  45.1 

1.04 

54  23.5 

0.76 

54    8.4 

0.50 

53  59. 1 

0.27 

53  55.3 

-0.06 

53  56.  7 

+0.17 

54    3.6 

0.41 

54  16.5 

0.67 

54  35. 8 

0.94 

55    2.1 

+L24 

54  58.5 

-1.19 

54  33. 5 

0.90 

54  15.2 

0.63 

54    3.1 

0.38 

53  56.  5 

-0.16 

53  55. 3 

+0.06 

53  59. 4 

0.29 

54    9.3 

0.54 

54  25. 3 

0.80 

54  48. 0 

1.09 

55  17.9 

+1.39 

21      3.8 

1.71 

21  44.3 

1.67 

22  24. 6 

1.68 

23    5.4 

1.73 

23  47. 7 

1.81 

6 

0  32.2 

1.90 

1  19.0 

2.01 

2    8.2 

2.10 

2  59,3 

2.15 

3  51.  2 

2.16 

24.6 

25.6 

26.6 

27.6 

28.6 

29.6 

0.9 

1.9 

2,9 

3,9 

4.9 


MAY. 


28 
29 


16  44.  6 

16 

38.5 

15 

47.0 

15 

59.4 

16  42. 1 
16  33.  7 

15  53.  2 

16  5.6 


61  20,1 

-0..53 

60  57. 8 

-1.29 

57  48,  8 

+1.86 

58  34,3 

+1.90 

61  11.3 

-0.93 

60  40.  2 

-1.62 

58  11.4 

+  1.90 

58  57. 1 

+L88 

12  36,  6 

2.66 

13  41,2 

2.69 

5  55.3 

1.95 

6  42.5 

1.98 

14.9 

15.9 

7.3 

8.3 


25 
26 

27 


15  49.  8 

15  58.  7 

16  7.2 


JUNE. 


15 

54.3 

16 

3.0 

16 

11.1 

57 

59.1 

1 

37 

58  31.7 

1 

34 

59 

3.0 

1 

25 

58 

15.5 

1.36 

58  47.  6 

1.30 

59 

17.5 

1.17 

4  40.1 

5  27.0 

6  15.6 

1.94 
1.98 
2.08 

5.7 
6.7 

7.  7 


168 


EXTRACTS    FROM    NAUTICAL    ALMANAC. 


[Extracts:  Pages  V-XII.] 
GREENWICH  MEAN  TIME. 


THE   MOOX'S   RIGHT   ASCENSION    AND   DECLINATION. 

Hour. 

Right  Ascension. '  j^^^^^ 

1 

Declination.        j^^iff^ 

Hour. 

Right  Ascension.  f»\«^ 

Declination. 

Diff. 
for  1  m. 

■ 

I-* 
h.     m.      #.             s. 

1 

O          1            H                     II 

h.    m.       s. 

s. 

o        <         "1         "1 

THURSDAY,  APRIL  10. 

WEDNESDAY,  MAY  28. 

17 
18 
19 

17  18  38.57  1  2.6448 
17   21   17.16   i  2.6414 
17  23  55.54     2.6379 

S.  26  19  38. 3 

26  19  41. 1 

S.  26  19  33. 0 

-  0.138 
+  0.044 
+  0.225 

6 

7 
8 

10  19     4.23 
10  21     7.  78 
10  23  11.  34 

2.0.591 
2.0592 
2.0593 

N.  7    4  18.5 

6  49  52.4 

N.  6  35  23. 4 

-14.411 

14. 459 

-14.507 

WEDNESDAY,  APRIL  16. 

THURSDAY,  JUNE  26. 

t 

6 

22  12  47. 08 
22  14  39.  29 
22  16  31.  30 

1.8718 
1.8685 
1.86.53 

S.    8  12  37.4 

7  59  36. 1 

S.     7  46  33.5 

+13.010 

13.032 

+  13.054 

2 

3 
11 

11  37  41.96 
11  39  46.49 
11  56  28.  42 

2. 0743  i    S.     2  35  36.  4 
2.0767  i          2  50  44.4 
2.0989     S.    4  51  36.5 

-15.135 

15.  l;?3 

-1.5.069 

FRIDAY,  APRIL  25. 

:\rONDAY,  DECEMBER  8. 

16 
17 
18 

5  41  33. 19 
5  43  48.  55 
5  46    3.  93  . 

2. 2558 
2.2562 
2.2566 

N.  26     5  43.  8 

26    4  23. 5 

N.  26    2  55.  2 

-  1.272 
1. 405 

-  1.5.37 

2 
3 
4 

12  23  13.52     2.1615     S.    8     9  24.4 
12  25  23.37     2.1668           8  23  44.9 
12  27  3.'].54  !  2.172-2     S.    8  38     3.8 

14.  354 
14.328 
14.302 

TUESDAY,  APRIL  29. 

11 
12 
13 

9     2  56.  23     2. 1384 
9     5     4.49     2.1369 
9     7  12.66     2.13.56 

X.  15  27     3.  6 

15  14  52.  7 

N.  15    2  36.3 

-IJ.lSo 

12. 227 

-12.318 

EXTRACTS    FROM    NAUTICAL    ALMANAC. 

[Extracts:  Pages  relating  to  Planets.] 
GREENWICH   MEAN  TIME. 


169 


JXJPITKR. 


VEJiTXJS. 


April. 


April. 


Apparent 

Right 
Ascension. 


Noon. 


22  25  51.70 
22  26  35.54 
22  27  19.02 
22  28    2.14 


Var.  of 
R.  A. 
fori 
Hour. 


Noon. 


Apparent 
Declination. 


Noon. 


+1.834  —10  44  29.6 
1.819  10  40  28.0 
1-804!       10  36  28.1 

+1.789,  _io  32  30.0 


Var.  of 
Pec. 
fori 
Hour. 


Noon. 


+10.10 

10.03 

9.9d 


Meridian 
Passage. 


Apparent 

Right 
Ascension. 


Var.  of 
R.  A. 
fori 
Hour. 


Noon. 


Noon. 


h.  m. 
20  50.0 
20  46.8 
20  43.6 


+9.89  20  40.3 


h.  III.       n.  s. 

4  19  14.43+12.686 
4  24  19.28'  12.718 
4  29  24.88+12.748 


Day  of  the  Month. 


Polar  Semidiameter 
Horizontal  Parallax 


1st. 


11th. 


16.4 
1.5 


16.7 
1.6 


17.1 


Day  of  the  month. 


17.5 


1.6      1.6 


Semidiameter 
Hor.  Parallax 


1st. 


6.0 


Apparent 
Declination. 


Noon. 


+22  40  33.2 

22  55    4.9 

4-23    8  59.5 


Var.  of 
Dec. 
fori 

Hour. 


Noon. 


Meridian 
Passage. 


+37.08 

35.55 

+34.00 


h.  m. 
2  10.7 
2  11.9 
2i3.0 


6th. 


6.2:      6.3 


6.2 
6.4 


16th. 


6.3 

6.5 


6.4 


26th. 


6.6 


6.7    6.8 


September. 


M^RS. 


Apparent 

Right 
Ascension. 


Var.  of 
R.  A. 
fori 
Hour. 


Noon. 


Noon. 


h.   m.      s. 
22  32    5.11 
22  31  38.03 


Apparent 
Decimation. 


Noon. 


-1.134 
-1.120 


-10  44  20.5 
-10  46  57.2 


Var.  of 
Dec. 
for  1 
Hour. 


-6.58 
-6.47 


March. 


Meridian 


h.  m. 
10  49.8 
10  45.5 


Day  of  Month. 


Polar  Semidiameter 
Horizontal  Parallax 


23.6 
2.2 


nth. 

21st. 

II 

II 

23.5 

23.2 

2.2 

2.2 

Apparent 
Right 

Ascension. 


h.   ni.      s. 
20    5  56.83 
20    9    1.27 
20  12    5.45 


Noon. 


s. 
+7.690 

7.680 
+7.669 


Apparent 
Declination. 


Noon. 


-21  13  58.1 
21  5  40.4 
-20  57  10.7 


Var.  of 
Dec. 
fori 

Hour. 


Noon. 


+20.48 

20.98 

+21.48 


Meridian 
Passage: 


h.      m. 
20  26.4 
20  25.6 
20  24.7 


22.8 
2.2 


Note. — North  declinations  are  marked  +,  south  declinations  — . 

+  prefixed  to  the  hourly  change  of  declination,  indicates  that  north  declinations  are  increasing  and  south 
declinations  are  decreasing;  —  indicates  that  north  declinations  are  decreasing  and  south  declinations 
increasing. 


170 


EXTKACTS    FROM    NAUTICAL    ALMANAC. 


[Extracts:  Pages  relating  to  Fixed  Stars.] 
FIXED   STARS. 

MEAN  PLACES  FOR  1879.0.     (J.\n.  O+0.OI6,  Washington.) 


Star'»Name. 

Magni- 
tude. 

Right  Ascension.   An.  Variation. 

Declination. 

An.  Varia- 
tion. 

• 
(x Ursse  Min.  (Polanfi) *.. 

2 

//.    Vi.         8. 

1  14  24.861 
1  33  12.133 
4  28  58.716 
6  15  38.457 
6  39  48.935 

13  18  49.216 

14  10    8.551 
16  21  59.432 

+21.485 
+  2.233 
+  3.437 
+  3.633 
+  2.645 
+  3.154 
+  2.735 
+  3.670 

0      /        ff 
+88  39  49.92 
—57  51     5.79 
+16  15  53.35 
+22  34  26.94 
-16  33    4.30 
-10  31  44.21 
+19  48  48.59 
-26    9  41.94 

n 

+19.00 
+18.40 
+  7.59 

-  1.48 

-  4.68 
—18.90 
—18.87 

-  8.34 

orEridani  {Acheriiar) 

a  Tauri  {Aldebaran) 

1 
1 
3 
1 
1 
1 
1.2 

Jit  Geminorum 

a  Canis  Maj.  {Sirius) 

a  Virginis  { Spica ) 

cc  Bootis  {Arctui'ua) 

a  Seorpii  (Antares) 

*  Circnmpolar  Star. 
APPARENT  PLACES  FOR  THE  UPPER  TRANSIT  AT  WASHINGTON. 


oUrsae 

Minorls.     {Polaris.) 

a  Erldani.     ( Achertiar. ) 

a  Tauri.    ( Aldebaran. ) 

Mean  Solar 

Right 

Declination 

Mean  Solar 

Right          Declination 

Mean  Solar         Right 

Declination 

Date. 

Ascension. 

North. 

Date. 

Ascension. 

South. 

Date.           Ascension. 

North. 

h.  m. 

0      1 

h.   m. 

0      1 

h.  m. 

0       1 

1  13 

+88  39 

1  33 

-57  50 

4  28 

+16  15 

June  10.8 

63.54 

n 

47.1 

July  27. 7 

14.91  +.47 

II 
28.6  +0.5 

Apr.  9.1 

59.66  -.10 

58.7  -0.2 

11.8 

64.35 

47.0 

Aug.  6.7 

15.37  +•« 

28.3     0.0 

19.1      59.57     .07 

58.6  -0.1 

12.8 

65.21 

46.9 

29.1      59.52  -.02 

58.5     0.0 

aCani 

s  Majoris.     (Si 

rius.) 

a  Virginis.    (Spica.) 

a  Bootis.     ( Arcturus. ) 

Mean  Solar 

Right 

Declination 

Mean  Solar 

Right 

Declination 

Mean  Solar 

Right          Declination  1 

Date. 

Ascension. 

Soidh. 

Date. 

Ascension. 

South. 

Date. 

Ascension. 

North. 

h.  m. 

0     , 

h.   TO. 

0      I 

■  h.  TO. 

0      1 

6  39 

-16  32 

13  18 

-10  31 

14  10 

+19  48 

(Dec.  30.5) 

51'.  06  +.10 

63.7  -2.5 

Apr.  29.5 

52^28  +.02  !   64.6  -o.i 

May  9.4 

8.                  " 

11.71  +.02 

II 
32  A  +1-6 

Jan.   9.5 

51.14  +.05 

66.1  -2.3 

May  9.4 

52.29     .00  !  64.7     0.0 

19.4 

11.71  -.01    33.7  +1.6  1 

Apr.  9.2 

50.09  -18 

76.2  +0.3 

19.4 

52.28  -.03 

64.6  +0.1 

1 

19.2 

49.92     -16 

75.8     0.6 

29.4 

52.24     .04 

64.4      0.3 

29.2 

49.77     -13 

75.0     0.9 

June  8.3 

52.19  -.60 

64.1  +0.4 

May  9.2 

49.65  -10 

74.0  +1-1 

• 

aSC( 

)rpli.     (Antare 

8.) 

Mean  Solar 

Right 

Declination 

Date. 

Ascension. 

South. 

h.  m. 
16  21 

0     1 
-26  9 

May     9.5 

63;il  +19 

II 
53.8  -0.5 

19.5 

63.28      16 

54.3     0.4 

29.5 

63.43      12 

54.7     0.4 

June    8.5 

63.53      09 

55.0     0.3 

18.4 

63.60  +-05 

55.3  -0.3 

1 

July  28.3 

63.49  -10 

56.0     0.0 

Aug.    7.3 

63.38     -13 

55.9  +0.1 

17.3 

63.24  -i-i 

55.8  +0.2 

FORMS    FOR    WORK. 


171 


APPENDIX    II. 


A  COLLECTION  OF  FOEMS  FOE  WOEKING  DEAD  EECKONINa  AND  YAEI- 
OUS  ASTEONOMICAL  SIGHTS,  WITH  NOTES  EXPLAINING  THEIE 
APPLICATION  UNDEE  ALL  CIECUMSTANCES. 


(The  figures  in  parenthesis  refer  to  the  Notes  following  these  forms.) 

FOKM  FOK  DAY'S  WORK,  DEAD  BEUKOMNG. 


Time. 

Compass  Course. 

Var. 

Dey. 

Lee- 
way. 

Total 
error. 

True  Course. 

Patent 
log. 

Dist. 

N. 

S. 

E. 

W. 

Diflf.(i) 
Long. 

' 

Laliti 

0 

de. 

Longiixidf. 

Left  at  departure 

(or  noon) 

.   (S)  N.  or  S. 

.  (2)  E.  or  W 

Run  to 

N.  or  S. 
N.  or  S. 

E.  orW 

ByD.  R.at 

E.  or  W 

Run  to 

N.  or  S. 

E.  or  W. 

By  D.  R.at 

N.  or  S. 

E.  or  W. 

FURM  FOK  TLVE  SIGHT  OF  SUN'S  LOWER  LIMB  (SIMNER  LIKE). 


h.    m.    s. 


W.  T. 
C-W 


Chro. 
C.C. 


(11)  G.  M.  T 
(T)Eq.t. 

G.  A.  T. 


Obs.  alt.  Q  . 
Corr.         ± 


(3)  S.  D. 
i.*)  L  C. 


dip 
p.  &  r. 


(MDec. 

H.D. 
G.M.T. 


N.orS. 


Corr.     ± . 


Dec. 


(«)!> 


N.orS. 


(5)  Eq.  t. 

H.  D. 
G.  M.  T. 

Corr. 

Eq.  t. 


Corr. 


2). 


h.    m.    s. 


G.A.T.  .. 
L.A.T.I.. 


(h.    m.    S.I 
(8)  Long.Ji----,----„4E.orW. 


sec 
cosec 


cos 

sin 


sin  i  ti 


2). 


DLo 


(10) 


So-ll 


h.   m.   s. 

G.A.T 

L.A.T., 


Jll.      7)1.      S.' 
i"'T"„-\E.orW. 


sec 
cosec 


cos 

sin 


sin  i  ti 


2). 


172  FORMS    FOR    WORK, 


W.  T, 

C-W 

Chro, 

,  t. 

C.  C. 

(!•)  G.M. 

T. 

R.  A. 

M.S. 

Red. 

(Tab.  9) 

G.  S. 

T. 

R.  A. 

* 

FORM  FOK  TIME  SIGHT  OF  A  STAR  (SUMKEB  LIXE). 

h.    m.    s.                                                 o    ,    „                                                      ^     ^     g_ 
Obs.  alt.  * R.  A , 


+ Corr.         ± 


Dec N.orS. 


+  .....«L. 
+ 


(*).I.C.  + («)p 


dip 
xef. 


(IS)  H.  A.  from  Gr E.  or  VV. 

Corr.         ± 


h  °    '    " 

Li  sec  (9)  La  sec 

p  cosec  cosec 


«1 

si-h. 

cos 
sin 

Gr.  H.  A. 

(18)  H.  A.i 

h. 

m. 

f:. 

2 
..  E.orW. 
.  E.orW.  8ini?i 

h. 

m. 

f. 

(14)  Long.i 

o 

, 

II 

•'Ie.oj-W. 

(1")  «■>  cos 

sin 


*)-/t 

Gr.  H.  A. 

li. 

m. 

s. 

H.  A.» 

h. 

m. 

8. 

Long.o 

o 

' 

II 

sin  i  U 


>¥..  or  W. 


FORM  FOB  TIME  SIGHT  OF  A  PLANET  (SUMNER  LINE). 


W.  T. 
C-W 

S. 
.b.9 

h.  m.  s. 
+ 

Chro.  t. 
C.  C. 

^..".\.. 

(11)  G.  M.  T. 
R.  A.  M. 
Red.  (Ta 

+ 

)  + 

G.  S.  T. 
R.  A.* 

(i2)H.A.fromGr E.orW. 


Obs. 

alt. 

* 

R.  A. 

Corr. 

4- 

h 

H.  D. 

'       II 

G.  M.  T 

(15)  par. 

+ 

(4)  I.  C. 

+ 

Corr. 

+ 

'       // 

R.  A. 

dip 

- 

ref. 

- 

'       II 

Corr. 

i 

h.  m.  .V.                                         o    '    " 
Dec.  N.orS. 


h.  TO.  «. 


H.  D. 
G.  M.  T. 

Corr. 

Dec.  N.orS. 


(«)p 


7i. 

/     // 

o 

'         II 

O         ; 

'         II 

For  the  remainder  of  the  work,  by  which  the  hour  angles  and  thence  the  longitudes  are  found,  employ  the  method 
given  under  "  Form  for  Time  Sight  of  a  Star  (Sumner  Line)." 


W.  T. 
C-W 

S. 
b.9 

h.  m.  8. 
+ 

Chro.  t. 
C.  C. 

± 

(")G.  M.  T. 
R.  A.  M. 
Red. (Ta 

+ 

')+ 

G.  S.  T. 
R.  A.  C 

FORMS    FOR   WORK.  173 

FORM  FOR  TIME  SIGHT  OF  MOON'S  LOWER  LIMB  (SUMXER  LINE). 

°    '    "                                       !i.  m.  8.                                     o    I    II 
Obs.alt.  C  (i-)R.  A.  (i-)Dec.  N.orS. 


(i«)S.  D.  + M.I).         + M.  D. 

Aug.  + m. 


(*)I.  C.  + No.  mill.   ± No.  mill.   ±. 


^— —  Corr.  ± Corr. 

dip  — h.  m.  8, 

— —  R.  A.  Dee. 

/    // 

(i2)H.A.fromGr E.orW.        1st  corr.  ± (6)p 

O       /       fl 

Approx.  alt 

p.ct-r.(Tab.24)+ 


For  the  remainder  f)f  the  Wf)rk,  by  which  the  hour  angles  and  thence  the  longitude.s  are  found,  employ  the  method 
given  under  "  Form  for  Time  Sight  of  a  Star  (Sumner  Line)." 

FORM  FOR  MERIIUAX  ALTITIDE  OF  SIN'S  L(MVER  LIMB. 

O  I  II  I         II  O  I         II 

Obs.alt.Q  (3)S.D.    +  (")  Dec N.orS. 

Corr.        ±  (*)I.  C.     +  


(18)  c  N.orS.  dip      — 

rf  N.  or  S.  p.ii-r.  — 


Lat.  N.orS. 


H.  D.    4-  

Long.  ±  

h. 

Corr.    4-  

O           1          II 

Dec 

N.orS. 


Corr.    ±   

FORM  FOR  MERIDIAN  ALTITUDE  OF  A  STAR. 

O  I         II  I         II  O  I  II 

Obs.alt.*  (<)  I.  C.  +  Dec N.orS. 

dip     -  

ref.     - 


h                

(18)  Z 

d 

N.orS. 

N.orS. 

Lat. 

N.orS. 

Corr.  ±  

•  FORM  FOR  MERIDIAN  ALTITUDE  OF  A  PLANET. 

O        I         II  I        II  ii^    „j  o      /      // 

Obs.alt.  =)< (15)  par.  + G.  M.  T.,  Gr.  trans Dec N.orS. 

Corr.        4: (4)1.  C.  + Corr.  for  Long.  + — ^— 


L.  M.  T.,  local  trans H.  D.   + 

Long.  ± h. 

G.M.T 


(18);  N.orS.  dip- G.  M.  T.,  local  trans. 

d  N.orS.  ref.   - 

Lat.  N.orS.  — 


Corr.  ± 


Dec N.orS. 


174 


FORMS    FOR    WORK. 


(IS); 


FORM  FOR  MERIDIAN  ALTITUDE  0¥  MOON'S  LOWER  LIMB. 

°    '    "  h.  VI. 


O         I         II 


Obs.  alt.  ^ 


N.orS.      (W}S.D. 

X.orS.  Aujr. 

(<)I.C. 


Lat N.orS. 


dip 


G.  M.  T.,  Gr.  trans. 

■^-^—  Corr.  for  Long.(Tab.  11)  ± 

+ L.  M.  T.,  local  trans. 

+ Long.  +  . 

+ 

+  .. 


G.  M.  T.,  local  trans. 


('■)  Dec 


II 

M.  D.       ±... 

m. 

Xo.  min.  ±  . . . 

I    II 

Corr.        +  . . . 

0 

t    II 

Dec. 

N.orS. 


N.orS. 


Ist  corr. 


Approx.  Alt. 
jj.<fcr.  (Tab.24)  +. 


ALTERNATIVE  FORM  FOR  MERIDIAN  ALTITUDE  OF  A  BODY.  (»)) 
±  90°  00'  00"  Jiules/or  signs. 


(M)  Dec. 
Corr. 


Constant : 
Obs.  alt. 


Lat. 


Case     I.  Lat.  &  Dec.  same  name,  Lat.  greater -i-  90°  +  Dec.  —  Corr.  —  Alt- 
Case   II.  Lat.  &  Dec.  same  name,  Dec.  greater —90°  +  Dec.  +  Corr.  +  Alt. 

Case  III.  Lat.  and  Dec.  opposite  names +  90°  —  Dec.  —  Corr.  —  Alt. 

Ca.se  IV.  Lower  transit +90°  — Dec.  +Corr.  +  Alt. 


N.orS. 

FORM  FOR  LATITUDE  SIGHTS  OF  SUN'S  LOWER  LIMB  (SUMNER  LINE). 


W.T. 

■i 

h. 

III.    s. 

Obs.  alt. 
Corr. 

h 

S.D. 
LC. 

C-W 

Chro.  t. 

C.C.  + 

(")G.M.T. 
(T)  Eq.t. 

4_ 

+ 

G.A.T. 
Long.  1    ± 

L.A.T., 

(«)  Long,  g   rt 
L.A.T.2 


h.   m.  s. 


dip 
p.  &r. 


Corr. 


(6)  Dec. 


H.D. 
G.  M.  T. 

Corr. 

Dec. 


N.  or  S. 


(*)  Eq.  t 


N.  or  S. 


T 

». 

H.D.       ±  . 

h. 

G.M.T. 

s. 

Corr.       ±  . 

m. 

& 

Ea.t. 

h.   m.   s. 


<!>'  <t>"  Method. 


(s*)9>i"     N.orS. 

a>  1 '     N.  or  8. 


Lat.  1 N.  or  S. 


h         

«>j"     

<Pi'      

Lat.  2 N.  or  S. 


sec. 
tan . 


sec. 
tan  . 


sni. 
sin. 


sin. 
sin. 


(25)  a 
h 

(20)  fl  <  1  2  rt 

H, 


d 


Reduction  to  Meridian. 


N.  or  S. 

N.  or  S. 


Lat.  1      N.  or  S. 


h 
atn^  ± 


Lat.s     N.orS. 


W.  T. 

C-W 

+ 

Chro.  t. 

0.  C. 

± 

(")  G.  M.  T. 

R.  A.  M.  S. 

+ 

Red.  (Tab.  9) 

+ 

G.  S.  T. 

R.  A.* 

FORMS    FOR    WORK  175 

FORM  FOB  LATITUDE  SKiHTS  OF  A  STAR  (SUMXER  LINE). 

h.    m.    8.  0     1     It  fi^    „j_    g^ 

R.A 


(12)  H.A.fromGr E.  or  W. 

(!")  Long.i  E.orW. 


(h.    m.    «.| 

Ie.  or  W. 


(«3)  Long.2 


f^.    m.    «. 


Corr. 

-t-    .. 

h 

I.e. 

+  .... 

'     " 

dip 
ref. 

,     „ 

Corr. 

± 

/     // 

Dec.  N.  orS. 


For  the  remainder  of  the  work,  by  which  the  latitudes  are  found  from  either  the  <p'  <p"  formula  or  the  reduction  to  the 
meridian,  employ  the  methods  given  under  "  Form  for  Latitude  Sights  of  Sun's  Lower  Limb  (Sumner  Line)." 

FORM  FOR  LATITUDE  SItiHTS  OF  A  PLACET  (SUMNER  LINE). 

h.  in.  8.                                             °      ' 
W.  T.  Ob8.alt.5(< R.A.  Dec.  N.  or  S. 


C-W  + Corr. 


Chro.  t. 
C.  C. 


(")G.  M.  T.  (»6)  par.         +. 

R.  A.  M.S.        + (<)   I.e.         +. 

Red.  (Tab.9)    + 

G.S.T.  


R.A.*  ^jp  _ R-A Dec N.orS. 


R.  A. 

4; 

h. 

m. 

8. 

Dec. 

H.  D. 

8. 

H.  D. 
G.  M.  T. 

G.  M.  T. 

h. 

Corr. 

8. 

Corr. 

R.A. 

h. 

in. 

8. 

Dec. 

(W)  H.A.fromGr E.orW.        reL 

(«)Long.,  E.orW. 


h.   m.   8. 


h.    m.    8. 
(58)  Long.o  

I  h.   in.  8. 


Corr. 


E.  or  W. 


For  the  remainder  of  the  work,  by  which  the  latitudes  are  found  from  either  the  <p'  <p"  formula  or  the  reduction  to  the 
meridian,  employ  the  methods  given  under  "  Forms  for  Latitude  Sights  of  Sun's  Lower  Limb  (Sumner  Line)." 


176 


FORMS    FOR    WORK. 


FORM  FOR  LATITUDE  SIGHTS  OF  MOOX'S  LOWER  LIMB  (SUMXER  LINE). 


h.  m.  s. 


W.T. 
C-W 

Chro.  t. 
C.  C. 

(11)  G.  M.  T. 
R.  A.  M.  S. 


+  . 


Iljd.  (Tab.  9)      + 

G.  S.  T.  

R.A.C  

(12)  H.  A.  from  Gr K.or W. 

(«)  Long.]  E.orW. 


Obs.alt.C 


(16)  S.  D. 

Aug. 

(*)I-C. 


dip 


h.  VI.  g. 


('■)  R.  A. 


^E.orW. 


1st  Corr. 


Approx.  alt. 

p.  dr.  (Tab.  24)  +. 


M.  I>. 

+  ... 

«. 

No.  min. 

-4-  .. 

«). 

Corr. 

-1- 

*•• 

R.  A. 

/(. 

m.  i<. 

(•■)  Dec 


^ 

^__ 

II 

i\r 

D. 

4-  ... 

m. 

No 

.ram 

■  dt-  ■ 

Coi 

rr. 

1  II 

_ 

De( 

B. 

0 

1  II 

N.orS. 


N.orS. 


Long.o 


//.  m.  i. 


h.  m.  s. 


E.orW 


For  the  remainder  of  the  work,  by  which  the  latitudes  are  found  from  either  the  9'  q>"  formula  or  the  reduction  to  the 
meridian,  employ  the  method.s  given  under  "  Forms  for  Latitude  Sights  of  Sun's  Lower  Limb  (Sumner  Line)." 

FORM  FOR  CHRONOMETER  CORRECTION  BY  EQUAL  ALTITUDES  OF  SUN. 


W.  T.,  A.  M. 

h.  m. 

s.                                     h.  m.   s. 
W.  T.,P.  M 

(28)  Dec. 

H.  D.  a 
merid. 

Long. 
Corr. 
Dec. 

(31)  Tab.  37 

H.  D. 

L 

1st  pt. 
2dpt. 

Eq.eq.l 

± . 

±. .. 
0 

± . .. 

±... 

±  -  -. 

0 

1    II 

N.orS. 

H.  D.  ( 
noon; 

H.    D. 
noon) 

Diff.  24" 
Diff.  li> 
Diff.  for 
H.  D.  at 

0 
..  d  ±... 

P'-e^-}  ± 

Wll.Ji 

i             4- 

n 

+ 

C-W               + 

C-W 

h. 

A.  M.  Chro.  t. 

P.  M.  Chro.  t 

P.  M.  Chro.  t. 

+ 

A.M.Chro.t.- 

2) 

4- , 

■" — 

Mid.  Chro.  t. 

" 

1    II 

-1-.. 

Eq.  eq.  alt. 

long.     4- 

" 

0 
II 

s. 

N.orS. 

]ogA(±)... 
log      (±)... 
tan      (  +  )... 
log      (±)... 

}  

Chro.  t.  L.  Ai 

noon 
C)  Eq.  t. 

merid.  ± 

II 

TO.      S. 

—     (2'*)Eq.  t.                  

logB(  +  ). 

log     (±)., 

...  tan     (±).. 

log     (±).. 

Chro.  t.  L.  M. 
noon 
(29)  Long. 

}  

S. 
H.  D.              -4- 

— 

/j 

]- 

G.  M.  T. 

Corr.              ± 

m.    8. 
Eq.  t.                  

\~.. 

~ 

FORM  FOR  FINDING  THE  TIME  OF  HIGH  (OR  LOW)  WATER. 

d.   h.   m. 


G.  M.  T.  of  Greenwich  transit 
(32)  Corr.  for  Long.  (Tab.  11) 

L.  M.  T.  of  local  transit 
'    Lunitidal  int.  (App.  IV) 

L.  M.  T.  of  high  (or  low)  water 


FORMS    FOR    WORK.  177 

NOTES  KELATIXG  TO  THE  FORMS. 

1.  It  Is  not  necessary  to  convert  departure  into  difference  of  longitude  for  eacli  course;  it  will  suffice  to  make  one 
conversion  for  the  sum  of  all  the  departures  used  in  bringing-  forward  the  position  to  any  particular  time. 

2.  In  D.  R.  it  will  be  found  convenient  to  worli  Lat.  and  Long,  in  minutes  and  tenths,  rather  than  in  minutes  and 
seconds. 

3.  If  upper  limb  is  observed,  the  correction  for  S.  D.  should  be  negative,  instead  of  positive. 

4.  A  positive  I.  C.  has  been  assumed  for  illustration  throughout  the  forms;  if  negative,  it  should  be  included  with  the 
minvs  terms  of  the  correction. 

6.  For  time  sights  and  9'  q>"  sights,  take  Dee.  and  Eq.  t.  from  Naut.  Aim.,  p.  II  (G.  M.  noon). 
0.  To  obtain  p,  subtract  Dec.  from  90°  if  of  same  name  as  Lat.:  add  to  90°  if  of  opposite  name. 

7.  Sign  of  Eq.  t.  that  of  application  to  mean  time. 

8.  If  G.  A.  T.  is  later  than  L.  A.  T.,  Long,  is  west;  otherwise  it  is  east. 
P.  If  Lat.  is  exactly  known,  a  second  latitude  need  not  be  employed. 

10.  So  and  So— /(  may  be  obtained  by  applying  half  the  difference  between  Lj  and  L.^,  with  proper  sign,  to  Sj  andsj— ^, 
respectively. 

11.  The  G.  M.  T.  must  represent  the  proper  number  of  hoiirs  from  noon,  the  beginning  of  the  astronomical  daj';  to  obtain 
this  it  may  be  necessary  to  add  V2^  to  the  Chro.  t. 

12.  H.  A.  from  Greenwich  is  the  difference  between  G.  S.  T.  and  R.  A.,  and  should  be  marked  W.  if  the  former  is  greater; 
otherwise,  E. 

1;^.  Local  H.  A.  is  marked  E.  or  W.,  according  as  the  body  is  east  or  west  of  the  meridian  at  time  of  observation. 
11.  Subtract  local  hour  angle  from  Greenwich  hour  angle  to  obtain  longitude;  that  is,  change  name  of  local  hour  angle 
and  combine  algebraically. 

15.  The  forms  include  a  correction  for  the  parallax  of  a  planet,  but  in  most  cases  this  is  small,  and  may  be  omitted.  When 
used,  take  hor.  par.  from  Kaut.  Aim.  and  reduce  to  observed  altitude  by  Table  17.  The  semidiameter  of  a  planet  may  be 
disregarded  in  sextant  work  if  the  center  of  the  body  is  brought  to  the  horizon  line. 

16.  If  upper  limb  is  observed,  the  corrections  for  S.  D.  and  Aug.  should  be  negative,  instead  of  positive. 

17.  R.  A.  and  Dec.  are  to  be  picked  out  of  Naut.  Aim.  for  nearest  hour  of  G.  M.  T.,  and  to  be  corrected  for  the  number 
of  minutes  and  tenths. 

IS.  Mark  zenith  di.stance  N.  or  S.  according  as  zenith  is  north  or  south  of  the  body  observed:  mark  Dec.  according  to  its 
name,  subtracting  it  from  180°  for  cases  of  lower  transit;  then,  in  combining  the  two  for  Lat.,  have  regard  to  their  names. 

19.  For  meridian  altitudes,  take  Dec.  from  Naut.  Aim.,  p.  I  (G.  A.  noon). 

20.  This  form  enables  "Constant"  to  be  worked  up  before  sight  is  taken,  and  gives  latitude  directly  on  completion  of 
meridian  observation.  Longitude  and  altitude  at  transit  must  be  known  in  advance  with  sufficient  accuracy  for  correcting 
terms. 

21.  The  details  of  obtaining  Dec.  at  transit  and  correction  for  altitude  are  shown  in  the  meridian  altitude  forms  for  each 
of  the  various  bodies. 

22.  In  an  a.  m.  sight  subtract  L.  A.  T.  from  24''  to  obtain  t;  in  a  p.  m.  sight  L.  A.  T.  is  equal  to  t. 

23.  If  Long,  is  exactly  known,  a  second  longitude  need  not  be  employed. 

24.  Mark  <p"  N.  or  S.  according  to  name  of  Dec,  and  subtract  it  from  180°  when  body  is  nearer  to  lower  than  to  upper 
transit;  mark  q>'  N.  or  S.  according  as  zenith  is  north  or  south  of  the  body;  then  combine  for  Lat.  having  regard  to  the  names. 

25.  Take  a  from  Table  26  and  at-  from  Table  27. 

26.  Add  for  upper,  subtract  for  lower  transits. 

27.  Subtract  longitude  from  Greenwich  hour  angle  to  obtain  local  hour  angle;  that  is,  change  name  of  longitude  and 
combine  algebraically. 

28.  For  equal  altitude  sights,  take  Dec.  and  Eq.  t.  from  Naut.  Aim.,  p.  I  (G.  A.  noon). 

29.  Add  longitude  if  east;  subtract  if  west. 

80.  If  error  is  +,  the  chronometer  is  fast,  and  the  correction  is  subtractive;  and  the  reverse. 

31.  Mark  log  A  and  log  B  as  indicated  in  Table  37;  mark  N.  Lat.,  N.  Dec,  an<l  H.  D.  toward  the  north  +,  and  the 
reverse.  If,  in  combining  the  three  logarithms  for  the  respective  parts  of  the  equations,  one  or  three  of  them  should  be 
minus,  the  sign  of  that  part  is  minus;  otherwise,  plus. 

32   Add  for  west,  subtract  for  east  longitude. 

22489—03 12 


178 


KULES    AND   PRINCIPLES    OF   MATHEMATICS. 


APPENDIX  III. 

EXPLANATION  OF  OEETAIN  EULES  AND  PRINCIPLES  OF  MATHEMATICS 
OF  USE  IN  THE  SOLUTION  OF  PEOBLEMS  IN  NAVIGATION. 


DECIMAL  FRACTIONS. 

Fractions,  or  Vulgar  Fractions,  are  expressions  for  any  assignable  part  of  a  unit;  they  are  usaually 
denoted  by  two  numbers,  placed  one  above  the  other,  with  a  line  between  them;  thus  \  denotes  the 
fraction  one-fourth,  or  one  part  out  of  four  of  some  whole  quantity,  considered  as  divisible  into  four 
equal  parts.  The  lower  number,  4,  is  called  the  denominator  of  the  fraction,  showing  into  how  many 
parts  the  whole  is  divided;  and  the  upper  number,  1,  is  called  the  numerator,  and  shows  how  many  of 
those  equal  parts  are  contained  in  the  fraction.  It  is  evident  that  if  the  numerator  and  denominator  be 
varied  in  the  same  ratio  the  value  of  the  fraction  will  remain  unaltered;  thus,  if  both  the  numerator 
and  denominator  of  the  fraction,  \,  be  multiplied  by  2,  3,  4,  etc.,  the  fractions  arising  will  be  f,  -^t^,  ^, 
etc.,  all  of  which  are  evidently  equal  to  \. 

A  Decimal  Fraction  is  a  fraction  whose  denominator  is  always  a  unit  with  some  number  of  ciphers 
annexed  and  the  numerator  any  number  whatever;  as,  -f^,  yifjj,  rMfft  etc.  And  as  the  denominator  of 
a  decimal  is  always  one  of  the  numbers  10,  100,  1000,  etc.,  the  necessity  for  writing  the  denominator 
may  be  avoided  by  employing  a  point;  thus,  fV  is  written  .3,  and  j^j^  is  written  .14;  the  mixed  number 
3tA>  consisting  of  a  whole  number  and  a  fractional  one,  is  written  3. 14. 

In  setting  down  a  decimal  fraction  the  numerator  must  consist  of  as  many  places  as  there  are 
ciphers  in  the  denominator;  and  if  it  has  not  so  many  figures  the  defect  must  be  supplied  by  placing 
ciphers  before  it;  thus,  yVV  =  -16,  y^f  (y  =  .016,  xjyVVff  =  -0016,  etc.  And  as  ciphers  on  the  right-hand  side 
of  integers  increase  their  value  in  a  tenfold  proportion,  as  2,  20,  200,  etc.,  so  when  set  on  the  left  hand 
of  decimal  fractions  they  decrease  their  value  in  a  tenfold  proportion,  .as  .2,  .02,  .002,  etc.;  but  ciphers 
set  on  the  right  hand  of  these  fractions  make  no  alteration  in  their  value;  thus,  .2  is  the  same  as 
.20  or  .200.  -" 

The  common  arithmetical  operations  are  performed  the  same  way  in  decimals  as  they  are  in  inte- 
gers, regard  being  had  only  to  the  particular  notation,  to  distinguish  the  integral  from  the  fractional 
part  of  a  sum. 

Addition  of  Decimals. — Addition  of  decimals  is  performed  exactly  like  that  of  whole  numbers, 
placing  the  numbers  of  the  same  denomination  under  each  other,  in  which  case  the  separating  decimal 
points  will  range  straight  in  one  column. 

Ex.\MPLES. 


Add: 


Sum: 


Miles. 
26.7 
32.15 

143.206 
.003 

202.059 


Feet. 

1.26 

2.31 

1.785 

2.0 

7.355 


Inches. 
272.3267 
.0134 
2.1576 
31.4 

305.8977 


Subtraction  of  Decimals. — Subtraction  of  decimals  is  performed  in  the  same  manner  as  in  whole 
numbers,  observing  to  set  the  figures  of  the  same  denomination  and  the  separating  points  directly 
under  each  other. 

Examples. 


From : 
Take: 

31.267 
2.63 

36.75 
.026 

1.254 
.316 

1364.2 
25.163 

Difference: 

28.637 

36.724 

.938 

1339.037 

Multiplication  of  Decimals. — Multiply  the  numbers  together  as  if  they  were  whole  numbers, 
and  point  off  as  many  decimals  from  the  right  hand  as  there  are  decimals  in  both  factors  together;  and 
when  it  happens  that  there  are  not  so  many  figures  in  the  product  as  there  must  be  decimals,  then 
prefix  such  number  of  ciphers  to  the  left  hand  as  will  supply  the  defect. 


Example  I. 
Multiply  3.25  by  4.5. 

3.25 
4.5 


1.625 
13.00 


Answer:        14.625 
In  one  of  the  factors  is  one  decimal,  and  in  the 
other  two;  their  sum,  3,  is  the  number  of  decimals 
of  the  product. 


Example  II. 
Multiply  .17  by  .06. 

.17 
.06 


Answer: 


.0102 


In  each  of  the  factors  are  two  decimals;  the  pro- 
duct ought  therefore  to  contain  4;  and,  there  being 
only  three  figures  in  the  product,  a  cipher  umst  be 
prefixed. 


RULES    AND    PRINCIPLES    OF   MATHEMATICS. 


179 


Example  III. 
Multiply  0.5  by  0.7. 


Answer: 


0.5 

0.7 

0.35 


Example  IV. 

Multiply  .18  by  24. 

.18 
24 


Answer: 


72 
36 

4.32 


Division  of  Decimals. — Division  of  decimals  is  performed  in  the  same  manner  as  in  whole  num- 
bers. The  number  of  decimals  in  the  quotient  must  be  equal  to  the  excess  of  the  number  of  decimals 
of  the  dividend  above  those  of  the  divisor;  when  the  divisor  contains  more  decimals  than  the  dividend, 
ciphers  must  be  affixed  to  the  right  hand  of  the  latter  to  make  the  number  equal  or  exceed  that  of  the 
divisor. 


Examplk  I. 

Divide  14.625  by  3.25. 

3.25  )  14.625  (  4.5 
1300 


1625 
1625 


In  this  example  there  are  two  decimals  in  the 
divisor  and  three  in  the  dividend;  hence,  there  is 
one  decimal  in  the  quotient. 

Example  II. 

Divide  3.1  by  .0062. 
Previous  to  the  divishm  affix  three  ciphers  to 
the  right  hand  of  3.1,  to  make  the  numl)er  of  deci- 
mals in  the  dividend  equal  the  number  in  the 
divisor. 

.0062)  3.1000(500 
310 


Example  III. 

Divide  17.256  by  1.16. 

1.16  )  17.25600  ( 14.875 
116 


565 
464 

1016 
928 

880 
812 

680 
580 

100 


000 

Multiplication  of  Decimals  by  Contraction. — The  operation  of  multiplication  of  decimal  fractions 
may  be  very  much  abbreviated  when  it  is  not  required  to  retain  any  figures  beyond  a  certain  order  or 
place;  this  will  constantly  occur  in  reducing  the  elements  taken  from  the  Nautical  Almanac  from  Green- 
wich noon  to  later  or  earlier  instants  of  time. 

In  multiplying  by  this  method,  omit  writing  down  that  part  of  the  operation  which  involves  decimal 
places  below  the  required  order,  but  mental  note  should  be  made  of  the  product  of  the  first  discarded 
figure  by  the  multiplying  figure,  and  the  proper  number  of  tens  should  be  carried  over  to  insure  accuracy 
in  the  lowest  decimal  place  sought. 

Example:  Required  the  reduction  for  the  sun's  declination  for  7'".43,  the  hourly  difference  being 
58^''.  18,  where  the  product  is  required  to  the  second  decimal. 


By  ordinary  method. 

58'M8 
7\43 

By  contraction 

58'M8 
7^43 

17454 
23272 
40726 

1.74 

23.27 

407.26 

432^^2774,          ^. 

432.^^27 

In  the  contracted  method,  for  the  multiplier  .03  it  is  not  necessary  to  record  the  product  of  any 
figures  in  the  multiplicand  below  units;  for  the  multiplier  .4,  none  below  tenths;  but  in  each  case 
observe  the  product  of  the  left-hand  one  of  the  rejected  figures  and  carry  forward  the  number  of  tens. 


180 


RULES    AND   PRINCIPLES   OF   MATHEMATICS. 


REDrcTioN  OF  Decimals. — To  reduce  a  vulgar  fraction  to  a  decimal,  add  any  number  of  ciphers  to 
the  numerator  and  divide  it  by  the  denominator;  the  quotient  will  be  the  decimal  fraction.  The  decimal 
point  must  be  so  placed  that  there  may  be  as  many  figures  to  the  right  hand  of  it  as  there  were  added 
ciphers  to  the  numerator.  If  there  are  not  so  many  figures  in  the  quotient  place  ciphers  to  the  left  hand 
to  make  uj)  the  number. 


Example  I. 

Reduce  ^V  to  a  decimal. 
50)^.00 

.02  Answer. 
Example  II. 

Reduce  |  to  a  decimal. 
8)3.000 


.375  Answer. 
Example  III. 

Reduce  3  inches  to  the  decimal  of  a  foot. 
Since  12  inches  =  1  foot  this  fraction  is  xi- 
12)3.00 


Example  IV. 

Reduce  15  minutes  to  the  decimal  of  an  hour. 
Since  60"'  =  1\  this  fraction  is  f§. 

60)15.00 


.25  Answer. 

Example  V. 

Reduce  1 

7m 

22'  to  the  decimal  of  an  hour 

22» 

22"' 
=  —  =0'".37. 
60 

IT^.S? 

iT'-.s: 

= =0\289  Answer. 

60 

.25  Answer. 

Any  decimal  may  be  reduced  to  lower  denominations  of  the  same  quantity  by  multiplying  it  by  the 
number  representing  the  relation  Vjetween  the  respective  denominations. 
Example  VI:  Reduce  7.231  days  to  days,  hours,  minutes,  and  seconds. 


01.231 
24 

924 

462 

5\544 


0\544 
60 

32".  640 


0™.640 
60 

38\400 


Answer:  7*  5''  32'»  38'. 4. 


GEOMETRY. 


Geometry  is  the  science  which  treats  of  the  description,  properties,  and  relations  of  magnitudes,  of 
which  there  are  three  kinds;  viz,  a  line,  which  has  only  length  without  either  breadth  or  tnickness;  a 
surface,  comprehended  by  length  and  breadth;  and  a  solid,  which  has  length,  breadth,  and  thickness. 

A  point,  considered  mathematically,  has  neither  length,  breadth,  nor  thickness;  it  denotes  position 
simply. 

A  line  has  length  without  breadth  or  thickness. 
A  surface  has  length  and  breadth  without  thickness. 
A  solid  has  length,  breadth,  and  thickness. 

A  straight  or  right  line  is  the  shortest  distance  between  two  points  on  a  plane  surface. 
A  plane  surface  is  one  in  which,  any  two  points  being  taken,  the  straight  line  between  them  lies 
wholly  within  that  surface. 

Parallel  lines  are  such  as  are  in  the  same  plane  and  if  extended  indefinitely  never  meet. 

A  circle  is  a  plane  figure  bounded  by  a  curve  line  of  which  every  point  is 
equally  distant  from  a  point  within  called  the  center.  The  bounding  curve  of 
the  circle  is  called  the  circumference. 

The  radius  of  a  circle,  or  semi-diameter,  is  a  right  line  drawn  from  the 
center  to  the  circumference,  as  AC  (fig.  65) ;  its  length  is  that  distance  which 
is  taken  between  the  points  of  the  compasses  to  describe  the  circle. 

A  diameter  of  a  circle  is  a  right  line  drawn  through  the  center  and  termi- 
nated at  both  ends  by  the  circumference,  as  ACB,  its  length  being  twice  that 
of  the  radius.  A  diameter  divides  the  circle  and  its  circumference  into  two 
equal  parts. 

An  arc  of  a  circle  is  any  portion  of  the  circumference,  as  DFE. 
The  chord  of  an  arc  is  a  straight  line  joining  the  ends  of  the  arc.    It  divides 
the  circle  into  two  unequal  parts,  called  segmivti,  and  is  a  chord  to  them  both; 
thus,  DE  is  the  chord  of  the  arcs  DFE  and  DGE. 
A  semicircle,  or  half  circle,  is  a  figure  contained  between  a  diameter  and  the  arc  terminated  by  that 
diameter,  as  AGB  or  AFB. 


RULES    AND   PRINCIPLES    OF   MATHEMATICS.  181 

Anypart  of  a  circle  contained  between  two  radii  and  an  arc  is  called  a  sector,  as  GCH. 

A  quadnmt  is  half  a  semicircle,  or  one-fourth  part  of  a  whole  circle,  as  CAG. 

All  circles  are  supposed  to  have  their  circumferences  divided  into  360  equal  parts,  called  degrees; 
each  degree  is  divided  into  60  equal  parts,  called  minutes;  and  each  minute  into  60  equal  parts,  called 
seconds;  an  arc  is  measured  by  the  number  of  degrees,  minutes,  and  seconds  that  it  contains. 

A  aphere  is  a  solid  bounded  by  a  surface  of  which  every  point  is  equally  distant  from  a  point  within 
which,  as  in  the  circle,  is  called  the  center.  Substituting  surface  for  circumference,  the  definitions  of  the 
radius  and  diameter,  as  given  for  the  circle,  apply  for  the  sphere. 

An  angle  is  the  inclination  of  two  intersecting  lines,  and  is  measured  by  the  arc  of  a  circle  inter- 
cepted between  the  two  lines  that  form  the  angle,  the  center  of  the  circle  being  the  point  of  intersection. 

A  i-ig}tt  angle  is  one  that  is  measured  by  a  quadrant,  or  90°.  An  acute  angle  is  one  which  is  less  than 
a  right  angle.     An  obtuse  angle  is  one  which  is  greater  than  a  right  angle. 

A  plane  triangle  is  a  figure  contained  by  three  straight  lines  in  the  same  plane. 

When  the  three  sides  are  equal,  the  triangle  is  called  equilateral;  when  two  of  them  are  equal,  it  is 
called  isosceles.  When  one  of  the  angles  is  90°,  the  triangle  is  said  to  be  right-angled.  When  each  angle 
is  less  than  90°,  it  is  said  to  be  acute-angled.  When'one  is  greater  than  90°,  it  is  said  to  be  obtuse-angled. 
Triangles  that  are  not  right-angled  are  generally  called  oblique-angled. 

A  quadrilateral  figure  is  one  bounded  by  four  sides.  If  the  opposite  sides  are  parallel,  it  is  called  a 
parallelogram.  A  parallelogram  having  all  its  sides  equal  and  its  angles  right  angles  is  called  a  square. 
When  the  angles  are  right  angles  and  only  the  opposite  sides  equal,  it  is  called  a  rectangle. 

In  a  right-angled  triangle  the  side  opposite  the  right  angle  is  called  the  hi/potenuse,  one  of  the  other 
sides  is  called  the  base,  and  the  third  side  is  called  the  }>erjiendicular.  In  any  oblique-angled  triangle, 
one  side  having  been  assumed  as  a  base,  the  distance  from  the  intersection  of  the  other  two  sides  to  the 
base  or  the  base  extended,  measured  at  right  angles  to  the  latter,  is  the  j)erpendicular.  In  a  parallelo- 
gram, one  of  the  sides  having  been  assumed  as  the  base,  the  distance  from  its  opposite  side,  measured 
at  right  angles  to  its  direction,  is  the  perpendicular.  The  term  altitude  is  sometimes  substituted  for 
perpendicular  in  this  sense. 

Every  section  of  a  sphere  made  by  a  plane  is  a  circle.  A  great  circle  of  a  sphere  is  a  section  of  the 
surface  made  by  a  plane  which  passes  through  its  center.  A  small  circle  is  a  section  by  a  plane  which 
intersects  the  sphere  without  j)assing  through  the  center. 

A  great  circle  may  be  drawn  through  any  two  points  on  the  surface  of  a  sphere,  and  the  arc  of  that 
circle  lying  between  those  points  is  shorter  than  any  other  distance  between  them  that  can  be  measured 
upon  the  surface.     All  great  circles  of  a  sphere  have  equal  radii,  and  all  bisect  each  other. 

The  extremities  of  that  diameter  of  the  sphere  which  is  perpendicular  to  the  plane  of  a  circle  are 
called  the  poles  of  that  circle.  In  the  case  of  a  small  circle  the  poles  are  named  the  adjacent  pole  and 
the  remote  pole.  All  circles  of  a  sphere  that  are  parallel  have  the  same  poles.  All  points  in  the  circum- 
ference of  a  circle  are  equidistant  from  the  poles.  In  the  case  of  a  great  circle,  the  poles  are  90°  distant 
from  every  point  of  the  circle. 

Assuming  any  great  circle  as  a  primary,  all  great  circles  which  pass  through  its  poles  are  called  its 
secondaries.     All  secondaries  cut  the  primary  at  right  angles. 

Useful  Formll.e  Derived  from  Geometry. — In  these  formulae  the  following  abbreviations  are 
adopted: 

h,  base  of  triangle  or  parallelogram.  r,  radius  of  sphere  or  circle. 

h,  perpendicular  of  triangle  or  parallelogram.  d,  diameter  of  sphere  or  circle. 

/,  height  of  cylinder  or  cone.  A,  major  axis  of  ellipse. 

7t,  ratio  of  diameter  to  circumference  a,  minor  axis  of  ellipse. 

( =  3.141593).  s,  side  of  a  cube. 

Area  of  parallelogram  =  bxh. 

Area  of  triangle  =  ^  b  X  h. 

Area  of  any  right-lined  figure  =  sum  of  the  areas  of  the  triangles  into  which  it  is  divided. 

Sum  of  three  angles  of  any  triangle  =  180°. 

Circumference  of  circle  =  27tr,  or  Ttd. 

Area  of  circle  =  TCr',  or  —j-- 

Angle  subtended  by  arc  equal  to  radius  =  57°. 29578. 

Volume  of  sphere  =  -^  • 

Surface  of  sphere  =  7td\  or  47rr*. 

Area  of  ellipse  =  — r — 

Volume  of  cube  =  s*. 

Volume  of  cylinder  =  Area  of  base  X  I- 

Volume  of  pyramid  or  cone  =  Area  of  base  X  "3  • 


182 


EULES    AND   PRINCIPLES    OF   MATHEMATICS. 


TRIGONOMETRIC  FUNCTIONS. 

The  trigonometric  functions  of  the  angle  formed  by  any  two  lines 
are  the  ratios  existing  between  the  sides  of  a  right  triangle  formed  by 
letting  fall  a  perpendicular  from  any  point  in  one  line  upon  the 
other  line;  no  matter  what  point  is  chosen  for  the  perpendicular 
nor  which  line,  the  ratios,  and  therefore  the  respective  functions, 
will  be  the  same  for  any  given  angle. 

Let  ABC  (lig.  66)  be  a  plane  right  triangle  in  which  C  is  the 
right  angle;  A  and  B,  the  other  angles;  c,  the  hypotenuse;  a  and 
b  the  sides  opposite  the  angles  A  and  B,  respectively.  In  considering 
the  functions  of  the  angle  A,  its  opposite  side,  a,  is  regarded  as  the 
perpendicular  and  adjacent  side,  b,  as  the  base;  for  the  angle  B,  b  is 
the  perpendicular  and  a  the  base.  Then  the  various  ratios  are 
designated  as  follows: 

perpendicular   .       „    ,  ^,       .        ,        ,     .      ,  , 
hypotenuse  '  ^^  called  the  sine  of  angle  A,  abbreviated  sin  A; 

hvpotenuse'  ^^  called  the  cosine  of  angle  A,  abbreviated  cos  A; 

])erpendicular   .       ,,    ,    , 

is  called  the  tangent  of  the  angle  A,  abbreviated  tan  A; 


base 
base 


is  called  the  cotangent  of  the  angle  A,  abbreviated  cot  A; 


a 

c' 

b 

a 

v 
b 

a' 
c 

F 

c^ 

a' 

1- 

1  —  sine  A,  is  called  the  co-versed  sine  of  A,  abbreviated  covers  A. 

The  following  relations  may  be  seen  to  exist  between  the  various  functions: 

c  . 

=  -  =  cosec  A; 


>  is  called  the  secant  of  the  angle  A,  abbreviated  sec  A; 


perpendicular' 

hypotenuse 

base 

hvpotenuse      .       ,,    ,    ,  ,   ,  ,     .      ,  ,        .       , 

or  rtprnendicular'  ^^  called  the  cosecant  of  the  angle  A,  abbreviated  cosec  A; 

cosine  A,  is  called  the  versed  sine  of  A,  abbreviated  vers  A. 


=  1 


cosA  =  l-^7=ft=^^«^' 

!HLA^£_ii  =  «=tanA. 
cos  A       c    '   c       h 


Hence  the  cosecant  is  the  reciprocal  of  the  sine,  the  secant  is  the  reciprocal  of  the  cosine,  the  cotan- 
gent is  the  reciprocal  of  the  tangent,  and  the  tangent  equals  the  sine  divided  by  the  cosine. 

The  complement  of  an  angle  is  equal  to  90°  minus  that  angle,  and  thus  in  the  triangle  ABC  the 
angle  B  is  the  complement  of  A.     The  supplement  is  equal  to  180°  minus  the  angle. 

From  the  triangle  ABC,  regarding  the  angle  B,  we  have: 

8inB=  — =  cosA; 
tan  B  =     =  cot  A ; 


sec  B  =  —  =  cosec  A. 


RULES    AND    PRINCIPLES    OF    MATHEMATICS. 


183 


Fig.  67. 


Hence  it  may  be  seen  that  the  sine  of  an  angle  is  the  cosine  of  the  complement  of  that  angle;  the 
tangent  of  an  angle  is  the  cotangent  of  its  complement,  a 

and  the  secant  of  an  angle  is  the  cosecant  of  its  com- 
plement. 

The  functions  of  angles  vary  in  sign  according  to 
the  quadrant  in  which  the  angles  are  located. 

Let  AA^  and  BB^  (fig.  67)  be  two  lines  at  right 
angles  intersecting  at  the  point  O,  and  let  that  point 
be  the  center  about  Avhich  a  radius  revolves  from  an 
initial  position  OB,  successively  passing  the  points 
A,  B',  A'.  In  considering  the  angle  made  bv  this 
radius  at  any  position,  P^  P^^  V'^',  V'^,  with  the  line  , 
OB,  its  position  of  origin,  the  functions  will  depend  * 
upon  the  ratios  existing  between  the  sides  of  a  right 
triangle  whose  base,  h,  will  always  lie  within  BB,^ 
and  whose  perpendicular,  a,  will  always  be  parallel  to 
AA/',  while  its  hypotenuse,  c  (of  a  constant  length 
equal  to  that  of  the  radius),  will  depend  upon  tlie 
position  occupied  by  the  radius.  Now,  if  OB  and  OA 
be  regarded  as  the  positive  directions  of  the  base  and 
perpendicular,  respectively,  and  OB^  and  OA^  as  their 
negative  directions,  the  sign  of  the  hypotenuse  being 
always  positive,  the  sign  of  any  function  may  be  deter- 
mine'd  by  the  signs  of  the  sides  of  the  triangle  upon 
which  it  depends. 

For  example,  the  sine  of  the  angle  P^'OB  is  -,  and  since  a  is  positive  the  quantity  has  a  positive 

value;  its  cosine  is  -,  and  as  h  is  measure<l  in  a  negative  direction  from  O  the  cosine  must  therefore  be 

negative. 

In  the  first  quadrant,  between  0°  and  90°,  all  quantities  being  positive,  all  functions  will  also  be 
positive. 

In  the  second  quadrant,  between  90°  and  180°,  sin  A  f  =    J  is  positive;  cos  A  {  =--  \  has  a  nega- 

.tive  value  Wuse  ,,  i,  negative;  ,a„  A  (=|)  «  al»  negative  because  of  ..    The  cosea>nt,  recant,  and 

cotangent  have,  as  in  all  cases,  the  same  signs  as  the  sine,  cosine,  and  tangent,  respectively,  being  the 
reciprocals  of  those  quantities. 

In  the  third  quadrant,  between  180°  and  270°,  sin  A  {  =-  J  and  cos  A  f  =7  J  are  both  negative, 
because  both  d  and  h  have  negative  values;  tan  A  f  =r  )  is  positive  for  the  same  reason. 

In  the  fourth  quadrant,  between  270°  and  360°,  sin  A  f  =^  )  is  negative,  cos  A  f  =-  J  is  positive, 

and  tan  A  f  =r  J  is  also  negative. 

From  a  consideration  of  the  signs  in  the  manner  that  has  been  indicated  the  following  relations 
will  appear: 

sin  A  =  sin  (180°-A)  =  -sin  (180° +A)  =  — sin  (360° -A). 

cos  A  =  — cos  (180°— A)  =  -co8  (180°  +  A)  =  co8  (360°— A). 

tan  A  =  - tan  (180° -A)  =  tan  (180°  + A)  =  — tan  (360° -A). 

sin  A  =  cos  (90°  — A)  =  - cos  (90°+A)  =  -cos  (270° -A)  =  cos  (270°+ A). 

Any  similar  relation  may  be  deduced  from  the  figure. 

It  is  of  great  importance  to  have  careful  regard  for  the  signs  of  the  functions  in  all  trigonometrical 
solutions. 

LOGARITHMS. 

In  order  to  abbreviate  the  tedious  operations  of  multiplication  and  division  with  large  numbers,  a 
series  of  numbers,  called  Logarithms,  was  invented  by  Lord  Napier,  by  means  of  which  the  operation  of 
multiplication  may  be  performed  by  addition,  and  that  of  division  by  subtraction.  Numbers  may  be 
involved  to  any  power  by  simple  multiplication  and  the  root  of  any  power  extracted  by  simple  division. 

In  Table  42  are  given  the  logarithms  of  all  numbers,  from  1  to  9999;  to  each  one  must  be  prefixed 
an  index,  with  a  period  or  dot  to  separate  it  from  the  other  part,  as  in  decimal  fractions;  the  numbers 
from  1  to  100  are  given  in  that  table  with  their  indices;  but  from  100  to  9999  the  index  is  left  out  for  the 
sake  of  brevity;  it  may  be  supplied,  however,  by  the  general  rule  that  the  index  of  the  logarithm  of  any 


184  RULES    AND   PRINCIPLES    OF   MATHEMATICS. 

integer  or  mixed  number  is  always  one  less  than  the  number  of  integral  places  in  the  natural  number. 
Thus,  the  index  of  the  logarithm  of  any  number  (integral  or  mixed)  l)etween  10  and  100  is  1;  from  100 
to  1000  it  is  2;  from  1000  to  10000  it  is  3,  etc. ;  the  method  of  finding  the  logarithms  from  this  table  will 
be  evident  from  the  rules  that  follow: 

To  find  the  logarithm  of  amj  number  less  than  100,  enter  the  first  page  of  the  table,  and  opposite  the 
given  number  will  be  found  the  logarithm  with  its  index  prefixed.  Thus,  opposite  71  is  1.85126,  which 
IS  its  logarithm. 

To  find  the  logarithm  of  any  number  between  100  and  1000,  find  the  given  number  in  the  left-hand  col-, 
umn  of  the  table  of  logarithms,  and  immediately  under  0  in  the  next  column  is  a  number,  to  which  must 
be  prefixed  the  number  2  as  an  index  (because  the  number  consists  of  three  places  of  figures),  and  the 
required  logarithm  willjae  found.  Thus,  if  the  logarithm  of  149  was  required,  this  number  being  found 
in  the  left-hand  column,  against  it,  in  the  column  marked  0  at  the  toj)  (or  bottom)  is  found  17319,  pre- 
fixing to  which  the  index  2,  we  have  the  logarithm  of  149,  2.17319. 

To  find  the  logarithtn  of  any  number  between  1000  and  10000,  find  the  three  left-hand  figures  of  the  given 
number  in  the  left-hand  column  of  the  table  of  logarithms,  opposite  to  which,  in  the  column  that  is 
marked  at  the  top  (or  bottom)  with  the  fourth  figure,  is  to  be  found  the  required  logarithm,  to  which 
must  be  prefixed  the  index  3,  because  the  number  contains  four  places  of  figures.  Thus,  if  the  logarithm 
of  1495  was  required,  opposite  to  149,  and  in  the  column  marked  5  at  the  top  (or  bottom)  is  17464,  to 
which  prefix  the  index  3,  and  we  have  the  logarithm,  3.17464. 

To  find  the  logarithm  of  any  number  above  10000,  find  the  first  three  figures  of  the  given  number  in  the 
left-hand  column  of  the  table,  and  the  fourth  figure  at  the  top  or  bottom,  and  takeout  the  corresponding 
logarithm  as  in  the  preceding  rule;  take  also  the  difference  between  this  logarithm  and  the  next  greater, 
and  multiply  it  by  the  remaining  figure  or  figures  of  the  number  whose  logarithm  is  sought,  pointing  off 
as  many  decimal  places  in  the  product  as  there  are  figures  in  the  multiplier.  To  facilitate  the  calcula- 
tion of  the  proportional  parts  several  small  tables  are  placed  in  the  margin,  which  give  the  correction 
corresponding  to  the  difference,  and  to  the  fifth  figure  of  the  proposed  number.  Thus,  if  the  logarithm 
of  14957  was  required,  opposite  to  149,  and  under  5,  is  17464;  the  difference  between  this  and  the  next 
greater  number,  17493,  is  29;  this  multiplied  by  7  (the  last  figure  of  the  given  number)  gives  203; 
pointing  off  the  right-hand  figure  gives  20.3  (or  20)  to  be  added  to  17464,  which  makes  17484;  to  this, 

Prefixing  the  index  4,  we  have  the  logarithm  sought,  4.17484.  This  correction,  20,  may  also  be  found 
y  inspection  in  the  small  table  in  the  margin,  marked  at  the  top  29;  opposite  to  the  fifth  figure  of  the 
number,  7,  in  the  left-hand  column,  is  the  corresponding  correction,  20,  in  the  right-hand  column. 

Again,  if  the  logarithm  of  1495738  was  required,  the  logarithm  corresponding  to  149  at  the  left,  and 
5  at  the  top,  is,  as  in  the  last  example,  17464;  the  difference  between  this  and  the  next  greater  is  29; 
multiplying  this  by  738  (the  given  number  excluding  the  first  four  figures)  gives  21402;  crossing  off  the 
three  right-hand  figures  of  this  product  (because  the  number  738  consists  of  three  figures),  we  have  the 
correction  21  to  be  added  to  17464;  and  the  index  to  be  prefixed  is  6,  because  the  given  number  consists 
of  7  places  of  figures;  therefore  the  required  logarithm  is  6.17485.  This  correction,  21,  may  be  found  as 
above,  by  means  of  the  marginal  table  marked  at  the  top  29,  taking  at  the  side  7.38  (or  7^  nearly),  to 
which  corresponds  21,  as  before. 

To  find  the  logarithm  of  any  mixed  decimal  number,  find  the  logarithm  of  the  number,  as  if  it  Avere 
an  integer,  by  the  preceding  rules,  to  which  prefix  the  index  of  the  integral  part  of  the  given  number. 
Thus,  if  the  logarithm  of  the  mixed  decimal  149.5738  was  required,  find  the  logarithm  of  1495738,  with- 
out noticing  the  decimal  point;  this,  in  the  last  example,  was  found  to  be  17485;  to  this  prefix  the  index 
2,  corresponding  to  the  integral  part  149;  the  logarithm  sought  will  therefore  be  2.17485. 

lb  find  the  logarithm  of  any  decimal  fraction  less  than  unity,  it  must  be  observed  that  the  index  of  the 
logarithm  of  any  number  less  than  unity  is  negative;  but,  to  avoid  the  mixture  of  positive  and  negative 
quantities,  it  is  common  to  borrow  10  in  the  index,  which,  in  most  cases,  may  afterwards  be  neglected 
in  summing  them  with  other  indices;  thus,  instead  of  writing  the  index  —  1  it  is  written  -|-9;  instead 
of  —  2  we  may  write  +  8;  and  so  on.  In  this  way  we  may  find  the  logarithm  of  any  decimal  fraction 
by  the  followmg  rule:  Find  the  logarithm  of  a  fraction  as  if  it  were  a  whole  number;  see  how  many 
ciphers  precede  the  first  figure  of  the  decimal  fraction,  subtract  that  number  from  9,  and  the  remainder 
will  be  the  index  of  the  given  fraction.  Thus  the  logarithm  of  0.0391  is  8.59218  —  10;  the  logarithm  of 
0.25  is  9.39794  —  10;  the  logarithm  of  0.0000025  is  4.39794  —  10,  etc.  In  most  cases  the  writing  of  —  10 
after-  the  logarithm  may  be  dispensed  with,  as  it  will  be  quite  apparent  whether  the  logarithm  has  a 
positive  or  a  negative  index. 

To  find  the  number  corresponding  to  any  logarithm,  seek  in  the  column  marked  0  at  top  and  bottom 
the  next  smallest  logarithm,  neglecting  the  index;  write  down  the  number  in  the  side  column  abreast 
which  this  is  found  and  this  will  give  the  first  three  figures  of  the  required  number;  carry  the  eye  along 
the  line  until  the  next  smallest  logarithm  to  the  given  one  is  found,  and  the  fourth  figure  of  the  required 
number  will  be  at  the  top  and  bottom  of  the  column  in  which  this  stands;  take  the  difference  between 
this  next  smallest  logarithm  and  the  next  larger  one  in  the  table,  and  also  the  difference  between  the 
next  smallest  logarithm  and  the  given  one;  entering  the  small  marginal  table  which  has  for  its  heading 
the  first-named  difference  and  finding  in  the  right-hand  column  of  that  table  the  last-named  difference, 
there  will  appear  abreast  the  latter,  in  the  left-hand  column,  the  fifth  figure  of  the  required  number. 
Where  it  is  desired  to  determine  figures  beyond  the  fifth  for  the  corresponding  number,  the  difference 
between  the  next  lower  logarithm  and  the  given  one  may  be  divided  by  the  difference  between  the 
next  lower  and  next  higher  ones,  and  the  quotient  (disregarding  the  decimal  point,  but  retaining  any 
ciphers  that  may  come  between  the  decimal  point  and  the  significant  figures)  will  be  the  fifth  and  suc- 
ceeding figures  of  the  number  sought.  Having  found  the  figures  of  the  corresponding  number,  point 
off  from  the  left  a  number  of  figures  which  shall  be  one  greater  than  the  index  number,  and  there  place 
a  decimal  point.  In  this  operation  of  placing  the  decimal  point,  proper  account  must  be  taken  oi  the 
negative  value  of  any  index. 

Thus,  if  the  number  corresponding  to  the  logarithm  1.52634  were  required,  find  52634  in  the  column 
marked  0  at  the  top  or  bottom,  and  opposite  to  it  is  336;  now,  the  index  being  1,  the  required  number 
must  consist  of  two  integral  places;  therefore  it  is  33.6. 


EULES    AND    PRINCIPLES    OF    MATHEMATICS. 


185 


If  the  number  corresponding  to  the  logarithm  2.57345  were  required,  look  in  the  column  0  and  find 
in  it,  against  the  number  374,  the  logarithm  57287,  and,  guiding  the  eye  along  that  line,  find  the  given 
logarithm,  57345,  in  the  column  marked  5;  therefore  the  mixed  number  sought  is  3745,  and  since  the 
index  is  2,  the  integral  part  must  consist  of  3  places;  therefore  the  number  sought  is  374.5.  If  the  index 
be  1  the  number  will  be  37.45,  and  if  the  index  be  0  the  numljer  Avill  be  3.745.  If  the  index  be  8, 
corresponding  to  a  number  less  than  unity,  the  number  will  be  0.03745. 

Again,  if  the  number  corresponding  to  the  logarithm  3.57811  were  required,  find,  against  878  and 
under  5,  the  logarithm  57807,  the  difference  between  this  and  the  next  greater  logarithm,  57818,  being 
11,  and  the  difference  between  57807  and  the  given  number,  57811,  being  4:  in  the  marginal  table  headed 
11,  find  in  the  right  hand  column  the  number  4,  and  abreast  the  latter  appears  the  figure  4,  which  is  the 
fifth  figure  of  the  required  number;  hence  the  figures  are  37854;  pointing  off  from  the  left  3  +  1  =  4 
places,  the  number  is  3785.4. 

If  the  given  logarithm  were  5.57811,  since  the  index  5  requires  that  there  shall  be  six  places  in  the 
whole  number,  it  is  desirable  to  seek  accuracy  to  the  sixth  figure.  The  logarithmic  part  being  the 
same  as  in  the  example  immediateh'  preceding,  it  is  found  as  before  that  the  first  four  figures  are  3785, 
the  difference  between  the  next  lower  and  next  greater  logarithms  is  11,  and  between  the  next  lower 
logarithm  and  the  given  one  is  4;  divide  4  by  11  and  the  quotient  is  .36;  drop  the  decimal  point,  annex 
and  point  off,  and  the  number  required  is  found  to  be  378536. 

It  may  be  remarked  that  in  using  five-place  logarithm  tables  it  is  not  generally  to  be  expected  that 
results  will  be  exact  beyond  the  fifth  figure. 

To  show,  at  one  view,  the  indices  corresponding  to  mixed  and  decimal  numbers,  the  following 
examples  are  given: 


Mired  number.  Logarithms. 

40943.0 Log.  4.61218 

4094.  3 Log.  3.  61 21 8 

409.  43 Log.  2.  61218 

40.943 Log.  1.61218 

4.  0943 Log.  0.  61218 


Decimal  nnmher.  Logarithms. 

0. 40943 Log.  9.  61218  — 10 

0.  040943 Log.  8. 6121 8  —  1 0 

0.  0040943 Log.  7.  61218  - 10 

0. 00040943 Log.  6.  61218  —  10 

0. 000040943 Log.  5.  61218  — 10 


To  perform  multiplicaiitm  hi/  logarithms,  add  the  logarithms  (jf  the  two  numbers  to  be  multiplied  and 
the  sum  will  be  the  logarithm  of  their  product. 


Example  I. 

Multiply  25  by  35. 

25 Log.  1.  39794 

35 Log.  1.54407 

Product,  875 Log.  2. 94201 

Example  II. 

Multiply  22.4  by  1.8. 

22.4 Log.  1.35025 

1.8 Log.  0. 25527 


Product,   40.32 Log.  1.60552 


Example  III. 

Multiply  3.26  by  0.0025. 

3.  26 Log.  0.  51322 

0.  0025 Log.  7.  39794 

Product,  0.  00815 Log.  7.  91 116 

Example  IV. 

Multiply  0.25  by  0.(X)3. 

0. 25 Log.  9.  39794 

0.  003 Log.  7.  47712 


Product,  0. 00075 Log.  6.  87506 


In  the  last  example,  the  sum  of  the  two  logarithms  is  really  16.87506  —  20;  this  is  the  same  as 
6.87506—  10,  or,  remembering  that  the  quantity  is  less  than  unity,  simply  6.87506. 

To  perform  divivon  hg  logarithms,  from  the  logarithm  of  the  dividend  subtract  the  logarithm  of  tlie 
divisor;  the  remainder  will  be  the  logarithm  of  the  quotient. 


Example  I. 

Divide  875  by  25. 

875 Log.  2.  94201 

25 Log.  1 .  39794 

Quotient,    35    Log.  1. 54407 

Example  II. 

Divide  40.32  by  22.4. 

40.32 Log.  1.60552 

22.4 Log.  1.35025 


Quotient,   1.8 Log.  0. 25527 


Example  III. 

Divide  0.00815  by  0.0025. 

0.00815 Log.  7.91116 

0.0025 .Log.  7.39794 

Quotient,  3.26 Log.  0.  51322 

Example  IV. 

Divide  0.00075  by  0.025. 

0.00075 Log.  6.87506 

0.025 Lop:.  8.  39794 


Quotient,  0.03 Log.  8.47712 


In  Example  III  both  the  divisor  and  dividend  are  fractions  less  than  unity,  and  the  divisor  is  the 
lesser;  consequently  the  quotient  is  greater  than  unity.  In  Example  IV  both  fractions  are  less  than 
unity;  and,  since  the  divisor  is  the  greater,  its  logarithm  is  greater  than  that  of  the  dividend;  forxthis 
reason  it  is  necessary  to  borrow  10  in  the  index  before  making  the  subtraction,  that  is,  to  regard  the 
logarithm  of  .00075  as  16.87506  —  20;  hence  the  quotient  is  less  than  unity. 


186 


RULES    AND    PRINCIPLES    OB'    MATHEMATICS. 


The  arithmetical  complement  of  a  l>gan.thm  is  the  difference  between  that  logarithm  and  the  loga- 
rithm of  unity  (10.00000— 10,  of  0.00000).  It  is  therefore  the  logarithm  of  unity  divided  by  that 
num]>er  which  is  the  reciprocal  of  the  number;  and,  since  the  effect  of  dividing  by  any  number  is  the 
same  as  that  of  multiplying  by  its  reciprocal,  it  follows  that,  in  performing  division  bv  logarithms,  we 
may  either  subtract  the  logarithm  of  the  divisor  or  add  the  arithmetical  complement  of  that  logarithm. 
As  the  addition  Of  a  number  of  quantities  can  be  performed  in  a  single  operation,  while  in  subtraction 
the  difference  between  only  two  quantities  can  lie  taken  at  a  time,  it  is  frequently  a  convenience  to  deai 
with  the  arithmetical  complements  rather  than  with  the  logarithms  themselves. 


Example  I. 
Divide  875  by  25. 

875 Log.  2.  94201 

25 Log.  1.39794.... Colog.  8.60206 


Quotient,  85 Log.  1.54407 

Ex.\MPI.E   II. 

Divide  0.00075  by  0.025. 

0.00075 Log.  6.  87506 

0.025 Log.  8.39794 Colog.  1.60206 


Ex.\MPLE   III. 

Simplifv  the  expression,  40.32  X  .00815 
*      ■  ^  '     22.4  X. 0025 

40.32 Log.  1.  60552 

.00815 Log.  7.91116 

22.4 Log.  1.35025 Colog.  8.64975 

.0025 Log.  7.39794 Colog.  2.60206 


Result,  5.868 Log.  0.76849 


Quotient,  0.03 Log.  8.47712 

To  perform  involution  by  logarithms,  maltiply  the  logarithm  of  the  given  number  by  the  index  of  the 
power  to  which  the  quantity  is  to  be  raised;  the  product  will  be  the  logarithm  of  the  power  sought. 


Example  I. 
Required  the  square  of  18. 

18 Log.  1.25527 

2 


Answer,  324 Log.  2.51054 

Example  II. 

Required  the  square  of  6.4. 

6.4 Log.  0.80618 

2 


Answer,  40.96 Log.  1.  61236 


Example  III. 
Required  the  cube  of  13. 

13 Log.  1.11394 

3 


Answer,  2197 Log.  3.34182 

Example  IV. 

Required  the  cube  of  0.25. 

0.25 Log.  9.39794 

3 


Answer,  0.015625 Log.  8. 19382 


In  the  last  example,  the  full  product  of  the  multiplication  of  9.39794—10  by  3  is  28.19382—30,  Avhich 
is  equivalent  to  8.19382—10. 

To  perform  evolution  by  logarithms  divide  the  logarithm  of  the  number  by  the  index  of  the  power; 
the  quotient  will  be  the  logarithm  of  the  root  sought.  If  the  number  whose  root  is  to  be  extracted  is  a 
decimal  fraction  less  than  unity,  increase  the  index  of  its  logarithm  by  adding  a  number  of  tens  which 
shall  Ije  less  by  one  than  the  index  of  the  power  before  making  the  division. 


Example  I. 

Required  the  square  root  of  324. 
324 Log.  2)  2.  51055 


Answer,  18 Log.      1,25527 

Example  II. 

Required  the  cube  root  of  2197. 
2197 Log.3)3.34183 


Answer,     13 Log.       1.11394 


Example  III. 

Required  the  square  root  of  40.96. 

40.96 Log.2)  1.61236 


Answer,  6.4 Log.      0.80618 

Example  IV. 

Required  the  cube  root  of  0.015625. 

0.015625 Log.        8.19382 

Add  20  to  the  index 3)28. 19382 

Answer,  0.25 Log.       9.  39794 


In  the  last  example  the  logarithm  8.19382—10  was  converted  into  its  equivalent  form  of  28.19382— 30i 
which,  divided  by  3,  gives  9.39794—10. 

To  find  the  loganthm  of  any  function  of  an  angle,  Table  44  must  be  employed.  This  table  is  so 
arrangeJl  that  on  every  page  there  appear  the  logarithms  of  all  the  functions  of  a  certain  angle  A, 
together  with  those  of  the  angles  90°— A,  90°  + A,  and  180°— A;  thus  on  each  page  may  be  found  the 
logarithms  of  the  functions  of  four  different  angles.  The  number  of  degrees  in  the  respective  angles 
are  printed  in  bold-faced  type,  one  in  each  corner  of  the  page;  the  number  of  minutes  corresponding 
appear  in  one  column  at  the  left  of  the  i)age  and  another  at  the  right;   the  names  of  the  functions 


RULES    AND    PRINCIPLES    OF    MATHEMATICS.  187 

to  which  the  various  logarithms  correspond  are  printed  at  the  top  and  bottom  of  the  columns.  The 
invarial)le  rule  must  be  to  take  the  name  of  the  function  from  the  top  or  the  bottom  of  the  page, 
according  as  the  number  of  degrees  of  the  given  angle  is  found  at  the  top  or  bottom;  and  to  take  the 
minutes  from  the  right  or  left  hand  column,  according  as  the  number  of  degrees  is  found  at  the 
right  or  left  hand  side  of  the  page;  or,  more  briefly,  take  names  of  functions  and  number  of  minutes, 
respectively,  from  the  line  and  column  nearest  in  position  to  the  number  of  degrees. 

Taking,  as  an  example,  the  thirty-first  page  of  the  table,  it  will  be  found  that  30°  appears  at  the 
upper  left-hand  corner,  149°  at  the  upper  right-hand,  59°  at  the  lower  right-hand,  and  120°  at  the  lower 
left-hand  corner.  Suppose  that  it  is  desired  to  find  the  log.  sine  of  30°  10';  following  the  rule  given,  we 
find  10'  in  the  left-hand  column  and  Sine  at  the  top  of  the  page,  and  abreast  one  and  below  the  other  is 
the  required  logarithm,  9.70115.  But  if  the  log.  sine  of  59°  10'  were  sought,  as  59°  appears  below  and  at 
the  right  of  the  page,  the  logarithm  9.93382  would  be  taken  from  the  column  marked  Sine  at  the  bottom 
and  abreast  10'  on  the  right.  It  may  also  be  seen  that  log.  sin  30°  10'=log.  cos  59°  50'=log.  cos 
120°  10'=log.  sinl49°  50'=9.70115,theequality  of  the  functions  agreeingwith  trigonometrical  deductions; 
(in  this  statement  numerical  values  only  are  regarded,  and  not  signs;  the  latter  must,  of  course,  be  taken 
into  account  in  all  operations). 


Example  I. 

Required  the  log.  sine,  cosecant,  tangent,  cotan- 
gent, secant,  and  cosine  of  28°  37'. 

Log.  sin  9.  68029  Log.  cot  10.  26313 
Log.  cosec  10.  31971  Log.  sec  10.  05658 
Log.  tan       9.  73687        Log.  cos    9. 94342 


E.XAMPLE   II. 

Required  the  log.  sine,  cosecant,  tangent,  cotan- 
gent, secant,  and  cosine  of  75°  42'. 

Log.  sin  9. 98633  Log.  cot  9. 40636 
Log.  cosec  10. 01367  Log.  sec  10.  60730 
Log.  tan     10. 59364        Log.  cos     9. 39270 

When  the  angle  of  which  the  logarithmic  function  is  required  is  given  to  seconds,  it  becomes 
necessary  to  interpolate  between  the  logarithms  given  for  the  even  minutes  next  below  and  next  above; 
this  may  be  done  either  by  computation  or  (except  in  a  few  cases)  by  inspection  of  the  table. 

To  interpolate  by  computation,  let  n  represent  the  number  of  seconds,  D  the  difference  between  the 
logarithms  of  the  next  less  and  next  greater  even  minute,  and  d  the  difference  between  the  logarithm 
of  the  next  less  even  minute  and  that  of  the  required  angle.     Then, 

It  should  be  noted  when  the  number  of  seconds  is  30,  20,  15,  or  some  similar  nimiber,  permitting 
the  reduction  of  the  fraction  w^  to  a  simple  value,  such  as  i,  J,  J,  as  the  interpolation  by  this  method 

may  thus  be  made  with  greater  facility. 

Having  obtained  the  difference  of  the  logarithm  from  that  of  the  next  lower  even  minute,  it  must 
be  applied  in  the  proper  direction — that  is,  if  the  function  is  such  that  its  logarithm  increases  as  the 
angle  increases,  the  logarithmic  difference  must  be  added;  but  if  it  decreases,  then  that  difference  must 
be  subtracted. 

For  example,  let  it  be  required  to  find  the  log.  sin  and  log.  cosec  of  30°  10'  19".  The  log.  sin  of 
30°  10'  is  9.70115;  the  difference  between  this  logarithm  and  that  of  the  sine  of  30°  11'  (9.70137)  is  +  22, 
which  is  D.     Hence, 

d  =  ^X(  +  22)  =  -|-7; 

and  the  required  logarithm  is  9.70122.     The  log.  cosec  of  30°  10'  is  10.29885;  the  difference,  D,  between 
that  and  log.  sin  30°  11'  (10.29863)  is  —  22.     In  this  case 

rf  =  Wx(-22)  =  --; 

therefore,  log.  cosec  30°  11'  19"  =  10.29878. 

The  method  of  interpolating  by  inspection  consists  in  entering  that  column  marked  "Diff."  which 
ia  adjacent  to  the  one  from  which  the  logarithmic  function  for  the  next  lower  minute  is  taken,  and 
finding,  abreast  the  number  in  the  left-hand  minute  column  which  corresponds  to  the  seconds,  the 
required  logarithmic  difference;  and  the  latter  is  to  be  added  or  subtracted  according  as  the  logarithms 
increase  or  decrease  with  an  increa.sed  angle.  Thus,  if  it  be  required  to  find  log.  sin  30°  10'  19",  find  as 
before  log.  sin  30°  10'  =  9.70115;  then,  in  the  adjacent  column  headed  "Diff."  and  abreast  the  number 
of  seconds,  19,  in  the  left-hand  minute  column  will  be  found  7,  the  logarithmic  difference;  add  this,  as 
the  function  is  increasing,  and  we  have  the  required  logarithm  9.70122.  If  log.  cosec  30°  10'  19"  be 
sought,  find  log.  cosec  30°  10'  =  10.29885;  then  in  the  adjacent  difference  column,  which  is  the  same  as 
was  used  for  the  sines,  find  as  before  the  logarithmic  difference,  7;  and  since  this  function  decreases  as 
the  angle  increases,  this  must  be  subtracted;  therefore,  log.  cosec  30°  10'  19"  =  10.29878. 

This  method  of  interpolation  by  inspection  is  not  available  in  that  portion  of  the  table  where  the 
logarithmic  differences  vary  so  rapidly  that  no  values  will  apply  alike  to  all  the  angles  on  the  same 
page;  on  such  pages  the  difference  for  one  minute  is  given  in  a  column  headed  "Diff.  1',"  instead  of 
the  usual  difference  for  each  second;  in  this  case,  the  interpolation  must  be  made  by  computation,  the 
given  difference  for  one  minute  being  D.  In  other  parts  of  the  table  the  interpolation  by  inspection 
may  be  liable  to  slight  error  because  of  the  variation  in  logarithmic  difference  for  different  angles  on 
the  same  page;  but  the  tabulated  values  are  sufficiently  accurate  for  the  usual  calculations  in  navigation. 

It  will  be  evident  that  while  the  methods  explained  have  contemplated  entering  the  tables  with  a 
smaller  angle  and  interpolating  ahead,  it  would  be  equally  correct  to  enter  with  a  greater  angle  and 
interjwlate  hack  for  the  proper  number  of  minutes,  making  the  requisite  change  in  the  sign  of  the 
correction. 


188 


RULES    AND    PRINCIPLES    OF   MATHEMATICS. 


Example  I. 

Required  the  log.  sine,  cosine,  and  tangent  of 
42°  57'  06'''. 


For  42°  57 


For  42°  57'  06". 


Log.  sin 
Log.  cos 
Log.  tan 


9.83338  I 

9.86448 

9.96890 


9. 83339 
9. 86447 
9. 96893 


EXAMIM.H    II. 

Required  the  log.  secant,  cosecant,  and  cotangent 
of  175°  32'  36". 


For  175°  32' 


For  175°  32'  36" 


Log.  sec 
Log.  cosec 
Log.  cot 


10. 00132 
11. 10858 
11. 10726 


-  1 

+97 
4^8 


10.  00131 
11. 10955 
11. 10824 


It  should  be  observed  that,  for  uniformity  and  convenience,  all  logarithms  given  in  Table  44  have 
been  increased  by  10  in  the  index,  and  it  is  understood  that  —10  ought  properly  to  be  written  after 
each;  thus  all  logarithms  under  10.00000  represent  functions  whose  value  is  less  than  unity,  and  all 
over  10.00000  those  greater  than  unity;  for  example,  11.10726  is  the  logarithm  of  a  number  in  which 
the  decimal  point  should  be  placed  after  the  second  figure  from  the  left. 

To  find  the  angle  corresponding  to  anij  logarithmic  function,  the  process  is  the  reverse  of  the  one  just 
described.  Find,  in  the  column  marked  with  the  name  of  the  function,  either  at  top  or  bottom,  the 
two  logarithms  between  which  the  given  one  falls;  write  down  the  degrees  and  minutes  of  the  lesser  of 
the  two  corresponding  angles,  which  will  be  the  degrees  and  minutes  of  the  angle  required.  Call  the 
difference  between  the  two  tabulated  logarithms  D,  and  the  difference  between  the  given  logarithm  and 
that  which  corresponds  to  the  lesser  angle,  d;  then  if  n  represent  the  number  of  seconds,  we  have: 

n  =  p  X  60. 

Or,  the  same  may  be  obtained  by  inspection  (except  where,  as  before  explained,  the  differences 
for  seconds  are  not  tabulated)  byfinding,  in  the  "Diff."  column  adjacent  to  that  from  which  the  logarithm 
was  taken,  the  logarithmic  difference,  d,  and  noting  the  number  of  seconds  abreast  which  it  stands  in 
the  left-hand  minute  column. 

Interpolation  may  be  also  made  in  the  reverse  direction  from  the  next  greater  even  minute. 

Thus,  if  it  be  required  to  find  the  angle  corresponding  to  log.  sin  9.61400,  we  find  log.  sin  24°  16', 
9.61382,  and  log.  sin  24°  17',  9.61411;  hence  D  =  29,  and  d  =  18; 


18       ,^ 
n  =  29  X  60 


37; 


and  the  angle  is  24°  16'  37".  Or,  in  adjacent  column  headed  "Diff.,"  18  would  be  found  abreast  38, 
39,  or  40  (seconds)  in  the  left-hand  minute  column — a  correspondence  sufficiently  close  for  navigation 
work. 

If  the  angle  were  known  to  be  in  the  second  quadrant,  we  find  log.  sin  155°  43',  9.61411,  and  log. 
sin  155°  44',  9.61382;  here,  D  =  29,  and  d  =  11 ; 

n  =  29  X  60  =  23; 

therefore,  the  angle  is  155°  43'  23".     Or,  in  adjacent  "Diff."  column  find,  abreast  11,  23  or  24  seconds. 

Example  I.  Example  II. 


Find  angles  less  than  90°  corresponding  to  log. 
cot  10..3.3621,  log.  sec  10.11579,  and  log.  cos  8.70542. 


Log.  cot  10. 33621  24  45 
Log.  sec  10. 11579  40  00 
Log.  cos  8. 70542  87  05 


4 
116 


15 
22 

28 


Find  angles  in  second  quadrant  corresponding  to 
log.  tan  10.15593,  log.  sin  8.87926,  and  log.  cosec 
10.04944. 


Log.  tan  10. 15593 
Log.  sin  8. 87926 
Log.  cosec  10. 04944 


0 

' 

d 

II 

124 

55 

19 

42 

175 

39 

69 

25 

116 

49 

3 

27 

The  Hour  Columns  in  Table  44  give  the  measure  in  time  corresponding  to  twice  the  angular  distance 
given  in  arc.  Thus,  abreast  the  angle  13°  00'  stands  in  the  P.  M.  column  l""  44"  00",  corresponding  in 
time  to  2  X 13°  00',  and  in  the  A.  M.  column  lO*"  16™  00%  which  is  the  same  subtracted  from  12\  These 
columns  are  of  use  in  working  the  various  formula?  which  involve  functions  of  half  the  hour  angle. 
Interpolation  for  values  intermediate  to  those  given  in  the  tables  is  made  on  the  same  principle  as  for 
the  angular  measure;  this  operation  may  be  performed  by  inspection  by  the  use  of  the  small  tables  at 
the  bottom  of  each  page,  where  n,  the  number  of  seconds  of  time,  is  given  in  bold-faced  type,  and  (/,  the 
logarithmic  difference  for  the  respective  columns,  appears  below. 


Example  I. 

Given  t=V'  48'"  44%  find  log.  cot  J  t. 

For  1"  48'°  40",  log.  cot.  i  t  10. 61687 

Diff.  for  4%  Col.  B,  -  28 


For  1"  48'»  44', 


log.  cot  J  t     10.  61659 


Example  II. 

Given  log.  sin  §  t  9.91394,  find  the  Hour  A.  M. 
corresponding. 

For  9.91389,  4''39'°12» 

Diff.  for  5,  Col.  C,  -  5 


For  9.91394, 


4  39  07 


RULES    AND    PRINCIPLES    OF   MATHEMATICS. 


189 


jytlSCELLANEOUS  TJSEFTJL  DATA. 

Earth's  Polar  radius =6, 356, 583. 8  meters. 
Earth's  Equatorial  radius=6,378,206.4  meters. 

Earth's  Compression  =  ^qq  Anh- 

Earth's  Eccentricity  =^0.0824846 

Number  of  feet  in  one  statute  mile=5280 

Number  of  feet  in  one  nautical  mile=6080.27 

Sine  of  1^^=0.00000485 

Sine  of  1^=0.00029089 

The  Napierian  base  £=2.7182818 

The  modulus  of  common  logarithms=0. 4342945 

French  meter  in  Enplish  feet,  3.28087 

French  meter  in  En-^lish  statute  miles,  0.00062138 

French  meter  in  nautical  miles,  0.00053959 

1  pound  Avoirdupois=7,000  grains  Troy. 

French  gramme=0.00220606  Imperial  pound  Troy. 

French  kilogramme=0.0196969  English  cwts. 

Cubic  inch  of  distilled  water,  in  grains =252. 458. 

Cubic  foot  of  water,  in  ounces  Troy =908. 8488. 

Cubic  foot  of  water,  in  pounds  Troy=75.7374. 

Cubic  foot  of  water,  in  ounces  Avoirdupois=997. 1366691. 

Cubic  foot  of  water,  in  pounds  Avoirdupois =62. 3210606.  J 

Length  of  pendulum  which  vibrates  second  at  Greenwich,  39.1393  inches. 


log  8. 9163666. 
log  3.  7226339. 
log  3.  7839232. 
log  4. 6855749. 
log  6. 4637261. 
log  0. 4342945. 
log  9.  6377843. 
log  0. 5159890. 
log  6.  7933560. 
log  6.  7320620. 


Bar.  30.00  in. ;  ther.  62°  F. 


APPENDIX  IV. 
MARITIME  POSITIONS  AND  TIDAL  DATA. 


The  following  table  contains  the  latitude  and  longitude  of  a  large  number  of  places,  together  with 
lunitidal  intervals  and  tidal  ranges  at  the  more  important  ones.  It  is  arranged  geographically  and 
followed  by  an  alphabetical  index. 

The  geographical  position  generally  relates  to  some  specified  exact  location,  and  is  based  upon  the 
best  available  authority.  The  tidal  data  relate  to  the  waters  adjacent  to  the  point  whose  latitude 
and  longitude  are  given,  being  abstracted  from  the  Tide  Tables  published  by  the  United  States  Coast  and 
Geodetic  Survey  for  the  year  1903. 

The  high  water  and  low  water  lunitidal  intervals  represent  the  mean  intervals  between  the  moon's 
transit  and  the  time  of  next  succeeding  high  and  low  waters  throughout  a  lunar  month.  The  spring 
and  neap  ranges  are  the  differences  in  height  between  high  water  and  low  water  at  spring  and  at  neap 
tides.  For  those  places  where  the  tide  is  chiefly  of  a  diurnal  type,  and  where  there  is  usually  but  one 
high  and  one  low  water  during  a  lunar  day,  the  tidal  values  are  bracketed;  in  such  cases  the  lunitidal 
intervals  are  for  the  semi-diurnal  part  of  the  tide  ( which,  however,  is  only  appreciable  for  a  few  days  when 
the  moon  is  near  the  equator),  and  the  range  given  in  the  column  headed  "Spg."  does  not,  as  in  other 
cases,  apply  to  the  spring  tide,  but  to  the  greatest  periodic  daily  range,  which  usually  occurs  a  day  or 
two  after  the  moon  attains  its  extreme  of  declination,  and  is  therefore  near  one  of  the  tropics.  As  those 
places  where  the  diurnal  type  predominates  seldom  experience  large  tidal  effects,  the  general  data 
furnished  regarding  such  tides  will  suffice  for  the  ordinary  purpose  of  the  navigator.  The  method 
of  finding  the  time  of  high  or  low  water  from  this  table  is  illustrated  in  article  507,  Chapter  XX. 

190 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA. 


[Page  191 


Place. 


Salisbury  Island:  E.  pt 

Nottingham  Island :  S.  ]  )t 

Digges  Island :  W.  extreme 

Cape  AVostenholme 

Charles  Island:  E.  pt 

w.  pt :.... 

Cape  Weggs 

Prince  of  Wales  Sound :  Center  of  ent 

Cape  of  Hopes  Advance 

Akpatok  Island:  E.  pt 

Green  Island :  NE.  pt 

Button  Islands:  N.  pt 

Cape  Chidleigh 

Resolution  Island:  S.  pt.,  Hutton  h'dl'd 
E.  pt.,  C.  Resolution 

Black  Head 

Eclipse  Harbor:  E.  side 

Nachvack  Bay:  Islands  off  entrance 

Saddle  Island 

Port  Man  vers :  Entrance 

Nain:  Church 

Hopedale  Harbor:  Hill  to  E'd 

Aillick  Harbor:  Cape  Mokkivik 

Cape  Harrison :  N.  extreme 

Indian  Harbor:  Obs 

Outer  Gannet  Island:  Summit 

Gready  Harbor 

Cartwright  Harbor:  Caribou  Castle 

Indian  Tickle :  Summit 

Roundhill  Island :  Summit 

Occasional  Harbor:  E.  summit  of  Twin  I. 

Cape  St.  Lewis:  SE.  pt 

Battle  Islands:  NE.  extreme,  SE.  I 

Table  Head 

Belle  Isle;  Light-house 

Cape  Bauld :  Light-house 

Bell  Island :  S.  end 

Cape  St.  John:  Gull  Island  light 

Tilt  Cove,  L^nion  Copper 

Mine 

Funk  Island:  Summit 

Offer  Wadham :  Light-house 

Toulinguet  Islands:  Light-house 

Seldom-come-by  Harbor:  Shiphill 

Cape  Freels :  Gull  I 

Greenspond  Island 

Cape  Bonavista:  Light-house 

Catalina  Harbor:  Green  I.  light-house  .. 

Bonaventure  Head 

Hearts  Content:  Light-house 

Baccalieu  Island :  Light-house 

Harbor  Grace:  Light-house  on  beach 

Cape  St.  Francis:  Light-house 

St.  Johns  Harbor:  Chain  Rock  Battery.. 

Cape  Race:  Light-house 

Cape  Pine:  Light-house 

Trepassey  Harbor:  Shingle  Neck 

Cape  St.  Mary :  Light- house 

Little  Placentia  Harbor:  W.  side  Coopers 

Cove 

Burin  Island :  Light-house 

Laun :  Gr.  Laun  R.  C.  Church 

St.  Pierre:  U.  S.  Coast  Survey  Station .. . 
Brunet  Island:  Mercers  Hd.  light-house. 
Boar  Islands:  Burgeo  I.  lijiht-house 


Lat.  N. 

Long.  W. 

Liin. 

Int. 

Range. 

H.W. 

L.  W. 

Spg. 

Neap. 

o   /    // 

63  27  00 

O     /     II 

76  30  00 

77  50  00 

78  08  00 
77  33  00 

74  00  00 

75  20  00 
74  03  00 
72  25  00 
70  02  00 
67  05  00 
67  50  00 
64  40  00 

64  12  00 

65  00  00 
64  30  00 
64  28  00 
64  07  15 
63  20  00 

61  20  00 

62  07  00 
61  40  13 
60  12  34 
59  08  01 
57  56  40 
57  12  40 
56  31  31 
56  23  00 
56  59  50 
55  58  39 
55  35  48 
55  44  29 
55  38  08 
55  32  20 
55  41  00 

55  22  10 

55  25  12 
55  35  30 
55  21  33 

55  37  17 
53  10  56 

53  45  00 

54  47  35 
54  12  00 
53  25  12 
53  37  45 
53  04  42 
53  02  40 
53  23  35 
53  23  20 

52  47  42 

53  08  11 
52  47  20 

52  40  54 

53  04  30 
53  31  55 

53  22  10 

54  11  42 

53  58  43 

55  08  49 

55  32  00 

56  10  36 
55  51  40 

57  36  52 

h.    m. 

h.    m. 

ft. 

ft. 

63  06  00 
62  37  00 

8  58 

2   46 

13.5 

6.1 

62  35  00 

62  48  00 

62  50  00 

62  30  00 

62  07  00 

61  18  00 

60  10  00 

60  40  00 
60  52  00 

60  33  00 

61  21  00 
61  40  00 
60  00  00 
59  48  00 
59  07  00 
57  35  00 



' 

i 

8  00 
7  00 

1  48 
0  48 

5.0 
5.2 

2.0 
2.1 

57  00  00 

1      ; 

56  32  45 
55  27  04 
55  13  33 

7.00 
5  30 

0  48 
11  43 

6.5 
6.9 

3.0 
3.2 

54  55  50 

t 1 

54  26  55 
54  00  05 

6  10 

12  23 

7.0 

3.2 

53  oO  00 

53  42  37 

53  34  25 
53  26  00 
52  40  07 
52  21  16 
52  15  36 
52  06  00 

51  53  00 

51  38  48 
50  42  10 
49  59  54 

49  53  00 

6  27 

0  15 

6.0 

2.8 

6  38 
6  30 

0  26 
0  18 

5.0 
3.5 

2.3 
L6 

1 

'            i 

1     ' 

49  45  29 

1 

49  35  40 

1 

49  41  20 

;      1 

49  36  50 

49  15  20 
49  04  20 
48  42  01 
48  30  15 
48  16  55 

47  53  10 

48  08  58 
47  42  45 
47  48  30 
47  34  02 
46  39  24 
46  37  04 
46  43  20 

46  49  34 

47  17  55 
47  00  26 
46  56  30 

46  46  51 

47  15  30 
47  35  13 

i      1     1 

1      ; 

7  23 

1  11 

4.1 

1.9 

7  15 

1  03 

3.3 

r.5 

7  12 
6  50 

1  01 
0  38 

3.3 
6.5 

1.5 
3.0 

6  50 

8  20 

0  38 
2  08 

6.6 
7.2 

3.1 
3.3 

8  05 

8  23 

1  8  53 

8  22 

1  53 

2  11 
2  41 
2  10 

7.0 
6.6 
6.5 
6.2 

3.2 
3.1 
3.0 
2.9 

Page  192]  APPENDIX  IV. 

MAKITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


al 


0 


Place. 


Lat.  N. 


LaPoileBay:  (ir.  Espic  Church 

Cape  Ray :  Light-house 

Codrov  island:  S.  side  Boat  Harbor ' 

Cape  St.  George:  Red  I.,  SE.  pt 

Cow  Head :  N W.  extreme ' 

Port  Saunders:  NE.  point  of  entry 

Rich  Point:  Light-house j 

Ferolle  Point:  Cove  Point,  NE.  extreme  J 

Flower  Cove:  Capstan  Pt ' 

Green  Island:  150  fms.  from  NE.  end  . . .| 
Cape  Norman :  Light-house I 

Chateau  Bay:  S.  pt.  Castle  I 

Amour  Point :  Light-house | 

Wood  Island:  S.  pt ; 

Greenly  Island :  Light-house 

Bradore  Bav :  Obs.  Spot,  Jones  Pt i 

Old  Fort  Island :  Center 

Great  Mecatina  Island :  SE  pt 

Mecatina  Harbor:  S.  point  of  Dead  Cove. 
Little  Mecatina  I. :  S.  pt.  C.  McKinnon. . 

St.  INIary  Reefs 

South  Makers  Ledge 


Cape  Whittle , 

Natashquan  Point :  S.  edge , 

Clearwater  Point:  SW.  extreme. 

Carousel  Island:  Light-house 

Point  de  Monts:  Light-house 

Quebec:  Mann's  Bastion,  Citadel. 

Montreal :  Cathedral 

Father  Point :  Light-house 

Cape  Chatte:  Extreme 

Cape  iVIagdalen :  Light- house 

Cape  Rosier:  Light-house 

Cape  Gaspe :  Light-house 


Anticosti  Island:  Heath  Pt.  light-house 
SW.  pt.  light-house  . . 


E.  pt 


Bonaventure  Island: 

Leander  Shoal 

Macquereau  Point 

Chaleur  Bay :  Carlisle 

Dalhousie  I 

Miscou  Island:  NE.  pt.,  Point  Birch 
Miramichi  Bay:  Portage  I.,  N.  pt... 
Point  Escumenac:  Light-house 


North  Point:  Light-house 

Richmond  Harbor:  Royalty  Pt.. 

East  Point:  Light-house 

Charlottetown :  Flag-staff  on  fort 


47  39  50 
47  37  00 

47  52  30 

48  33  48 

49  55  20 

50  38  30 

50  41  39 

51  02  10 
51  17  25 
51  24  10 
51  38  00 

51  58  00 
51  27  35 
51  22  45 
51  22  35 
51  27  30 
51  21  40 
50  47  30 
50  46  44 
50  31  40 
50  14  00 
50  09  30 

50  11  00 
50  06  00 
50  12  27 
50  05  40 
49  19  35 

46  48  17 

45  30  24 

48  31  25 

49  06  00 
49  15  40 
48  51  37 

48  45  15 

49  05  20 
49  23  45 

48  29  30 
48  24  00 
48  12  00 
48  01  00 
48  04  24 
48  01  00 

47  14  00 
47  05  00 

47  03  46 

46  34  00 
46  27  15 
46  13  55 


Gt.  Bird  Rock :  Light-house 

East  Island :  E.  extreme 

Entry  Island :  Light-house 

Amherst  Hbr. :  N.  side  of  entrance 
Deadman  Rock:  W.  pt 


St.  Paul  Island:  Light-house,  NE.  end.. 
Light-house,  SW.  end.. 

Cape  North :  Light-house 

St.  Anns  Harbor:  K.  pt.  entrance 


50  40 
37  40 
16  30 
14  23 
16  03 


47  13  50 
47  11  20 

47  01  45 
46  21  00 


Sydney  Harbor:  Light-house 46  12  25 


Long.  \V. 


58  24  10 

59  18  00 
59  23  40 
69  13  10 
57  50  00 
57  17  07 
57  24  20 
57  02  40 
56  44  45 
56  33  40 
55  53  52 

55  50  20 

56  51  05 

57  08  00 
57  10  50 
57  14  12 

57  46  00 

58  51  00 

58  59  20 

59  20  00 
59  45  00 

59  57  00 

60  08  00 

61  44  00 

63  27  03 

66  22  44 

67  21  55 
71  12  19 
73  33  04 

68  27  40 
66  46  00 
65  19  30 

64  12  00 
64  09  35 

61  42  30 

63  35  46 

64  08  00 
64  18  00 

64  46  30 

65  19  00 

66  22  10 

64  29  00 

65  02  00 
64  47  33 

63  59  19 
63  43  00 
61  58  05 
63  07  23 

61  08  32 
61  24  30 
61  41  20 

61  49  38 

62  12  25 

60  08  32 
60  09  50 

60  23  27 
60  27  00 
60  12  50 


Lun.  Int. 


Range. 


H.W. 


/*.  m. 
8  50 


8  50 
"9'46' 


1  25 


1  43 

1  48 
6  07 


1  52 
1  46 
1  33 
1  25 


1  55 

2  20 

3  10 
2  00 

4  16 


L.  \v. 


Spg. 


h.    VI. 

2  38 


6.0 


2  32 
"3*13' 


4.3 
'I'd 


6  45 


4.0 


7  05 
7  18 
0  54 


8.1 
10.8 
14.6 


7  33 
7  13 
6  50 
6  40 


12.0 

10.5 

6.4 

5.5 


6  35 
6  40 


3.6 
4.9 


7  33 

8  07 

9  10 
8  25 

10  59 


4.7 
4.8 
8.1 
4.0 
2.3 


Neap. 


4  20 

5  15 
8  17 

11  07 


8  30 


8  35 
8  25 
8  10 


11  00 

11  55 

2  20 

4  23 


2.4 
1.8 
1.4 
6.4 


2  12 


2.7 


2  17 
2  13 
2  05 


3.1 
6.0 
5.0 


ft. 
2.8 


2.1 
"2."5 


2.0 


6.0 

8.0 

10.8 


8.9 
7.8 
4.7 
4.1 


1.8 
2.5 


2.3 
2.4 
4.1 
2.0 
1.2 


1.2 
0.9 
0.7 
3.2 


1.4 


1.6 
3.7 
3.1 


BSfl 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  193 


Place. 


Lat.  N. 


Scatary  Island:  Light-house,  NE.  pt 

Louisburg:  Light-house,  NE.  pt 

Madame  Island :  S.  pt 

Port  Hood :  Just-au-corps  I 


Sable  Island:  Light- house,  E.  end 


Pictou:  Custom-house 

Cape  St.  George 

North Canso:  Light-house,  NW.  entrance. 
Arichat  Harbor:  R.  C.  Church  steeple  . . 
Cape  Canso:  Cranberry  I.,  light-house  .. 

White  Head  Island:  Light- house 

Green  Island :  Light-house 

Wedge  Island :  Light-house 

Halifax :  Dock-yard  ob.«ervatory 

Sambro  Island:  Light-house 

Margaret  Bay :  Shut-in  I 

Tancook  Island 

Lunenburg:  Battery  Pt.  light 

Cape  Le  Havre:  Black  Rock 

Coffin  Island :  Light-house 

Little  Hope  Island :  Light-house 

Shelburne  Hbr.:  Two  lights,  McNutts  I 

Cape  Sable:  Light-house 

Seal  Island :  Light-house 

Yarmouth :  Cape  Fourchu  light 

Cape  St.  Mary.. 

Bryer  Island :  Light-house 

Annapolis  Harbor:  Prim  Pt.  light 

Haute  Island :  Light-house 

Cape  Chignecto 

Burntcoat  Head :  Light-house 


Cape  Enrag^:  Light-house 

Cape  Quaco:  Light-house 

St.  Johns:  Partridge  I.  light 

Cape  Lepreau :  Light- house 

L'Etang  Harbor:  S.  pt.  tower 

St.  Andrew:  S.  pt.  light 

Campo  Bello  Island:  Light-house,  N.  pt. 
Grand  Manan  Island:  Light-house,  NE.  pt. 

GannetRock:  Light-house,  NE.  pt 

Machias  Island:  Light-house 


46  02  15 
45  54  34 

45  28  00 

46  00  00 

43  58  14 

45  40  50 
45  52  00 
45  41  42 
45  30  48 
45  19  49 
45  11  58 
45  06  15 
45  00  35 

44  39  38 
44  26  10 
44  34  00 
44  29  00 
44  21  45 
44  12  00 
44  02  00 
43  48  30 
43  37  15 
43  23  19 
43  23  34 

43  47  28 

44  05  20 
44  14  57 

44  41  34 

45  14  55 
45  19  00 
45  18  40 

45  35  34 
45  19  30 
45  14  20 
45  03  40 
45  04  00 
45  04  06 
44  57  40 
44  45  52 
44  30  38 
44  30  07 


Long.  W. 


Calais:  Astronomical  station 45  11 

Eastport:  Cong.  Church 44  54 

Quoddy  Head:  Light-house [  44  48 

Machias:  Town  Hall 44  43 

Petit  Manan  Island :  Light-house 44  22 


Bakers  Island :  Light-house 

Mount  Desert  Rock :  Light-house 

Bangor:  Thomas  Hill 

Belfast:  Methodist  Church 

Rockland :  Episcopal  Church 

Matinicus  Rock :  Light-house 

Monhegan  Island :  Light-house 

Seguin  Island :  Light-house 

Bath:  Winter  St.  Church 

Brunswick:  College  spire 

Augusta:  Baptist  Churcli 

Portland:  Custom-house 

Portland  Head  light-house  . . . 

Cape  Elizabeth:  Li^ht-house  (west) 

Wood  Island :  Light-house 

Boon  Island :  Light-house 


44  14 

43  58 

44  48 
44  25 
44  06 
43  47 
43  45 
43  42 
43  54 

43  54 

44  18 
43  39 
43  37 
43  33 
43  27 
43  07 


59  40  25 
59  59  26 
61  03  00 
61  36  00 

59  46  08 


62  42 

61  52 
61  29 
61  01 

60  55 

61  08 
61  32 
61  52 

63  35 
63  33 

63  54 

64  06 
64  17 
64  18 
64  37 

64  47 

65  15 

65  37 

66  00 
66  09 
66  12 
66  23 
65  47 
65  00 
64  57 
63  48 


64  46  55 

65  32  00 

66  03  20 
66  27  40 

66  49  00 

67  02  52 
66  54  10 
66  44  00 

66  47  00 

67  06  13 


67  16 
66  59 

66  57 

67  27 

67  51 

68  11 
68  07 

68  46 

69  00 
69  06 

68  51 

69  18 
69  45 
69  49 
69  57 

69  46 

70  15 
70  12 
70  12 
70  19 
70  28 


Lun.  Int. 


H.  W. 


h.    TO. 


7  45 
7  55 
9  05 


9  34 
9  20 
9  26 

7  55 
7  43 
7  45 


7  34 
'7'32 


39 


8  17 

9  35 
10  00 


10  29 

10  49 

11  07 


0  27 


11  21 
11  07 
11  04 
11  09 
11  00 


11  02 

"io'si' 

11  36 
11  09 


11  02 


0  23 

11  35 
11  09 
10  45 


12  13 


2  54 
11  06 


11  12 


L.  W. 


h.    m. 


1  35 

1  47 

2  47 


Range. 


Spg.   Neap. 


ft. 


5.0 
5.0 
3.5 


3.9 
2.8 
3.1 
5.0 
6.5 


1  46 


1  30 
'i"36' 


2  05 

3  23 
3  41 


4  36 

4  41 

5  27 


7  27 


5  21 

'I'm 

5  40 
5  05 


5.2 


7.1 
'7."6' 


8.5 
12.8 
16.0 


20.8 
27.5 
33.0 


50.5 


30.0 
23.9 
24.5 
23.3 
24.9 


22.5 


18.0 

23.3 
20.9 


4  59  15.5 


6  47 
5  22 
4  55 
4  31 


15.1 
11.7 
11.0 
10.2 


6  16 


10  18 
4  51 


4.9 
10.1 


4  51 


10.2 


ft- 


3.1 
3.1 

1.8 


2.0 
1.4 
1.6 
3.1 
4.0 
4.1 


3.2 
"4.' 4 
"4.' 3 


5.2 

9.5 

11.8 


15.  4 
20.4 
24.4 


37.4 


22.2 

17.7 
18.2 
17.1 
18.2 


16.7 


13.2 

17.1 
15.2 


11.3 


11.0 
8.6 
8.1 
7.5 


5.8 


3.6 
7.3 


22489—03- 


-13 


Page  194]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


Place. 


Whale  Back:  Light-house 

Portsmouth :  Ntfvy-y ard  flagstaff 

Fort  Constitution 

Hampton:  Baptist  Church 

Isles  of  Shoals:  White  I.  light-house 


Newburyport:  Academy 

Plum  I.  light-house 

Ipswich :  Light-house  ( rear) 

Annisquam  Harbor:  Light-house 

Cape  Ann:  Thatchers  I.  light-house  (N.) . 

Gloucester:  Universalist  Church 

Ten-pound  I.  light-house 

Beverly :  Hospital  Pt.  light-house 

Salem :  Derbys  Wharf  light-house 

Marblehead :  Light-house 

Cambridge:  Harvard  Observatory 

Boston :  Navy-yard  flagstaff 

State  house 

Little  Brewster  I.  light-house. . . 

Minots  Ledge:  Light-house 

Plymouth :  Pier  head 

Gurnet  light-house 

Barnstable:  Light-house 

Cape  Cod :  Highlands  light- house 

Chatham :  Light-house  (south ) 

Monomoy  Point:  Light-house 

Nantucket:  South  Church 

Nantucket  South  shoal:  Light  ship 

Sankaty  Head :  Light-house 

Tarpaulin  Cove:  Light-house 

Vineyard  Haven:  W.  Chop  light-house.. 

Gay  Head:  Light-house 

Cuttyhunk:  Light-house 

New  Bedford :  Baptist  Church 


Sakonnet  Point:  Light-house 

Beaver  Tail:  Light-house 

Newport:  Flagstaff,  torpedo  station 

Bristol  Ferry:  Light-house 

Providence:  Unitarian  Church 

Point  Judith :  Light-house 

Block  Island:  Light-house  (SE) 

Watch  Hill  Point:  Light-house 


Lat.  N. 


43  03  32 
43  04  56 
43  04  16 
42  56  15 
42  58  02 


48  30 
48  55 
41  07 

39  43 
38  21 
36  46 

36  07 

32  48 
31  00 
30  20 
22  48 
22  22 
21  28 

19  41 
16  11 
58  44 
00  12 
43  20 
02  23 

40  15 

33  34 

16  55 

37  05 

17  01 
28  08 
28  51 

20  55 
24  52 

38  10 


41  26  30 
41  26  58 
41  29  07 
41  38  34 
41  49  26 
41  21  40 
41  09  10 
41  18  14 


Montauk  Point:  Light-house 41 

Stonington:  Light-house 41 

New  London :  (proton  Monument 41 

Little  Gull  Island :  Light-house 41 

Gardners  Island:  Light-house,  N.  pt 41 

Plum  Island:  Light-house,  W.  pt 41 

Say  brook:  Light-house,  Lynde  Pt 41 

New  Haven:  Yale  College  spire  (middle).  41 

Bridgeport  Harbor:  Light-house ;  41 

Norwalk  Island:  Light-house |  41 

Shinnecock  Bay :  Light-house  . . 

Fire  Island :  Light-house 

Albany:  Dudley  Observatory. .. 
New  York:  Navy-vard  flagstaff. 
City  Hall 


40 
40 
42 
40 
40 
Fort  Wadsworth :  Light-house ■  40 


04  16 
19  31 
21  16 
12  23 

08  29 
10  25 
16  17 
18  28 

09  24 
02  56 
51  03 
37  57 
39  50 
42  02 
42  44 
36  20 


Long.  W. 


70  41  49 
70  44  22 
70  42  34 
70  50  12 
70  37  25 

70  52  28 
70  49  10 
70  46  00 
70  40  55 
70  34  31 
70  39  59 
70  39  58 
70  51  23 
70  53  03 

70  50  03 

71  07  43 
71  03  05 
71  03  50 
70  53  26 
70  45  35 
70  39  12 
70  36  04 
70  16  52 
70  03  40 
60  57  01 
60  59  39 
70  05  57 
69  36  33 

69  57  57 

70  45  29 
70  36  01 
70  50  08 
70  57  01 

70  55  36 

71  13  30 
71  24  00 
71  19  40 
71  15  39 
71  24  19 
71  28  55 
71  33  08 
71  51  32 

71  51  27 

71  54  49 

72  04  47 
72  06  26 
72  08  44 
72  12  43 
72  20  37 

72  55  45 

73  10  49 
73  25  11 

72  30  16 

73  13  08 
73  44  56 

73  58  51 

74  00  24 
74  03  15 


Lun.  Int. 


H.  W. 


h.     m. 

"ii"23' 


11  19 
11  23 


11  17 
11  13 


11  02 


11  16 
11  09 


11  27 
"ii'69' 


11  23 
11  36 


12  11 

12  00 

0  04 


7  51 
11  34 
7  31 
7  86 
7  57 

7  40 
7  40 
7  48 

7  53 

8  12 
7  32 

7  33 

8  49 

8  20 

9  09 
9  26 
9  26 
9  40 


10  29 

11  08 
11  09 
11  03 

7  48 

7  19 
5  13 

8  44 


7  41 


L.  W. 


Range. 


Spg. 


h.   m.       ft. 

'5"69  Tio.'s' 


4  58 

5  10 


5  04 
5  00 


4  49 


5  03 

4  57 


5  17 
'4"56' 


5  11 
5  25 


5  57 

5  48 

6  00 


1  51 
4  33 
1  20 

0  59 

1  18 

1  05 
1  09 
1  00 
0  40 

0  57 

1  17 

1  25 

2  38 

2  03 

3  03 
3  32 
3  04 
3  35 


11 
54 
04 
56 
38 
20 
0  46 
2  49 


1  38 


10.0 
9.1 


10.1 
10.1 


10.2 


10.6 
10.6 


11.0 
i6.*9" 


10.8 
11.6 


4.6 
4.3 
3.8 


2.8 
2.0 
3.7 
4.3 
5.2 

4.5 
4.7 
4.4 
5.2 
5.4 
3.8 
3.7 
3.2 

2.3 
3.2 
2.9 
3.0 
2.5 


4.3 
7.0 
8.4 
8.2 
3.0 
2.2 
2.8 
5.3 


5.4 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  195 


Place. 


Lat.  N. 


Sandy  Hook:  Light-house  (rear) 

Light-ship 

Navesink  Highlands:  N.  Hght-house 

Barnegat  Inlet:  Light-house 

Tuckers  Beach :  Light-house 

Absecon  Inlet:  Light-house 

Five  Fathom  Bank:  Light-ship 

Cape  May :  Light-house 

Philadelphia,  Pa. :  Statehouse 

Navy-yard    flagstaff, 

League  I v . 

Wilmington,  Del. :  Town  hall 

Cape  Henlopen :  Light-house 

Assateague  Island:  Light-house 

Hog  Island:  Light-house 

Cape  Charles:  Light-house 

Baltimore:  Washington  Monument 

Annapolis:  Naval  Academy  observatory. 

Point  Lookout:  Light-house 

Washington,  D.  C. :  Navy-yard  flagstaff  . 

Naval  Observatory  . 

Capitol  dome 

Old  Point  Comfort:  Light-house 

Norfolk :  Navy-yard  flagstaff 

Richmond,  Va. :  Capitol 

Cape  Henry :  Light-house 


Elizabeth  City :  Court-house . . . 

Eden  ton :  Court-house 

Currituck  Beach :  Light-house  . 

Bodie  Island :  Light-house 

Cape  Hatteras:  Light-house 

Ocracoke:  Light-house 

Newbern,  Episcopal  spire 

Cape  Lookout:  Light-house  ... 
Beaufort,  N.  C. :  Court-house . . 
Frying- Pan  Shoals:  Light-ship 


Georgetown :  Episcopal  Church 

Light-house,  North  I 

Cape  Romain :  Light-house 

Charleston:  Light-house,  Morris  I 

St.  Michael's  Church 

Beaufort,  S.  C. :  Episcopal  Church 

Port  Royal:  Martins  Industry  light-ship. 

Tybee  Island :  Light-house 

Savannah :  Exchange  spire 

Sapelo  Island:  Light-house 

Darien :  Winnowing  House 

St.  Simon :  Light-house 

Brunswick:  Academy 


Amelia  Island :  Light-house 

Fernandina:  Astronomical  station  .. 

St.  Johns  River:  Light-house 

Jacksonville:  Methodist  Church 

St.  Augustine:  Presbyterian  Church 

Light-house 

Cape  Canaveral :  Light-house 

Jupiter  Inlet:  Light-house 

Fowey  Rocks:  Light-house 

Carysfort  Reef:  Light-house 


40  27  42 
40  28  15 
40  23  48 
39  45  52 
39  30  22 
39  21  59 
38  47  20 

38  65  59 

39  56  53 

39  53  14 
39  44  27 

38  46  42 
37  54  40 
37  23  46 

37  07  22 

39  17  48 

38  58  53 
38  02  19 
38  52  30 
38  53  39 
38  53  20 
37  00  06 

36  49  33 

37  32  16 
36  55  35 

36  17  58 
36  03  24 
36  22  36 
35  49  07 
35  15  17 
35  06  32 
35  06  21 
34  37  22 
34  43  05 
33  34  26 

33  22  08 
33  13  21 
33  01  06 
32  41  43 
32  46  34 
32  26  02 
32  05  33 

32  01  20 
32  04  52 
31  23  28 
31  21  54 
31  08  02 
31  08  51 

30  40  23 
30  40  18 
30  23  36 
30  19  43 
29  53  20 
29  53  07 
28  27  37 
26  56  54 
25  35  25 
25  13  17 


Long.  W. 


74  00  09 
73  50  09 

73  59  10 

74  06  24 
74  17  08 
74  24  52 
74  34  36 

74  57  39 

75  09  03 

75  10  32 
75  33  03 
75  05  03 
75  21  23 
75  41  59 

75  54  24 

76  36  59 
76  29  08 
76  19  20 

76  59  45 

77  03  06 
77  00  36 
76  18  24 

76  17  46 

77  26  04 
76  00  27 

76  13  23 

76  36  31 
75  49  51 
75  33  49 
75  31  16 

75  59  11 

77  02  24 

76  31  29 

76  39  48 

77  49  12 

79  16  49 
79  10  55 
79  22  19 
79  52  54 

79  55  49 

80  40  27 
80  33  15 

80  50  37 

81  05  26 
81  17  01 
81  25  39 
81  23  30 
81  29  26 

81  26  26 
81  27  47 
81  25  27 
81  39  14 
81  18  41 
81  17  12 
80  32  30 
80  04  48 
80  05  41 
80  12  40 


Lun.  Int. 


Range. 


H.W. 


h.    m. 
7  30 


7  50 
7  48 
9  59 


8  16 
1  28 

0  53 
12  00 

8  17 


8  03 

6  34 
4  39 
0  31 

7  42 


8  44 

9  05 
4  30 

7  53 


7  37 


7  00 


6  29 

7  21 


8  39 
"6"59' 


7  20 

8  10 


8  00 


7  39 
7  36 


8  12 
8  00 
8  00 
8  20 
8  21 


L.W. 


Spg. 


h.    TO. 
1  23 


1  43 
1  42 
3  57 


1  47 

8  58 

8  02 
6  40 
1  50 


2  19 

0  44 
10  53 

6  52 

1  56 


2  17 

2  47 

11  55 

1  43 


1  26 


0  45 


0  20 

1  08 


3  38 

"o'So' 


1  10 

2  06 


1  31 
1  33 


ft. 
5.6 


2.7 
4.2 
4.7 


5.6 
6.2 

7.0 
6.7 
5.4 


3.0 
1.4 
1.0 
1.7 
3.5 


3.0 
3.2 
4.3 
3.2 


3.4 


2.2 


4,4 
3.3 


4.3 
'5.'9' 


6.0 

8.5 


7.9 
7.6 
8.4 
7.5 
7.5 
7.8 


5.4 


5.3 
5.9 

1.8 
2.6 

2.7 


Neap. 


ft. 
3.6 


1.7 
2.7 
3.0 


3.6 
4.4 

5.2 
4.9 
3.5 


2.0 
1.0 
0.8 
1.1 
2.5 


2.0 
2.1 
2.8 
2.1 


2.2 


1.5 


3.0 
2.3 


2.9 
"4.'i 


4.2 
5.9 


5.5 
5.3 
5.8 
5.2 
5.3 
5.4 


4.8 
3.7 


3.6 
4.0 
1.2 
1.3 
1.4 


Page  196]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


Place. 


Alligator  Reef:  Light-house 

Sombrero  Key:  ^ight-house 

Sand  Key :  Light-house 

Key  West:  Light-house 

Loggerhead  Key :  Light-house 

Sanibel  Island:  Light-house 

Gasparilla  Island:  Light-house 

Tampa  Bay :  Egmont  Key  light 

Cedar  Keys:  Ast.  station,  Depot  Key 

Seahorse  Key  light 

St.  Marks:  Fort  St.  Marks 

Apalachicola:  Flag-staff 

Cape  St.  George:  Light-house 

Cape  San  Bias:  Light-house 

Pensacola:  Light-house 

Navy-yard  chimney 

Sand  Island:  Light-house  (front) 

Mobile  Point:  Light-house 

Mobile:  Episcopal  Church 

Horn  Island :  Light-house 

East  Pascagoula:  Coast-Survey  station. . . 
Mississippi  City:  Coast-Survey  station... 

Ship  Island :  Light-house 

Cat  Island:  Light-house 

Chandeleur:  Light-house 

Mouth  Mississippi  River:  Pass  a  1' Outre 
light 

S.   Pass  light 
(East  Jetty) 

SW.  Pass  light 

New  Orleans:  United  States  Mint 

Barataria  Bay :  Light-house 

Timbalier  Island :  Light-house 

Ship  Shoal:  Light-house 

Southwest  Reef:  Light-house 

Calcasieu  Pass:  Light-house 

Sabine  Pass:  Light-house 

Galveston:  Cathedral,  N.  spire 

Light-house,  Bolivar  Pt 

Matagorda:  Coast-Survey  station 

Light-house 

Indianola:  Coast-Survey  station 

Lavaca:  Coast-Survey  station 

Aransas  Pass:  Light-house 

Brazos  Santiago:  Light,  S.  end  Padre  I .. 

Point  Isabel :  Light-house 

Rio  Grande  del  Norte:  Obs.  N.  side  of 
entrance 

San  Fernando  River:  Entrance 

Santander  River:  Entrance 

Mount  Mecate:  Summit 

Tampico:  Light-house 

Cape  Roxo 

Lobos  Cay :  Light-house 

Tuspan  Reefs:  Middle  islet 

Mexico:  National  Observatory 

Bernal  Chico:  Middle  of  islet 

Zempoala  Point:  Extreme 

Vera  Cruz:  San  Juan  d'Ulloa  light 

Sacrificios  Island 

Orizaba  Mountain :  1 7, 400  feet 

Cofre  de  Perote  Mount:  14,000  feet 

Al varado :  E.  side  of  entrance 

Roca  Partida:  Summit 

Tuxtla,  volcano:  Summit 

Montepio:  Landing  place 


Lat.  N. 


24  51  02 
24  37  36 
24  27  10 
24  32  58 

24  38  04 
26  27  11 

26  43  06 

27  36  04 
29  07  29 

29  05  49^ 

30  09  03 
29  43  32 
29  35  18 

29  40  00 

30  20  47 
30  20  49 

30  11  19 
30  13  44 
30  41  26 
30  13  23 
30  20  42 
30  22  54 
30  12  53 
30  13  57 
30  02  58 

29  11  30 

28  59  28 

28  58  22 

29  57  46 
29  16  30 
29  02  49 

28  54  56 

29  23  36 
29  46  55 
29  43  04 

29  18  17 
29  22  05 
28  41  29 
28  20  18 
28  32  28 
28  37  36 
27  51  53 
26  04  16 
26  04  36 

25  57  22 

25  23  40 
23  46  20 
22  38  40 
22  15  50 
21  35  00 
21  28  12 
21  03  00 
19  26  01 
19  39  50 
19  27  26 
19  12  29 
19  10  10 
19  04  00 
19  29  30 
18  49  00 
18  44  00 
18  29  00 
18  40  00 


Long.  W. 


80  37  08 

81  06  40 
81  52  40 

81  48  04 

82  55  42 
82  00  43 
82  15  34 

82  45  40 

83  01  57 

83  03  58 

84  12  42 

84  59  12 

85  02  54 
85  21  30 
87  18  32 

87  16  06 

88  03  02 
88  01  26 
88  02  28 
88  31  39 

88  32  45 

89  01  57 

88  57  56 

89  09  41 

88  52  19 

89  02  28 

89  08  08 

89  23  30 

90  03  28 

89  56  43 

90  21  25 

91  04  15 
91  30  14 
93  20  43 

93  51  00 

94  47  26 

94  46  00 

95  57  26 

96  25  28 
96  31  01 

96  37  21 

97  03  23 
97  10  00 
97  12  28 

97  08  57 

97  21  25 

97  46  55 

98  04  55 
97  49  55 
97  22  00 
97  13  00 
97  13  35 

99  06  39 
96  24  39 
96  20  22 

96  07  57 
9()  05  30 

97  15  55 
97  07  30 
95  44  48 
95  11  14 
95  08  00 
95  05  12 


Lun.  Int. 


H.  W. 


h.  m. 
8  22 
8  24 

8  40 

9  20 
9  44 

12  17 
0  42 

11  32 
0  42 


2  00 
[12  10] 


[11  10] 

iii'28i 


[11  25] 
[1  35] 

[12  00] 
[0  20] 


[0  23] 
[11  53] 

[11  15] 

[10  55] 
[10  54] 


[11  00] 

[11  50" 

[0  18 

[0  40 

2  17 

3  17 

[4  18] 

[4  07] 


L.W. 


00 
05 
20 
36 
21 
6  10 

6  19 
5  07 

7  13 


Range. 


Spg.    Neap. 


■ft 

2.6 

1.9 

1.5 

1.6 

1.4 

2.3 

1.4 

1.8 

3.1 


8  30   2.  6 
[5  35]  i  [2.5] 


[4  55] 


[4  20] 


[3  09] 
[6  50] 
[5  40] 
[5  45] 


[6  35] 
[5  33] 

[5  00] 

[4  42] 
[4  41] 


[4  35] 


[4  25] 


[155] 


4  47] 

'5  38] 

6  33] 

6  56] 

8  41 

9  36 


[10  33] 
[10  23] 


[10  47] 


[10  35] 


[8  03] 


[1  06]   [7  19] 


[2  49]   [8  38] 


[2.1]; 


[1.7] 


J.  5] 

[2.1] 

2.0] 

2.3] 


[2.1] 
[1.8] 

[1.6] 

[1.7] 
[1.9] 


2.1] 

2.0] 

2.2] 

2.0] 

1.7 

0.9 

[1.4] 
[1.6] 


[1.6] 


[1.6] 


[1.4] 


[1.3] 


[2.4] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA, 
EAST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  197 


Place. 


Zapotitlan  Point:  Light-house 

San  Juan  Point:  Light-house 

Coatzacoalcos:  Light-house 

Santa  Ana  Lagoon:  Entrance 

Tupilco  River:  Entrance 

Tabasco  River:  Light-house 

Carmen  Island :  N  E.  pt 

Laguna  de  Terminos:  Vigia  tower,  W. 
end  Carmen  I 

Paypoton  Mount:  Summit 

Lerma:  Church 

Campeche:  Light-house 

Fort  San  Jo^6 

Point  Palmas 

Sisal :  Fort  light 

Madagascar  Reef:  Center 

Progreso:  Light-house 

Silan:  Village 

Lagartos:  Milage 

Cape  Catoche:  Light-house 

Areas  Cays:  Light-house 

Obispo  Shoal :  16-foot  spot 

New  Bank :  Center 

Triangles,  E.  reef:  Beacon 

Triangles,  W.  reef:  Cay  at  SW.  end 

Bajo  Nuevo  Reef:  Center 

Arenas  Cays:  N  W.  Cay 

Alacran  Reef:  Perez  Cay 

Con  toy  Island :  Light-house 

Mugeres  Island :  Light-house 

Cancun  Island:  Nisuc  Pt 

Cozumel  Island:  N.  pt.  light-house 

S.  pt.  light-house 

Ascension  Bay :  Allen  Pt 

Chinchorro  Bank:  Cayo  Lobos  light 

Half-Moon  Cay:  Light-house 

Mauger  Cav,  NW.  end:  Light-house 

Glover  Ree'f :  SW.  Cay 

English  C^y :  Light-house 

St.  Georges  Cay :  Center 

Sand-Fly  Cays":  II  ut,  S.  end 

South  Water  Cay :  Center 

Belize:  Fort  George  light 

North  Standing  Creek:  Entrance 

Sittee  Point:  Cay 

Cockscomb  Mount:  Summit,  4,000  feet.. 

Placentia  Point:  Huts  on  point 

Icacos  Point:  S.  extreme 

Sarstoon  River:  Entrance 

Dulce  River:  Entrance,  W.  side 

Dulce  Gulf:  Fort  St.  Philip 

Isabel 

Hospital  Bight:  Hut,  N.  pt.  of  entrance. 

Cape  Three  Points:  NAV.  extreme 

Seal  Cays:  S.  Cay 

Omoa:  Entrance 

Cape  Triunfo:  Bluff  pt 

Congrehoy  Peak:  Summit,  8,040  feet 

Truxillo:  Fort 

Utilla  Island:  S.  Cay 

Hog  Islands:  Highest  hill  on  W.  islet. . . 

Roatan:  Center  of  Coxen  Cay 

Port  Royal,  NW.pt.  of  GeorgeCay 

Bonacca  Island:  Summit,  1,200  feet 

Misteriosa  Bank:  S.  Point 

Swan  Islands:  NW.  pt.  of  W.  I 


Lat.  N. 

Long.  W. 

Lun. 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

O          1           II 

18  34  00 

O          1           II 

94  50  00 
94  38  57 
94  24  46 
93  51  53 
93  25  25 
92  42  00 
91  30  50 

91  50  17 

90  43  27 
90  36  11 
90  32  20 
90  30  51 
90  22  00 
90  02  37 

90  18  27 
89  39  30 
88  54  27 

88  10  27 
87  04  10 

91  57  45 

92  13  27 

91  52  27 

92  12  47 
92  18  57 
92  04  26 
91  24  21 

89  41  45 
86  48  00 
86  43  39 
86  46  45 
86  43  55 

86  59  04 

87  28  27 
87  23  40 

87  32  30 
87  46  30 

87  50  50 

88  03  20 
88  04  45 
88  06  05 
88  05  36 
88  11  20 
88  13  48 
88  15  15 
88  37  40 
88  22  13 
88  35  51 
88  56  20 

88  46  22 

89  01  36 
89  09  44 

88  33  22 
88  38  50 
88  20  15 
88  04  31 
87  27  46 
86  55  00 

85  59  18 

86  59  15 
86  32  09 
86  34  27 
86  18  41 
85  55  00 
84  02  00 
83  56  27 

h.    m. 

h.    m. 

ft. 

ft. 

18  19  45 

18  08  56 

18  18  49 

18  26  44 

18  39  30 

18  47  08 

18  38  44 

19  38  00 

[12  16] 

[6  00] 

[1.6] 

19  48  24 

1 

19  50  20 
19  51  36 

2  59 

9  28 

2.1    1.3 

21  02  00 

1 

21  10  06 
21  26  30 

10  20 

4  10 

1.8    0.9 

21  17  00 

21  23  00 

1 

21  36  30 

21  35  50 
20  12  45 
20  29  00 

9  30 
[12  06] 

3  19 

[5  50] 

1.5 
[1.6] 

0.8 

20  32  00 

20  54  54 
20  58  00 

[12  00] 

[5  45] 

[1.6] 

21  50  00 

22  07  10 

22  23  36 

.... 

21  33  00 

21  12  00 
21  03  00 

9  20 

3  08 

1.6 

0.9 

20  35  50 
20  16  20 

8  20 

2  08 

1.5 

0.8 

19  46  55 

18  23  20 

17  12  15 

17  36  15 

16  42  20 

17  19  30 

17  33  15 

16  57  50 

16  48  50 

17  29  20 
16  57  40 

8  00 

1  50 

1.5 

0.8 

16  47  45 

16  48  10 

16  30  54 

16  14  15 

15  54  00 

15  49  45 

15  38  00 

9  00 

2  50 

2.0 

1.1 

15  24  20 

15  52  20 

15  57  45 

16  08  00 

15  47  11 

I 

15  48  45 

15  38  00 

15  55  45 

16  03  40 

15  58  00 

16  18  00 
16  24  20 

7  35 

1  23 

3.5 

1.8 

16  28  00 
18  44  00 

8  50 

2  38 

1.5 

0.8 

17  24  30 

Page  198]                                      APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  NORTH  AMERICA— Continued. 

o 

s 

«  j 

§2 

8 

• 

s 
« 

■M 

i 

a 
1 

c 

0 

PS 

!fi 
S 

0 

5 

Place. 

L*t.  N. 

Long.  W. 

Lun.  Int. 

Range.         1 

H.  W. 

L.  W. 

Spg. 

Neap. 

• 

Great  Rock  Head :  Bluff  extreme 

Cape  Camaron 

o          /        « 

15  53  00 

16  00  00 
15  51  50 
15  48  50 
15  23  40 

15  00  00 

16  03  30 

o          /       // 

85  27  10 
85  03  00 
84  38  33 
84  17  10 
83  42  36 

83  10  00 
83  08  20 
82  23  27 
82  18  07 
82  42  08 
82  20  00 

82  45  57 
80  51  27 

79  50  53 

80  15  20 

81  08  21 
81  07  21 

80  05  05 

81  21  26 
81  43  06 
81  27  53" 

81  49  54 

83  21  27 
83  23  10 
83  37  12 
83  45  57 
83  41  57 

82  58  35 

83  03  35 
83  42  15 

83  47  27 
83  02  00 

82  39  06 
82  21  47 

82  20  31 

83  03  27 
82  20  33 
82  07  51 
81  55  02 
81  33  57 

h.    m. 

h.    m. 

ft. 

ft. 

Brewers  Lagoon:  E.  side  of  entrance 

Patook  River:  E.  side  of  entrance 

Carataska  Lagoon:  E.  side  of  entrance  . . 

Cape  Gracias-d-Dios:  Light-house 

Caxones  Reef:  Great  Hobby  Islet 

10  20 

4  07 

2.0 

1.1 

GordaBank:  Gorda  Cay '  15  52  00 

Farrall  Rock:  Center 

15  51  00 

Half-Moon  Cay:  Center 

15  08  50 

15  07  00 

14  21  12 

16  54  00 

15  47  45 
14  21  33 
14  08  00 
14  30  00 
13  34  30 

13  22  54 
12  31  40 
12  24  00 
12  10  00 

14  03  00 
12  22  35 
12  20  39 
12  15  30 

11  59  00 

12  17  30 
12  09  17 
10  56  15 

10  01  30 
10  00  05 

9  38  30 
9  25  45 
9  24  47 
9  16  30 
9  14  22 
9  14  30 
9  10  30 
9  06  30 

Alargate  Reef:  E.  pt 

Mosquito  Cays:  S.  end 

Rosalind  Bank :  N W.  extreme 

Serranilla  Bank:  Beacon  Cay 

4  00 
4  00 

10  13 
10  13 

2.0 
2.0 

1.1 
1.1 

Serrana  Bank :  Little  Cay 

Quita  Sueno  Bank:  S.  extreme  of  reef. . . 

Spit  at  NW.  end 

Roncador  Cay:  S.  pt 

j 

Old  Providence:  Isabel  House 

4  00 

io  13     i.6 

0.5 

St.  Andrews  Island :  SW.  cove,  Entrance  I . 
Courtown  Cays:  Middle  Cay 

1 

Albuquerque  Bank:  Smith  Cay 

' 

Brangmans  Bluff:  Extreme 

Pearl  Cays:  Colombilla  Cay 

1  50 

8  03 

2.0 

1.1 

Pearl  Cays  Lagoon:  Mosquito  Pt 

Cookra  Hill :  Summit 

Bluefields:  Schooner  Pt 

1  40 

7  52 

2.0 

1.1 

Little  Corn  Island :  Gun  Pt 

Great  Corn  Island:  Wells  N.  of  Quin  Bluff. 
Greytown :  Light-house 

1  35 
1  00 

7  47 
7  13 

2.0 
1.5 

1.1 

0.8 

Mount  Cartago:  Peak,  11,100  feet 

Port  Limon:  Grape  Cay  light 

1  00 

7  13 

1.6 

0.9 

Carreta  Point:  Extreme 

Tirby  Point:  Extreme 

Columbus  Island :  Lime  Pt 

Blanco  Peak:  Summit,  11,740  feet 

Shepherd  Island:  Hut  on  summit 

Cobbler  Rock:  Center 

Valiente  Peak:  Summit,  722  feet 

Escudo  de  Veragua:  W.  pt.  of  island 

1 

........I ..... 

1 

WEST  COAST  OF  NORTH  AMERICA. 

• 

1 

Point  Barrow:  Highest  lat.  of  U.  S 

Icy  Cape:  Extreme 

71  23  30 
70  16  00 
68  52  00 
67  09  00 
66  14  30 
66  32  00 
65  35  30 
65  33  30 
65  16  40 
65  00  00 
64  26  00 
63  26  00 
63  34  30 
61  40  00 
63  16  00 
63  50  00 
60  18  00 
60  13  00 
60  25  22 
58  48  31 

156  27  00 
161  47  30 
166  06  00 
163  34  00 

161  45  00 
163  36  00 
168  40  00 
168  00  00 
166  46  30 
168  02  00 

165  05  00 

162  02  30 
162  42  30 

166  15  00 
168  41  00 

171  31  00 

172  02  00 
172  36  00 
166  08  30 
160  50  00 

11  41 

5  33 

0.6 

0.2 

Cape  Lisburne:  849  feet 

Cape  Krusenstern :  Extreme 

Chamisso  Island :  Summit 

7  45 

1  50 

2.0 

0.6 

Cape  Espenberg:  Extreme 

Diomede  Island:  Fairway  Rock 

Cape  Prince  of  Wales:  W.  pt 

1  . 

Port  Clarence:  Point  Spencer 

6  10 

1  10 

1.1       0.9 

King  Island:  N.  pt 

Cape  Nome:  Extreme 

[2  05] 
;8  05] 

rs  25] 

r2.ni 

St.  Michael:  Fort 

[1  20]'  [4.5]i 1 

Stuart  Island:  W.  pt 

Cape  Romanzof :  Extreme 

St.  Lawrence  Island :  E.  pt 

NW.pt 

1 

St.  Matthew  Island:  SE.pt 

4  40 

11  0      3. 1 

1.6 

Pinnacle  Islet:  Summit,  930  feet 

Nunivak  Island :  Cape  Etolin 

Hagenmeister  Islant 

! 

1 

":r:       r  i 

APPENDIX  IV. 

MAKITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  NORTH  AMERICA— Continued. 


[Page  199 


Place. 


Cape  Menchikof :  Extreme 
Port  Moller 

St.  George  Island:  S. 


side 


Lat.  N. 


Attu  Island:  Chichagof  Harbor 

Kiska  Island :  Kiska  Harbor,  Ast.  sta . . . 
Amchitka  Island :  Constantine  Harbor . . 


Adakh  Island :  Bay  of  Islands 

Atka  Island:  Nazan  Bay  (church) 

Pribilof  Island:  St.  Paul  I.,  village 

Unalaska  Island:  C.  S.  station,  Iliuliuk  . 

Sannakh  Reefs:  S.  edge 

Sannakh  Island :  NE.  end 

Unga  Island 

Popof  Island :  Humboldt  I 

Nagai  Island :  Sanborn  Harbor 

Koniushi  Island:  NW.  harbor 

NE.  harbor 

Simeonof  Island :  Simeonof  Harbor 

Cape  Strogonof :  Extreme 

Chignik  Bay :  Anchorage 

Anowik  Island :  S.  end 

Chiachi  Islands 

Light-House  Rocks 

Chirikof  Island 

Kodiak  Island,  St.  Paul  Harbor:  Cove 

N  W.  of  village 

Port  Etches 

Middleton  Island 

Mount  St.  Elias:  Summit 

Yakutat  Bay:  Port  Mulgrave 

Lituya  Bay 

Sitka:  Middle  of  parade  ground 

Juneau  

Wrangell:  Ast.  station 


North  Island:  N.  pt 

Cape  Knox :  Extreme 

Port  Kuper:  Sansum  I 

Forsyth  Point:  Extreme 

St.  James  Cape:  S.  extreme 

Cumshewa  Harbor:  N.  side  of  entrance 

Skidegate  Bay :  Rock  on  bar 

Rose  Spit  Point:  J^xtreine 

Massett  Harbor:  Uttewas  village 

Cape  Edenshaw :  Extreme 


Hecate  Bay:  Observatory  Islet 

Stamp  Harbor:  Observatory  Islet... 
Island  Harbor:  Observatory  Islet... 

Cape  Beale:  Light-house 

Refuge  Cove:  Village  on  W.  side  . . . 

Hesquiat  Harbor:  Boat  Cove 

Estevan  Point:  S.  extreme 

Nootka  Sound :  Friendly  Cove 

Port  Langford:  Colwood  Islet 

Esperanza  Inlet:  Observatory  Rock. 

Kyuquot  Sound :  Shingle  Pomt 

Nasparti  Inlet:  Head  Beach 

Cook  Cape:  Solander  I 

North  Harbor:  Observatory  Rock. . . 


57  30  24 

55  54  59 

56  34  23 


52  56  01 
51  59  04 
51  23  39 

51  49  18 

52  10  36 
57  07  19 

53  52  54 

54  13  30 

54  26  12 

55  20  45 
55  19  17 
55  07  36 

55  03  17 
54  58  25 

54  55  30 

56  48  00 
56  19  20 

56  05  13 

55  51  58 
55  45  24 

55  48  22 

57  47  57 
60  20  43 

59  27  22 

60  20  45 
59  33  42 

58  36  57 

57  02  52 

58  18  00 

56  27  00 

54  15  00 
54  10  30 
52  56  31 

52  09  07 
51  54  00 

53  02  00 

53  22  20 

54  13  00 
54  01  40 
54  04  30 

49  15  22 
49  13  46 
48  54  41 

48  47  23 

49  20  50 
49  27  31 
49  22  07 
49  35  31 
49  47  20 
49  52  45 

49  59  55 

50  11  21 
50  06  31 
50  29  25 


Long.  W. 


157  58  30 
160  34  54 

169  39  50 

Long.  E. 
J  73  12  24 
177  30  00 
179  12  06 

Long.  W. 
176  52  00 
174  15  18 

170  17  52 
166  31  44 
162  38  00 
162  18  00 
160  38  39 
160  31  14 
159  56  06 
159  23  05 
159  22  18 
159  15  03 

158  46  00 

158  24  24 

156  39  19 

159  05  24 

157  27  04 
155  42  51 

152  21  21 
146  37  38 
146  18  45 
141  00  12 
139  46  16 
137  40  06 
135  19  31 
134  24  00 
132  23  00 

132  56  20 
132  57  50 
132  09  06 
131  03  20 
131  01  26 
131  31  00 
131  51  00 

131  34  00 

132  10  00 
132  20  56 

125  55  43 

124  50  07 

125  16  54 

125  13  14 

126  16  06 
126  24  53 
126  31  58 
126  36  58 
126  56  31 

126  59  21 

127  08  56 
127  37  24 

127  56  46 

128  03  05 


Lun.  Int. 


H.W. 


h.    m. 


3  35 
3  30 


3  25 


4  17 

3  50 

12  13 


2  40 


2  20 


1  45 


0  16 
0  50 


0  34 


0  06 
0  45 
0  30 


0  00 


0  07 


12  15 
0  45 


12  20 
12*65' 


12  05 


11  55 
11  50 
11  47 


L.  W. 


h.    m. 


9  48 
9  43 


9  38 


10  29 

9  58 
6  10 


8  55 


8  33 


7  58 


6  24 

7  05 


6  41 


6  17 
6  56 
6  39 


6  12 


6  19 


6  08 

7  20 


6  15 
'5'56' 


5  55 


5  45 
5  38 
5  34 


Range. 


Spg. 


ft. 


5.7 

5.2 


5.0 


2.7 
2.9 
5.7 


8.2 


7.5 


8.1 


9.0 
10.1 


9.5 


9.9 
18.6 
17.7 


11.5 


12.8 


10.0 
12.4 


9.9 

io.'s' 


9.7 
9.3 
9.3 


Neap. 


2.9 
2.7 


2.6 


1.4 
1.5 

2.8 


4.1 


3.8 


4.0 


4.5 

5.1 


5.0 


5.2 

9.7 
9.2 


5.7 


5.8 
7.1 


5.7 


5.9 


5.6 


5.5 
5.3 
5.3 


Page  200]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  NORTH  AMERICA— Continued. 


Place. 


Lat.  N. 


Lun.  Int. 


Long.  W. 


H.W. 


L.W. 


Range. 


Spg.       Neap. 


Koprino  Harbor:  Observatory  Rock 

Hecate  Cove :  Kitten  Islet 

Triangle  Island :  *NV.  side 

Cape  Scott:  Summit 

Bull  Harbor,  Hope  Island :  N.  pt.  Indian  I . 

Port  Alexander:  Islet  in  center 

Beaver  Harbor:  Shell  Islet 

Cormorant  I.:  Yellow  Bluff  in  Alert  Bay. 

Baynes  Sound :  Beak  Pt 

Nanoose  Harbor:  Entrance  Rock 

Nanaimo:  Light-house 

Benson's  House 

Victoria:  Light-house 

Esquimalt:  Fisgard  I.  light 

Race  Island :  Light-house 

Sooke  Inlet :  Secretary  I 

Port  Sail  Juan :  Pinnacle  Rock 


Port  Harvey :  Tide  Pole  Islet 

Port  Neville:  Robber's  Nob 

Knox  Bay,  Thurlow  Island:  Stream  at 
head  of  bay 

Valdes Island:  S.  pt 

Howe  Sound:  Plumper  Cove 

Atkinson  Point:  Light-house 

Vancouver,  Burrard  Inlet:  Govt.  Re- 
serve, English  Bay 

Eraser  River:  Garry  Pt 

New  Westminster:  Military  barracks 

Point  Roberts:  Parallel  station 

Semiamoo  Bay :  Parallel  station 


Admiralty  Head :  Light-house , 

Steilacoom:  Methodist  Church 

Seattle:  C.  S.  ast.  station 

Port  Townsend :  C.  S.  ast.  station 

Smith  Island :  Light-house 

New  Dungeness:  Light-house 

Port  Angeles:  Ediz  Hook  light-house 

Cape  Flattery :  Light-house 

Cape  Shoalwater:  Light-house 

Cape  Disappointment:  Light-house .. 

Kalama :  Methodist  Church 

Bremerton :  Navy-yard  flagstaff 

Tacoma:  St.  Luke  Church 


Astoria:  Flagstaff 

Yaquina  Head :  Light-house 

Cape  Arago,  or  Gregory:  Light-house  .. 
Cape  Blanco :  Light-house 


Crescent  City:  Light-house 

Trinidad  Head :  Light-house 

Eureka:  Methodist  Church 

Humboldt:  Light-house 

Cape  Mendocino:  Light-house 

Point  Arena:  Light-house 

Point  Reyes:  Light-house 

San  Francisco:  Coast  Survey  ast.  station . 

Presidio  station . 

Mare  Island:  Stone  block,  obs.  station. . 

Benicia:  Church 

Farallon  Islet:  Light-house 

Santa  Clara:  Catholic  Church 

Mount  Hamilton:  Obs.  peak 

San  Jos^:  Spire 

Pigeon  Point:  Light-house 


50  30  00 
50  32  26 
50  51  53 
50  46  41 
50  54  47 
50  50  49 
50  42  36 
50  35  02 
49  36  29 
49  15  43 
49  12  50 

49  10  1ft 
48  25  26 
48  25  50 
48  17  53 
48  19  .35 

48  33  30 

50  33  58 
50  31  09 

50  24  15 
50  02  42 

49  24  39 
49  19  42 

49  16  18 
49  07  04 
49  13  01 
49  00  00 
49  00  00 

48  09  19 

47  10  20 

47  35  54 

48  06  56 
48  19  07 
48  10  52 
48  08  24 
48  23  30 
46  43  00 
46  16  29 

46  00  26 

47  33  24 
47  15  32 

46  11  19 
44  40  35 
43  20  36 
42  50  22 

41  44  36 
41  03  01 
40  48  11 
40  41  37 
40  26  18 
38  57  12 
37  59  39 
37  47  55 

37  47  30 

38  05  53 
38  03  05 
37  41  51 
37  20  49 
37  21  03 
37  19  58 
37  10  49 


127  51  42 

127  35  44 
129  05  58 

128  26  11 
127  55  29 
127  39  23 
127  24  33 
126  56  56 
124  50  44 
124  07  32 
123  48  11 
123  56  02 
123  23  28 
123  26  46 
123  31  47 

123  42  40 

124  27  37 

126  16  06 
126  03  47 

125  38  26 
125  14  34 
123  28  46 
123  15  54 

123  11  26 
123  11  27 
123  53  52 
123  04  52 
122  44  56 

122  40  34 
122  35  51 
122  19  59 
122  44  58 

122  50  36 

123  06  31 

123  24  07 

124  44  06 
124  04  25 
124  03  11 
122  50  39 
122  37  33 

122  26  26 

123  49  42 

124  04  40 
124  22  31 
124  33  30 

124  12  10 
124  09  03 
124  09  41 
124  16  26 
124  24  25 
123  44  27 
123  01  24 
122  24  32 
122  27  49 
122  16  16 

122  09  23 

123  00  07 
121  56  26 
121  36  40 

121  53  39 

122  23  39 


ft. 


0  10 
0  32 
0  30 
0  55 
4  45 
4  52 


4  40 
[2  17] 
[2  00] 


4  59 


0  08 


12  22 

3  39 

4  27 
4  32 

0  15 
11  50 
11  55 


11  33 
11  27 
11  57 
11  33 
11  00 

10  36 

11  23 

12  07 
11  43 

1  05 

1  35 

10  40 


6  22 
6  44 

6  42 

7  08 
11  00 
11  18 


10.7 
11.6 
11.5 
12.8 
10.6 
10.2 


11  05 

[8  31] 

[8  14] 


[5.7] 
[5.8] 


8  10 
8  47 

10  00 

10  15 

11  58 

11  35 

12  01 
11  23 


14.1 
16.0 

15.7 
7.2 
9.0 

7.8 

8.2 
7.0 


11  10 


7.1 


11  04 
10  33 
9  32 
9  28 
8  34 
8  23 
6  16 


11.0 
9.2 


7.1 


6  19 
11  25 
10  35 
10  45 

6  42 
5  37 
5  49 


5  15 
5  11 
5  45 
5  19 
4  50 

4  21 

5  08 
5  34 
5  07 
7  15 
7  48 
4  25 


7.7 
3.2 
9.4 
9.8 

7.8 
7.3 
6.0 


4.1 
5.1 
5.1 
4.6 
5.6 
5.6 
4.5 


appp:ndix  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
*                                      WEST  COAST  OF  NORTH  AMERICA— Continued. 

[Page  201 

1 

Place. 

Lat.  N. 

Long.  W. 

Lun. 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

• 

£ 

u. 
© 

i 

s 

.0 

u 

0 

Santa  C  niz :  Warehouse  flagstaff 

Monterey:  C.  S.  azimuth  station 

Point  Pinos:  Light-house 

o         /         // 

36  57  31 
36  35  21 
36  37  55 
35  39  50 
34  26  49 
34  26  10 
34  15  46 

33  42  14 

34  03  05 
32  39  48 
32  43  06 

32  31  58 
34  04  19 

33  56  30 

34  03  12 
34  00  25 
33  28  16 
33  14  55 
33  23  09 

31  51  10 
31  33  04 
30  57  39 
30  28  58 
30  22  16 
29  47  20 
29  25  29 
29  10  50 
28  56  06 
28  40  16 
28  14  26 
28  03  52 
28  18  08 
27  39  35 
27  06  10 
26  45  45 
26  42  49 
26  18  56 
26  03  18 
24  58  00 
24  47  31 

24  38  23 
24  18  12 
24  20  17 
23  27  14 

22  53  07 

23  03  35 

23  32  48 

24  03  52 

24  15  31 
24  10  10 
24  24  10 

24  52  03 

25  29  23 

25  59  37 

26  00  41 
26  30  44 

26  53  37 

27  10  21 

27  26  06 

28  00  07 
28  25  04 

O           /          " 

122  01  29 
121  52  59 
121  56  02 
121  17  06 
120  28  18 
119  42  42 

119  15  56 
118  17  41 

118  14  32 
117  14  37 
117  09  41 

117  07  32 

120  21  55 

119  58  29 
119  33  51 
119  23  04 
119  02  29 
119  31  19 

118  24  05 

116  38  05 
116  40  51 
116  17  28 
116  06  46 
115  59  07 
115  48  12 
115  12  14 
118  18  30 
114  31  06 
114  14  15 

114  06  21 

115  11  32 
115  36  10 
114  54  27 

114  17  25 
113  16  25 
113  35  04 
112  41  44 
112  17  52 

115  51  54 
112  18  25 

112  08  54 
111  42  54 
111  30  21 
110  14  07 

109  54  50 
109  40  43 
109  28  57 

109  50  29 

110  20  34 
110  20  41 

110  20  35 
no  41  47 

111  01  43 
111  06  .53 
111  21  03 
111  27  14 

111  58  04 

112  05  39 
112  19  56 
112  47  36 
112  51  59 

h.    m. 
10  54 
10  43 

h.   m. 
4  27 
4  24 

ft. 

5.2 

4.8 

ft. 
3.3 
3.1 

Piedras  Blancas:  Light-house 

Point  Conception :  Light-house 

Santa  Barbara:  N.  tower,  Mission  Church 

San  Buenaventura:  C.  S.  ast.  station 

Pt.  Fermin,  San  Pedro  Bay:  Light-house. 
Los  Angeles:  Court-house 

9  37 
9  53 
9  36 

3  15 
3  21 
3  13 

4.8 
4.9 
5.5 

2.2 
2.2 
2.5 

Point  Lonia:  Light-house 

9  29 
9  32 

3  07 
3  20 

5.2 
5.1 

2.3 
2.3 

San  Diego:  C.  S.  ast.  station 

Mexican  Boundary :  Obelisk 

San  Miguel  Island":  Seal  Pt 

9  23 

3  02 

4.9 

2.2 

Santa  Rosa  Island :  P-.  pt  

Santa  Cruz  Island :  NE.  pt 

9  29 

3  06 

4.9 

2.2 

Anacapa  Island :  E.  pt        

Santa  Barl)ara  Island :  Summit 

: ::::::::  i 

San  Nicolas  Island:  Summit       

9  20 
9  28 

9  28 

3  04 
3  08 

3  06 

4.9 
5.1 

6.0 

2.2 
2.3 

2.2 

Santa  Catalina  Island:  Catalina  Peak  . . . 

Ensenada  Harbor:  Head  of  bay,  close  to 
beach  

San  Tomas:  NW.  shore  of  cove 

Colnett  Bay:  Head  of  bav 

9  27 

3  05 

5.8 

2.6 

San  Martin  Island:  Hassler  Cove 

Port  San  Quentin:  Sextant  Pt 

9  23 

3  00 

4.9 

2.2 

San  Geronimo  Island:  Bight  at  E.  end . . 
Canoas  Point:  High  bluff 

Guadeloupe:  North  pt 

La  Playa  Maria:  Mound  on  W.  side 

Santa  Rosalia  Bay:  Obs.  spot,  Cairn 

Lagoon  Head:  Highest  pt.  of  crater 

Cerros  Island :  SE.  extremity 

9  15 

2  53 

7.6 

3.4 

9  05 

2  42 

7.8 

3.5 

San  Benito  Island:  Summit  of  W.  island. 

San  Bartolom6:  N.  side  of  entrance 

Asuncion  Island:  Summit  of  island 

San  Ignacio  Point:  J*  xtreme 

9  00 

2  37 

8.2 

2.8 

Abreojos  Point:  Extreme  of  rocky  ledge. 

Sau  Domingo  Point:  Edge  of  clifi 

San  Juanico  f*oint:  Knoll 

Alijos  Rocks :  South  Rock 

9  00 

2  48 

6.7 

2.3 

8  29 

2  17 

5.7 

1.6 

Cape  San  Lazaro:  Extreme 

Magdalena  Bay:  Obs.  spot  (post)  N^  of 
Port  Magdalena 

8  25 

2  12 

5.5 

1.5 

Cape  Tosco:  Extreme 

El  Conejo  Point:  Extreme 

Todos  Santos:  Foot  of  hill,  Lobos  Pt 

San  Lucas:  Steep  sand  beach,  NW.  pt. 
of  bay 

San  Jose  del  Cabo:  NE.  side  of  entrance. 

Arena  Point :  Extreme l... 

Arena  de  la  Ventana:  Extreme 

8  36 

2  20 

4.5 

1.2 

Pichilinque  Bay:  SE.  pt.  of  San  Juan, 
Nepomezeino  I 

! 

La  Paz:  Obs.  spot,  El  Mogote 

Lupona  Point:  P^xtreme 

9  40 

3  34 

5.4 

1.3 

San  f^varisto:  3  m.  S.  of  S.  Evaristo  Hd. 
San  Marcial  Point :  E.xtreme 

Salinas  Bay:  Beach,  NE.  pt.  of  bay. 

Loreto:  Cathedral 

Pulpito  Point:  Summit 

Muleje:  Equipalito  Pt 

San  Marcos  Is'and:  S.  sand  spit 

Santa  Maria  Cove:  Beach  on  NW.  shore. 
San  Carlos  Point:  Extreme 

Santa  Teresa  Bay:  Beach  on  N.  side 

11  50 

5  47 

11.2 

2.6 

Page  202]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
"WEST  COAST  or  NORTH  AMERICA— Continued. 


Place. 


Las  Animas:  Lo^  pt 

Raza  Island:  Landing  place,  S.  side. 
Angeles  Bay:  Bight  on  NW.  shore.. 
Remedios  Bay:  Beach  on  W.  shore  . 

Mejia  Island:  S.  side 

San  Luis  Island:  SE.  side 

San  Firinin:  Beach,  N.  of  bight 

San  Felipe  Point:  Peak,  1,000  feet 


28  47  40 
28  49  11 

28  56  39 

29  13  52 
29  33  08 

29  57  27 

30  25  16 

31  02  57 
Philips  Point:  Beacon !  31  46  10 


Lat.  N. 


Long.  W. 


Georges  Island :  NE.  shore 

Cape  Tepoca:  Hill,  300  feet 

Libertad  Anchorage:  Beach 

Patos  Island :  SE.  end 

Tiburon  Island:  SE.  end 

Kino  Point:  0.2  mile  N.  88°  W.  of  mound. 

San  Pedro:  N.  side  of  bay 

Guaymas:  Light-house 

Claris  Island :  NW.  part 

Santa  Barbara:  N W.  side  of  bay 

Agiabampo:  SE.  side  of  entrance 

Topolobampo :  SE.  end  of  Santa  Maria  I . . 

Navachista:  W.  side  of  creek 

Playa  Colorado:  N.  side  of  entrance 

Altata:  N.  side  of  entrance 

Mazatlan :  Light-house 

Palenita  Village:  Boca  Tecapan 

San  Bias:  Custom-house 

Maria  Madre  Island:  SE.  extreme 

Mita  Point:  Extreme 

Penas  Anchorage:  Mouth  of  Rio  Real . . . 

Cape  Corrientes:  Extreme 

Perula  Bay :  Smooth  Rock 

San  Benedicto  Island:  S.  extreme 

Socorro  Island :  SE.  part 

Roca  Partida:  Summit 

Clarion  Island :  S.  end 

Clipperton  Island:  Summit 

Navidad  Bay:  W.  end  of  sandy  beach... 
ManzanillaBay:  Flagstaff, U.  S.consulate. 
Sacatula  River:  Beach,  W.  side  of  bay. . . 
Isla  Grande:  Tripod  on  NW.  summit  ... 

Sihuatanejo  Point:  Tree  on  beach 

Morro  Petatlan:  Junction  of  stony  and 

sandy  beaches 

Tequepa  Harbor:  Limekiln 

Acapulco:  Light-house 

Maldonado:  El  Recordo  Pt 

Port  Angeles:  Light-house 

Sacrificios  Point:  Highest  pt.  of  cape 

Port  Guatulco:  Cross 

Morro  Ayuca:  SummitofN.  edge  of  cape. 
Salina  Cruz:  Light-house 


Champerico:  Inshore  end  of  iron  wharf. . 

San  Jos6  de  Guatemala:  Light-house 

Acajutla:  Light-house 

Libertad:  Light-house 

La  Union :  Light-house 

Chicarene  Point:  Extreme 

Corinto:  Light-house 

San  Juan  del  Sur:  Signal  station 

Salinas  Bay :  Salinas  Islet 

Port  Culebra:  Extremity  of  Mala  Pt 

Ballena  Bay:  N.  Estero  Toussa .' 

Parida  Anchorage:  S.  pt.  of  Deer  Id 

Port  Nuevo:  Entrada  Pt 

Bahia  Honda:  W.  end  of  Centinela  I 

Coiba  (Quibo)  Island:  Observation  pt. . , 


31  00  54 
30  16  05 
29  54  12 
29  16  12 
28  45  55 
28  45  28 
28  03  22 
27  50  28 
26  58  59 
26  41  09 
26  16  35 
25  33  56 
25  23  06 
25  11  42 
24  38  52 
23  10  40 
22  30  26 
21  32  30 
21  30  45 
20  45  50 
20  36  26 
20  25  00 
19  34  48 
19  17  15 
18  42  57 
18  59  41 

18  20  55 

10  17  00 

19  13  25 
19  03  15 
17  58-  21 
17  40  15 
17  37  50 

17  31  28 
17  16  13 
16  49  10 
16  19  37 
15  39  09 
15  40  41 
15  44  58 

15  52  17 

16  09  49 

14  17  44 
13  55  15 
13  34  20 
13  28  49 
13  20  00 
13  17  09 
12  27  54 

11  14  45 
11  03  10 
10  36  46 

9  43  45 
8  10  13 
8  04  30 
7  43  32 
7  24  20 


113  12  48 
113  00  05 
113  34  35 
113  40  00 

113  35  19 

114  25  49 
114  39  47 
114  52  10 
114  43  31 

113  16  30 
112  53  26 
112  45  04 
112  28  51 
112  21  46 
111  58  37 

111  16  00 
110  54  28 
109  57  17 
109  40  48 
109  17  30 

109  10  23 
108  49  00 

108  23  37 
107  59  37 
106  26  47 
105  44  25 

105  18  40 

106  33  14 
105  33  37 
105  16  00 
105  39  21 
105  08  54 

110  49  22 
110  56  53 

112  04  07 

114  44  17 

109  13  00 
104  43  26 
104  19  50 
102  07  06 
101  40  25 
101  33  23 

101  27  14 
101  04  32 
99  55  50 
98  35  05 
96  30  43 
96  15  04 
96  08  10 
95  46  43 
95  12  31 

91  55  36 
90  49  45 
89  50  26 
89  19  25 
87  51  00 
87  47  06 
87  12  31 
85  52  59 
85  43  38 
85  42  46 
85  00  46 
82  14  32 
81  43  30 
81  31  58 
81  41  51 


Lun.  Int. 


Range. 


H.W. 


h.    m. 


11  30 


10  07 
9  08 


08 


9  07 


9  07 


50 


L.W. 


h.    m. 


2  50 
2  50 

2  55 

3  05 
3  15 


2  55 

3  00 
2  50 
2  45 


3  15 


3  10 


3  59 
2  51 


5.8 
3.8 


2  52   3.  2 


2  53 


2.5 


2  54  I  1.9 
'2'38T'2.'6* 


9  02 
9  02 
9  08 
9  18 
9  28 


9  08 
9  12 
9  02 
8  58 


9  28 


9  22 


8.5 

9.0 

9.5 

10.0 

10.5 


10.5 

10.0 

9.5 

9.0 


Neap. 


5  26  i  5.0   1.2 


1.4 
0.9 


1.0 


1.1 


1.3 


0.9 


4.6 
4.9 
5.1 
5.4 
5.7 


5.7 
5.4 
5.1 
4.9 


10. 5   5.  7 


11.0   5.9 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  NORTH  AMERICA— Continued. 

[Page  203 

o 

Place. 

Lat.  N. 

Long.  W. 

Lun 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

ii 

s 

Cocos  Island :  Head  of  Chatham  Bay 

Panama:  NE.  bastion,  ast.  station 

Taboga  Island :  Church 

O          1           II 

5  32  57 
8  57  12 
8  47  45 
7  27  40 
4  03  00 

O           1           II 

86  59  17 
79  32  05 
79  33  16 
79  59  25 
81  36  00 

h.     m. 

h.    m. 

ft. 

ft. 

3  00 
3  00 
3  10 

9  14 
9  13 
9  22 

16.0 
15.4 
13.0 

8.7 
8.3 
7.0 

Cape  Mala :  Extreme 

Malpelo  Island:  Summit 

i 1 1 

WEST  INDIA  ISLANDS. 

i 

K 
M 

& 

P 
s 

Memory  Rock :  Center 

Bahama  Island :  W.  pt 

26  56  53 

26  41  18 

79  06  54 
79  00  38 

77  10  45 

76  57  36 

78  23  48 

79  06  00 
79  18  26 
78  06  02 

77  34  26 
75  44  39 
75  10  34 
75  45  17 
75  28  20 
75  51  41 

74  51  54 

75  46  24 

74  59  00 

76  13  00 

76  51  48 

77  21  58 
77  46  45 
77  53  55 
77  57  06 

75  26  00 
75  07  27 
74  28  20 
74  50  08 
74  20  37 
74  22  54 
74  20  21 
74  22  48 
73  49  15 
73  38  03 

72  47  03 

73  50  29 
73  40  17 

73  42  33 
72  28  18 
72  12  51 
72  07  14 
71  31  12 
71  07  29 
70  29  54 
69  21  24 
68  47  24 

74  09  41 
74  29  34 

74  53  44 

75  .33  18 
75  36  59 
75  47  18 
75  47  40 

75  52  18 

76  07  48 

7  40 

1  28 

3.2 

L7 

Abaco  Island :  Light-house 

25  51  30 

26  31  10 

27  15  42 
26  02  00 
25  34  30 
22  45  10 
22  22  30 

21  42  00 

22  01  15 
22  14  02 
22  20  44 
22  31  15 

22  51  00 

23  32  15 

23  06  00 
25  00  00 
25  31  20 
25  05  37 

24  43  45 

25  49  40 
25  49  12 
24  06  15 
23  50  50 
23  56  40 
23  37  45 
22  06  40 
22  32  40 
22  47  30 

22  51  00 

23  05  30 
22  34  38 
22  16  30 
21  40  30 

20  56  00 

21  30  40 
21  37  30 
21  30  00 
21  54  00 
21  29  33 
21  30  55 
21  06  30 
20  35  00 
20  02  00 

20  15  10 
20  21  40 
20  41  41 

20  47  14 

21  04  24 
21  09  00 
21  07  00 
21  07  30 
21  07  05 

1 

Little  Guana  Cav :  Light-house 

Walker  Cay:  Highest  part 

Great  Isaac  Cay:  Light-house 



Gun  Cay :  Light-house 

8  20 

2  08 

...... 

3.0 



1.5 

Ginger  Cay:  Center 

Cay  Lobos:  Light-house 

St.  Domingo  Cav :  Center 



Cay  Verde:  Hill  at  S.  end 

Ragged  Island :  Gun  Pt 

Nairn  Cay :  E.  pt 

Nurse  Channel  Cay :  Beacon 

Long  Island:  S.  pt        

Great  Emma  Island :  Beacon 

1 

Clarence  Harbor:  Light-house 

8  20 
7  00 

2  08 
0  48 

4.1 
4.0 

2.1 
2.1 

Eleuthera  Island :  Light-house 

Royal  Island :  Eastern  Pass 

Nassau:  Light-house 

7  20 
7  40 

1  08 
1  28 

4.0 
3.0 

2.1 

L5 

Andros  Island :  Light-house 

Great  Stirrup  Cav :  Light-house 

Little  Stirrup  Cay :  W.  end 

San  Salvador  ( Cat  I. ) :  Light-house 

Concepcion  Island :  AY.  bay 

7  00 

0  48 

4.0 

2.1 

AVatlings  IslarSd:  Hunchinbroke  Rock  .. 
Rum  Cay :  Harbor  Pt 

1 

1 

Castle  Island :  Light-house 

Fortune  Island :  S.  end 

1 

Crooked  Island:  Moss  flagstaff " 

Bird  Island:  Light-house 

Samana  Cay:  W.  pt 



1 

Plana  Cay:  NW.  pt. 

j 

Mariguana  Island :  SE.  pt 

7  20 

1  08 

3.0 

1.5 

Hogsty  Reef:  NW.  Cay 

Inagua  Island:  Light-house 

7  50 

1  38 

3.5 

1.8 

Little  Inagua  Island:  N W.  pt 

W.  CaicosCay:  Hill,  SE.  end 

French  Cay:  W^.  pt 

I 

Fort  George  Cay:  Old  magazine 

Caicos  Island:  Parsons  Pt.,  S.  islet 

Turk  Island :  Light-house 

7  30 

1  18 

3.0 

1.5 

Square  Handkerchief  Bank:  NE.  breaker 
Silver  Bank :  E.  extreme 

f 

Navidad  Bank :  Center  of  E.  side 

Cape  Maysi :  Light-house 

5  40 

11  53 

2.8 

1.6 

Port  Baracoa:  Light-house 

Port  Cavo  Moa:  Carenero  Pt 

Port  Nipe:  Roma  Pt 

Lucrecia  Point:  Light-house 

Port  Sama:  E.  side  of  entrance 

Peak  of  Sama:  Summit,  885  feet 

Port  Naranjo:  E.  side  of  entrance 

Jibara:  Fort  San  Fernando 

6  20 

0  08 

2.4 

1.4 

Port  Padre:  Guinchos  Pt 

21  18  30     76  35  34 
21  37  30      77  04  ,34 

Port  Nuevitas:  Light-house 

7  00 

0  48 

2.2 

1:2 

1 

Page  204] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

WEST  INDIA  ISLANDS— Continued. 


Place. 


Maternillos  Point:  Light-house 

Cay  Verde:  NW.  «nd 

Cay  Contites:  S.  pt 

Paredon  Grande  Cay :  Light-house 

Cay  Sal :  Light-house 

Bahia  de  Cadiz  Cay:  Light-house 

Piedras  Cay :  Light-house 

Matanzas:  Summit  of  peak 

Habana:  Morro  Hght- house 

Transit  pier,  arsenal  yard 

Cape  San  Antonio :  Light-house 

San  Felipe  Cays:  SW.  pt 

Isle  of  Pines:  Port  Frances 

Piedras  Cay :  Light-house 

Cienfuegos:  Colorados  Pt.  light 

Cape  Cruz:  Light-house 

Santiago  de  Cuba:  Light-house 

Port  Guantanamo :  Fisherman  Pt 

Cayman  Brae:  E.  pt 

Little  Cayman :  W.  pt 

Grand  Cayman:  Fort  George,  W.  end 

Morant  Point :  Light-house 

Port  Antdnio :  Folly  Pt.  Light 

Port  Maria:  NW.  wharf 

St.  Ann  Bay:  Long  wharf 

Falmouth :  Fort 

Montego  Bay :  Fort 

St.  Lucia:  Fort 

Savanna-la-Mar :  Fort 

Kingston :  Plum  Pt.  light 

Port  Royal:  Fort  Charles,  flagstaff 

Morant  "Cays:  NE.  Cay 

Pedro  Bank:  Portland  Rock,  E.  end 

Baxo  Nuevo:  Sandy  Cay 

Samana  Town :  Fort 

Cape  Cabron :  Extreme 

Port  Plata:  Light-house 

Grange  Point:  W.  end 

Manzanilla  Point:  Presidente  Pt 

Cape  Haitien :  Town  fountain 

Port  Paix:  Wharf 

Nicolas  Mole:  Fort  George,  flagstaff 

Gonaives:  Verreur  Pt 

Gonave  Island :  W.  pt 

Arcadius  Islands:  Light-house 

Port  au  Prince:  Fort  Islet  light 

Petite  Riviere  Village:  Sand  beach   in 

front  of  huts 

Jeremie:  Fort 

Navassa  Island:  N.  extreme 

Formigas  Bank:  Shoal  spot 

Vache  Island:  Sand  beach,  near  NW.  pt. 

Jacmel :  Wharf .•. 

Beata  Island :  NW.pt 

Frayle  Rock:  Center 

Alta  Vela:  Summit 

Avarena  Point:  Extreme 

Salinas  Point  ( Caldera) :  Extreme 

St.  Domingo  City :  Light-house 

Point  Espada:  Extreme 


Lat.  N. 


21  40  02 

22  08  45 
22  11  14 

22  29  10 

23  56  30 
23  12  34 
23  14  10 
23  01  54 
23  09  21 
23  08  03 
21  51  44 
21  55  00 
21  35  30 

21  57  45 

22  01  58 
19  50  13 
19  57  31 
19  54  39 

19  45  15 
19  39  10 
19  17  45 

17  55  05 

18  11  31 
18  23  00 
18  26  24 
18  30  34 
18  29  25 
18  27  45 

18  12  20 
17  55  32 
17  55  56 
17  26  30 

17  06  20 
15  53  00 

19  12  29 
19  21  17 
19  49  15 
19  54  45 
19  45  34 
19  46  20 
19  57  40 
19  49  15 
19  25  42 

18  55  26 
18  48  13 
18  33  54 

18  37  15 
18  38  15 
18  25  10 
18  33  00 
18  06  00 
18  13  30 
17  36  45 
17  37  00 

17  28  50 

18  07  00 
18  12  00 
18  27  54 
18  19  43 


Long.  W. 


77  08 
77  37 

77  39 

78  09 
80  27 

80  29 

81  07 

81  43 

82  21 

82  21 
84  57 

83  31 
83  09 
81  07 
80  26 
77  43 
75  52 
75  09 


79  46  07 

80  07  17 

81  23  17 

76  11  08 
76  26  31 

76  54  22 

77  12  52 
77  39  52 

77  56  16 

78  10  52 
78  08  54 
76  46  45 

76  50  38 
75  58  20 

77  26  28 

78  39  04 


19  23 
16  00 

41  23 
39  03 
47  20 
11  42 
49  45 
23  07 

42  52 
18  34 
39  05 
22  01 


74  23  55 

74  05  54 

75  02  03 
75  44  24 
73  43  40 
72  34  30 
71  33  44 
71  41  00 
71  39  11 
70  59  18 
70  35  18 
69  52  00 
68  27  34 


Lun.  Int. 


Range. 


H.  W, 


h.  TO. 


7  20 


30 

18 


30 


4  47 


8  20 
7  50 


9  00 


6  50 


L.  W. 


h.  TO. 


Spg.  I  Neap. 


1  08 


2  18 
1  56 


2  18 


11  00 


2  30 
2  00 


2  48 


0  39 


[1.3]!. 

I 
[1.1]. 


[1.2] 


[LI] 


3.0 


5.5 


[1.2] 


[2.5] 


[2.2] 


ft.     I  ft. 


2.8  t   1.6 


2.2  1.2 

1.3  I   0.7 


1.5  I   0. 


2.0  i   1.1 


2.2  I   1.1 
2.6  I   1.3 


1.5 


2.9 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  INDIA  ISLANDS— Continued. 


[Page  205 


Place 


Mona  Island :  Light-house 

Mayaguez :  Mouth  of  Mayaguez  R 

Aguadilla  Bay :  Village 

San  Juan  de  Porto  Rico:  Morro  light- 
house   

Cape  San  Juan :  Light-house 

Guanica:  Meseta  Pt 

Culebrita  Island :  Light-house 

Vieques  (Crab)  Island:  Port  Ferro  light. 

St.  Thomas:  Fort  Christian,  SW.  bastion. 

St.  John  Island :  Ram  Head 

Tortola:  Fort  Burt 

Virgin  Gorda:  Vixen  Pt 

Anegada:  W.  pt 

E.  extreme  of  reefs 

Christiansted,  Santa  Cruz:  SW.  bastion 
of  fort 

Sombrero :  Light-house 

Dog  Island :  Center 

Anguilla:  Custom-house 

St.  Martin :  Fort  Marigot  light 

St.  Bartholomew :  Fort  Oscar 

Saba :  Diamond  Rock 

St.  Eustatius:  Fort  flagstaff 

St.  Christopher:  Basseterre  Church 

Booby  Island :  Center 

Nevis:  Fort  Charles 

Barbuda:  Flagstaff,  Martello  Tower 

Antigua,    English    Harbor:      Flagstaff, 

dockyard  

Sandy  Island :  Light-house . . 

Redonda  Islet:  Center 

Montserrat:  Plymouth  Wharf 

Guadeloupe,  Basseterre:  Light  on  mast. 
Port  Louis:  Light  on  mast 
Gozier  Islet:  Light-house. 
Manroux  Id. :  Light-house 
Point  h  Pitre:  Jarry  Mill. . 

Desirade:  E.  pt 

Petite  Terre :  Light-house 

Marie  Galante:  Light-house 

Saintes  Islands:  Tower  on  Chameauhill 

Dominica,  Prince    Ruperts    Bay:    Sand 

beach  W.  of  church 

Roseau:  Flagstaff,  Fort  Young 

Aves  Island :  Center 

Martinique,  Fort  de  France:    Fort  St. 

Louis  light 

St.  Pierre:  Ste.  Marthe  Bat- 
tery   

CaravellePen.:  Light-house 
Cabrit  Islet:  Summit 

St.  Lucia,  Port  Castries:  Light-house... 

Barbados,  Bridgetown:  Flagstaff,  Rick- 

ett's  Battery 

S.  Point:  Light-house 

Ragged  Point:  Light-house  . 

St.  Vincent,  Kingstown:  Light-house.. 

Bequia  Island,  Admiralty  Bay:  Church 

Grenada:  St.  George  light-house 

Tobago,  Rocky  Bay:  Light-house 


Lat.  N. 

Long.  W. 

Lun. 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

0  '  n 
18  02  43 

o  /  r/ 

67  50  30 
67  09  04 
67  16  08 

66  07  28 

65  36  31 

66  54  11 
65  13  34 
65  25  26 

64  55  52 
64  42  03 
64  36  47 
64  21  48 
64  24  58 
64  10  45 

64  42  16 
63  28  13 
63  16  00 
63  04  39 
63  05  45 

62  51  30 

63  15  16 
62  59  09 
62  43  14 
62  35  25 
62  37  29 
61  49  54 

61  46  07 

61  55  11 

62  19  10 

62  13  24 
61  44  09 
61  32  15 
61  29  40 
61  32  05 
61  33  15 
61  00  44 
61  06  45 
61  19  15 
61  35  55 

61  28  14 
61  23  52 

63  37  46 

61  04  30 

61  11  12 
60  53  20 

60  52  33 

61  00  48 

59  37  19 
59  31  50 

59  26  04 
61  14  34 
61  14  09 
61  45  06 

60  42  38 

h.     m. 

h.     TO. 

ft. 

ft- 

18  11  56 
18  25  09 

7  04 

2  00 

2.0 

1.0 

18  28  56 
18  23  05 

8  21 

2  20 

1.3 

0.9 

17  57  10 

[1.0] 
1.0] 

;i-i] 

[1.2] 

18  18  44 
18  05  20 

18  20  23 
18  18  08 

[7  31] 
[7  35] 

[7  11] 

[1  30] 
[1  40] 

[0  58] 

18  25  04 

18  30  39 

18  45  11 

18  36  30 

17  45  09 

18  35  37 

18  16  42 

18  13  06 

18  04  07 

17  53  58 

[1.5] 

17  39  10 

17  29  10 

17  18  12 

17  13  38 

17  07  52 

17  35  50 

17  00  00 

[2.0] 

17  06  54 

16  55  18 

16  42  12 

15  59  50 

16  25  09 

16  11  57 

[1.3] 

16  13  14 

16  13  56 

16  19  56 

16  10  17 

15  52  59 

15  51  32 

15  34  34 
15  17  27 

4  00 

10  12 

1.5 

0.8 

15  42  00 

14  35  44 

14  43  54 

14  46  13 
14  23  23 

3  50 

10  02 

1.1 

0.6 

14  01  54 

13  05  42 
13  02  45 

2  50 

9  02 

3.0 

1.5 

13  09  40 

1 

13  09  19 
13  00  25 

2  50 

9  05 

1.6 

0.8 

12  03  02 
11  10  08 

2  30 

3  50 

8  42 
10  02 

1.5 
2.1 

0.8 

1.1 

Page  206]                                       APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  INDIA  ISLANDS— Continued. 

Place. 

Lat.  N. 

Long.  w. 

Lun.  Int. 

Range.          1 

H.  W.         L.  W. 

Spg. 

Neap. 

Testigos  Islets:  Center  of  Testigo  Grande. 
Sola  Island :  Center 

O           t         II 

11  25  02 
11  19  00 
10  59  43 

10  57  45 

11  47  57 

11  56  16 

12  02  06 

11  59  30 

12  06  45 
12  06  36 
12  31  05 

O           1         II 

63  05  48 
63  36  00 

h.   m. 

h.   m. 

ft. 

ft. 

Pampatar,  Margafttal. :  San  Carlos  Castle . 

•Tortugas  Island:  S.  end  of  W.  Tortugillo 

Islet 

63  48  00 

65  26  38 

66  12  31 
66  39  10 
68  14  10 
68  39  19 
68  56  44 
68  56  36 
70  02  34 

Orchila  Island :  S.  side 

Roques  Islands:  Pirate  Cay 

. 

Bonaive  Island:  Light-house 

Little  Curasao  Island :  Light-house 

Curasao  Island:  Time-ball  station 

Light-house 

Oruba  Island:  Light-house 

' 

NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA. 

i 
s 

9 

0 

W 

i 

a 

> 

•9 

« 

1 

Chagres:  San  Lorenzo  Castle 

9  19  27 
9  22  39 
9  22  09 
9  32  30 
8  54  52 
8  47  00 

8  37  30 

9  24  00 
9  24  00 

10  25  50 

11  00  15 

10  07  00 

11  15  28 

11  33  30 

12  12  34 
12  23  09 

12  04  00 

10  57  30 

11  48  56 

12  11  00 
12  29  15 
11  27  56 

10  47  00 

11  10  00 
10  29  53 
10  36  57 
10  35  00 
10  34  06 
10  49  30 
10  13  30 
10  27  20 
10  40  00 
10  42  00 
10  40  00 
10  40  15 
10  42  00 
10  43  27 
10  45  00 
10  44  19 
10  43  48 
10  38  15 

8  39  25 

10  38  37 
10  40  03 
10  50  02 
10  03  29 
10  16  59 

80  00  22 
79  57  16 
79  54  45 
79  39  40 
77  42  25 
77  38  00 
76  52  55 
76  10  45 
75  48  00 
75  32  50 
74  57  55 
74  49  51 
74  14  33 
72  54  50 
72  09  42 
71  45  42 

71  07  55 
71  37  00 
70  17  21 
70  04  55 
70  57  00 
69  34  20 
68  19  55 
68  22  54 
68  00  55 
66  56  06 
66  06  15 
66  04  13 
66  09  25 
64  44  00 
64  11  33 
64  17  55 
63  50  25 
63  31  55 
63  18  00 
63  14  00 
63  09  43 
62  41  55 
62  44  29 
61  50  50 
61  51  18 

60  10  15 

61  30  38 
61  45  54 

60  54  10 

61  55  41 
61  28  12 

Toro  Point:  Light-house 

Colon:  Light-house 

0  06 

6  18 

1.1 

0.6 

Porto  Bello :  Ft.  St.  Geronimo 

Caledonia  Harbor:  Scorpion  Cay 

Carreto  Port:  Peak 

11  30 

5  17 

L5 

0.8 

Caribana  Point:  Extreme 

Fuerte  Island:  N.  extreme 

Cispata  Port:  Zapote  Pt 

Cartagena:  Light-house 

Sa vanilla:  Light-house 

Magdalena  River:  NW.  pt.  of  Gomez  I.. 
Santa  Marta:  Light-house 

Rio  de  la  Hacha:  Light  on  church 

Cape  La  Vela:  Sand  beach  inside  cape  . . 
Baiia  Honda:  E.  pt.,  S.  side 

Espada  Point:  Extreme 

Maracaibo:  Zapara  I.  light 

5  05 

11  17 

2.5 

1.5 

Estangues  Point:  500  ft.  from  extreme  . . 
Cape  San  Roman :  Extreme  . 

Marjes  Islets:  N.  islet 

Vela  de  Coro:  Light-house 

Tucacas  Island :  Ore  house 

St.  Juan  Bay:  Cay 

Puerto  Cabello:  Light-house 

La  Guaira:  Light-house 

6  00 

12  12 

,2.8 

L7 

Cape  Codera:  Morro.         

Corsarios  Bay:  W.  pt 

Centinela  Islet:  Center 

Barcelona:  Morro 

Cumana:  Light-house 

Escarseo  Point:  Extreme 

Chacopata:  Morro 

Esmeralda  Islet:  Center 

Carupano :  Light-house 

Pt.  Herman  Vasquez 

Puerto  Santo  Bay:  Sand  spit  S.  of  Morro. 
Tres  Puntas  Cape :  Extreme 

UnareBay:  Obs.  spot,  200yds.  S.  of  Morro 
Pena  Point:  Extreme 

Pato  Island:  E.  pt 

........ 

Mocomoco  Pt. :  Extreme 

Port  of  Spain:  King's  Wharf  light 

Chacachacare  Island:  Rocks  off  SW.  pt. . 
Galera  Point:  NE.  extreme,  light-house. 
Icacos  Point:  Light-house 

4  20 

10  30 

3.2 

1.9 

San  Fernando :  Pierhead 

APPENDIX  IV.                                        [Page  207 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued. 

1 

Place. 

Lat.  N. 

Long.  W. 

Lun. 

Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

S 

a 

g 

Demerara:  Georgetown  light-house 

Nickerie  River:  Light-house 

0  1         II 

6  49  20 
5  58  30 
5  49  30 
5  44  50 
5  16  50 
5  02  40 
4  56  20 
4  49  30 
4  23  20 

4  20  45 
2  46  30 

1  40  17 
Lat.  S. 

0  17  00 

1  26  59 
0  35  03 

2  10  11 
2  31  48 
2  16  22 
2  41  55 

2  53  20 

3  42  05 

4  25  35 

5  03  15 
5  29  15 
5  45  05 

5  46  41 

6  56  30 

7  06  35 

8  00  50 
8  03  22 
8  20  45 

8  43  40 

9  39  35 

10  30  30 

10  58  20 

11  09  45 

11  27  40 

12  12  05 

12  33  40 

13  00  37 

12  52  48 

13  22  37 

13  56  42 

14  17  40 
14  47  40 

14  56  40 

15  13  27 

15  21  00 

16  17  20 

16  25  38 

17  21  40 
17  31  45 
17  43  30 

17  57  31 

18  06  15 
20  19  23 
20  38  25 
20  49  00 

20  57  35 

21  38  40 

22  02  00 
22  23  45 

O         1         II 

58  11  30 
57  00  30 
55  08  48 
54  00  30 
52  34  53 
52  21  11 
52  20  26 
51  55  36 
51  50  36 

51  27  46 
50  54  46 
49  56  46 

48  23  30 
48  30  01 
47  20  54 
44  25  56 
44  18  45 
43  37  30 
42  18  02 
41  40  35 
38  28  25 
37  44  55 
36  02  52 
35  15  52 
35  11  55 
35  12  43 
34  49  30 
34  53  04 
34  50  36 
34  51  57 

34  56  05 

35  05  06 

35  44  54 

36  21  51 

37  04  00 

37  12  36 
37  24  00 

37  45  46 

38  02  16 
38  32  06 
38  41  28 

38  54  38 

39  07  05 
39  00  45 
39  03  25 
39  01  45 
39  01  15 
39  16  45 
39  02  05 
39  04  15 
39  13  15 
39  12  00 
39  14  36 

38  41  46 

39  31  16 

40  16  36 
40  23  46 
40  40  45 

40  46  35 

41  02  21 

40  59  00 

41  47  35 

h.    m. 
'  4  18 

h.    m. 
9  50 

St. 
8.6 

ft. 
3.9 

Parainaribo :  Stone  steps 

5  50 

12  00 

9.5 

4.3 

Maroni  River:  W.  light-house 

Salut  Islands:  Light-house 

Enfant  Perdu  Islet:  Light-house. 

Cayenne:  Light-house 

4  27 

10  30 

6.0 

2.7 

Connetable  Islet:  Center 

Cariniare  Mount:  Summit 

Orange  Cape :  Extreme 

Maye  Mountain :  Summit 

i 

North  Cape:  Extreme 

i 

Cape  Magoari :  Extreme 

Para:  Custom-house    

ii  50 

5  37 

11.0 

5.2 

Atalaia  Point:  Light-house 

Itacolomi  Point:  Light-house 

Maranhao  Island:  Landing  place 

Santa  Anna  Island :  Light-house 

Tutoya:  Entrance 

Paranahiba  River:  Amargao  Village 

Ceara:  Light-house 

6  50 
5  35 
5  05 

0  38 
11  47 
11  17 

16.5 
13.1 
11.7 

7.9 
6.2 
5.6 

5  25 
5  50 

11  37 

12  00 

8.2 
8.0 

3.9 
3.8 

Jaguaribe  River:  Pilot  station 

Cai^ara:  Village 

Cape  St.  Roque :  Extreme 

Rio  Grande  do  Norte:  Light-house 

Natal :  Cathedral 

4  05 

10  17 

8.8 

4.2 

Parahiba  River:  Light-house  at  entrance. 
Parahiba:  Cathedral 

Olinda:  Light-house 

Pernambuco:  Picao  light-house 

4  33 

10  50 

7.0 

3.3 

Cape  St.  Augustine:  Light-house 

Tamandare:  Village 

Maceio:  Light-house 

4  20 
4  17 

10  32 
10  29 

8.5 
7.8 

4.1 
3.7 

San  Francisco  River:  Light-house  at  en- 
trance   • 

Cotinguiba  River:    Light-house  at  en- 
trance   

Vaza  Barris  River:    Semaphore  at  en- 
trance   

Real  River:  Light-house 

Conde:  Village 

Garcia  d' Avila:  Tower 

' 

Bahia:  Santo  Antonio  light-house 

Itaparica :  Fort  on  N.  pt 

4  10 

10  22 

7.6 

3.6 

Morro  de  Sao  Paulo:  Light-house 

Camamu :  Village 

3  50 
3  50 

10  00 
10  00 

6.0 
6.3 

2.9 
3.0 

Contas:  Church 

Ilheoa:  Church 

Oliven^a:  Center  of  village 

3  35 

9  47 

6.4 

3.1 

Una:  Center  of  village 

Comandatuba:  Center  of  village 

Santa  Cruz:  Church 

3  25 

9  37 

6.0 

2.9 

Porto  Seguro:  INIatriz  Church 

Prado :  River  entrance 

Alcobaga:  Center  of  village 

Caravellas:  Center  of  village 

j 

3  10 
3  15 

9  23 
9  27 

6.4 
7.5 

3.1 
3.6 

Abrolhos  Island:  Light-house 

Porto  Alegre:  Center  of  village 

Espiritu  Santo  Bay :  Light-house 

Guarapiri  Islets :  E.  islet 

2  50 

9  00 

4.0 

L9 

Benevente:  Village 

2  40 

8  52 

5.0 

2.4 

Itapemirim:  Moscas  Islet 

Sao  Joao  da  Barra:  Light-house 

Cape  St.  Tl  .ome :  Extreme 

Macahe :  Fort  at  entrance 

1 

2  20 

8  30 

9.2 

4.4 

Page  208]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued. 


riace. 


Santa  Anna  Island :  Summit 

Barra  Sao  Joao:  Village 

Busies:  Church 

Cape  Frio:  Light-house 

Port  Frio:  Village 

Maricas  Islands:  S.  islet 

Rio  de  Janeiro:  Fort  Villegagnon  Light. 
Imperial  Observatory. . . 

Raza  Island :  Light-house 

Petropolis:  Center  of  town 

Cape  Guaratiba:  Summit 

Marambaya  Island:  Summit  of  SW.  end. 

Mangaratiba:  Village 

Palmas  Bay :  Beach  at  head  of  bay 

Angra  dos  Reis:  Landing-place 

Ilha  Grande:  Light-house 

Parati :  Fort 

Ubatuba:  Cathedral 

Porcos  Grande  Islet:  Summit 

Busios  Islets:  Summit 

St.  Sebastian  Island:  Boi  Pt.  light 

Villa  Nova  da  Princessa:  Center 

Santos:^  Moela  I.  light-house 

Quay 

Alcatrasses  Island:  Summit,  880  ft 

Conceigao:  Church i 

Quemada  Grande  Island:  Summit, 628ft. 

Iguape:  Quay  

Bom  Abrigo  Islet:  Light-house 

Ilha  do  Mel :  Light-house : 

Paranagua:  Quay 

Antonina:  Quay 

Coral  Islet:  Center 

Itacolomi  Islet:  Center 

Sao  Francisco:  Center  of  town 

Itapacaroya:  Church 

Cambria:  Church 

Arvoredo  Island :  Light-house 

Anhatomirim:  Light-house 

St.  Catharine  Island:  Rapa  Pt 

Naufragados  light 

Nostra  Senhora  do  Deserto :  Quay 

Coral  Island:  Summit,  230  feet 

Cape  St.  Martha:  Light-house 

Torres  Point:  Extreme 

Rio  Grande  do  Sul:  Light-house 


Lat.  s. 


Castillos:  Beuna  Vista  Hill,  184  feet. 

Cape  Santa  Maria:  Light-house 

Lobos  Island :  Center 

Maldonado :  Light-house 

Flores  Island :  Light-house 

Montevideo:  Cathedral,  SE.  tower.. 
Colonia:  Light-house 


Martin  Garcia  Island :  Light-house 

Buenos  Ayres:  Cupola  of  custom-house. 

La  Plata 

Indio  Point :  Light-house 

Piedras  Point:  Extreme 

Cape  San  Antonio:  Light-house 

Madanas  Point:  Light-house 

Cape  Corrientes:  E.  summit 

Port  Belgraoo:  Anchor.-Stock  Hill 

Argentina:  Fort 


22  26  00 
22  37  00 

22  46  00 

23  00  42 

22  53  15 

23  01  43 
22  54  46 

22  54  15 

23  03  40 

22  32  00 

23  03  40 
23  04  20 

22  57  20 

23  09  20 
23  00  30 
23  09  50 
23  12  20 
23  25  55 
23  32  57 
23  45  15 
23  58  30 

23  47  20 

24  03"  06 

23  56  00 

24  06  30 
24  10  32 
24  28  45 

24  42  35 

25  06  40 
25  30  55 
25  31  20 
25  26  30 
25  44  10 

25  50  15 

26  14  17 

26  46  45 

27  01  35 
27  18  00 
27  25  30 
27  22  55 
27  50  27 
27  36  00 

27  56  40 

28  38  00 

29  20  20 
32  06  40 

34  21  19 

34  40  01 

35  01  39 
34  58  15 
34  56  55 
34  54  33 
34  28  20 


34  10  50 
34  36  30 

34  54  30 

35  15  45 

35  26  50 

36  18  24 
36  53  00 
38  05  30 
38  57  00 
38  43  50 


Long.  W. 


43  15 
59  45 
54  05 

00  00 

01  15 
54  05 

09  24 

10  16 
08  45 

11  01 

33  24 
59  26 

02  29 
08  24 
19  04 
05  45 

42  04 
04  04 

03  50 
00  39 
15  20 

21  04 
15  57 
19  09 

40  49 
47  44 

41  04 

32  54 
51  50 
19  53 
31  03 

43  14 
23  14 

25  51 
39  29 
36  59 
36  44 

22  20 

34  25 

26  09 

35  16 
34  14 

33  44 
49  45 
43  39 
07  44 


Lun.  Int. 


53  47  16 

54  09  14 
54  53  16 

54  57  10 

55  55  04 

56  12  15 

57  52  27 

58  15  40 
58  22  14 
57  54  15 
57  10  45 
57  05  28 
56  44  15 

56  38  54 

57  30  01 

61  59  15 

62  15  27 


H.  W. 


h.   m. 


2  30 


2  50 


1  35 


2  50 


2  55 


2  35 


4  00 
8  20 


2  00 
6  30 


6  43 


9  50 


6  00 


L.  W. 


h.   m. 


Range. 


Spg.    Neap. 


ft. 


8  42   4. 9 


9  00   4.  2 


7  47 


9  05 


8  47 


10  12 

2  08 


8  12 
0  00 


12  15 


3  35 
'6'66' 


2.0 


3.5 

4.0 


5.3 


15.8 


2.3 


2.0 


5.  3    2.  5 


9  00   5. 0    2. 


6:4    3.1 


5.9  I   2. 


1.8    0.9 


0.9 


2.3 

2.7 


2.1  I   1.4 


3.5 


8.2 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
NORTH  AND  EAST  COASTS  OF  SOUTH  AMERICA— Continued 


[Page  209 


Place. 


Labyrinth  Head :  Summit 

Union  Bay:  Indian  Head 

San  Bias  Harbor:  SW.  end  of  Hog  Islet. 

San  Bias  Bay:  Summit  of  Rubia  Pt 

Rio  Negro:  Main  Pt 

Bermeja  Head :  E.  summit 

Port  San  Antonio:  Point  Villarino 

San  Antonio  Sierra:  Summit 

Port  San  Jos6:  San  Quiroga  Pt 

Delgado  Point:  SE.  cliff 

Cracker  Bay:  Anchorage 

Port  Madryn:  Anchorage  off  cave  bluff 

Chupat  River:  Entrance 

Port  St.  Elena:  St.  Elena  pen 

Leones  Island:  SE.  summit 

Melo  Port:  W.  pt 

Port  Malaspina :  S.  pt 

Cape  Three  Points:  NE.  pitch 

Port  Desire:  Largest  ruin 

Sea  Bear  Bay :  Wells  Pt 

Port  San  Julian:  Sholl  Pt 

Port  Santa  Cruz :  Mount  at  entrance 

Coy  Inlet:  Height  S.  side  of  entrance. . . 

Gallegos  River:  Observation  mound 

Cape  Virgins:  SE.  extreme 

Cape  San  Diego:  Extreme 

Staten  Island,   Cape    St.  John:  Light- 
house, W.  pt 

Port  Cork:  Observation 
mark,  summit 

Cape  St.  Bartholomew: 

Middle  pt 

Good  Success  Bay:  S.  end  of  beach 

Lennox  Cove:  Bluff,  N.  end  of  beach  . . . 

Goree  Road:  Guanaco  Pt 

Wollaston  Island :  Middle  Cove 

Barneveldt  Islands:  Center 

Cape  Horn:  South  summit,  500  ft 

Hermite  Island:  St.  Martin  Cove 


Lat.  S. 


39  26  30 

39  57  30 

40  32  52 

40  36  10 

41  02  00 
41  11  00 

40  49  00 

41  41  10 

42  14  15 
42  46  15 
42  57  00 

42  45  40 

43  20  45 

44  30  40 

45  04  00 
45  03  00 
45  10  10 
47  06  20 
47  45  05 
47  57  15 

49  15  20 

50  08  30 

50  58  27 

51  33  21 

52  18  35 
54  40  35 

54  43  24 

54  45  16 

54  53  45 

54  48  02 

55  17  00 
55  19  00 
55  35  30 
55  48  54 
55  58  41 
55  51  20 


Long.  W. 


62  03  22 
62  07  46 
62  09  30 
62  10  12 

62  45  11 

63  08  16 

64  54  41 

65  12  29 
64  27  56 

63  37  16 

64  28  20 

64  59  00 

65  03  36 
65  22  10 
65  36  01 

65  52  30 

66  32  36 
65  51  46 
65  54  45 
65  45  40 

67  42  30 

68  23  00 

69  09  47 
69  00  31 
68  22  12 
65  05  53 

63  47  00 

64  03  00 

64  45  45 

65  13  48 

66  49  00 

67  10  00 
67  19  00 

66  43  48 

67  16  15 
67  34  00 


Lun.  Int. 


H.W.    L.W. 


h.    m.  h.    m. 


10  50 


10  35 


7  05 


0  00 


10  35 
9  20 
9  00 
8  40 
8  18 
4  20 

4  19 


3  50 


4  07 


4  38 


4  23 


0  52 


3  50  I  10  03 


6  12 


10  33 
10  32 


10  03 


10  02 


Range. 


14.7 


23.5 


13.2 


16.8 


18.3 


29.5 
39.6 
40.0 
45.6 
38.7 
9.9 


6.7 


4.8 


Neap. 


St. 


7.7 


12.3 


6.9 


9.6 


15.4 
20.7 
20.9 
23.9 
20.2 
5.2 

6.0 


5.2 


3.8 


WEST  COAST  OF  SOUTH  AMERICA. 


False  Cape  Horn:  S.  extreme 55  43  15 

Ildefonso  Island:  Highest  summit 55  52  30 

Diego  Ramirez  Island :  Highest  summit .  56  28  50 

York  Minster  Rock:  Summit,  800  ft \  55  24  50 

Cape  Desolation :  S.  summit 54  45  40 

Mount  Skyring:  Summit,  3,000  ft 54  24  48 

Noir  Island:  SE.  extreme 54  30'  00 

Landfall  Island:  Summit  of  Cape  Inman  J  53  18  30 

Cape  Deseado:  Peaked  summit 52  55  30 

Apostle  Rocks:  W.  rocks 52  46  15 

Cape  Pillar:  N.  cliff 52  42  50 

Dungeness  Point:  Light-house 52  23  55 

Cape  Espiritu  Santo:  NE.  cliff 52  39  00 

Catharine  Point:  NE.  extreme !  52  32  00 

Cape  Possession :  Light-house 52  17  54 

Cape  Orange:  N.  extreme 52  28  40 

Delgada  Point:  Light-house 52  28  00 

Cape  Gregory :  Light-house 52  38  18 

Cape  San  Vicente:  W.  extreme 52  46  20 


04  40 

17  30 

41  30 

01  30 

36  10 

10  20 

00  00 

18  15 

36  30 

46  50 

42  20 

25  45 

34  00 

45  20 

57  10 

24  00 

33  00 

14  16 

25  25 

3  50 


2  20 
1  50 


0  32 
8  19 
8  20 
8  24 
8  35 


8  47 

9  23 


10  03 


8  33 
8  03 


6  45 
2  07 
2  08 
2  12 
2  25 


6.0 


4.8 
4.7 


2  40 

3  20 


4.0 
39.4 
39.0 
30.0 
39.0 


39.0 
21.0 


3.9 


3.7 
3.7 


3.1 
20.6 
20.4 
15.7 
20.4 


20.4 
11.0 


'22489—03- 


-14 


Page  210J                                      APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  SOUTH  AMEBICA— Continued. 

1 

Place. 

■ 

Lat.  S. 

Long.  W. 

Lun 

Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

6 

Elizal)eth  Islanc^  NE.  ])luff 

O           t        II 

52  49  18 

53  10  10 
53  33  30 
53  38  12 
53  47  00 
53  53  43 
53  51  45 
53  41  45 
53  43  57 
53  42  00 
53  37  10 
53  34  20 
53  31  45 
53  32  10 
53  30  50 
53  30  05 
53  25  00 
53  18  45 
53  15  30 
53  13  40 
53  06  30 
53  11  40 
53  06  35 

52  55  46 

53  01  00 
52  55  00 
52  42  00 
52  44  58 

51  18  29 
49  25  19 
49  12  40 

49  07  30 

48  54  20 

52  37  18 
52  24  00 
52  16  10 
51  51  50 

50  42  00 
50  17  20 
50  02  00 
50  00  18 

49  48  00 
48  06  15 
48  02  20 

47  39  30 
46  49  31 
46  58  57 
46  49  10 
46  35  00 
46  04  00 
45  53  20 
44  55  50 
44  09  00 
43  48  30 
43  41  50 
43  19  35 
43  17  10 
43  11  20 

42  48  00 
42  27  45 

O          f          II 

70  37  51 
70  54  24 
70  34  27 
70  58  31 

70  55  03 

71  17  15 
71  55  30 

71  59  41 

72  04  45 
72  10  42 
72  19  30 
72  27  10 
72  34  15 
72  32  25 
72  38  00 
72  47  30 

72  47  55 

73  00  30 
73  12  05 
73  21  30 
73  15  30 
73  17  45 
73  16  15 
73  44  28 

73  59  33 

74  17  45 
74  13  30 
74  38  14 
74  04  00 
74  17  39 
74  23  27 
74  25  10 
74  20  55 

74  23  10 

75  06  00 

74  55  00 

75  13  20 
75  27  45 

74  51  30 

75  22  00 
75  13  20 
75  31  00 
75  40  30 
75  28  20 

75  10  00 
75  18  20 
75  25  30 
75  37  55 
75  31  30 
75  12  00 
?5  06  00 
75  08  45 
74  07  45 

73  59  35 

74  42  00 

73  41  50 

74  22  00 
72  44  40 

72  30  30 

73  45  20 

//.    m. 

10  24 

11  03 

h.    in. 

4  24 

5  03 

ft. 

8.0 

5.0 

ft. 

4.2 

2.6 

Sandy  Point:  Light-house  

Cape  St.  Valentine:  Sununit,  at  extreme. 
Port  Famine:  Observatory 

11  58 

12  21 
0  28 

5  58 

6  21 
6  53 

6.0 
8.0 
7.0 

3.1 
4.2 
3.7 

Cape  San  Isidro:  Extreme 

Cape  Fro  ward :  Summit  of  bluff 

Mount  Pond:  Summit 

Port  Gallant:  Wigwam  Pt 

1  20 

7  40 

8.0 

4.2 

Charles  Island:  White  rock  near  NW.  end 
Rupert  Island :  Summit 

Mussel  Bay :  Entrance 

Tillv  Bav:  Sarah  I 

Borja  Bay :  Bluff  on  W.  shore 

1  54 

8  11 

5.5 

2.9 

Cape  Quad :  P^xtreme 

Barcelo  Bay :  J^ntrance 

Swallow  Bay :  Shag  I 

Cape  Notch :  Extreme 

Playa  Parda  Cove:  Summit  of  Shelter  I . . 

Pollard  Cove:  Entrance 

Port  Angosto:  Hay  Pt 

St.  Anne  Island :  Central  summit 

Half  Port  Bay :  Point  ^ 

Upright  Port:  Entrance 

Port  Tamar :  Mouat  Islet 

1  53 

8  08 

5.0 

3.9 

1  31 

7  44 

4.5 

3.5 

1  09 

7  21 

4.0 

3.1 

0  55 

7  07 

6.0 

4.6 

Port  Churruca:  Summit  of  Blanca  Pen  . . 
Valentine  Harbor:  Observation  mount . . 
Cape  Parker:  W.  summit 

Mercy  Harbor:  Summit  of  Battle  I 

Mayne  Harbor:  Observation  spot 

Port  Grappler:  Observation  spot 

Port  Riofrio:  Vitalia  I 

Eden  Harbor:  Observation  spot 

Halt  Bav :  Observation  islet 

Westminster  Hall  Islet:  E.  summit 

Evangelistas  Island:  Light-house 

Cape  Victory:  Extreme 

0  55 

7  08 

4.4 

3.4 

Cape  Isabel:  W.  extreme 

Cape  Santiago:  Summit. 

Molyneux  Sound :  Romalo  I 

Cape  Tres  Puntas:  Summit,  2,000  ft 

Port  Henry :  Observation  spot 

0  30 

6  45 

4.5 

3.5 

Mount  Corso:  SW.  summit 

Rock  of  Dundee:  Summit 

Santa  Barbara  Port:  N.  extreme  obs.  pt. 
Guaineco  Islands:  Speedwell  Bay,  hill, 
np:.  pt 

0  15 

6  30 

5.3 

4.1 

Port  Otwav :  Observation  spot 

0  10 

6  25 

5.3 

4.1 

Cape  Tres  Montes:  Extreme 

Cape  Raper:  Rock  close  to  cape 

Christmas  Cove:  SK.  extreme 

Hellyer  Rocks:  Middle 

Cape  Taytao:  W.  extreme 

Socorro  Island:  S.  extreme 

Mayne  Mountain:  Summit,  2,080  ft 

Port  Low :  Observation  islet 

0  00 

6  13 

4.4. 

3.4 

12  20 
12  10 

6  10 
6  00 

6.2 
6.1 

4.8 
3.1 

Huafo  Island :  S.  extreme 

Port  San  Pedro:  Cove  on  S.  shore 

Cape  Quilan:  SW.  extreme 

Corcovado  Volcano:  Summit,  7,510  ft... 
Minchinmadiva    Volcano:    S.   summit, 
8,000  feet 

Castro:  E.  end  of  town 

0  01 

6  21 

18.0 

9.1 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

WEST  COAST  OF  SOUTH  AMERICA— Continued. 


[Page  211 


Place. 


Dalcahue:  Chapel 

Oscuro  head :  Observation  pt 

Coman  Inlet:  Olvidada  I 

Port  Calbuco:  Lg,  Picuta 

San  Carlos  de  ARcud:  Light-house 

Condor  Cove:  Landing 

Eanu  Cove:  Anchorage 

Muilcalpue  Cove:  Landing  place 

Milagro  Cove:  Landing  place 

Laruehuapi  Cove:  Landing  place 

Valdivia :  Niebla  Fort  light 

Queule  Bay :  Choros  Pt 

Mocha  Island :  Light-house 

Lebu  River:  Tucapel  Head 

Yanez  Port:  Anchorage 

Lota:  Light-house 

Santa  Maria  Island :  Light-house 

Talcahuano :  Fort  Galvez 

Light  on  Quinquina  I 

Llico:  Village 

Port  San  Antonio:  Village 

Aconcagua  Mountain:  Summit 

Santiago :  Observatory 

Valparaiso:  Playa  Ancha  Pt.  light 

Site  of  Fort  San  Antonio 

Quintero  Point:  Summit 

Pichidanque:  SP].  pt.  of  island 

Tablas  Point:  SW.  extreme 

Chuapa  River:  S.  entrance  pt 

Maitencillo  Cove:  N.  head 

Talinay  Mount:  Summit 

Lengua  de  Vaca:  Light-house 

Port  Tongoi:  Obs.  spot.  W.  of  village 

Coquimbo :  Tortuga  Pt.  light 

Smelting  works,  N.  of  town. 

N.  islet 

Pajaros  Islets :  Light-house 

Choros  Islands:  SW.  pt.  of  largest  id 

Chaiiaral  Island:  Light-house 

Huasco:  Light  on  mole 

Herradura  de  Carrizal:  Landing  place. . . 

Port  Carrizal":  Middle  Point 

Matamoras  Cove:  Outer  pt.  S.  side 

Salado  Bay:  Summit  of  Cachos  Pt 

Copiapo:  Landing  place 

Caldera:  Light-house 

Light  on  mole  head 

Cabeza  de  Vaca  Point:  Extreme 

Flamenco:  SE.  corner  of  bay 

Chanaral  Bay :  Observation  pt 

St.  Felix  I. :  Peterborough  Cathedral  Rock 

Pan  de  Azucar  Island :  Summit 

Lavata:  Cove  near  SW.  pt 

San  Pedro  Point:  Summit 

Port  Taltal :  Light-house 

Grande  Point:  Outer  summit 

Paposo  Road :  Huanillo  Pt 

Reyes  Head :  Extreme  pitch 

Cobre  Bay:  Pt.  W.  of  village 

Jara  Head :  Summit 

Antofagasta:  Light-house 

Chimba  Bay:  E.  pt.  of  large  island 


Lat.  S. 

O    /    l> 

42  23  00 

42  04  00 

42  03  00 

41  46  08 

41  46  40 

40  46  19 

40  43  18 

40  35  52 

40  21  04 

40  11  47 

39  51  37 

39  23  00 

38  21  22 

37  35  20 

37  22  30 

37  05  20 

36  59  07 

36  42  00 

36  36  45 

34  46  02 

33  34  13 

33  38  30 

33  26  42 

33  01  08 

33  01  52 

32  46  00 

32  07  55 

31  51  45 

31  39  30 

31  17  05 

30  50  45 

30  14  00 

30  15  14 

29  56  15 

29  56  24 

29  55  10 

29  34  40 

29  15  45 

29  00  50 

28  27  20 

28  05  45 

28  04  30 

27  54  10 

27  39  20 

27  20  00 

27  03  15 

27  03  15 

26  51  05 

26  34  30 

26  20  00 

26  16  12 

26  09  15 

25  39  30 

25  31  00 

25  25  20 

25  07  00 

25  05  25 

24  34  30 

24  15  00 

23  53  00 

23  38  50 

23  33  05 

Long.  W. 


36  00 

25  00 
45  00 
07  15 
52  54 

51  00 
49  50 
45  00 
45  20 
41  50 

26  25 

14  00 
58  06 

39  55 

40  00 

11  13 
32  30 
07  27 

02  49 
06  12 
38  00 
56  30 

41  32 
38  52 

38  42 

32  56 

33  22 

34  51 

35  20 

39  21 
39  00 
39  00 

31  09 
21  00 

21  53 

22  21 

33  20 

34  38 

36  40 

15  45 

12  48 
11  32 
09  38 

03  26 
58  45 

52  54 

53  45 
51  55 
44  25 

37  25 
11  43 

43  57 

44  03 
41  18 
34  10 
30  16 
29  50 
36  29 
33  00 

32  28 

25  18 

26  55 


Lun.  Int. 


H.  W. 


1  10 
0  04 


0  00 
10  25 
10  18 
10  20 
10  15 
10  10 
10  05 
10  10 
10  04 
10  05 
9  57 
9  44 


9  37 


9  35 
9  30 
9  26 


9  15 

8  58 


8  23 
8  50 


8  21 
8  50 


9  00 
9  05 


9  10 


9  20 
9  35 
9  30 


9  05 


L.  W. 


Range. 


7  35 
6  20 


14.8 
5.9 


6  13 


3  25 
3  20 
3  16 


3  05 
2  48 


2  10 

2  38 


2  08 
2  37 


2  47 
2  52 


2  57   5. 0 


7.2 
5.6 
4.9 
3.3 
4.9 
5.3 
4,9 
6.0 
5.3 
5.0 
4.1 
4.0 


3  26   3.9 


4.1 
3.9 
4.2 


4.1 
4.9 


4.9 
4.9 


5.0 
4.9 


5.0 
4.9 


3  07  :  4.  9 
3  22  I  5.  0 
3  17  i  4.9 


2  52  I  4.  7 


Neap. 


7.5 
3.0 


3.7 
2.8 
2.5 
1.7 
2.5 
2.7 
2.5 
3.0 
2.7 
2.5 
2.1 
2.0 


2.0 


2.1 
2.0 
2.1 


2.1 
2.5 


2.5 
2.5 


2.5 
2.5 


2.5 
2.5 


2.5 


2.5 
2.5 
2.5 


2.4 


Page  212]                                    APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  SOUTH  AMERICA— Continued. 

■g 

Place. 

Lat.  s. 

Long.  W. 

Lun 

.Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

Moreno  Mountain!  Summit 

o       /       ;/ 

23  28  30 
23  26  42 
23  06  30 
22  34  00 
22  06  00 
21  55  50 
21  28  00 
21  05  30 
20  n  40 
20  51  05 
20  12  30 
19  05  01 
19  36  30 
19  19  00 
18  45  40 
18  28  43 
17  58  35 

17  42  00 

17  37  00 

17  01  00 

17  00  00 

16  42  20 

16  23  50 

16  13  30 

15  48  00 

15  33  15 

15  20  56 

14  57  00 

14  41  00 

14  09  50 

13  50  00 

13  48  00 

13  45  00 

13  38  20 

13  01  00 

12  48  00 

12  31  00 

12  11  30 

12  04  03 

12  08  15 

11  47  10 

11  27  10 

10  49  45 

10  06  15 

9  38  35 

9  15  30 

9  04  40 

8  46  30 

8  34  50 

8  05  40 

7  42  40 

7  23  40 

6  55  50 

6  46  00 

6  46  45 

6  26  45 

5  55  30 

5  12  00 

5  05  00 

4  40  50 

4  1^  40 

3  30  42 

O         1         II 

70  34  56 
70  37  11 
70  31  39 
70  17  42 
70  13  40 
70  11  17 
70  02  45 
70  12  12 
70  10  26 
70  14  40 
70  11  20 
70  10  30 
70  15  21 
70  17  50 
70  21  50 
70  20  00 

70  52  31 

71  22  31 

71  20  01 

72  02  53 
72  07  16 

72  27  16 

73  16  41 

73  41  31 

74  27  16 

74  51  01 

75  09  36 
75  30  46 

75  49  56 

76  16  36 
76  27  31 
76  18  31 
76  10  00 
76  24  15 
76  31  06 
76  38  11 

76  48  56 

77  02  31 
77  15  44 
77  14  45 
77  16  11 
77  50  04 

77  43  42 

78  10  02 
78  21  33 
78  30  03 
78  35  57 
78  45  16 

78  56  53 

79  06  46 
79  26  00 
79  33  15 
79  51  30 

79  57  55 

80  42  54 

80  51  56 

81  09  19 
81  05  36 
81  07  03 
81  17  01 
81  12  01 
80  28  12 

h.    TO. 

h.  m. 

ft. 

A 

Constitution  Cove:  Shingle  pt.  of  island. 
Mexillones  Mount:  Summit 

9  35 
9  44 
8  55 

3  22 
3  31 
2  42 

3.9 
4.0 
4.8 

2.0 
2.0 
2.4 

Port  Cobija:  Landing  place 

Tocopilla:  Extremity  Point 

San  Francisco  Head :  W.  pitch 

Loa  River:  Mouth 

i 

Lobos  Point :  Outward  pitch 

9  00 

2  47 

4.9 

2.5 

Pabellon  de  Pica:  Summit 

6 

Patache  Point:  Extreme 

, 

Iquique:  Light-house 

8  35 

2  22 

5.0 

2.5 

Mexillon  Bay :  Landing  place 

Pisagua:  Pichalo  Pt.,  extreme 

8  32 

2  20 

5.0 

2.5 

Gorda  Point:  W.  low  extreme 

Lobos  Point:  Summit 

Arica:  Iron  church 

7  49 

1  37 

5.6 

2.8 

Schama  Mount:  Highest  summit 

Coles  Point:  Extreme 

« 
ft* 

Ho:  Mouth  of  rivulet 

7  55 

1  43 

5.3 

2.7 

Port  Mollendo :  Light-house 

Islay:  Custom-house 

7  39 

1  27 

6.2 

3.1 

Quilca:  W.  head  of  cove 

Pescadores  Point:  SW.  extreme 

Atico:  E.  cove 

Chala  Point:  Extreme 

Lomas:  Flagstaff  on  pt 

San  Juan  Port:  Needle  Hummock 

Nasca  Point:  Summit 

6  47 

0  35 

3.9 

2.0 

Mesa  de  Dofia  Maria:  Central  summit. . . 
Carreta  Mount:  Summit 

San  Gullan  Island:  N.  summit 

Paraca  Bay:  N.  extreme  of  W.  pt 

Pisco:  Light-house 

6  16 

0  04 

3.8 

1.9 

Chincha  Islands:  Boat  slip,  E.  side  N.  id. 
Frayles  Point:  Extreme 

" 

Asia  Rock:  Summit 

Chilca  Point:  SW.  pitch 

Morro  Solar:  Summit 

San  Lorenzo  Island:  Light-house 

Callao:  Palominos  Rock  Light 

5  47 

12  00 

3.5 

1.8 

Pescadores  Islands:  Summit  of  largest. . . 
Pelado  Island :  Summit 

Sup^ :  W.  end  of  village 

Huarmey :  W.  end  of  sandy  beach 

Colina  Redonda:  Summit 

5  08 

11  21 

2.1 

1.1 

Saraanco  Bay :  Cross  Pt 

Chimbote :  Village,  N.  part 

4  50 

11  03 

2.0 

LO 

Chao  Islet:  Center 

Guanape  Islands:  Summit  of  highest 

Huanchaco  Point:  SW.  extreme 

Malabrigo  Bay :  Rocks 

4  19 

10  32 

2.1 

1.1 

Pacasmayo :  Light-house 

Eten  Head :  Light-house 

4  04 

10  17 

2.5 

1.3 

Lambayeque:  Beach  opposite 

Lobos  de  Afuera  Island:  Cove  on  E.  side. 
Lobos  de  Tierra  Island:  Central  summit. 
Aguja  Point:  W.  cliff  summit 

Paita,  Saddle:  S.  summit 

Paita:  Light-house 

3  20 

9  33 

3.5 

1.8 

Parinas  Point:  Extreme 

Cape  Blanco:  Under  middle  of  high  cliff. 
Tumbez:  Malpelo  Pt 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  SOUTH  AMERICA— Continued. 


[Page  213 


Place. 


Guayaquil  River:  Lighten  Santa  Clara  I. 

Guayaquil,  Concejo:  S.  pt.  of  city 

Puna:  Mandinga  Pt.  light 

Point  Santa  Elena:  Veintemilla  light 

Plata  Isle:  E.  pt 

Cape  San  Lorenzo:  Marlingspike  Rock.. 

Manta  Bay:  Light-house 

Caraques  Bay:  Punta  Playa 

Cape  Pasado:  Extreme 

Point  Galera:  N.  extreme 

Cape  San  Francisco:  S\V.  extreme 


Lat.  S. 


10  40 

12  24 

44  30 

12  00 

16  55 

03  30 

0  56  50 

0  35  25 

0  21  30 

Lat.  N. 
0  50  10 
0  40  00 


Esmeralda  River :  Light-house 

Mangles  Point:  S.  pt.  of  creek  entrance. 

Tumaco:  S.  pt.  of  El  Morro  I 

Guascama  Point:  Extreme 

Gorgona  Island:  Watering  Bay 

Buenaventura:  Basan  Pt 

Chirambiri  Point:  N.  extreme 

Cape  Corrientes:  SW.  extreme 

Cupica  Bay:  Entrance  to  Cupica  River. 

Cape  Marzo:  SE.  extreme 

Isla  del  Rey:  Extreme  of  Cocos  Pt 

Darien  Harbor:  Graham  Pt 

Flamenco  Island :  N.  Pt 

Chepillo  Island:  Center 

Point  Cham^:  Extreme 


03  30 

36  00 
49  36 

37  10 
58  10 
49  27 
17  06 
28  46 
41  19 

6  49  45 
8  12  30 
8  28  50 
8  54  30 
8  56  32 
8  39  00 


Long.  W. 


80  25  29 
79  52  19 

79  53  45 

80  59  00 

81  03  55 
80  55  55 
80  42  50 
80  25  24 
80  30  37 

80  05  40 
80  07  55 

79  42  00 
79  03  30 
78  45  29 
78  24  24 
78  11  16 
77  11  45 
77  29  44 
77  33  28 
77  30  31 

77  40  55 

78  54  40 

78  05  35 

79  31  15 
79  07  55 
79  41  45 


Lun.  Int. 


Range. 


H.  W. 


h.     m 
4  00 
7  00 


3  00 


3  10 


3  15 


3  35 


6  00 


3  40 
3  30 


3  00 


3  05 
3  30 


L.  W. 


10  13 
1  00 


Spg. 

ft. 

10.0 
11.0 


9  13 


9  23 


7.5 


9  28 


9  48 


13.2 


12  13 


13.2 


9  53 
9  43 


13.1 
13.3 


9  13 


15.7 


9  18 
9  42 


16.0 
15.0 


Neap. 

ft. 

5.1 

5.6 


4.0 


3.8 


5.0 


7.1 


7.1 


7.0 
7.2 


8.5 


8.7 
8.1 


ISLAITDS  nr  THE  ATLANTIC  OCEAN. 


Faeroe  Islands,  Strom  Islet:  Thorshaven 

Fort  flagstaff 

Halderoig  Islet:  Halde- 

roig  Church 

Numken  Rock 

Rockall  Islet:  Summit,  70  feet 

Corvo  Island:  S.  pt 

Flores  Island :  Santa  Cruz  Fort 

Fayal  Channel :  N.  Magdalen  Rock 

Fayal  Island,  Horta:  Castle  of  Santa  Cruz 
Caldera:  summit  3,351  ft  . 

Pico  Island :  Summit 

St.  George  Island :  Light-house 

Graciosa  Island:  Santo  Fort  light 

Terceira  Island:  Monte  del  Brazil,  near 

Angra 

St.  Michael  Island :  Custom-house,  Ponta 

Delgada 

Pt.  Arnel  light 

Santa  Maria  Island:  Villa  do  Porto  light 
Formigas  Islands :  Highest  rock 

Porto  Santo  Island :  Light-house 

Desertas:  Chao  I.,  Sail  Rock 

Madeira  Island :  Funchal  light 

Fora  I.  light-house 

Pico     Ruivo,     summit 

6,056  ft 

Pargo  (W.)  Pt 


62  02  26 

62  18  20 

61  23  00 

57  35  52 

39  40  07 

39  27  00 

38  32  09 

38  31  45 

38  34  30 

38  25  00 

38  40  30 

38  05  24 

38  38  20 

37  44  16 

37  49  20 

36  56  00 

37  16  44 

33  03  15 

32  35  45 

32  37  42 

32  43  14 

32  45  00 

32  48  07 

6  43  08 

7  GO  36 
6  45  30 

13  42  21 

31  08  00 
31  08  49 
28  34  00 
28  37  39 
28  44  00 
28  28  12 
28  13  00 
28  00  45 

27  13  45 

25  40  40 
25  08  21 
25  10  00 
24  47  06 

16  16  20 
16  33  30 
16  55  16 
16  39  31 

16  57  30 

17  16  05 


11  30 


0  20 


0  15 


0  40 


0  35 


5  18 


3.9 


6  32 


4.4 


6  27 


5.7 


6  52 


6  47 


6.6 


1.8 


2.0 


2.6 


3.0 
"3."6 


Page  214]                                      APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  IN  THE  ATLANTIC  OCEAN— Continued. 

1 

Place. 

Lat.  N. 

Long.  W. 

Lun. 

Int. 

Range.         1 

H.  W. 

L.  W. 

Spg. 

Neap. 

i 

s 

m 

g 

7 

M    - 
9 

t 

s 

N 
u 

|2 

Salvage  Islands:  Cight-house,  Gran  Sal- 
vage I -\. 

O         1         II 

30  08  00 

29  23  50 

28  57  24 
28  50  56 
28  45  25 
28  03  00 
28  10  42 
28  07  06 
28  35  25 

28  28  12 

28  16  35 
28  08  00 

27  46  30 

28  50  06 

17  06  50 
17  04  00 
16  54  36 
16  49  00 
16  38  00 
16  34  00 
16  50  50 
16  34  00 
16  13  20 
16  11  00 
16  09  10 
15  07  30 
15  18  06 
14  53  40 
14  53  00 

14  50  30 

32  19  22 
32  19  37 
32  15  05 
32  21  40 

0  55  30 

Lat.  S. 
3  51  30 
3  50  30 
7  55  20 

15  55  00 
20  27  42 
20  30  32 
37  19  00 
37  02  48 

40  19  11 

51  21  26 
51  04  11 
51  32  20 
51  41  10 
51  40  40 

54  04  45 
53  48  00 
59  34  00 

55  57  00 

O         /         II 

15  54  00 

13  29  31 
13  33  07 
13  52  05 

13  49  13 

14  31  35 

15  25  11 

15  24  56 

16  08  11 

16  15  09 

16  38  02 

17  05  55 
17  54  22 
17  47  01 

24  59  15 

25  17  00 

25  01  12 
24  47  08 
24  38  08 
24  16  00 
22  54  55 
22  55  42 
22  55  44 
22  42  00 

22  57  20 

23  12  42 
23  47  06 

23  31  45 

24  30  38 
24  40  00 

64  49  35 
64  49  15 
64  49  40 
64  38  40 

29  22  28 

33  49  29 

32  25  29 

14  24  35 

5  43  03 

28  46  57 

29  14  56 
12  23  00 
11  18  39 

9  56  11 

60  04  52 
58  30  56 
58  08  04 
57  51  30 
57  41  48 

38  15  00 
43  25  00 
27  45  00 

26  33  00 

h.    m. 

h.    m. 

ft. 

ft. 

Alegranza  Island:  Delgada  Pt.  light 

Lanzarote  Island:  Port  Naos  light 

Pechinguera  Pt.  light. 

Lobos  Island :  Martino  Pt.  light 

Fuerta  Ventura  Island:  Jandia  Pt.  light. 

Gran  Canada:  Isleta  Pt.  light 

Palmas  light 

0  50 

7  00 

8.5 

3.9 

0  40 

6  50 

9.3 

4.3 

Teneriffe  Island:  Anga  Pt.  light 

Santa  Cruz,  Br.    con- 
sulate   

1  15 

7  27 

7.8 

3.6 

Summitof  peak,  12,180 
ft 

Gomera  Island :  Port  Gomera 

Ferro  Island :  Port  Hierro 

Palma  Island :  Light,  NE.  pt 

0  20 

6  30 

8.6 

4.0 

San  Antonio  Island:  Bull  Pt.  light 

Summit,  7,400ft... 
St.  Vincent  Island:  Porto  Grande  light  . 
St.  Lucia  Island:  N.  pt 

5  50 

12  00 

3.3 

1.5 

Raza  Island :  E.  pt 

St.  Nicholas  Island :  Light-house 

Sal  Island:  N.  pt.  light 

s.  pt:.... 

Boavista  Island :  N W.  pt 

NE.  pt 

Light-house 

Mayo  Island :  English  Jload 

7  30 

1  20 

4.4 

2.0 

St.  Jago  Island:  Reta  Pt.  light 

Porto  Praya,  S.  light 

Fogo  Island :  N.  S.  da  Luz,'village 

Brava  Island:  Light-house 

5  50 

12  00 

4.8 

2.2 

Ireland  Island:  Dock  yard  clock  tower. . 
Bastion  C 

7  04 

0  52 

4.0 

2.6 

Hamilton  Island:  Gibbs  Hill  light 

St.  Davids  Island :  Light-house 

St.  Paul  Rocks:  Summit,  64  ft 

Rocas  Reef:  NW.  sandy  islet 

5  05 
5  00 
5  20 
3  00 
3  35 
3  40 

11  18 

11  13 

11  30 

9  10 

9  48 

9  53 

10.0 
6.0 
2.0 
2.8 
3.5 
4.0 

4.6 
2.7 
0.9 
1.3 
1.6 
1.8 

Fernando  Noronha:  The  Pyramid 

Ascension  Island :  Fort  Thornton 

St.  Helena  Island:  Obs.  Ladder  Hill . . . . 

Martin  Vaz  Rocks:  Largest  islet 

Trinidad  Island:  SE.  pt 

Inaccessible  Island:  Center 

Tristan  d' Acunha  Islands:  NW.  pt 

Gough  Island :  Penguin  Islet 

12  50 

5  40 

5.  .2 

2.4 

Port  Egmont:  Observation  spot 

7  20 

1  08 

10.7 

5.6 

Mare  Harbor:  Observation  spot 

Port  Louis:  Flagstaff,  govt,  house 

Port  Stanley:  Governor's  house 

Cape  Pembroke:  Light-house 

5  31 

11  27 

4.3 

2.2 

South  Georgia  Island:  N.  cape 

Shag  Rocks:  Center 

Sandwich  Islands:  S.  Thul6 

Traverse  I.  volcano  . . 

i 

1 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  IN  THE  ATLANTIC  OCEAN— Continued. 


[Page  216 


Place. 


New  S.  Orkney  Is. :  E.  pt.  Laurie  I 

E.  summit  Corona- 
tion I.,  5,397  ft... 
New  S.    Shetland    Islands,    Deception 
Island:  Port  Foster 


Bouvets  Island  (Circumcision):  Center.. 


Lat.  s. 


60  54  00 
60  46  00 
62  55  36 
54  16  00 


Long  W. 


44  25  00 

45  53  00 

60  35  00 
Long.  E. 
6  14  00 


Lun.  Int. 


H.  W. 


h.    m. 


L.  W. 


h.    TO. 


Range. 


Spg. 


ft. 


Neap. 


ft. 


ATLANTIC  COAST  OF  EUROPE. 


Greenwich :  Observatory 

Oxford :  University  Observatory ... 

Cambridge :  Observatory 

North  Foreland:  Light-house 

South  Foreland:  Light-house 

Dungeness:  Light-house 

Beachy  Head :  Light-house 

Southsea  Castle :  Light-house 

Portsmouth :  Observatory 

Southampton :  Royal  Pier  light 

Hurst  Castle:  W.  light 

Needles  Rocks:  Old  light-house 

St.  Catharine:  New  light-house 

Portland :  Notch  Bill  light 

Start  Point:  Light-house 

Plymouth:  Breakwater  light 

Eddystone:  Light-house 

Falmouth:  St.  Anthony  Pt.  light 

Lizard  Point:  W.  light-house 

Porthcurnow:  SE.  cor.  telegraph  co.'ssta 

Lands  End:  Longships  lignt-house 

Scilly  Hands:  St.  Agnes  light-house 

Trevose  Head :  Light-house 

Bideford :  High  light-house 

Lundy  Island :  Light-house,  N.  pt 

Bristol:  Cathedral 

Cardiff:  Light-house,  W.  pier 

Swansea:  Light-house,  W.  pier 

Caldy  Island :  Light-house 

St.  Anns:  Upper  light-house 

Smalls  Rocks:  Light-house 

Aberystwith :  Light-house 

Bardsey  Island :  Light-house 

South  Stack:  Light-house  on  rocks 

Holyhead:  Light-house  on  old  pier 

Skerries  Rocks :  Light-house,  highest  I . 

Bidstone:  Light-house  on  hill 

Liverpool :  Rock  light 

Observatory 

Morecambe  Bay:  Fleetwood  highlight. 

Calf  of  Man:  Upper  light-house 

Isle  of  Man :  Ayre  Pt.  light-house 

St.  Bees:  Light-house 

White  Haven:  W.  pier-head  light 

Mull  of  Galloway:  Light-house 

Ayr, Firth  of  Clyde:  Light-house,  N.  side 

harbor 

Troon:  Light-house,  inner  pier 


Lat.  N. 

51 

28  38 

51 

45  34 

52  12  52 

51 

22  28 

51 

08  23 

50  54  47  1 

50 

44  15 

50  46  35 

50  48  03 

50 

53  45 

50  42  07 

50  39  42 

50  34  30 

50  31  10 

50 

13  18 

50  20  02  1 

50 

10  49 

50  08  30 

49  57  40 

50  02  44 

50  04  10 

49  53  33 

50 

33  00 

51 

04  00 

51 

12  05 

51 

27  24 

51 

27  48 

51 

36  50 

51 

37  52 

51 

41  00 

51 

43  15 

52 

24  20 

52  45  00  1 

53 

18  30 

53 

18  54 

53  25  15 

53  24  02 

53 

26  38 

53  24  04  1 

53 

55  03 

54  03  14  I 

54 

24  56 

54  30  50 

54  33  00 

54  38  10 

55  28  10 

55 

32  55 

Long.  W. 

0  00  00 

1  15  04 

0  05  40 

Long.  E. 

1  26  48 
1  22  22 
0  58  18 
0  13  00 

Long.  W. 


05  15 
05  58 
24  00 
33  04 
35  25 
17  47 
27  30 

38  28 
09  27 
15  53 

01  00 
12  06 

39  18 
44  45 

6  20  38 

5  01  55 

12  30 

40  35 

35  55 

09  42 
56  00 
40  59 

5  10  30 
5  40  15 
05  40 
47  50 
42  00 
37  01 

36  20 

10  42 

02  27 
04  16 
00  20 
49  37 
22  01 

37  50 
36  00 
51  20 


4  38  10 
4  41  00 


1  10 


11  24 
11  09 

10  35 

11  10 


11  31 

0  35 

11  05 


6  29 
5  25 
5  20 


4  45 


4  15 


5  45 

5  00 
7  00 

6  45 
5  45 
5  40 
5  41 
5  40 

7  25 
7  24 


10  00 


11  08 
11  00 


10  55 


11  00 
11  05 

11  40 


7  46 


18.8 


5  53 
5  43 
4  23 

4  58 


16.8 
19.8 
21.5 
19.8 


4  19 
6  48 
4  53 


1.3.2 
12.8 
12.2 


0  09 
11  38 
11  33 


6.7 

14.9 
15.3 


10  58 


14.2 


10  28 


15.9 


11  58 

11  13 

0  48 

0  33 
11  58 
11  53 
11  54 
11  53 

1  13 
1  12 


22.7 
26.9 
31.3 
36.2 
27.1 
25.3 
24.0 
20.9 
14.2 
14.9 


3  48  i  15. 8 


5  27 
4  48 


27.6 

27.4 


4  43 


19.7 


4  48 

4  53 

5  28 


25.9 
14.8 


12.6 


8.4 
10.0 
11.0 
10.1 


6.7 
6.5 
6.2 


1.0 
6.8 
7.0 


6.5 


7.3 


11.4 
13.5 
15.7 
18.1 
13.6 
12.7 
12.0 
10.5 
7.1 
7.5 


7.9 


14.0 
13.9 


10.0 


13.1 

8.9 

5.2 


Page  216] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


Place. 


Ardrossan :  S.  breakwater  light 

Pladda  Island :  *Light-hou8e 

Glasgow:  Observatory 

Cantyre:  Light-house 

Rhynns  of  Islay :  Light-house 

Oban:  Light-house  on  N.  pier 

Skerry vore  Rocks:  Light-house 

Barra  Head:  Light-house 

Glas  Island:  Light-house,  Scalpay  I 

Stornoway :  Arnish  Pt.  light 

Butt  of  Lewis:  Light-house 

Cape  Wrath :  Light-house 

Dunnet  Head :  Light-house 

Kirkwall    (Orkneys):  New  pier-head 

light 

Startpoint  (Orkneys):  Light-house 

North  Ronaldeay:  Light-house 

Fair  Isle  Skroo:  Light-house 

Sumburgh  Head:  Light-house 

Blackness    (Shetland  Is.):  Light-house 

pier 

Lerwick  (Shetland  Is. ) :  Fort 

Hillswickness  (Shetland  Is. ) :  S.  extreme. 
Balta  I.  (Shetland  Is.):  Cairn  on  E.  side. 
Pentland  Skerries:  Upper  light-house... 

Tarbertness:  Light-house 

Buchanness:  Light-house 

Aberdeen  (Girdleness) :  Light-house 

Buddonness:  Upper  light-house 

Bell  Rock:  Light-house 

May  Island:  Light-house 

Inch  Keith  Rock:  Light-house 

Edinburgh :  Observatory 

Berwick:  Light-house 

Farn  Island:  NW.  light-house 

Coquet  Island:  Light-house 

Tynemouth:  Souter  Point  light-house. . . 

North  Shields:  Light-house 

Sunderland:  N.  pier  light 

Hartlepool :  Light-house 

Flam  borough :  New  light-house 

Humber    River:  Kilhngholme    middle 

light 


Lat.  X. 


Spurn  Head:  Upper  light-house 

Lowestoft:  Light-house 

Orfordness:  N.  light-house 

Harwich:  Landguard  Pt.  light.. 


Cape  Clear:  Old  light -house 

Fastnet  Rock :  Light-house 

Mount  Gabriel :  Ordnance  survey  station . 

Castlehaven :  Light-house 

Mizen  Hill:  Ordnance  survey  station 

Ban  try  Bay :  Roancarrig  light 

Bull  Rock :  Light-house 

Skelligs  Rocks:  Light-house 

Valentia:  Light-house 

Port  Magee 

Dingle  Bay:  Light  at  entrance 

Blasket  Islands:  Westernmost  rock 

Smerwick :  Signal  tower 

Tralee  Bay:  Light-house 

Beeves  Rocks :  Light-house 

Limerick :  Cathedral 

Shannon  River:  Loop  Head  light 


55  38  27 
55  26  00 
55  52  43 
55  18  39 

55  40  20 

56  24  50 
56  19  22 

56  47  08 

57  51  25 

58  11  28 
58  30  40 
58  37  30 
58  40  16 

58  59  15 

59  16  45 
59  23  24 
59  33  00 

59  51  15 

60  08  02 
60  09  22 
60  27  20 
60  44  25 
58  41  22 
57  51  54 
57  28  15 
57  08  33 
56  28  07 
56  26  03 
56  11  00 
56  02  09 
55  57  23 
55  46  00 
55  37  00 
55  20  06 

54  58  10 

55  00  30 
54  55  07 
54  41  51 
54  07  00 

53  39  00 


53  34  45 
52  29  14 
52  05  00 
51  56  05 

51  26  02 
51  23  18 
51  33  24 
51  31  00 
51  27  41 
51  39  10 
51  35  30 
51  46  14 
51  56  00 

51  53  08 

52  07  15 
52  04  30 
52  13  46 
52  16  14 
52  39  00 
52  40  04 
52  33  38 


Long.  W. 


4  49  28 

5  07  09 

4  17  39 

5  48  00 

6  30  46 

5  28  20 

7  06  32 
7  39  09 

6  38  28 
6  22  10 
6  16  01 
4  59  41 
3  22  25 

2  57  33 
2  22  25 
2  22  45 
1  36  30 
1  16  20 

1  16  02 
1  08  41 

1  29  50 
0  47  30 

2  55  25 
46  30 
46  22 
04  06 
44  53 
23  06 
33  22 
08  05 
10  54 
59  00 
39  00 
32  00 
21  30 
26  00 
21  30 
10  19 


3 
1 
2 
2 
2 
2 
3 
3 
1 
1 
1 
1 
1 
1 
1 
0  05  00 

0  12  00 

Long.  E. 

0  07  10 

1  45  24 
1  34  30 
1  19  10 

Long.  W 

9  29  03 

9  36  25 

9  32  44 

9  10  20 

9  48  19 

9  44  49 

10  18  03 

10  32  45 

10  19  16 

10  23  17 

10  15  30 

10  40  00 

10  21  40 

9  52  53 

9  01  18 

8  37  23 

9  55  54 


Lun.  Int. 


H.  W. 


h.    m. 
11  35 


0  55 
10  20 


5  10 
"5*35' 


9  57 


10  50 
9  35 


10  20 


9  30 
10  00 


0  24 

0  50 

1  56 


1  58 

2  08 


3  11 
3  12 

3  21 

4  20 


5  16 

9  47 

11  05 

11  56 


3  50 


4  10 


3  30 


3  40 


3  40 
3  50 


6  00 


L.  W. 


h.      VI. 

5  23 


7  08 
4  08 


11  22 
"ii'47" 
"6'22' 


3  44 


4  37 
3  22 


4  17 


3  17 
3  47 


6  36 

7  02 

8  08 


8  11 

8  28 


9  31 

9  32 

9  43 

10  36 


11  29 

3  35 

4  53 

5  44 


10  03 


10  23 


Range. 


Spg. 


ft. 
8.8 


11.2 
4.0 


12.8 

ii.'i' 

13.' 4" 


5.0 
5.2 


6.0 
'6.4" 


11.2 
11.7 

15.5 


16.5 
15.0 


14.8 
14.5 
14.2 
15.8 


18.5 
6.2 
7.8 

11.2 


10.6 


9  43 


10.8 


9  53 


10.7 


9  53 
10  03 


10.7 
12.3 


0  13 


18.7 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


[Page  217 


Place. 


Eeragh  Island :  Light-house 

Arran  Island:  Light-house 

Gal  way :  Mutton  I.  light 

Golam  Head:  Tower 

Slyne  Head :  N.  light-house 

Clifden  Bay:  Gortrumnagh  Hill 

TuUy  Mountain:  Ordnance  survey  station 

Inishboffin :  Lyon  Head  light 

Inishturk  Island :  Tower 

Clew  Bay:  Inishgort  light 

Newport:  Church 

Clare  Island:  Light-house 

Blacksod  Point:  Light-house 

Eagle  Island:  W.  light-house 

Broadhaven :  Guba  Cashel  light 

Dounpatrick    Head:    Ordnance    survey 

station 

Anghris  Head:  Ordnance  survey  station. 

Knocknarea:  Tumulus 

Sligo  Bay:  Black  Rock  light 

Knocklane:  Ordnance  survey  station 

Killvbegs  (Donegal  Bay):  St.  Johns  Pt. 

light.- .....: 

Rathlin  O'Birne  Islet:  Li^ht-house 

Aran  Island :  Rinrawros  light 

Bloody  Foreland:  Ordnance  survey  sta- 
tion   

Tory  Island:  Light-house 

Horn  Head:  Ordnance  survey  station  . . . 

Melmore  Head :  Tower 

Fanad  Point:  Light-house 

Glashedy  Island:  Ordnance  survey  station 

Malin  Head :  Tower 

Inishtrahull :  Light-house 

Inishowen  Head :  E.  light-house 

Moville:  New  Pier 

Londonderry:  Cathedral 

Scalp  Mountain :  Ordnance  survey  station 

Benbane  Head :  Summit 

Rathlin  Island:  Altacarry  light-house... 

Maiden  Rocks:  W.  light-house 

Lough  Larne:  Farres  Pt.  light-house 

Belfast  Bay :  Light,  east  side 

Mew  Islands:  Light-house 

Donaghadee:  Light-house 

South  Rock :  Light  vessel 

Dundrum  Bay:  St.  John  Pt.  light 

Carlingford  Lough:  Haulbowline  Rk.  It. . 

Drofiheda:  Light-house 

Rockabill :  Light-house 

Howth  Peninsula:  Bailey  light 

Dublin :  Observatory 

N.  wall  light., 

Poolbeg:  Light-house 

Kingstown :  IC.  pier  light 

Killiney  Hill:  Mapas  obelisk 

Bray  Head:  Ordnance  survey  station  ... 

Wicklow :  Upper  light 

Tara  Hill:  Summit 

Black  Stairs  Mountain :  Ordnance  survey 
station 

Tory  Hill:  Ordnance  survey  station 

Wexford :  College 

Forth  Mount:  Ordnance  survey  station. . 

Tuskar  Rock :  Light-house 

Great  Saltee:  S.  end 

Waterford :  Hoop  Pt.  light 


53  08  55 
53  07  38 
53  15  13 
53  13  46 
53  23  58 
53  29  47 
53  35  00 
53  36  40 
53  42  27 
53  49  34 
53  53  06 

53  49  30 

54  05  45 
54  17  00 
54  16  00 

54  19  36 
54  16  33 
54  15  30 
54  18  00 
54  20  50 

54  34  08 

54  39  47 

55  00  52 

55  08  13 
55  16  26 
55  12  31 
55  15  14 
55  16  33 
55  19  07 
55  22  50 
55  25  55 
55  13  38 
55  10  20 

54  59  40 

55  05  23 
55  15  03 
55  18  05 
54  55  47 
54  51  07 
54  40  20 
54  41  50 
54  38  45 
54  24  04 
54  13  30 
54  01  10 
53  43  00 
53  35  47 
53  21  40 
53  23  13 
53  20  47 
53  20  30 
53  18  10 
53  15  52 
53  10  39 
52  57  54 
52  41  55 

52  32  55 
52  20  53 
52  20  04 
52  18  57 
52  12  09 
52  06  41 
52  07  25 


Long.  W. 


9  51  30 

9  42  06 

9  03  10 

9  46  03 

10  14  01 

10  03  54 

10  00  15 

10  09  40 

10  06  41 

9  40  12 

9  32  56 

9  59  00 

10  03  34 

10  05  31 

9  53  00 

9  20  41 
8  46  02 
8  34  25 
8  37  00 
8  40  14 

8  27  33 
8  49  52 
8  33  48 

8  15  38 
8  15  00 
7  57  15 
47  12 
37  53 
23  51 
22  22 
13  37 
55  38 
7  02  20 
7  19  25 
7  21  51 
6  28  45 
6  10  45 
44  18 
47  21 
49  30 

31  30 

32  01 
22  20 
39  30 

6  04  45 
6  15  00 
6  00  20 
6  03  06 
6  20  30 
6  13  33 
6  09  00 
6  07  30 
6  06  37 
6  04  55 
6  00  08 
6  13  01 

6  48  17 

7  07  31 
6  28  15 
6  33  41 
6  12  35 
6  37  15 
6  55  53 


Lun.  Int. 


Range. 


H.  W. 


h.    m. 


4  15 
4  19 


4  16 


4  20 


4  50 


5  03 


5  28 


6  65 

7  48 


10  30 


10  42 

"ii"66' 


10  45 
10  45 


10  55 


11  00 
10  52 


10  30 
10  10 


7  05 


5  30 


Spg. 


h.    m. 


10  28 
10  19 


13.4 
15.1 


10  29 


13.2 


10  33 


12.1 


11  03 


10.4 


5  10  !  11  23 


11.4 


11  16 


11.2 


11  41 


11.6 


0  43 

1  35 


7.5 
8.0 


4  18 


4  06 

"4'48' 


9.3 

ii.'i' 


4  33 
4  33 


15.8 
11.6 


4  43 


12.7 


4  48 
4  27 


13.0 
10.9 


4  18 
3  58 


11.8 

8.7 


0  53 


4.9 


11  43 

'ii'is' 


12.3 


Neap. 


ft. 


5.7 
6.4 


5.2 


4.5 


5.3 


4.8 


5.3 


3.4 
3.6 


4.5 
"6."3 

"7.'4 


9.2 
6.8 

"7.' 5 


7.6 
6.4 


6.9 
5.1 


2.9 


5.1 
6.' 2 


Page  218]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


Place. 


Waterford:  Cath^ral 

Great  Newton  Head:  Metal  Man  Tower. 

Dungarvan:  Ballinacourty  light 

Knockmealdown  Mount:  Ordnance  sur- 
vey station 

Helvick  Head:  Ordnance  survey  station. 

Mine  Head :  Light-house 

Youghal:  Light-liouse 

Capel  Island :  Tower 

Ballycottin :  Light-house 

Cork  Harbor:  Haulbowline  Coal  Wharf. 

Queenstown :  Roches  Pt.  light 

Kinsale:  Light-house,  S.  pt 

Seven  Heads:  Tower 

Galley  Head :  Light  on  summit 

Stag  Rocks :  Largest 

Alderney  Harbor:  Old  pier  light 

St.  Heliers:  Light  on  Victoria  Pier 


Lat.  N. 


52  15  33 
52  08  13 
52  04  27 

52  13  39 
52  03  00 
51  59  33 
51  56  34 
51  52  54 
51  49  30 
51  50  33 
51  47  33 
51  36  11 
51  34  14 
51  31  50 
51  28  05 
49  43  00 
49  10  29 


Vardo:  Fortress 70 

Vadso :  Light-house 70 

North  Cape :  Extreme ;  71 

Fruholm :  Light-house 71 

Hammerfest :  Light-house 70 

Tromso:  Observatory ]  69 

Hekkingen:  Light-house 69 

Andenes:  Light-house 69 

Lodingen  (Hjertholm):  Light-house 68 

Lofoten  Island:  Skraaven  I.  light 68 

Glopen  light 67 

Grvto :  Light-house 67 

Stot:  Light-house 66 

Tra?nen:  Soe  Islet  light 66 

Bronnosnnd:  Light-house 65 

Villa:  Light-house 64 

Halten  Island :  Light-house 64 

Koppem '63 

Agdenes:  Light-house 63 

Trondheini:  Mumkholmen  flagstaff ■.  63 

Grip:  Church :.'  63 

Christiansund :  Storvaden 63 

Freikallen • 63 

Hestskjaer:  Light-house 63 

Steinshesten 62 

62 
62 
62 


^ratenen :  Light-house 

Svinoen  Islet 

Hjcerringa  Mountain :  Summit 

Hornelen  Mountain:  Summit 61 

Batalden  Island :  Store 61 

Kinnsund :  Light-house 61 

Alden 61 

Helliso:  Light-house 60 

Bergen :  Cathedral 60 

Lorstakken  Mountain :  Summit 60 

Marstenen  Islet:  Light-house 60 

Furen  Islet 59 

Ulsire:  Light-house 59 

Hvidingso :  Light-house I  59 

Port  Stavanger :  Light-house '  58 

Obristadbrci'kke:  Light-house .58 

Synesvarde  Mountain :  Summit j  58 


Kompas  Mountain:  Summit. 

Lister:  Light-house 

Lindesnes :  Light-house 

Ryvingen  Island:  Light-house.. 
Christianssand:  Odderoen  light. 


22  00 

04  00 
11  00 

06  00 
40  15 
39  12 
36  05 
19  30 

24  40 

09  20 
53  15 

23  15 

56  35 

25  50 
28  40 

32  55 

10  25 
48  25 
38  45 
27  04 
13  11 

07  01 
03  04 

05  00 
58  49 
48  20 
19  38 

11  12 
51  21 

38  40 

33  35 
19  16 
45  05 
23  37 
21  39 
07  50 

57  44 
18  20 
03  10 

58  30 

39  25 
36  56 
25  51 

06  25 
58  55 
58  00 

07  50 


Long.  W. 


7  06  24 
7  10  15 
7  33  05 

7  54  54 
7  32  39 
7  35  08 
7  50  34 
7  51  10 

7  59  00 

8  18  20 
8  15  14 
8  31  58 
8  42  51 

8  57  10 

9  13  27 
2  12  00 
2  06  44 


Long. 
31  07 
29  45 
25  40 
23  59 
23  40 
18  57 
17  50 
16  08 
16  02 
14  40 
13  04 
13  52 
13  28 

11  59 

12  13 
10  42 

9  24 
9  44 
9  45 
10  23 
7  36 
7  43 
7  46 
7  29 
7  12 
6  36 
5  16 
5  07 


5  20 
5  19 
5  01 
5  03 

4  52 

5  24 
5  45 
5  33 
5  49 

5  58 

6  34 

7  03 

7  29 

8  00 


Lun.  Int. 


Range. 


H.W. 


h.    m. 


5  00 


5  02 


4  40 


4  33 
4  30 
4  20 


6  21 
6  09 

5  40 


2  20 
1  35 


0  42 


11  35 


11  18 


11  00 


lO  15 


9  43 


4  16 


L.W. 


Spg.   Keap. 


h.    m. 


11  13 


12.4 


11  15 


12.6 


10  53 


11.8 


10  59 
10  43 
10  33 


11.6 
11.4 
10.7 


0  16 
0  00 

11  57 


17.2 
3L2 

9.0 


8  40 

7  48 


8.3 

7.8 


6  55 


7.0 


5  23 


6.9 


5  04 


8.4 


4  48 


5.0 


3  55 


4.1 


3  40 


6.2 


6.3 


5.9 


5.8 
5.7 
5.3 


7.6 
13.6 

5.1 


4.7 
4.4 


4.0 


3.3 


4.1 


2.9 


2.1 


0.8 


10  15 


1.1 


0.5 


APPENDIX  IV.                                       [Page  219 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  ETJK.OPE— Continued. 

o 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

i 

9 

1 

Okso:  Light-house 

O          1         II 

58  04  15 
58  15  02 
58  24  40 
58  51  50 

58  59  25 

59  00  01 
58  59  34 

58  58  05 

59  01  35 
59  10  30 
59  23  10 
59  25  34 
59  29  23 
59  39  52 
59  40  21 
59  54  44 
59  09  00 
59  07  08 
58  59  45 
58  54  05 

58  56  24 
58  54  12 
58  32  45 
58  20  12 
57  53  49 
57  40  58 
57  18  15 
57  06  26 
56  54  08 
56  40  21 
56  14  40 
56  18  06 
56  02  37 
55  52  00 
55  36  47 
55  23  00 
55  22  00 
55  25  42 

55  22  58 

56  00  54 
56  10  04 
56  09  45 
56  11  50 

56  55  18 

57  26  29 
57  57  24 

57  45  38 

58  08  52 
58  17  55 

58  44  26 

59  20  35 
59  51  31 
59  45  24 

59  45  15 

60  10  35- 
60  15  19 
60  20  26 
60  22  15 
60  22  26 
60  31  41 
60  40  29 
60  43  48 

60  55  57 

61  18  22 
61  32  54 

o          /          // 

8  03  30 
8  31  36 

8  47  55 

9  36  15 
9  45  50 
9  45  14 

10  03  28 
10  09  26 
10  31  55 
10  36  25 
10  32  45 
10  29  52 
10  19  15 
10  38  08 
10  36  55 
10  43  35 

10  50  15 

11  24  09 

10  47  20 

11  00  45 

11  10  28 
11  00  36 
11  02  16 
11  13  24 
11  28  04 
11  53  54 

11  54  16 

12  14  32 
12  29  48 
12  51  38 
12  51  47 
12  27  11 
12  41«30 
12  49  48 
12  59  49 
12  49  02 

h.    in. 

h.    m. 

/'. 

St. 

Hamberg:  Mill 

Arendal  Inlet:  Inner  Torungerne  light.. 

Jomf ruland :  Light-house 

Langotangen :  Light-house 

4  17 

10  10 

LO 

0.7 

Langesund:  Church 

Frederiksvsern :  Lookout  tower 

4,34 

10  00 

1.3 

1.0 

Svenor:  Light-house     

Foerder  Islet:  Light-house. 

Fulehuk :  Light-house    

Basto :  Light-house       

' 

Horten :  Church                    

Holmestrand :  Church 

Drobak :  Church 

Oscarsberg:  Fort  flagstaff  . . 

Christiania:  Observatory 

5  22 

10  37 

1.2 

0.9 

Strom tangen  (Torgauten):  Light-house. 
Fredriksten :  Fort  clock  tower 

Torbjornskjter:  Light-house 

Koster;  Light-house 

Stromstad :  Steeple 

Nord  Koster  Islands :  Light-house 

Wadero  Island:  Light-house . 

Hollo  Island:  Light-house 

Paternoster  Rocks:  Light-house 

Gottenburg:  Signal  station 

Nidingen  Islet:  Light-house 

Warberg:  Castle  tower 

Falkenberg:  Church 

Halmstad :  Palace 

Engelholm :  Church 

Kullen  Point;  Light-house 

Helsingborg:  Light-house 

Landskrona :  Light-house 

Malmo:  Light-house 

Falsterbo:  Light-house 

Trelleborg:  Light-house 

13  09  20 

13  49  38 

14  n  10 
14  50  57 

14  52  02 

15  36  05 

16  24  04 

Ystad :  Light-house 

Sandhammaren :  Light-house ^.. 

Hano  Island :  Light-house ;.. 

Karlshamn :  Light-house 

Karlskrona:  Stum  holm  Tower 

Oland  Island :  Light  on  S.  pt 

Gottland  Island:  Hoburg  light,  S.  pt 

Ostergarns  light 

Faro  Island:  Holmadden  light 

Sparo  Vestervik :  Granso  light 

18  11  06 

18  59  27 

19  22  36 
16  40  36 
16  59  22 

16  11  28 

17  52  09 

18  03  30 

17  37  39 

18  41  34 

19  24  34 
18  49  49 
18  22  36 
18  26  33 
18  24  21 
18  09  49 
18  22  38 
17  08  29 
17  33  50 
17  02  57 
17  04  18 
17  01  51 

Haradsskar  Islet:  Light-house 

Norrkopings  Inlopp :  Light-house 

Landsort:  Light-house 

Stockholm :  Observatory 

Upsala:  Observatory 

Norrtelge:  Inn 

Soderarm :  Light-house 

Svartklubben :  Light-house 

Osthammar :  Church 

Oregrund :  Clock  tower 

Djursten :  Light-house 

Forsmark:  Church 

Orskar  Rock :  Light-house 

Gefle:  Church 

Eggegrund  Islet:  Light-house 

Hamrange:  Church 

Soderhamm :  Court-house 

Enanger:  Church 

::::::;:::::  i 

1 

Page  220] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

ATLANTIC  COAST  OF  ETTROPE— Continued. 


Place. 


Hudiksvalls :  Coyrt-house 

Gnarp:  Church 

Sundsvall:  Church 

Lungo:  Light-house 

Skags  Head :  Light-house 

Holmogadd :  Light-house 

Umea:  Bredekar  Light 

Bjuroklubb:  Light-house 

Pitea 

Rodkallen :  Light-house 

Maloren :  Light-house 

Tomea:  Light-house 

Uleaborg:  Karlo  I.  light 

Ulko  Kalla  Rock:  Light-house 

Norrsher  Islet:  Kvarken  light 

Kaske:  Shelgrund  I.  light 

Bierheborg:  Sebsher  light 

Nuistad:  Ensher  light 

Abo:  Observatory 

Aland  Island;  Shelsher  light 

Ekkere  light 

Logsher  light 

Bogsher:  Beacon 

Ute  Islet:  Light-house 

Gauge:  Gange  I.  light 

Rensher:  Light-house 

Helsingfors:  Observatory 

8oder  Skars:  Light-house 

Kalboden  Island:  Light  vessel 

Rodsher  Island:  Light-house 

Hogland  Island:  Lower  light 

Upper  light 

Sommer  Island :  Light-house ,. 

Vieborg  Bay:  Nelva  I.  light 

Stirsudden :  Light-house 

Kronstadt:  Light  on  Frederikstadt  t 

tion 

Cathedral 

St.  Petersburg:  Observatory 

Pulkowa :  Observatory 

Peterhof :  Pier-head  light 

Oranienbaum:  Light-house 

Seskar  Islet:  Light-house 

Narva:  Light  S.  pt.  of  entrance 

Stensher  Rock:  Light-house 

Ekholm  Islet:  Light-house 

Koksher:  Light-house 

Revel:  Light  N.  end  of  W.  mole  . . . 

Cathedral 

Nargen  Island :  Light-house 

Surop:  W.  light 

Baltic  Port:  Light-house 

Odenskholm  Island:  Light-house 

Takhkona  Point:  Light-house 

Dago  Island :  Dagerort  light 

Filzand  Island:  Light-house 

Svalferort  Tzerel :  Light-house 

Kuino:  Light-house 

Pernau:  Light  at  S.  entrance 

Riga:  Light  on  Fort  Kametskoi  dike 

Cathedral 

Runo  Island:  Light-house 

Domesnes :  Light-house 

Windau :  Light  on  S.  jetty 

Libau:  Light  at  entrance  of  port 


Lat.  N. 


61  43  57 

62  02  51 
62  23  30 

62  38  35 

63  11  55 
63  35  34 

63  39  33 

64  28  50 

65  19  10 
65  18  53 
65  31  30 


65 
65 
64 
63 
62 
61 
60 
60 
60 
60 
59 
59 
59 
59 
59 
60 
60 
59 
59 
60 
60 
60 
60 
60 

59 

59 
59 
59 
59 
59 
60 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
59 
58 
58 
57 
58 
58 
57 
56 
57 
57 
57 
56 


48  30 
02  20 
20  05 
14  08 

20  06 
28  29 
43  10 

26  57 
24  45 

13  20 
50  50 
31  11 
46  30 
46  00 
56  10 
09  43 
06  40 
58  45 
58  08 
00  40 
06  22 
12  31 

14  43 
11  05 

58  14 

59  44 
56  30 
46  19 

53  26 
55  40 

02  08 
28  04 

49  10 

41  06 

42  00 

27  05 

26  28 
36  22 

27  55 

21  30 
18  06 
05  25 

55  02 
23  02 

54  37 
05  50 

23  10 

03  28 

56  36 
48  02 
48  10 

24  00 
31  01 


Long.  E. 


17  07  37 
17  16  22 

17  19  05 

18  05  05 

19  02  50 

20  45  35 

20  18  35 

21  34  45 

21  30  00 

22  21  55 

23  34  00 

24  12  00 
24  34  00 

23  27  00 

20  37  40 

21  11  24 
21  22  34 

21  01  00 

22  17  03 
19  34  00 
19  31  20 

19  54  05 

20  25  50 

21  22  00 

22  58  08 

24  24  43 

24  57  17 

25  25  51 

25  37  30 

26  41  05 

27  01  40 

26  58  44 

27  33  46 

27  58  36 
29  03  01 

29  47  12 

29  46  07 

30  19  22 
30  19  40 
29  54  54 
29  46  38 

28  23  01 
28  03  31 
26  23  00 
25  48  58 
25  02  37 
24  46  10 
24  44  45 
24  31  57 
24  24  05 
24  04  30 

23  23  15 
22  36  15 
22  11  36 

21  49  56 

22  04  15 

23  59  34 

24  49  25 
24  00  59 
24  08  25 
23  15  00 
22  39  15 
21  34  00 
20  59  40 


Lun.  Int. 


Range. 


L.  W. 


h.    m. 


Spg.    Neap. 

ft. 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

ATIiANTIC  COAST  OF  EUROPE— Continued. 


[Page  221 


Memel:  Light-house 

Heiligen  Creutz:  Church  tower 

Brusterort :  Light-house 

Pillau :  Light-house 

Fischausen:  City-hall  tower 

Konigsberg:  Observatory 

Tolkemit:  Church  tower 

Elbing:  Church  tower 

Tiegenort :  Church  tower 

Danzig:  Observatory 

Neufahrwasser  light 

Weichselmunde:  Fortress  tower 

Putziger  Heisternest:  Church  tower 

Oxhoft:  Light-house 

Hela:  Light-house 

Rixhoft:  Light-house 

Leba:  Church  tower 

Stopelmunde:  Church 

Jershoft:  Light-house 

Rugenwalde:  St.  Mary's  Church 

Coslin:  St.  Mary's  Church 

Funkenhagen :  Light-house 

Colberg:  St.  Marv's  Church 

Gross-Horst :  Light-house 

Cammin:  Cathedral  tower 

Wollin:  Church  tower 

Stettin;  N.  Castle  tower 

Swinemunde :  Light-house 

Streckelsberg:  Survey  station  near  beacon 

Usedom:  Church  tower 

Lassau:  Church  tower 

Wolgast:  Church  tower 

Grieiswald:  St.  Nicholas  Church 

Griefswalder  Oie :  Light-house 

Granitz:  Castle  tower 

Bergen :  Church  tower 

Arkona:  Light-house 

Stralsund:  St.  Mary's  Church 

Darsserort:  Light-house 

Wustrow :  Church 

Ribnitz:  Church  tower 

Wamemunde:  Church 

Rostock :  St.  Jacob' s  Church 

Diedrichshagen :  Survey  station 

Basdorf :  Survey  station 

Wismar:  St.  Nicholas  Church 

Hohenschonberg:  Survey  station 

Travemunde:  Light-house 

Burg:  Church  tower 

Manenleuchte:  Light-house 

Petersdorf :  Church  tower 

Hessenstein :  Flagstaff  of  lookout  tower . 

Schonberg:  Church 

Bulk :  Light-house 

Kiel :  Observatory 

Eckemforde :  Church 

Schleswig:  Cathedral 

Kappeln:  Church 

Flensberg:  Church 

Duppel:  Survey  station 

Schleimunde:  Light-house 

Augustenburg:  Church 

Hugeberg :  Survey  station 

Apenrade:  Church 

Skoorgaarde :  Survey  station 

Ballum :  Church 

List:  E.  light-house 


Lat.  N. 


55  43  45 
54  53  47 
54  57  40 
54  38  25 
54  43  49 
54  42  51 
54  19  19 
54  09  44 
54  16  30 
54  21  18 
54  24  28 
54  23  51 
54  12  16 
54  33  09 
54  36  06 
54  49  55 
54  45  29 
54  35  16 
54  32  29 
54  25  27 
54  11  28 
54  14  40 
51  10  40 
54  05  47 
53  58  29 
53  50  41 
53  25  41 

53  55  03 

54  03  08 
53  52  17 

53  56  59 

54  03  18 
54  05  49 
54  15  02 
54  22  56 
54  25  08 
54  40  53 
54  18  42 
54  28  28 
54  20  47 
54  14  42 
54  10  42 
54  05  27 
54  06  32 
54  08  00 
53  53  50 
53  58  54 

53  57  44 

54  26  16 
54  29  43 
54  28  54 
54  19  47 
54  23  52 
54  27  25 
54  20  30 
54  28  25 
54  80  55 
54  39  48 
54  47  05 
54  54  28 
54  40  23 
54  56  48 

54  58  05 

55  02  46 
55  03  52 
55  05  31 
55  03  04 


Long.  E. 


Lun.  Int. 


Range. 


H.  W. 


21  06 
20  01 
19  59 

19  53 

20  00 
20  29 
19  31 
19  23 
19  08 
18  39 
18  39 
18  41 
18  40 
18  33 
18  49 
18  20 
17  33 
16  51 
16  32 
16  24 
16  11 
15  52 
15  34 
15  04 
14  46 
14  37 
14  33 
14  17 
14  01 
13  55 
13  51 
13  46 
13  22 
13  55 
13  37 
13  26 
13  26 
13  05 
12  30 
12  24 
12  26 
12  05 
12  08 
11  46 
11  41 
11  28 
11  05 

10  52 

11  11 
11  14 
11  04 
10  32 
10  22 
10  12 
10  08 

9  50 
9  34 
9  56 
9  26 
9  45 
10  02 
9  52 
9  58 
9  25 
9  23 
8  39 
8  26 


h.     m. 


0  20 


L.  W. 


Spg. 


h.     m. 


6  33 


5.2 


Page  222] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

ATLANTIC  COAST  OF  EUROPE— Continued. 


Place. 


Keitum:  Church 

Fohr:  St.  Nicholaf  Church 

Ualgenberg:  Survey  station 

Husum :  Church '... 

Tonning:  Church 

Busuin:  Church 

Helgoland :  Ijight-house 

Scharhorn :  Beacon  

Neuwerk :  Li^ht-house 

Cux  haven :  Light-house 

Stade:  Church  steeple 

Steinkirchen :  Church 

Altona :  Observatory 

Hamburg:  Observatory 

Berlin:  Observatory 

Harburg:  Light-house 

Hohe  Weg:  Light-house 

Langwarden :  Church 

Bremerhaven:  New  harbor  light. 

Minsener  Sand:  Light  vessel 

Schillighorn:  Light-house 

Wilhelmshaven:  Observatory 

Wangeroog:  Light-house 

Spikeroog:  Church 

Langeoog:  Belvedere 

Balstrum :  Church 

Norderney:  Light-house 

Juist:  Church 

Emden:  City  Hall  tower 


Lat.  N. 


Falster:  Gjedser  light 

Moen  Island :  Stege  Church  spire 

Moen  light,  SE.pt 

Prceste :  Church  spire 

Kjorge:  Church  tower 

Amager  Island:  Holloenderby  Ch.  spire. . 

Nordse  Rase  light 

Copenhagen:  New  observatory 

Bornholm:  Ronne  light 

Christianso  Island:  Great  tower 

Kronberg:  High  spire 

Nakkehooed :  Upper  light 

Hesselo  Island :  Light-house 

Anholt  Island :  Light-house 

Spodsbjerg:  Light-house 

Roeskilde:  Cathedral 

Nykjobing:  Church  tower 

Oddensby :  Church  tower 

Sejro  Island :  Sejro  Point  light 

Kallundborg:  Church 

Omo  Island:  Church 

Vordingborg:  Waldeniar's  tower 

Veiro  Island:  Light-house 

Langeland  Island:  Fakkebjerg  light 

JEto  Island :  Church  spire 

Lyo  Island:  Church  tower 

Assens:  Church  tower 

Baago  Island :  Light-house 

Kolding:  Castle  tower 

Bogense:  Church  spire 

Nyborg:  Church  spire 

Turo  Island :  Church  spire 

Svendborg:  Frue  Church 

Endelave  Island:  Church  tower 

Samso  Island :  Koldby  Church  tower 

Horsens :  Frelser  Church  spire 


54  54  13 
54  41  51 
54  41  21 
54  28  43 
54  19  08 
54  07  52 
54  10  57 
53  57  15 
53  55  01 
53  52  25 
53  36  12 
53  33  43 
53  32  45 
53  33  07 

52  30  17 

53  28  30 
53  42  50 
53  36  20 
53  32  52 
53  46  57 
53  42  21 
53  31  52 
53  47  25 
53  46  19 
53  45  06 
53  43  46 
53  42  39 
53  40  45 

53  22  06 

54  33  50 
54  59  03 

54  56  46 

55  07  24 
55  29  44 
55  35  45 
55  38  10 
55  41  14 
55  05  40 

55  19  19 

56  02  20 
56  07  10 
56  11  50 
56  44  16 
55  58  36 
55  38  34 
55  55  30 
55  57  52 
55  55  09 
55  40  50 
55  09  48 
55  00  26 
55  02  19 
54  44  23 

54  51  14 

55  02  34 
55  16  09 
55  17  44 
55  29  31 
55  34  03 
55  18  41 
55  03  00 
55  03  37 
55  45  32 
55  48  02 
55  51  44 


Long.  E. 


8  22  03 
8  33  13 

8  33  58 

9  03  21 
8  56  38 
8  51  53 

7  53  11 

8  24  35 
8  29  58 

8  42  43 

9  28  48 
9  36  40 
9  56  35 
9  58  25 

13  23  44 
9  59  37 
8  14  48 
8  18  30 
8  34  25 
8  04  47 
8  01  43 
•8  08  48 


54  09 
41  45 
35  41 
22  03 
13  58 

6  59  53 

7  12  25 


n  58  03 
12  17  16 
12  32  40 
12  03  07 
12  07  36 
12  38  24 
12  41  26 
12  34  47 

14  42  00 

15  11  39 
12  32  02 
12  20  50 
11  42  50 
11  39  15 

11  51  36 

12  05  02 
11  40  29 
11  24  06 
11  05  07 
11  05  04 
11  09  32 
11  54  59 
11  22  23 
10  42  13 
10  24  11 
10  09  16 

9  53  50 

9  48  09 

9  28  40 

10  05  29 

10  47  47 

10  40  02 

10  36  48 

10  16  20 

10  33  37 

9  51  19 


Lun.  Int. 


Range. 


H.  W. 


h.  m. 


1  35 


2  10 

1  45 

1  11 

11  29 


0  39 


4  00 
'5"66' 


L.  W. 


Spg. 


h.  m. 


7  47 


8  23 

7  57 
7  24 
5  17 


10.8 

11.0 

11.7 

8.1 


6  51 


10.1 


10  13 

"ii'i2' 


8.5 

'e.'i' 


0  25 


6  38 


10.1 


0  54  i   7  07 
0  10  !   6  23 


10.4 
9.5 


0  04 
11  27 


11  05 
"'6"24" 


6  17 
5  15 


13.2 
8.0 


4  53 


7.3 


6  36 


9  33 


3  21 


0.6 


Neap. 


ft. 


4.5 


6.2 
6.4 
6.8 
4.7 


5.8 


4.9 


3.5 


5.7 


5.8 
5.3 


7.4 
4.5 


4.1 


5.0 


0.3 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  ETJROPE— Continued. 


[Page  223 


Lat.  N. 


Tuno  Island :  Light-house 

Samsoe  Island:  Nordby  Church  tower  . 

Aarhns:  Cathedral  spire 

Hjelm  Islet:  Light-house 

Fornpes :  Light-Jiouse 

Hals:  Church  tower 

Aalborg:  St.  Rudolph's  Church 

Cape  Skaw,  or  Skagen:  Old  light-house 

Hirtshals:  Light-house .' 

Haustholm :  Light-house 

Boobjerg :  Light-house 

Ringkjobing:  Church  spire 

Loune:  Church  tower 

Blaabjerg:  Summit,  100  ft 

Guldager:  Church 

Fano  Island :  Nordby  Church 

Mano  Island:  Church  spire 


Niewe  Diep:  Time-ball  station 

Amsterdam :  W.  church  tower 

Utrecht:  Observatory 

Leyden :  Observatory 

The  Hague:  Church  tower 

Scheveningen :  Light-house 

Brielle:  Light-house 

Rotterdam :  Time-ball  station 

Hellevoetsluis:  Time- ball  station , 

Willemstadt:  Light-house 

Goedereede:  Light  on  church  tower 

Flushing:  Time-ball  station 

Light,  Westhaven  bastion . '. 


Brussels:  Observatory , 

Antwerp:  Observatory 

Notre  Dame  Cathedral . 
Blankenberghe:  Fort  light-house . 

Ostend :  Light- house 

Church  tower 

Nieuport:  Templars  tower 


Paris:  Observatory 

Dunkerque :  Tower 

Gravelines:  Light  on  N.  breakwater  . . . 

Calais:  Light  on  old  fort 

Cape  Gris  Nez :  Light-house 

Boulogne,  C.  Alprech:  Light-house 

Abbeville:  Tower 

Cay eux :  Light-house 

Dieppe:  W.  jetty  light 

Ailly  Point:  Light-house 

St.  Valery  en  Caux :  Light  on  W.  break- 
water   

Fecamp:  N.  jetty  light 

Cape  La  Heve:  S.  light 

Havre:  S.  jetty  light 

Honfleur:  Hospital  jetty  light 


Caen :  Church  tower 

Port  Corseulles:  W.  jetty  light 

Point  De  Ver:  Light-house 

Cape  La  Hougue:  Light-house 

Cape  Bartieur:  Light-house 

Cherbourg:  Light,  W.  head   of  break- 
water   

Naval  Observatory 

Cape  La  Hague:  Light-house 

Casquets  Rocks:  Light  on  NW.  rock  . . . 


55  56  58 

55  57  06 

56  09  26 
56  08  00 
56  26  36 

56  59  54 

57  02  54 
57  43  46 
57  35  06 
57  06  50 
56  30  48 
56  05  27 
55  47  17 
55  44  50 
55  31  52 
55  26  26 
55  16  11 


52  57  50 
52  22  30 
52  05  10 
52  09  20 
52  04  40 
52  06  16 
51  54  29 
51  54  30 
51  49  19 
51  41  48 
51  49  08 
51  26  33 
51  26  24 

50  51  11 

51  12  28 
51  13  17 
51  18  47 
51  14  13 
51  13  50 
51  07  53 

48  50  11 
51  02  09 
51  00  18 
50  57  45 
50  52  10 
50  41  57 
50  07  05 
50  11  42 

49  56  06 
49  55  04 

49  52  28 
49  46  05 
49  30  04 
49  29  01 
49  25  32 

49  11  14 
49  20  18 
49  20  28 
49  34  19 
49  41  50 

49  40  29 
49  38  54 
49  43  22 
49  43  17 


Long.  E. 


10  26  51 

10  33  00 

10  12  50 

10  48  32 

10  57  40 

10  18  53 

9  55  22 

10  36  38 

9  56  44 

8  36  10 

8  07  23 

8  14  52 

8  14  36 

8  14  43 

8  24  12 

8  24  03 

8  32  38 


46  36 
53  04 
07  50 
29  03 
18  30 
15  10 
10  45 
28  50 
07  40 
26  26 
58  35 
35  48 
34  32 


4  22  18 
4  24  44 
4  24  12 
3  06  54 
2  55  51 
2  55  22 
2  45  34 

2  20  14 
2  22  31 
2  06  34 
1  51  07 
1  35  02 
1  33  47 


49  56 
30  46 
05  01 


0  57  35 

0  42  34 
0  22  12 
0  04  08 
0  06  22 
0  13  43 

Long.  W. 
0  21  10 
0  27  24 

0  31  08 

1  16  21 
1  15  56 

1  43  44 
1  38  08 

1  57  15 

2  22  41 


Lun.  Int. 


Range. 


H.  W. 


5  46 
4  18 


2  35 


2  35 
2  34 


7  17 


2  50 

3  35 

2  20 

3  20 


0  44 


4  15 


0  05 
0  02 


0  10 


11  58 
11  59 
11  39 
11  17 
11  18 


10  54 


10  29 
10  06 


9  03 


8  13 
8  14 


7  30 


6  20 


Spg.  I  Neap. 


h.    m. 


ft- 


11  58 
10  30 


1.0 

1.2 


8  47   2. 1 


47  !  4.5 
46  i  4.7 


1  05  I  3. 9 


9  02 
9  47 

8  32 

9  32 


6  56 


10  27 


6  17 
6  32 


6  22 


5  58 

6  16 
6  13 
5  51 
5  52 


5  48 


5  33 
5  02 


4  14 


2  45 
2  37 


1  44 


0  15 


4.8 
6.7 
5.2 


14.7 


14.8 


12.5 
16.1 


15.7 


16.8 
19.0 
21.0 
21.5 
25.2 


27.3 


26.8 
23.3 


22.5 


18.5 
17.0 


17.6 


15.5 


ft. 


0.5 
0.7 


1.2 


2.6 

2.7 


2.0 


2.5 
3.5 

2.8 
5.2 


5.7 

i.i 


8.4 


8.5 

9.6 

10.7 

11.0 

12.8 


13.3 


13.1 
11.4 


11.0 


8.2 
7.5 


6.9 


Page  224J 


APPENDIX  IV. 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUROPE— Continued. 


Place. 


Port  St.  Peter,  Guernsey:  Light  on  Cas- 
tle Coonet  Breakwater 

Douvres  Rocks:  Light-house 

Cape  Carteret:  Light-house 

Coutances:  Cathedral  tower 

Granville :  Light-house 

Chausey  Is. :  Light  on  SE.  end  of  large  id 

St.  Malo:  Roehebourne  light 

Cape  Frehel:  Light-house 

Heau  de  Brehat:  Light-house 

Morlaix,  He  Noire:  Light-house 

De  Bas  Islet:  Light-house 

Abervrach :  Light  on  Vrach  Islet 

Usiiant:  Stiff  Point  light 

Brest:  Observatory 

Brest  (approach ) :  Quelern  light 

De  Sein  Islet:  Light-house 

Bee  du  Raz:  Light-house 

Audierne:  Pier-head  light 

Penmarch  Rocks:  Light-house 

Glenan  Islands:  Light,  Penfret  I 

De  Groix  Island:  Light-house 

Lorient:  Church-tower  light 

Belle  Isle:  Light-house 

Port  Haliguen :  Light  on  N.  jetty 

Haedic  Island :  Light-house 

Port  Navalo:  Light-house 

Vannes:  St.  Pierre  Church 

Le  Four  Rock :  Light-house 

Croisic:  End  of  breakwater 

Guerande:  Steeple 

Port  St.  Nazaire:  Light-house 

Paimbffiuf :  Steeple 

Nantes :  Cathedral 

Noir  Moutier  Island:  Light-house 

Le  Pilier  Island :  Light-house 

D'Yeu  Island:  Light-house 

La  Chaume:  Light-house 

Point  de  Grouin  du  Cou:  Light-house.. 

R6  Island:  Light,  NW.pt 

Rochelle:  E.  Quay  light 

Aix  Island :  Light-house 

Rochefort:  Hospital 

Oleron  Island:  Light  NW.  pt 

Point  de  la  Coubre:  Light-house 

Point  Cordouan:  Light-house 

Point  de  Grave:  Light-house 

Bordeaux:  St.  Andr6 

Bayonne:  Cathedral 

Biarritz :  Light-house 

St.  Jean  de  Luz;  St.  Barbe  Point  light . 

Fuenterrabia:  Light  on  Cape  Higuera.. 

Port  Pasages :  Light  at  entrance 

San  Sebastian:  Monte  Igueldo  light 

Bilbao:  Light  on  Galea  Castle 

Castro  Urdiales:  Santa  Ana  Castle  light 

Santofia:  Pescador  Point  light 

Santander:  Cape  Mayor  light 

San  Martin  de  la  Arena:  Light-house. . . 
San  Vincent  de  la  Barquera:  End  of  new 

mole 

Rivadesella:  Mount  Somos  light 

Gijon:  Santa  Catalina  light 

Aviles:  Light-house 

Rivadeo:  Light-house 

Estaca  Point:  Light-house 


Lat.  N. 


49  27  13 
49  06  28 
49  22  27 
49  02  54 
48  50  07 
48  52  13 
48  40  18 
48  41  05 
48  54  33 
48  40  23 
48  44  45 
48  36  57 
48  28  31 
48  23  32 
48  19  10 
48  02  40 
48  02  28 
48  00  47 
47  47  52 
47  43  17 
47  38  51 
47  44  53 
47  18  42 
47  29  10 
47  19  18 
47  32  53 
47  39  30 
47  17  53 
47  18  30 
47  19  44 
47  16  18 
47  17  17 
47  13  08 
47  00  41 
47  02  35 
46  43  04 
46  29  38 
46  20  41 
46  14  40 
46  09  25 
46  00  36 

45  56  37 

46  02  49 
45  41  39 
45  35  14 
45  34  10 
44  50  19 
43  29  29 
43  29  38 
43  23  58 

43  23  30 
43  20  05 
43  19  22 
43  22  36 
43  24  20 
43  28  36 
43  29  30 
43  26  50 

43  23  35 
43  31  00 
43  32  48 
43  38  05 
43  34  40 
43  47  20 


Long.  W. 


2  31  31 
2  48  49 
1  48  25 
1  26  39 
1  36  46 
1  49  20 
58  41 
19  08 

05  11 
52  33 

01  38 
34  34 
03  26 

29  36 
34  28 
52  03 
45  25 
32  50 
22  30 
57  15 

30  35 
21  31 
13  38 

06  09 
50  07 
55  08 
45  28 
38  05 

31  25 
25  48 
11  50 

02  09 

32  59 
13  16 

21  37 

22  56 
47  45 
27  49 

33  40 
1  08  57 
1  10  40 

0  57  50 

1  24  37 
1  15  16 
1  10  24 
1  04  27 

0  34  42 

1  28  43 
1  33  16 
1  39  53 


Lun.  Int. 


Range. 


47  30 
56  05 
01  40 
04  06 
16  10 
28  06 
47  40 
01  00 

24  55 
07  10 
40  11 
56  00 
03  00 
42  00 


H.  w. 


h.    m. 
6  12 


6  07 


5  50 
5  55 
5  43 


5  35 
5  00 
4  35 
4  00 
3  35 
3  23 


3  25 


3  04 
3  05 
3  00 


3  09 
3  25 
3  35 
3  20 
3  45 
5  47 


3  25 


3  35 

4  18 

5  50 
■3  05 


3  18 
3  20 


3  27 
3  27 
3  45 


3  35 


6  30 


3  07 


3  00 


2  50 
2  45 
2  45 


L.  W. 


h.     TO. 
0  07 


ft. 
26.0 


0  15 


30.8 


0  09 
0  04 
0  04 


36.7 
34.7 
36.0 


12  00 
11  25 
11  00 
10  25 
10  00 
9  45 


30.4 
23.1 
22.0 
20.6 
18.9 
19.5 


9  53 


17.2 


9  31 
9  34 

9  27 


11.1 
13.3 
13.0 


9  36 
9  50 
9  58 
9  46 
10  08 
12  11 


13.8 
16.6 
16.9 
16.7 
16.6 
15.8 


9  47 


16.7 


9  56 
10  39 
12  28 

9  26 


16.6 
17.0 
16.5 
16.7 


9  40 
9  44 


14.7 
12.7 


9  22 
9  22 
9  55 


16.6 
16.6 
16.7 


9  53 


16.8 


0  12 


15.3 


9  14 


12.3 


9  05 
9  03 
9  03 
9  07 
9  18 
9  14 

9  14 


11.7 
12.7 
11.8 
12.3 
14.8 
1L7 

10.4 


9  03 
8  58 
8  58 


13.5 
12.0 
14.4 


Neap. 

ft. 
11.5 


13.5 


16.0 
15.2 

15.7 


13.3 

10.6 

10.1 

9.5 

8.7 
9.0 


5.1 
6.1 
6.0 


6.3 

7.7 
7.9 
7.7 
7.7 
7.4 


7.7 


7.7 
7.9 

7.7 
7.7 


6.8 
5.9 


7.7 
7.7 
7.7 


7.8 


7.1 


5.8 


5.5 
5.9 
5.5 
5.7 
6.9 
5.5 

4.9 


6.3 
4.9 
3.9 


APPENDIX  IV.                                       [Page  225 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ATLANTIC  COAST  OF  EUKOPE— Continued. 

1 

Place. 

Lun.  Int. 

Range.          1 

H.  W.    1     L.  W. 

spg. 

Neap. 

1 

© 

s 
<s 

B 
a. 

Port  Cedeira:  Light-house 

O       /       1/ 

43  39  00 
43  29  30 
43  27  30 
43  23  10 

o     /      ri 

8  05  30 
8  13  29 
8  20  20 
8  24  26 

h.  VI. 
2  43 
2  44 

h.  m. 
8  56 
8  57 

ft. 

14.8 
14.9 

fl. 
6.1 
6.1 

Ferrol:  Old  naval  observatory 

Priorino  Chico  light 

Corufia:  Hercules  Tower  light 

2  43 
2  42 

8  56 
8  55 

14.8 
10.0 

6.1 
4.6 

Cape  Finisterre:  Light-house 

42  52  45       9  15  28  1 

Vigo"  Cres  I.  light 

42  12  30 
41  09  10 
40  10  47 
39  24  49 
39  21  00 
38  46  49 
38  42  31 
38  29  15 
37  01  20 
37  07  48 

36  58  23 

37  11  00 
37  15  08 
36  43  58 
36  27  40 
36  31  30 
36  10  50 

35  59  53 

36  07  19 
36  07  10 
36  06  25 

8  54  00 
8  40  35 

8  54  15 

9  30  29 
9  22  30 
9  29  46 
9  11  10 
8  56  00 
8  58  00 
8  39  53 
7  51  48 
7  24  00 
6  57  12 
6  26  30 
6  12  20 
6  19  00 
6  02  08 
5  36  31 
5  26  12 
5  21  17 

Oporto :  Light,  N.  S.  de  Luz 

2  25 
2  20 

8  38 
8  35 

10.0 

7.0 

4.3 
3.0 

Cape  Mondego :  Light-house 

Berlanga  Island'  Light-house 

Peniche:  Light-house       

2  05 

8  15 

7.8 

3.4 

Cape  Roca :  Light-house        

Lisbon :  Royal  Observatorv 

2  20 
2  10 

8  05 
8  20 

11.1 
11.6 

4.8 
5.0 

Setubal:  Light-house             

Cape  St  Vincent:  Light-house 

Lagos :  Church 

1  55 

8  08 

13.0 

5.6 

Cape  Sta.  Maria:  Light-house 

Ayanionte  ■  Lio'ht-house         ....         ... 

Huelva*  Plaza  at  head  of  mole 

San  Lucar:  Chipiona  light 

1  15 

7  28 



12.3 

5.6 

Cadiz:  Observatory^  of  San  Fernando 

San  Sebastian  light 

1  45 

7  58 

11.8 

5.4 

Cape  Trafalgar:  Light-house 

Tarifa:  Light-house. 

1  32 

7  52 

5.6 

2.6 

Algeciras:  Verde  I.  light         

Gibraltar:  Dockyard  flagstaff     

Europa  Pt.  light 

5  20  42 

1  35 

7  55 

3.7 

1.7 

COASTS  OF  THE  MEDITEBBANEAN,  ADBIATIC,  AND  BLACK  SEAS. 

B 

SB 
fa 

Malaga:  Light-house 

36  42  39 
36  50  12 

36  42  57 

37  33  28 
37  35  50 
37  33  22 

37  34  38 

38  12  30 

4  24  38 
2  27  50 
2  11  12 
1  15  12 
0  59  09 
0  57  58 
0  50  20 
0  .30  12 

2  15 

8  35 

2.9 

1.5 

Almeria:  Light-house 

Cape  de  Gata:  Light-house 

Mazarron :  Light-house 

Cartagena :  Arsenal  gate 

Esconibrera  light 

Porman :  Light-house 

Santa  Pola  Bay:  Jjight-house 

Alicante :  N.  mole  light 

38  20  12  !     0  28  48 
38  30  00  :     0  11  42 
38  30  57  ;     0  10  06 
38  33  30  1     0  04  02 

Villajoyose:  Light-house 

Benidonne:  Tower 

Altea:  Light-house 

Calpe :  Church  tower 

38  38  36 

Long.  E. 
0  02  52 
0  09  17 
0  12  02 
0  07  30 

Long.  W. 
0  13  37 
0  19  48 
0  18  50 

Long.  E. 
0  41  19 
0  08  56 
0  28  48 
0  39  45 

0  53  55 

1  14  42 

2  10  52 

3  08  28 
3  17  10 
3  18  55 

3  07  30 
3  06  50 

Morayva:  Tower 38  40  51 

Jarea:  Cape  San  Antonio  light 38  48  06 

Denia:  Mole-head  light 38  51  00 

Cape  Cullera:  Light-house 

39  12  15 
39  28  05 

39  27  50 

39  53  57 

Valencia :  Light-house 

Mole-end  light 

5  00 

11  30 

1.5 

0.8 

Columbretes  Islands:  Light-house 

Oropesa  Cape:  Light-house 

40  04  53 
40  27  48 
40  33  30 
40  43  10 

Vinaroz :  Mole-head  light 

Port  Alfaques:  Baila  light 

Cape  Tortosa:  Light-house 

Tarragona:  E.  mole  light 

41  06  00 
41  22  10 

41  50  04 

42  16  15 
42  19  10 

42  30  59 
42  31  18 

Barcelona:  E.  mole-head  light 

Palamos  Bay:  Molino  Pt.  light 

Cadaques :  Clock  tower 

Cape  Creux :  Light-house 

Cape  Bear:  Light-house 

Port  Vendres:  Fort  Fanal  light 

22489—03- 


-15 


Page  226]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


Place. 


Port  Nouvelle:  S.  jetty  light 

Cette:  Light,  St.  liiouis  mole 

Aigues  Mortes:  Espignette  Pt.  light. 

Planier  Rock :  Light-house 

Marseille:  Janet  Cliff  light 

New  observatory 

Ciotat:  Berouard  mole  light 

Toulon:  St.  Mandrien  li^ht 

Grand  Riband  Island :  Light-house.. 

Cannes:  Light-house 

Antibes :  Garoupe  light 

Nice:  Light-house 

Ville  Franche:  Mole-head  light 

Cape  Ferret  light  . . . 


Port  Ibiza:  Light-house 

Cabrera  Island :  Light-house 

Pi  (Majorca) :  Light-house 

Port  Mahon  (Minorca):  Light-house 

Cape  Spartivento:  Light-house 

Cape  Sandalo:  Light  on  San  Pietro  I 

Porte  Conte:  Cape  Caccia  light , 

Port  Torres:  Light-house 

Cape  Testa:  Light-house 

Razzoli  Island :  Light-house 

Caprera  Island :  Galera  Pt , 

Cape  Figari :  Signal  station 

Cape  Tavolara:  Light-house 

Cape  Bellavista:  Light-house 

Cape  Carbonera:  Cavoli  I.  light 

Cagliari;  Light  on  mole 


Bonifacio:  Mount  Pertusato  light. 

Ajaccio:  Light-house 

Corti:  Church  tower 

Calvi:  Light-house 

Cape  Corso:  Giraglia  I.  light 

Bastia:  Light-house 

Porto  Vecchio:  Chiape  Pt.  light .. 


Cape  Melle:  Light-house 

Genoa:  San  Benigno  light 

Spezzia:  Fort  Santa  Maria  light 

Florence:  Observatory 

Leghorn  (Livorno):  Light  on  S.  end  of 
curved  breakwater 

Capraia  Island:  Cape  Ferrajone  light 

Elba  Island,  Porto  Longone:  Fort  For- 
cado  light 

Pianosa  Island:  Light  on  battery,  W. 
side  of  fort , 

Africa  Rock :  Light-house 

Monte  Christo  Islet:  Summit 

Giglio  Island,  Cape  Rosso:  Light-house 

Civita  Vecchia:  Light  N.  end  of  break- 
water   

Rome:  Observatory 

Gaeta:  Orlando  tower 

Ponza  Islet:  Punto  della  Guardia  light . 

Naples:  Observatory 

Light  on  elbow  of  mole 

Capri  Island:  Carena  Pt.  light 

Lipari  Island :  Casa  Bianca  light 

Ustica  Island :  NE.  point  light 

Faro  of  Messina:  Capo  di  Faro  light 

Milazzo:  Light-house 

Palermo:  Observatory 

Light  on  mole  head 

Trapani:  Pal  umbo  Rock  light 


Lat.  N. 


43  00  47 
43  23  50 
43  29  17 
43  11  57 
43  20  43 
43  18  22 
43  10  21 
43  05  10 
43  01  01 
43  32  51 
43  33  61 
43  41  32 
43  41  58 
43  40  30 

38  54  10 

39  06  34 
39  33  00 
39  51  53 

38  52  34 

39  08  44 

40  33  50 

40  50  25 

41  14  36 
41  18  24 
41  14  15 
40  59  52 

40  54  55 
39  55  45 
39  05  15 

39  12  35 

41  22  10 

41  52  50 

42  18  14 

42  35  10 

43  01  45 

42  41  47 

41  35  45 

43  57  17 

44  24  15 
44  04  00 
43  46  04 

43  32  33 
43  02  57 

42  45  14 

42  35  06 
42  21  28 
42  20  15 
42  19  13 

42  05  38 
41  53  54 
41  12  27 

40  52  38 
40  51  46 
40  60  15 
40  32  07 
38  28  43 
38  42  40 
38  16  02 
38  16  10 
38  06  44 
38  07  56 
38  00  39 


LongE. 


04  08 
42  08 
08  32 
13  51 
20  46 
23  43 
36  42 
56  06 


6  08  39 


00  54 
08  02 

17  13 

18  42 

19  41 


1  27  25 

2  57  20 
2  37  00 
4  18  20 

8  51  08 
8  13  29 
8  10  00 

8  23  56 

9  08  35 
9  20  21 
9  29  40 
9  39  07 
9  44  22 
9  43  25 
9  32  35 
9  07  20 

9  11  15 

8  35  45 

9  09  04 

8  43  25 

9  24  10 
9  27  00 
9  22  05 

8  10  22 

8  54  19 

9  50  48 
11  15  22 

10  17  25 
9  51  07 

10  24  38 

10  05  50 
10  03  54 
10  18  39 

10  65  24 

11  46  50 

12  28  40 

13  35  16 

12  57  17 

14  14  44 
14  15  38 
14  11  40 

14  51  40 

13  12  00 

15  39  11 
15  13  42 
13  21  16 
13  22  04 
12  29  50 


Liin.  Int. 


H.  W. 


7  31 


8  22 


4  00 


L.  W. 


h.  m. 


2  00 


2  24 


Range. 


Spg.    Neap. 


ft. 


0.6 


0.6 


10  13 


0.7 


ft. 


0.3 


0.2 


0.2 


APPENDIX  IV.  [Page  227 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


Place. 


Maritimo  Island:  Light  on  SW.  pt 

Marsala:  W.  mole  light 

Girgenti :  Port  Empedoche  light 

Gozo  Island :  Light  on  NW.  pt 

Malta  Island,  Valetta   Harbor:    Light- 
house   

Linosa  Island :  Landing  Cove 

Lampedusa  Island:  Carallo  Bianco  light 

Cape  Passaro :  Light-house 

Syracuse:  Maniace  Castle  light 

Augusta  Port:  Torre  d' Avola  light 

Catania:  Sciari  Biscari  light 

Cape  Taormina:  Semaphore 

Messina:  San  Ranieri  light 

Cape  Peloro :  Light-house 

Cape  Spartivento :  Light-house 

Cape  Colonna:  Light-house 

Cotrone:  Mole-head  light 

Taranto:  Cape  St.  Vito  light 

Gallipoli :  St.  Andrea  light 

Cape  Sta.  Maria  di  Leuca:  Light-house. 

Cape  Otranto :  Light-house 

Port  Otranto:  Castle 

Brindisi:  Light-house 

Bari:  St.  Catalolo  light 

Viesti:  Light  on  St.  Croce  Rock 

Manfredonia:  Light-house 

Tremiti  Islands:  Caprara  I.  light 

Ancona:  Monte  Cappucini  light 

Malamocco:  Rocchetta  Mole  light 

Venice:  Site  of  tower  of  St.  Mark 

Grado:  Church  tower 

Monfalcone:  Church  tower 

Trieste:  Observatory  Nautical  Academy 

Theresa  Mole  light 

Capo  d'Istria:  Light-house 

Isola:  Light-house 

Pirano :  Light-house 

Salvo  re  Point:  Light-house 

Citta  Nuova:  Light-house 

Parenzo:  Cathedral  tower 

Rovigno:  St.  Eufemia  light 

Pola:  N.  cupola  of  observatory 

Promontore  Point:  Porer  Rock  light 

Nera  Point:  Light-house 

Fiume:  Cathedral  tower 

Porto  Re :  Light-house 

Veglia:  Mole  head 

Prestenizza  Point:  Light-house 

Cherso:  Kimen  Point  light 

Galiola  Rock:  Light-house 

Unie  Island:  Netak  Point  light 

Lussin  Piccolo:  Sta.  Maria  Church 

St.  PietrodiNenibo  Island:  Health  office 

Gruizza  Rock :  Light-house 

Zengg:  Mole-head  light 

Terstenik  Rock :  Light-house 

Carlobago :  Light-house 

Zara:  Church  tower 

Bianche  Point:  Light-house 

Zara  Vecchia:  Church  tower 

Port  Tajer:  Lestrice  I.  light 

Lucrietta  Island :  Light-house 

Sebenico:  Mount  Tartaro 

Rogosnizza  Port:  Mulo  Rock  light 

Zirona     Grande     Island:     St.     George 

Church  tower 

Trani:  Cathedral  tower 


Lat.  N. 


37  57  13 
37  47  10 
37  16  55 
36  04  10 

35  54  00 
35  51  50 

35  29  37 

36  41  03 

37  03  04 
37  12  39 
37  29  35 

37  50  25 

38  11  33 

38  16  02 
37  55  29 

39  01  29 

39  04  38 

40  24  41 
40  02  48 

39  47  43 

40  06  23 
40  09  06 

40  39  36 

41  08  19 
41  53  17 

41  37  39 

42  08  14 

43  37  14 
45  20  30 
45  25  58 

45  41  06 
45  48  33 
45  38  51 
45  38  54 
45  33  00 
45  32  34 
45  31  54 
45  29  24 
45  19  16 
45  13  45 
45  05  00 

44  51  49 
44  45  30 

44  57  24 

45  19  36 

46  16  18 
45  01  30 
45  07  12 
44  57  36 
44  43  36 
44  37  20 
44  31  49 
44  27  42 
44  24  42 
44  59  24 
44  40  06 
44  31  30 
44  07  05 
44  09  06 
43  56  16 
43  51  15 
43  37  36 
43  45  08 
43  31  00 

43  27  00 
43  31  02 


Long.  E. 


12  02  55 

12  25  59 

13  32  27 

14  12  55 

14  31  30 
12  52  09 

12  36  12 

15  07  45 
15  17  37 
15  13  20 
15  05  19 
15  18  30 
15  34  36 

15  39  11 

16  03  31 

17  12  09 
17  08  07 
17  12  23 

17  56  55 

18  22  17 
18  31  25 
18  28  45 
17  59  37 
16  50  52 
16  11  13 
15  55  34 
15  31  36 

13  31  18 
12  19  09 
12  20  29 


13  22 
13  32 
13  46 
13  45 
13  43 
13  39 
13  33 
13  29 
13  33 
13  35 
13  38 
13  50 

13  53 

14  08 
14  26 
14  33 
14  34 
14  16 
14  23 
14  10 
14  14 
14  28 
14  33 
14  34 
14  53 

14  34 

15  04 
15  14 

14  49 

15  26 
15  12 
15  34 
15  58 
15  55 


16  08  51 
16  15  09 


Lun.  Int. 


H.W. 


h.  m. 


L.  W. 


h.  m. 


3  12 


9  25 


3  00 


9  13 


3  30 


10  15 


9  20 


9  00 


8  15 


8  10 


6  10 


Range. 


Spg.    Neap. 


0.9 


9  43 


4  45 


3  50 


3  25 


2  35 


2  25 


1.8 


3.3 


2.0 


3.4 


1.2 


0.2 


0.3 


0.5 


0.9 


0.6 


0.9 


0.3 


1.1  !   0.3 


0  20   1.0 


0.3 


Page  228]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


Place. 


Lat.  N. 


Port  Spalato:  Cathedral  tower 

Soltal.,  PortOliveTto:  St.  Nicholas  tower. 

Spalato  Passage:  Speo  Pt.  light 

Makarska:  Church  tower 

Porno  Rock:  Center 

St.  Andrea  Rock:  Summit 

Lissa  Island :  Hoste  Rock  light 

Pakonjidol  Rock:  Light-house 

Lesina  Island:  Port  Gelsa  light 

St.  Giorgio  Pt.  light 

Sabioncello    Peninsula:    Cape    Gomena 

light 

Sorelle  Rocks:  Light-house 

Curzola  Island:  Porto  Bema  mole  head. . 
Porto     Valle     Grande, 

church  tower 

Lagostini  Island:  Glavat  Rock  light 

Lagosta  Island :  St.  George  Chapel 

Cazza  Island :  Light-house 

Pelagosa  Rock :  Light-house 

Meleda  Island:  Port  Palazzo  Ruin 

Olipa  Rock :  Light-house 

Pettini  di  Ragusa  Rocks:  Light-house... 

Bobara  Rock :  Summit 

Molonta  Peninsula:  Summit 

Ostro  Point:  Light-house 

Cattaro:  Health  office 

Budua:  Mole-head  light 

Katie  Rock :  St.  Domenica  Chapel 


Antivari:  Pt.  Valovica  light 
Dulcigno:  W.  windmill 


Cape  Rodoni:  Guard-house... 

Cape  Pali:  Guard-house 

Durazzo:  Light-house 

Cape  Laghi :  Ruin 

Skumbi  River:  Pyramid  at  mouth. 
Semeny  River:  Samana  Pt.  light . . 
Vojazza  River:  Pyramid  at  mouth 

Saseno  Island:  Light-house 

Avlona:  Light-house 

Cape  Linguelta:  Extreme 

Mount  Cica:  Pyramid 

Port  Palermo:  Pyramid 

Cape  Kiefali :  Pyramid 

Fano  Island:  Pt.  Kastri  light 

Port  Pagonia:  Ruin 

Port  Gomenitza:  "Well  Dogana 

Port  Parga:  Madonna  I 


Port  St.  Spiridione:  Convent 

Corfu :  Light-house 

Paxo  Island:  Madonna  I.  light 

Prevesa;  Fort  Nuovo  minaret 

Port  Drepano:  Observation  island 

Port  Vliko:  Custom-house 

Port  Vathi :  Lazaretto  light 

Port  Argostoli :  St.  Theodoro  light 

Patras:  Light-house 

Katakolo:  Light-house 

Zante:  Mole  light 

Strovathi,  or  Strivali  Island:  Stamphani 

Llight 

Proti  Passage:  Marathon  Pt 

Navarin :  Light-house 

Mothoni:  Round  tower 

Koroni  Anchorage:  Mole  light 

Petalidi  Bay:  Petalidi  Pt 

Candia  Island,  Port  Suda:  Light-house.. 

Megalo    Kastron:    Mole 

light 


43  30  07 
43  23  50 
43  19  12 
43  17  46 
43  05  28 
43  01  43 
43  04  30 
43  09  24 
43  09  50 
43  07  30 

43  02  50 
42  57  42 
42  54  19 

42  57  37 
42  45  54 

42  45  05 

43  45  05 
42  23  30 
42  47  06 
42  45  30 
42  39  00 
42  35  08 
42  27  04 
42  23  36 
42  25  30 
42  16  42 
42  11  43 

42  05  15 
41  55  47 

41  35  10 
41  23  31 
41  18  40 
41  08  44 
41  02  12 
40  47  00 
40  36  14 
40  30  12 
40  25  30 
40  25  17 
40  12  00 
40  02  57 
39  54  29 
39  51  53 
39  39  27 
39  29  50 
39  16  32 

39  39  54 
39  37  05 
39  11  30 
38  56  30 
38  47  25 
38  40  40 
38  22  04 
38  11  36 
38  15  00 
37  38  20 
37  47  10 

37  15  12 
37  03  38 
36  54  10 
36  48  40 
36  47  50 
36  57  20 
35  28  55 

35  20  30 


Long.  E. 


16  26  06 
16  11  10 

16  24  30 

17  01  36 
15  27  30 

15  45  29 

16  12  28 
16  27  14 

16  41  55 

17  12  00 

17  00  19 
17  12  44 
16  51  32 

16  43  07 

17  08  54 
16  51  45 
16  29  29 

16  15  12 

17  22  51 

17  46  48 

18  03  08 
18  10  49 
18  25  36 
18  32  00 
18  46  12 
18  50  36 

18  56  25 

19  04  19 
19  12  29 

19  27  15 
19  24  54 
19  27  14 
19  26  47 
19  26  30 
19  20  14 
19  19  14 
19  16  15 
19  27  55 
19  17  45 
19  38  33 
19  47  53 
19  54  55 

19  26  06 

20  07  12 
20  17  09 
20  24  55 

19  43  09 

19  56  30 

20  12  34 
20  45  40 
20  44  16 
20  42  44 
20  43  37 

20  29  30 

21  43  50 
21  18  55 

20  55  26 

21  01  14 
21  34  35 
21  40  29 
21  42  40 
21  58  00 
21  56  42 

24  09  39 

25  09  44 


Lun.  Int. 


H.  W. 


h.  m. 


4  00 


3  40 


L.  W. 


h.   m. 


Range. 


Spg.    Neap. 


ft- 


10  30 


9  53 


2.4 


1.0 


ft. 


0.7 


0.3 


APPENDIX  IV.                                       [Page  229 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITERRANEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 

1 
o 

Place. 

Lat.  N. 

Long.  E. 

Lun.  Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

« 

V 
V 

s> 

u 

d 

i 

s 

Kandeliupa  Island :  Light-house 

StampaU  Island,  Maltezana  Port:  Agios 
loanes 

o        /          // 

36  29  40 

36  34  25 
36  15  20 
36  40  27 

36  59  12 

37  06  32 
37  00  01 

37  08  38 
37  26  12 
37  07  36 
37  25  55 
37  38  00 
37  39  28 
37  44  00 
37  57  30 

36  47  05 

37  18  42 
37  31  45 
37  44  30 
37  56  14 
37  58  20 
37  38  45 

37  52  48 

38  01  28 
38  28  15 

o       r         II 

26  59  25 

26  24  28 
25  13  00 
24  23  15 

24  40  30 

25  23  00 
25  14  21 

25  14  08 
24  56  14 

h.     m. 

h.     m. 

fl. 

ft. 

Christiana  Islands:  N.  pt                    ..   .. 

Milo  Island:  Summit,  Mt.  St.  Elias 

Siphano  Island :  Light-house 

Naxos  Island,  Naxia:  Gate  on  Bacchus  I. 

Paros  Island,  Port  Trio:  Trio  Pt 

Port  Naussa:    St.    Yanni 
Church 

! 

Syra:  Mole  light                

Sermo  Island :  Aniyno  Pt 

24  32  23 
24  23  35 
24  44  32 
24  19  44 
24  04  12 
24  42  30 
23  05  40 
23  08  53 
23  25  45 
23  25  30 
23  38  10 

23  43  55 

24  02  15 
24  03  00 
24  16  42 

Therm ia  Island:  Ruins  of  Cythnus 

Jura  Island:  North  pt            .. ...   .. 

1 

1 

Port  St.  Nikolo:  Light-house                 

•-(■--■■■ 

St.  Nikalao  Island:  Port  Mandri 

Andros  Island,  Cape  Fasse:  Light-house, 
leraka :  Acropolis 

i 

i 

Port  K  heli :  Light-house 

Poros  Island:  Light-house 

1 

1 

JEgina:  Light-house    

Pirajus:  Light-house 

\ 

Athens:  Observatory 

< 

Cape  Colonna:  Extreme 

1 

Port  Raphti:  Statue  I 

Petali  Island :  Trago  I.  peak 

Euripo  Strait:  Light-house 

1 

23  36  45 

Skiathos  Island:  Mount  Stavros 

Salonika:  S.  bastion 

Port  Baklar:  Cape  Xeros 

39  10  48      23  27  07 

40  37  28 
40  32  40 
39  52  10 
39  50  52 
39  31  58 
39  12  35 

39  06  10 
39  03  20 
38  32  00 
38  19  55 
37  41  24 
37  16  33 

22  58  00 
26  45  00 
25  03  20 
25  14  14 

24  59  13 

25  50  00 

26  34  54 
26  31  39 

25  35  00 

26  17  45 

26  58  42 

27  36  55 

Lemnos  Island :  Kastro  Castle 

Port  Moudros:  Sangrada  Pt 

Strati  Island :  St.  Strati  Church 

1 

Mityleni  Island,  PortSigri:  Light-house. 
Mitvleni:  LightonMity- 
leni  Pt             

! 

Port  lero:  Sidero  Islet . 
Psara  Island:  Fort 

Tchesm6:  C.  K^zil  light 

Samos  Island :  Fonia  Pt.  light 

Port  Isene:  Tower 

Kos:  Light-house 

36  55  00  !  27  18  25 
36  48  00  ;  28  18  00 
36  39  33  '  29  06  13 
36  26  00     28  16  24 

Marmorice  Harbor:  Adassi  Pt.  light 

Makrv  Harbor:  Kasil  I 

Rhodies  Port:  Arab's  Tower  light 

Port  Lindo:  Tower 

36  05  53 

40  02  30 

40  24  27 

41  01  20 
41  01  02 
41  00  35 
41  00  16 
41  21  15 

41  52  04 

28  08  10 

26  10  54 

26  41  24 

29  01  00 
29  00  29 
29  01  14 
28  58  59 
28  42  14 

27  58  45 

Dardanelles:  Hellas  Pt.  light 

(jallipoli :  Light-house 

:::::::;:::  i 

Bosphorus:  Tofana  Pt.  light 

Scutari:  Leander  Tower  light 

Constantinople:  Seraglio  Pt.  light 

St.  Sophia  Mosque 

Cape  Kara  Burnu:  Light-house 



Yuiada  Road :  Fort  Tersana 

Burghaz :  Light-house 

42  27  52     27  35  54 

43  10  00     27  58  35 

44  10  20     28  39  14 

45  09  47      29  41    14 

Varna  Bav :  Light-house 

Kusterjeh:  Cape  Kusterjeh  light 

Danube  River:  Salina  light 

Fidonisi  Island:  Light-house 

Odessa :  Observatory 

45  16  00 

46  28  36 
46  34  27 
44  36  55 

44  29  50 

45  21  03 

46  45  00 
42  58  00 
41  39  30 

30  14  14 

30  45  34 

31  33  36 
33  36  26 
33  36  25 
36  28  30 
36  46  40 

40  55  10 

41  38  15 

Dnieper  Bay:  Fort  Nikolaeo  light 

Sebastopol:  E.  light-house 

Balaklava  Bav :  Hospital 

Kertch:  Light-house 

Berdiansk:  Breakwater  light 

Saukhoum :  Light-house 

Batoum:   Light-house       

Page  230]  APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
COASTS  OF  THE  MEDITERBAXEAN,  ADRIATIC,  AND  BLACK  SEAS— Continued. 


Plac'o. 


Trebizond :  Light>4iouse 

Sinope :  Light-house 

Bender  ErekH :  Light-house 

Marmora  Island :  Light  off  E.  pt 

Artaki  Bay:  Zeitijn  Adasi  Islet 

Tenedos  Island:  Ponente  Pt.  light 

Port  Ajano:  Nikolo  Rock 

Port  Ali-Agha:  W.  pt.  of  entrance 

Smyrna:  English  consulate  flag-staff . . . 

Vourlah :  Custom-house 

Sighajik  Harbor:  Beacon  on  islet 

Budrum :  Light-house 

Adalia:  Light-house 

Alexandretta:  Light-house 

Latakiyah:  Light-house 

Tripoli  Roadstead:  Bluff  Islet  light 

Ruad  Island :  Light-house 

Beirut:  Light-house 

Saida  ( ancient  Sidon ) :  Light-house 

SAr  (ancient  Tyre) :  Light-house 

Acre:  Li^ht-house 

Haifa:  Light-house 

Famagusta:  Light-house 

C.  Gata:  Light 

Lamaka:  Light-house 

Port  Said :  High  light-house 

River  Nile:  Damietta  Mouth 

Rosetta  Mouth  light 

Aboukir  Bay:  Nelson  I.  peak 

Alexandria:  Eunostos  Pt.  light 

Ben  Ghazi :  Castle 

Tripoli  Harbor:  Light-house 

Sfax:  Ras  Tina  light 

Mehediah :  Sidi  Jubber 

Monastir:  Burj  el  Kelb  battery 

Hammamet  Bay:  Castle  flag-staff 

Kalibia  Road :  Light-house 

Cape  Bon :  Light-house 

Tunis:  Goletta  light 

Cape  Farina:  Extreme 

Benzert:  N.  Jetty  light 

Galita  Island:  Monte  Guardia 

Bona:  Fort  Genois  light 

Stora:  Singe  I.  light 

Cape  Bougaroni :  Light-house 

Cape  Carbon :  Light-house 

Algier :  Light-house  near  Admiralty 

Cape  Tenez :  Light-house 

Oran:  Mers  el  Kebir  light 

Habibas  Island :  Light-house 

Zafarin  Islands:  Light  Isabel  Segunda  I 

Alboran  Island :  Light-house 

Ceuta:  Light-house 

Tangier:  Casbah  tower 

Cape  Spartel :  Light-house 


41  01  00 

42  01  20 
41  18  03 
40  38  10 
40  23  30 
39  50  00 
39  01  21 
38  50  10 
38  25  40 
38  21  48 
38  12  21 
37  02  00 
36  52  00 
36  35  30 
35  30  30 
34  29  25 

34  52  00 
33  54  10 
33  34  20 

33  16  30 
32  54  35 
32  47  40 

35  07  10 

34  33  45 
34  54  00 

31  15  41 
31  31  40 
31  29  30 
31  21  23 

31  11  43 

32  06  51 
32  54  03 

34  39  01 

35  30  24 

35  45  24 

36  23  20 

36  50  12 

37  04  45 

36  48  19 

37  10  42 
37  16  38 
37  31  16 
36  57  15 

36  54  29 

37  05  17 
36  46  41 
36  47  16 
36  33  07 


35  44  21 
35  43  22 

35  11  05 
35  58  00 
35  53  44 
35  47  00 
35  47  14 


Long.  E. 


39  46  25 

35  13  20 

31  25  49 
27  46  09 
27  47  30 

25  58  34 

26  47  57 

26  57  20 

27  09  10 
26  47  00 

26  47  32 

27  27  05 

30  45  34 

36  10  20 
35  46  30 
35  44  24 
35  51  00 
35  28  25 
35  21  30 
35  14  40 
35  08  00 
35  05  00 

33  57  22 
33  01  30 
33  38  59 

32  18  45 

31  51  00 
30  19  10 
30  06.00 
29  51  40 

20  02  40 
13  10  50 

10  41  17 

11  05  15 
10  50  42 

10  37  10 

11  07  00 
11  03  15 
10  18  31 

10  17  30 
9  53  21 
8  56  12 
7  46  40 
6  53  11 
6  28  37 
5  06  22 
3  04  13 
1  20  36 

Long.  W. 

0  41  38 

1  07  57 

2  25  45 

3  03  29 
5  16  46 
5  48  31 
5  55  41 


Lun.  Int. 


H.  W.  i  L.  W. 


h.     m.        h.     m. 


9  15 


9  45 


9  40 


9  40 


9  45 

9  55 
10  00 

3  35 


3  33 


2  46 


1  55 
1  30 


Range. 


3  15  i  2.5 


3  35 


3  30 


3  30 


3  15 

3  45 
3  50 

9  57 


9  55 


8  58 


8  07 
7  40 


1.2 


1.4 


LO 


1.1 

1.2 
1.9 

4.2 


3.0 


2.6 


3.3 

8.0 


Neap. 


0.7 


0.3 


0.4 


0.3 


0.3 

0.3 
0.5 

1.1 


0.8 


L3 


1.5 
3.7 


WEST  COAST  OF  AFRICA. 


El  Araish:  S.  pt.  of  entrance  ... 
Sali:  Fort 

Cape  Dar  el  Beida:  Light-house 


35  12  50 
34  04  10 
33  36  00 


6  09  13 

6  48  00 

7  33  00 


1  35 


7  45 


10.4 


4.8 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

WEST  COAST  OF  AFRICA— Continued. 


[Page  231 


Place. 


Cape  Blanco,  North :  Extreme 

Mogador  Harbor:  English  consulate 

Cape  Ghir:  Extreme 

Cape  Noun :  Extreme 

Cape  Juby :  Extreme 

Cape  Bojador:  Extreme 

Penha  Grande 

Ouro  River  entrance:  Dumford  Pt 

Pedra  de  Galha 

Cape  Blanco,  South :  Extreme 

Portendik:  Village 

St.  Louis:  Light-house 

Almadie  Point:  Light-house 

Cape  Verde:  Light-house 

Port  Dakar:  Light-house 

Cape  Manoel :  Light-house 

Goree  Island:  Fort 

Bird  Island :  Flagstaff  

Bathurst:  Flagstaff 

Carabane:  Light-house 

Nunez  River:  Sand  I 

Ponga  River  entrance:  Observation  pt  . . 

Isles  de  Los:  Light-house 

Matacong  Island:  House 

Scarcies  River:  W.  end  of  Yellaboi  I 

Sierra  Leone:  Light  on  cape 

N.  battery 

Sherbro  Island:  N.  island 

Sherbro  River:  Manna  Pt 

Gallinas  River:  AV.  elbow  of  Kamaaounl. 

Cape  Mount:  W.  peak 

Cape  Mesurado :  Light-house 

Monrovia:  Light-house 

Marshall:  Agent's  house 

Grand  Bassa:  Agent's  house 

Cestos:  Factory 

Sangwin  River:  Sangwin  Pt 

Sinon :  Bloobarra  Pt 

Cape  Palnias:  Light-house 

Tabou  River:  Tabou  Pt 

Axim  Bay:  Ft.  St.  Anthony 

Cape  Three  Points:  Light-house 

Dix  Cove:  Fort 

Tacorady  Bay:  Tacorady  Pt 

Chama  Bay:  Dutch  Fort 

El  Mina  Bay:  Ft.  St.  George 

Cape  Coast  Castle:  Light-house 

Accra:  Light-house 


Lat.  N. 


Volta  River  entrance:  Dolbens  Pt 

Lagos  River:  Light-house 

Benin  River  entrance:  N.  pt 

Brass  River:  Entrance  (approx. ) 

Calebar  River  (New) :  Rough  Corner  . . . 
Opobo  River:  W.  pt.  beacon  (approx. ) . . 

Quaebo  River:  Bluff  Pt 

Calebar  River  (Old) :  Townsend  flagstaff 

( Dunketown) 

Fernando  Po  Island:  Light-house 

San  Bento  River:  Joho  Pt.  (approx.)  ... 
Princes  Island:  Diamond  Rocks,  center 

of  largest 

St.  Thomas   Island:   Ft.  San  Sebastian 

light 


Anno  Bon  Island:  Turtle  Islet. 

Cape  Lopez:  Light-house 

Mayumba  Bay:  Light- house . . . 


33  08  00 

31  30  30 

30  38  00 

28  45  00 

27  56  00 

26  07  57 

25  07  06 

23  36  03 

22  12  37 

20  46  27 

18  18  45 

16  01  31 

14  44  45 

14  43  20 

14  40  30 

14  38  55 

14  39  55 

13  39  45 

13  28  00 

12  35  00 

10  36  37 

10  03  15 

9  30  30 

9  16  10 

8  57  05 

8  30  00 

8  29  57 

7  40  36 

7  22  45 

7  00  08 

6  44  30 

6  19  10 

6  19  00 

6  08  06 

5  54  08 

5  26  25 

5  12  42 

59  15 

22  10 

24  47 

52  18 
45  00 
47  45 

53  00 
5  01  00 
5  04  48 
5  06  20 
5  31  50 

5  46  00 

6  25  15 
5  46  01 
4  16  40 
4  23  07 
4  27  00 
4  30  40 

4  56  24 
3  46  10 
1  35  00 

1  40  42 

0  20  30 
Lat.  S. 

1  24  18 
0  36  25 
3  23  00 


Long.  W. 


8  35  05 

9  43  30 
9  50  00 

11  02  00 

12  56  00 
14  29  00 

14  50  44 

15  58  00 

16  48  11 

17  05  40 
16  02  00 

16  30  22 

17  32  25 
17  30  55 
17  25  28 
17  26  47 
17  24  30 
16  40  30 
16  35  00 
16  44  00 
14  42  00 
14  04  30 

13  44  00 
13  26  20 
13  18  25 
13  18  30 
13  14  30 
13  04  30 
12  31  55 
11  38  45 
11  22  51 
10  49  25 
10  50  00 
10  22  45 
10  04  05 

9  34  45 
9  20  16 
9  02  05 
7  44  15 
7  21  30 
2  14  45 
2  05  45 


1  56  40 


45  00 
38  00 
21  05 
13  50 


0  11  30 
Long.  E. 
0  41  00 
3  25  15 

5  03  05 

6  15  00 

7  07  00 
7  40  00 

7  59  00 

8  20  46 

8  47  05 

9  39  00 

7  27  56 
6  42  45 

5  38  12 

8  43  10 
10  38  00 


Lun.  Int. 


Range. 


H.W.    L.W.    Spg.    Neap 


1  05 


11  55 
11  50 


11  35 


h.    m. 

"r'ii 


5  43 

5  38 


ft. 

'i6."9' 


8.5 
7.3 


5  23 


9  00 


7  30 


7  40 


5  50 


5  40 


4  50 
4  30 


4  00 


2  50 


1  20 


1  30 


12  00 


11  54 


11  05 
10  43 


10  13 


4  20   10  32 


4  20   10  33 
4  50   11  05. 


4  25 


10  38 


5.5 


5.9 


11.4 


11.6 


10.4 


6.0 


4.8 
4.3 


4.7 


6.0 


4.2 
3.3 


7.0 


ft. 


5.0 


3.9 
3.4 


2.5 


2.7 


5.2 


5.3 


4.8 


2.5 


2.0 

1.8 


1.9 


2.5 


1.8 
1.3 


2.9 


1    Page  232]                                        APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
WEST  COAST  OF  ATRICA— Continued. 

1 

Place. 

Lat.  S. 

Long.  £. 

Lun.  Int.                     Range.          1 

H.  W. 

L.  W. 

Spg.    1     Neap.    1 

Loango  Bav :  Indian  Pt.  light 

o         /         // 

4  40  00 

4  49  00 

5  18  30 

5  32  30 

6  04  36 
6  31  50 

8  48  24 
12  20  00 

12  34  43 

13  12  30 
13  26  05 
15  09  00 

15  47  30 

16  30  00 
18  23  00 
22  57  00 
26  17  00 
26  37  52 
26  58  30 

29  15  12 

30  18  33 
30  33  07 
33  07  51 
33  48  52 

33  56  04 

34  21  12 

O           1         If 

11  46  30 

11  45  00 

12  08  00 
12  11  00 
12  15  00 

12  25  25 

13  13  20 
13  32  00 

13  23  45 
12  48  55 
12  36  00 
12  12  00 
11  52  40 
11  42  00 
11  57  12 

14  30  00 

14  57  20 

15  07  02 

15  12  22 

16  52  02 

17  16  20 

17  27  30 

18  01  21 
18  22  33 
18  28  40 
18  29  26 

*.     7?!. 

4  13 

/(.    m. 
10  26 

ft. 
6.5 

St. 
2.7 

Black  Point  Bay :  Sandy  Pt 

Malemba  Bay :  Landing  Cove 

Kabenda  Bay:  Kabenda  Pt.  light 

Congo  River  entrance:  Shark  Pt 

Margate  Head:  Summit 

4  10 

10  25 

6.0 

2.5 

St.  Paul  de  Loando:  Flag  staff,  Ft.  San 
Miguel 

3  40 

9  53 

4.8 

2.0 

Lobito  Point :  Extreme 

Benguela:  Telegraph  office 

3  30 

9  43 

5.5 

2.3 

Elephant  Bay :  Friar  Rocks 

St.  Marv  Bay:  Bav  I 

Little  Fish  Bay :  Light-house 

Port  Alexander:  Bateman  Pt 

Great  Fish  Bay:  Tiger  Pt 

3  00 

9  12 

5.7 

2.4 

Cape  Frio:  Extreme 

Walfisch  Bay :  Light-house 

Ichabo  Island 

Angra  Pequena:  Diaz  Pt 

Elizabeth  Bay:  S.  pt.  of  Possession  I 

Port  Nolloth:  Magistrate's  house 

Hondeklip  Bay 

2  35 

2  25 

8  47 
8  38 

5.5 
5.3 

2.3 
2.2 

Roodewal  Bay 

Saldanha  Bav :  Constable  Hill 

2  20 

8  33 

5.1 

2.1 

Table  Bay:  Robben  I.  light 

Cape  Town :  Observatory 

1  36 

7  47 

4.6 

2.0 

Cape  of  Good  Hope:  Light-house 

EAST  COAST  OF  AFRICA  AND  THE  RED  SEA. 

34  10  45 
34  23  48 
34  46  45 
34  49  45 
34  23  47 
34  11  10 
34  04  35 
34  06  15 
34  12  30 
34  01  41 
33  57  43 
33  50  27 
33  36  09 
33  28  00 
33  23  10 
33  05  10 

18  27  30 

18  50  20 

19  38  17 

20  00  37 
20  48  40 

22  09  31 

23  03  38 

23  24  23 

24  50  20 

25  42  12 

25  37  21 

26  17  13 

26  54  10 

27  03  00 
27  20  48 
27  49  12 

27  55  02 

28  22  36 

29  06  40 
29  21   15 
29  33  16 
29  48  40 
31  03  50 

31  51  39 

32  27  39 
32  38  10 
32  35  52 
35  29  45 
35  31  41 
35  29  00 

35  29  30 
34  53  30 
34  46  00 

36  11  47 

36  58  30 

37  01  09 

2  35 

8  48 

5.2 

2.2 

Cape  Hangklip:  Extreme 

Quoin  Point:  Extreme 

Cape  Agulhas :  Light-house 

2  40 

8  53 

5.2 

2.2 

Port  Beaufort:  Flag-staff 

St.  Blaize:  Light-house 

3  18 

9  31 

5.6 

2.0 

Knysna  Harbor:  Fountain  beacon 

Plettenberg  Bay:  Summit  of  Seal  Pt 

St.  Francis:  Light-house 

Cape  Recife:  Light-house  . 

Port  Elizabeth :  Light-house 

3  21 

9  33 

5.4 

1.9 

Bird  Islands:  Light-house 

Port  Alfred:  Signal  staff 

■ 

Waterloo  Bay:  Maitland  Signal  Hill 

Madagascar  Reef'  Center 



Cove  Rock:  Center 

East  London:  Light-house 

33  01  45 
32  42  00 
32  02  30 
^^  4«  1."^ 

3  37 

9  50 

5.0 

1.8 

Cape  Morgan:  Extreme 

Hole-in-the-Wall 

Rame  Head*  Extreme 

Cape  Hermes:  Extreme 31  38  06 

Waterfall  Bluff !  31  26  15 

Port  Natal  (Durban):  Light-house I  29  52  40 

Dumford  Point:  Extreme |  29  00  12 

Cape  St.  Lucia:  Extreme '  28  32  30 

CapeVidal-  Extreme                                     ^s  f^f  ^(^ 

3  58 

10  11 

5.6 

1.6 

Delagoa  Bay:  Reut^en  Pt.  light 

Cape  Corrientes:  Small  rock 

25  58  49 
24  05  30 

5  10 

11  22 

n.9 

3.4 

Innamban  Bay:  Barrow  Hill  light 

Cape  St.  Sebastian:  Extreme 

23  45  30 
22  05  00 
21  31  00 
20  38  10 
20  10  42 
18  52  50 
18  01  24 
17  51  50 

4  30 

10  42 

n.o 

3.2 

Bazaruto  Island:  N  pt  light 

Chuluwan  Island*  Light-house 

Sofala:  Fort  on  N.  side  of  entrance 

Zambesi  River:  Kangoni  Mouth 

Quillimane  River:  Light-house 

4  15 

10  27 

13.5 

3.9 

Quillimane:  Town 

Mazemba  River:  Entrance 

17  15  00     M8  04  00 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  AFRICA  AND  THE  RED  SEA— Continued 

[Page  233 

1 

Place. 

Lat.  S. 

Long.  E. 

Lun 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

Premeira  Islands:  Center  of  Casuarina  I. 

Angoxa  Islands:  Center  of  Hurd  I 

Mafamale  Island :  Center 

O           /           II 

17  06  30 
16  33  24 
16  20  30 
15  08  00 
15  02  12 
15  00  45 
14  58  20 
14  53  00 

13  23  40 
12  55  45 
12  19  30 
11  09  18 
10  41  20 
10  19  22 
10  16  31 
10  06  43 

9  59  30 
9  44  22 
9  25  36 
8  57  15 
7  38  10 
6  49  41 
6  26  10 
6  09  43 
5  00  35 
4  04  30 
3  12  48 
2  15  42 
2  13  35 
1  13  00 

0  22  35 

Lat.  N. 

1  06  48 

1  42  06 

2  01  48 
2  30  00 

10  26  30 

11  50  30 

12  26  00 
12  11  15 
12  39  00 
11  27  30 
11  13  00 

10  25  00 

11  22  00 

12  39  00 

14  44  00 

15  28  10 
15  37  12 

18  15  12 

19  07  00 

20  44  00 

23  36  20 

24  56  30 
26  06  24 

O           1           II 

39  06  27 

39  49  57 

40  03  57 
40  36  12 
40  48  45 
40  45  06 
40  45  10 
40  40  00 
40  46  00 
40  31  15 
40  40  09 
40  43  21 
40  38  35 
40  26  34 
40  10  33 
40  02  14 
39  46  41 
39  47  07 
39  39  31 
39  30  42 
39  54  42 
39  17  05 

38  54  27 

39  11  08 
39  10  20 

39  41  13 

40  11  21 
40  56  21 

40  59  40 

41  54  15 

42  33  57 

44  03  27 

44  53  49 

45  24  39 

46  07  00 
51  22  55 

51  16  45 

52  09  35 

52  25  35 

53  59  31 
49  35  40 

47  17  00 
44  59  35 

43  29  35 
43  25  35 

40  52  00 
39  45  30 
39  27  23 
38  19  30 
37  19  09 
37  15  30 
36  10  15 
35  51  00 
.34  17  03 

h.    m. 

h.    m. 

Jt. 

ft. 

:::::::::::::::      i 

Port  Mokamba:  Mokambo  Pt 

i 

Port  Mozambique:  St.  George  I.  light... 

San  Sebastian  light. . 

Cape  Cabeceira:  Light-house 

1 

4  00 

10  12 

11.8 

3.4 

Port  Conducia:  Bar  Pt  

i 

Lurio  Bay :  Pando  Pt             

1 

Peniba  Bav :  N.  pt.  light 

:::::::::::::::::  i 

Querimba  Islands:  Ibo  I.  light 

Numba  Island :  K.  pt 

\ 

Cape  Delgado :  Light-house 

3  59 

10  11 

11.3 

3.3 

Msimbati :  Ran  Matunda 

Mikindini  Harbor:  Kinizi 

Mgan  Mwania:  Madjori  Rock 

Lindi  River:  Fort  flagstaff 

3  55 



10  08 

10.9 

4.5 

Mchinga  Bay :  Observation  spot 

Kiswere  Harbor:  Rustmigi 

Kilwa  Kisiwani:  Fort 

Mafia  Island:  Moresby  Pt 

Dar-Es-Salaam :  Flagstaff 

1 

Bagauioyo;  French  Mission 

Zanzibar:  English  consulate 

4  05 

10  17 

14.5 

6.0 

Tanga  Bay:  Light-house 

Mombasa:  Light-house 

:::::;::::  i 

Port  Melinda:  Vasco  de  Gama's  Pillar  . . 
Lamo  Bay :  Lamo  Castle 

4  00 

10  13 

12.1 

5.0 

Manda  Roads:  E.  side  of  Manda  Toto  I  . 
Port  Durnford:  Foot  Pt 

4  30 

10  42 

n.7 

4.9 

Kisimayu  Bay:  S.  pt.  of  Kisimayu  I 

Brava:  Well 

4  15 

10  27 

7.5 

3.1 

Meurka  Anchorage:  S.  pt.  of  town 

Magadoxa:  Tower 

Murat  Hill:  Peak 

Ras  Hafun:  E.  extreme  of  Africa 

Cape  Guardafui :  E.  pt 

6  00 

12  12 

6.1 

2.5 

Kal  Farun  Islet:  Center 

Abd-al-Kuri  Island :  NE.  pt 

1 

Socotra  Island:  Tamarida,  mosque 

Ras  Antareh:  Extreme  of  rocky  pt 

Miiit  Island :  Center 

7  05 

1  17 

7.5 

3.1 

1 

Port  Berbera:  Light-house 

1 

Zeyla:  Mosque 

7  30 

7  50 

1  18 
1  38 

8.5 

7.2 

3.5 
3.0 

Perim  Island:  Light- house 

Hanfelah  Bay:  Hanfelah  Pt 

Disei  Island :  Village  Baj' 

Massaua  Harbor:  N.  pt.  of  entrance 

Khor  Nowarat:  Shatireh  Islet 

0  45 

6  57 

4.0 

1.7 

Suakin :  Light-house 

2  10 

8  22 

L7 

0.7 

Makaua  Island :  S.  pt 

St.  Johns  Island :  Peak 

Daedalus  Shoal :  Light-house 

[ 

Kosair  Anchorage:  SW.  angle  of  fort 

Brothers  Island :  Light- house 

.1  _   ._   ..1 

26  18  50  1  34  50  45 
26  45  48  '  33  59  43 

6  40 

0  28 

2.0 

0.8 

Safajah  Island:  N.  summit 

Ashrafi  Island:  Light-house 

27  47  21 

28  20  52 

29  06  29 
29  53  05 
28  13  47 
27  35  45 
27  33  00 
26  13  00 
24  38  35 
24  05  15 

33  42  28 
33  06  31 
32  39  43 

32  32  50 

33  36  56 
35  30  30 

35  32  30 

36  27  00 

37  17  45 

38  02  45 

1 

Ras  Gharib:  Light-house 

10  35 
10  40 
10  45 

4  23 

4  28 
4  32 

1.5 
5.5 

6.8 

0.6 
2.3 

2.8 

Zafarana:  Light-house 

Suez :  Newport  Rock 

Tor:  Ruined  fort 

Sherm  Yahar:  Entrance 

i 

Sherm  Joobbah :  Entrance 

t 

Sherm  Wej :  Light-house 

Sherm  Hassejy :  Anchorage 

1 

Yembo:  Anchorage 

::::::  i 

« 

Page  234]                                      APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
PIAST  COAST  OF  AFRICA  AND  THE  RED  SEA— Continued. 

o 

Place. 

Lat.  N. 

Long.  E. 

Lun. 

Int. 

Range.          1 

H.W. 

L.W. 

Spg. 

Neap.   1 

i 

Sherm  Rabigh :  ^ichorage 

Jiddah:  Jezirah  el  Mifsaka  I 

0      /      // 

22  43  50 

O         1         II 

39  00  30 

39  10  38 

40  12  00 

40  30  00 

41  03  20 
41  27  30 

41  58  15 

42  29  00 
42  38  45 
42  34  00 
42  56  00 

42  45  28 

43  13  36 

h.    m. 

h.    VI. 

ft.             ft. 

21  28  00 
20  09  00 

3  30 

9  42 

2.  0         0.  8 

Lith:  Agha  Islet 

Jelalil:  Anchorage 19  55  30 

Kunfidah:  Islet '  19  07  40 

j 

Khor  Nohud:  Entrance 

18  15  50 

Farisan  I.  Anchorage:  Jebel  Mandhakh . 
Gizau :  Fort     .. 

16  50  15 
16  53  00 
15  42  00 
15  20  30 
14  47  00 
14  03  53 
13  19  43 

Loheiya:  Hill  Fort 

1  15 

7  27 

2.9 

1.2 

Kauiardn  Bay :  Harbor. .... 

Hodeida  Road 

Jebel  Zukur  Island:  N.  pt 

Mokha:  N.  Fort 

11  45 

5  33 

4.5 

L9 

ISLANDS  OF  THE  INDIAN  OCEAN. 

i 

d 

> 

• 

fl 
e 

g 

ss 

Chitlac  Islet:  S.  end 

11  40  45 
11  35  00 
11  27  30 
11  13  00 
11  06  00 
10  47  00 
10  32  00 
10  06  00 
10  03  00 
8  16  00 

6  55  00 
6  59  00 

6  25  00 
5  26  30 
5  01  30 
4  25  45 
4  44  00 

4  10  15 
3  41  00 

2  57  00 

3  16  00 
2  10  30 

2  07  00 
0  14  30 

Lat.  S. 
0  41  30 

5  40  56 

4  52  26 

5  53  00 

4  37  15 

3  43  06 

5  15  00 

7  13  37 
16  25  12 
19  40  22 

19  52  36 

19  59  45 

20  08  46 
20  24  20 

72  42  54 
72  09  54 
72  59  00 
72  44  00 

72  41  00 

73  40  00 
72  37  40 

72  15  10 

73  35  54 
73  01  15 

72  55  54 

73  12  54 

72  41  54 

73  20  00 
72  53  00 

72  57  24 

73  28  00 
73  30  24 
73  24  54 
73  34  24 

72  48  00 

73  03  00 
73  35  54 
73  13  00 

73  06  54 

53  41  03 
53  23  38 
55  27  10 

55  27  23 
55  12  19 

71  43  47 

72  23  50 

59  46  40 

63  25  38 

57  39  14 
57  32  35 
57  29  26 
57  47  14 

Betrapar  Islet:  N.  Island 

Kittau  Islet :  S.  end 

10  20 

4  00 

6.3 

3.0 

Cardamum  Islet:  Center 

Ameni  Islet:  N.  end 

Underut  Islet:  Center 

Cabrut  Islet:  E.  end 

Seuheli  Par:  N.  islet 

Kalpeni  Islet:  S.  end 

Minikoi  Island :  Light-house 

11  27 

5  15 

2.5 

1.2 

Heawandu  Island :  S.  end 

Kee-lah  Island :  N.  end . 

Mah  Kundu  Island:  NE,  extreme 

Nar  Foree  Island 

Hee-tah-doo  Island 

To-du  Island :  Center .. 

Gafor  Island :  Center 

Male,  or  Kings  Island:  Flagstaff 

Pha-li-du  Island :  Northern  end 

0  20 

6  25 

2.9 

1.4 

Moluk  Island:  Center 

Himniittee  Island 

Kimbeedso  Island :  S.  end 

Esdu  Island :  NE.  pt 

Wahdu  Island :  E.  end 

Addu  Atoll:  Gung  I 

Amirante  Islands:  Iledes Roches, N. beach 

African  Islands 

Seychelle  Is.,  Platte  I. :  S.  end 

Port  Victoria:  End  of  Ho- 
doul  Jettv 

4  22 

10  35 

4.3 

1.2 

Bird  Island:  Tree 

Chagos  Archipelago,  Peros  Banhos:  Dia- 
mond Islet 

Diego  Garcia :  N.  end 

of  Middle  I 

Cargados  Carajos:  Establishment  I.,  flag- 
staff   

1  30 
1  50 
0  20 

7  43 

8  03 
6  32 

5.8 
4.0 
5.5 

L7 
1.2 
1.6 

Rodriguez  Island:  Mathurina  Bay,  Point 
Venus  

Flat  Island :  Light-house 

Cannonier  Point:  Light-house 

Port  Louis:  Martello  tower.  Ft.  George.. 
Grand  Port:  Fouquet  I.  light 

0  48 

7  00 

1.6 

0.3 

APPENDIX  IV.                                        [Page  235 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  INDIAN  OCEAN— Continued. 

1 

Place. 

Lat.  s. 

Long.  E. 

Lun.  Int. 

Range.          1 

H.W. 

L.  W. 

Spg. 

Neap. 

it 
-0 

Reunion  Island:  St.  Denis  light 

Bel- Air  light    

O         1         II 

20  51  38 
20  53  11 

20  59  45 

21  19  47 

15  51  .37 
10  21  30 

10  06  45 
7  00  30 
7  06  00 

25  39  10 
25  12  30 
25  03  00 

23  38  25 

22  05  18 
21  54  24 

20  18  18 
19  49  30 
17  53  00 
17  29  00 

16  12  10 
16  07  00 
15  46  30 
15  43  45 
15  11  42 

14  40  18 
13  59  00 
13  55  40 
13  27  15 
13  23  38 
12  49  30 
12  27  20 
12  03  18 

11  57  30 

12  23  20 
12  44  02 
12  49  00 

12  56  48 

13  21  15 

15  15  48 
15  54  50 

15  27  55 

16  14  00 

17  00  05 

16  42  30 

17  23  16 

18  09  47 

19  55  00 

21  58  10 

24  46  25 
24  59  42 

24  58  50 

25  01  30 

22  22  30 
21  29  00 
12  26  30 
12  47  02 

12  16  20 
L2  25  00 
LI  34  48 
LI  40  44 
9  46  20 
9  22  35 
9  41  20 

O         /         II 

55  26  59 
55  36  18 
55  16  18 

55  28  58 
54  28  46 

56  32  00 

51  10  21 

52  44  57 
56  22  00 

45  06  50 
44  17  57 
44  07  20 
43  38  20 
43  15  20 

43  20  21 

44  19  21 
44  31  30 
44  02  20 

43  45  18 

44  29  05 

45  17  09 

45  43  09 

46  18  45 

46  57  29 

47  24  36 
47  58  21 
47  48  05 

47  59  30 

48  17  34 
48  38  57 

48  45  45 

49  11  21 
49  17  25 
49  35  56 
49  45  06 
49  54  00 

49  56  25 

50  01  59 
50  31  21 
50  16  05 
49  49  11 
49  50  59 
49  50  59 
49  56  15 
49  32  04 
49  25  31 
48  52  10 
48  14  50 
47  10  34 
47  07  20 
47  04  24 
46  59  11 

40  24  10 
39  40  39 

46  32  35 

45  16  27 

44  24  54 
43  47  00 

47  24  09 
43  19  15 

46  31  07 

46  14  52 

47  32  25 

h.     m. 

h.     m. 

ft- 

ft. 

St.  Paul  light       

St.  Pierre  light 

Tromelin  Island :  N.  end 

Agalegas  Island:  NW.  pt 

11  50 

5  38 

3.5 

0.6 

FarQuhar  Islands"  Hall's  house 

Alphonse  Island:  SE.  part  (Trees) 

Coetivv  Island :  N.  en(       

Cape  St.  Mary :  S.  extreme 

Lev  en  Island :  Center         

Port  Machikora :  Barracouta  I . 

St.  Augustine  Bay :  Nosi  Vei  I 

5  40 

11  52 

9.8 

2.9 

Murderers  Bay:  Center  of  Murder  I 

Cape  St.  Vincent'  Extreme          .... 

Mourondava :  Village 

Tsniano:  Village 

Kovra  Rythi  Point:  Extreme 

Coffin  Island :  Nosi  Vao 

Cape  St.  Andrew :  Extreme 

Boyanna  Bay :  Barabata  Pt ........ 

Cape  Tauzon :  Extreme 

Majunga  (Mojanga):  Light-house 

Majamba  Bay :  W.  pt 

4  15 

11  28 

10.9 

3.2 

Narendri  Bay :  Modrmora  Pt 

Port  Radama:  Pt.  Blair ... 

Radama  Islands:  N.  pt.  Nossuvee  I 

Baratoube  Bay :  Ambubuka Pt. 

Nosi  Be :  Hellville  jetty 

Minow  Islands:  N.  pt.  Great  I 

Cape  San  Sebastian :  Extreme 

Port  Liverpool:  N.  pt.  of  entrance 

Cape  Amber:  NE.  extreme 

Port  Lady  Frances:  Sunson  Pt 

Port  Looke:  Pt.  Bathurst 

PortLeven:  S.  pt.  Nosi  Haul . 

Andrava  Bav :  Berry  Head 

Vohemar :  Flagstaff 

Cape  East:  Ugoncy  I 

Venangue  Be  Bay :  Entrance 

Port  Choiseul:  Maran  Seelzy  Village 

Cape  Bellone :  Extreme 

3  45 

9  57 

5.1 

1.5 

St.  Marys  Island:  Light  on  Madame  I  .. 
Port  Tantang:  Flagstaff 

::::::::.:::  i 

1 

Fenerive  Point:  Flagstaff 

Tamatave:  Pt.  Hastie 

Mahanuru :  Town 

4  00 

10  12 

7.3 

2.1 

Matatane:  Village 

Santa  Lucia:  N.  end  of  town,  Obs.  Rock. 
Point  Ytapere :  Extreme 

Ytapere  Ba v :  N.  pt 

! 

Fort  Dauphin :  Flagstaff 

4  15 

10  27 

4.7         1.3 

Europa  Island :  Center 

Bassas  da  India:  E.  pt 

j 

Geyser  Reef:  SE.  extreme 

Mayotta  Island :  Zaoudzi 

4  00 

10  13 

1L9 

2.0 

Johanna  Island:  Landing  place,  Pomoni 
Harbor 

Mohilla  Island:  Numa  Choa  Harbor 

Glorioso  Islands:  W.  islet 

Comoro  Island:  Islet  in  Mauroni  Bay... 
Assumption  Island :  Hummock 

4  45 

10  58 

10.0 

L7 

Aldabra  Island:  Westl.,  E.  sideentrance. 
Cosmoledo  Islands:  Observation  islet 

1 

Page  236J                                       APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  INDIAN  OCEAN— Continued. 

1 

Place. 

Lat.  S. 

Long.  E. 

Lun. 

iHt. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

M 
N 

2 
•s 

M 

e 
« 

s 

« 

Prince  Edwards  Islands:  Marion  I.,  Obs. 
spot,  NE.  side.? 

o          /         // 

46  49  30 

46  36  00 
46  22  00 
46  01  00 
46  28  18 
46  10  40 
46  26  00 

48  40  00 

48  26  45 

49  42  00 

49  21  22 

o         r        II 

37  49  15 

50  41  30 

51  30  15 

50  40  00 

51  50  00 
50  35  00 

52  13  00 

69  04  00 
68  48  20 
68  54  00 

70  04  31 
70  15  00 
70  29  50 

73  15  30 
73  52  00 
72  31  45 
77  31  53 
77  29  15 
96  53  02 
105  45  57 

A.      TO. 

h.    m. 

ft. 

ft. 

Penguin  Islands:  Center  of  SW.  islet ... 
Possession  Island :  N W.  pt 

Twelve  Islands:  Summit  NE.  I 

Navire  Bav         

Hog  Island:  Summit 

East  Island:  Center 

Christmas  Harbor 

Blighs  Cape 



Cape  Bourbon 

::::::        i 

Mollov,  Port  Roval  Sound:  U.  S.  Tr.  of 
Venus  Obs.,  18*74 

0  14 

6  36 

4.6 

L3 

Cape  Challenger 

49  41  00 

Balfour  Rock 

49  29  00 

53  02  45 
53  13  00 
53  02  50 
38  42  51 
37  50  00 
12  06  22 
10  25  19 

:::::::::::  i 

Heard  Island:  Cape  Laurens,  NW.  end.. 
Sealing  station . 

McDonald  Island,  Summit 
St.  Pauls  Island :  Ninepin  Rock 

10  40 

10  50 

5  20 

7  10 

4  28 

4  38 

11  32 

1  00 

3.0 
3.3 
5.1 
4.5 

0.9 
1.0 
1.5 
L3 

Amsterdam  Island:  Summit,  2,750  feet.. 

Keeling  or  Cocos  Islands:  Direction  I 

Christmas  Island:  Flying  Fish  Cove 

SOUTH  COAST  OF 

ASIA. 

1 

i 
£ 

Aden :  Telegraph  station 

Lat.  N. 

12  47  16 

13  22  00 
13  24  50 

13  28  45 

14  20  10 
14  31  15 
14  43  50 
14  49  00 

14  54  40 

15  12  00 

15  38  00 

16  30  00 

16  59  00 

17  32  45 
17  53  15 

19  00  25 

20  10  00 
20  31  30 

22  32  40 

23  38  00 
23  52  00 

23  51  30 

24  21  50 

25  21  00 

26  24  13 
26  30  00 
25  21  34 

24  29  02 

25  17  24 

26  10  55 
26  13  56 
30  32  00 
29  22  56 

29  15  25 
28  59  07 
26  47  40 
26  33  37 

Long.  E. 

44  59  07 

45  40  50 

46  26  35 

46  39  00 

48  56  45 

49  07  35 
49  35  05 

49  57  05 

50  16  35 

51  10  30 

52  14  20 

52  48  00 

54  43  29 
56  03  05 

56  20  35 

57  51  35 

58  38  35 

58  58  35 

59  48  35 
58  30  50 
58  08  00 
57  26  00 
56  46  12 
56  22  56 
56  32  22 
56  31  29 

55  24  12 
54  22  14 
51  33  32 
51  13  46 
50  32  17 

47  51  23 

48  00  55 

50  21  11 
50  50  35 

53  23  36 

54  02  21 

7  49 

1  41 

4.9 

2.0 

Sughra:  Sheik's  house 

Mokatein :  Black  ruin 

Howaivuh:  Sheik's  house 

Banderburum :  SE.  house  of  town 

Makalleh  Bay:  Flagstaff 

8  20 

2  07 

6.8 

2.8 

Shahah  Roads:  Custom-house 

Sharmoh :  Single  house 

Kosair:  High  house 

Sihut :  Center  of  town    .           

Ras  Fartak:  Extreme  pt 

Damghot:  Town 

Merbat:  Town 

8  50 

2  38 

7.0 

2.9 

Kuria  Maria  Is.,  Hullaniyeh  I. :  NE.  bluff 
Ras  Sherbedat :  Point 

Cape  Isolette:  Islet         

Masirah  Island :  Point  Abu-Rasas 

Point  Ras  Ye 

9  45 
9  15 
9  30 

3  32 
3  03 
3  20 

9.6 
8.9 
6.0 

4.4 
4.1 

2.8 

Ras-al-Hed :  Extreme  pt 

Maskat  ( Muscat ) :  Maskat  Pt 

Deimaniveh  Islands:  E.  islet 

Sueik :  Fort 

Sohar'  SE  tower  of  town  hall 

Khaur  Fakan  Bay:  W.  end  of  village... 

Ras  INIusendom :  N.  end  of  island 

Great  Quoin  Islet:  Center 



Sharjah:  High  tower  with  flagstaff 

Abu-Thabi:  Fort  flagstaff 

Al  Beda'a  Harbor:  Nes8ahPt.,N.  extreme 
Ras  Rakkin:  NW.  pt 

Bahrain  Harbor:  Portuguese  fort 

Basrah:  Custom-house  flagstaff 

6  15 

11  30 

6.4 

3.7 

Kuweit  Harbor:  N.  end  of  town 

Khdrig  Islet:  Fort  fla^taff 

0  06 

6  17 

8.3 

4.8 

Abu  Shahr:  Residencv  flagstaff 

7  12 

1  13 

2.6 

1.5 

Shaikh  Shu'aib  Islet:  E.  end. 

Kais  Islet:  NE.  pt 

0  30 

6  40 

6.6 

3.8 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
SOUTH  COAST  OF  ASIA— Continued. 


[Page  237 


Place. 


Lat.  N. 


Basidiih:  Chapel 26  39  12 

Haujam  Islet:  Ruined  mosque '  26  40  49 

Kasm:  Fort '  26  57  27 

Jashak  Bay:  Telegraph  office 25  38  19 

KubKalat:  High  peak,  1,680  feet 25  29  45 

ChahbarBay:  Telegraph  office 25  16  43 

GwatarBay:  Islet 25  03  17 

! 

Gwadar  Bay :  Telegraph  office |  25  07  19 

Pasni:  Telegraph  office 25  15  52 


Onnarah:  Telegraph  office 
Sunmiyani:  Jam's  house.. 
Cape  Monze:  Peak 


Karachi :  Manora  light 

Observatory 

Mandavi :  Light-house 

Bey t  ( Bet ) :  Light-house 

Dwarka:  Light-house 

Temple  spire 

Porebander:  Light-house 

Mangarol:  Light-house 

Diu  Head :  Light-house 

Kutpur:  Light-house 

Bhaunagar:  Light-house 

Perim  Island :  Light-house 

Cambay :  Flagstaff 

Surat  River:  Tapti  light 

Surat:  Minaret  Adrusah 

Bassein :  Center  of  town 

Bombay :  Observatory 

Kenery  Island  light 

Bankot:  Fort  Victoria 

Ratnagherry :  Fort 

Viziadrug:  Fort  flagstaff 

Cape  Ramas:  W.  bastion  of  fort  ... 

Goa:  St.  Denis  Church 

Agaada  light 

Vingorla:  Signal-station  light 

Vingorla  Rocks:  Light-house 

Sedashigar  Bay:  Oyster  Rock  light. 

Kumpta:  Light-house 

Hindwar:  Monument 

Kundapur:  Light-house 

Mangalore:  Light-house 

Kannanur:  Light-house 

Tellicherri :  Flagstaff 

Mahe :  Light-house 

Calicut:  Light-house 

Cochin :  Light-house 

Alipee :  Light-house 

Quilon:  Tongacherri  Point  light 

Trevandrum :  Observatory 

Cape  Comorin :  Light-house 

Trichendore :  Pagoda  on  pt 

Tuticorin :  Light-house 

Paumben  Pass :  Light-house 


Manaar:  Center  of  town 

Colombo :  Light-house , 

Dondra  Head :  Light-house , 

Point  de  Galle:  Light-house 

Great  Bassas  Rocks:  Light-house 
Little  Bassas  Rocks:  Light-house  , 

Batticaloa:  Light-house 

Trincomali :  Dock-yard  flagstaff. . 


Calimere  Point:  Light-house 

Negapatam :  Light-house 

Pondicherri:  Light-house  ... 


25  11  55 
25  25  19 
24  50  03 


47  37 

49  50 

50  00 
29  20 
14  00 

14  00 
38  00 
06  00 

41  20 
02  21 
47  00 
35  54 
17  00 
05  20 
12  19 

20  10 
53  45 

42  08 

58  00 

59  30 
33  26 
05  12 

21  24 

29  25 

51  10 
53  20 
49  00 
25  00 
17  28 
38  15 

52  17 
5i  10 
45  00 
42  00 

15  10 
58  00 

30  00 

53  20 
30  47 
04  00 
29  55 
47  10 
17  20 


8  59  00 
6  55  40 

5  55  30 

6  01  25 
6  10  10 

6  25  00 

7  45  00 

8  33  30 

10  18  00 

10  45  28 

11  55  40 


Long.  E. 


55  16  47 

55  54  25 

56  17  37 

57  46  14 

59  40  32 

60  37  40 

61  26  24 

62  19  42 

63  28  37 

64  37  02 
66  35  39 

66  39  58 

60  58  06 

67  01  33 
69  20  15 
69  04  40 

68  57  06 

68  58  54 

69  36  00 

70  06  32 

70  50  45 

71  49  35 

72  14  00 
72  21  08 
72  35  10 
72  38  40 
72  49  27 
72  48  44 
72  48  56 

72  48  49 

73  02  40 
73  15  56 
73  19  39 
73  54  50 
73  54  00 
73  46  10 
73  37  00 

73  27  15 

74  03  40 
74  22  30 
74  26  40 
74  39  50 

74  50  40 

75  21  51 
75  29  40 
75  31  10 

75  46  40 

76  14  40 
76  20  40 
76  34  00 

76  56  45 

77  32  35 

78  07  47 

78  11  26 

79  12  50 

79  53  52 

79  50  40 

80  34  12 

80  13  04 

81  28  15 
81  44  00 
81  41  00 
81  13  42 

79  51  30 
79  50  47 
79  50  10 


Lun.  Int. 


h.  m. 


10  50 
9  20 


9  20 


8  50 
10  15 
"i2'65' 


4  27 


11  26 


'Ai 


10  34 


10  50 


11  21 
11  33 


0  18 


1  55 


2  02 


8  10 


8  37 


L.  W. 


h.  m. 


4  35 
3  05 


3  05 


2  35 
4  00 
'5*39' 


11  18 


5  08 


4  10 


4  11 


4  28 


4  59 

5  06 


6  16 


1  52    7  51 
1  37    7  36 


7  49 


8  07 


1  44 


2  37 


Range. 


Spg. 


11.6 

7.8 


^.1 


7.3 


10.8 


12.0 


5.2 


5.0 


6.5 


2.7 
2.1 


2.5 


3.0 
2.0 


2.0 


2.0 


2.1 


Neap. 


5.3 
3.6 


3.7 


3.8 
3.4 


5.2 


29.  8   15. 1 


4.9 


2.5 


2.4 


3.4 


1.4 
1.0 


1.3 


0.8 
0.5 


0.4 


0.4 


0.5 


0.9 


Page  238] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

SOUTH  COAST  OP  ASIA— Continued. 


Place. 


Madras:  Observatory 

Light-house 

Pulicat:  Light-house 

Armeghon :  Light-house 

Kistna:  Light-house 

Masulipatam :  Flagstaff 

Coconada:  Light-house 

Vizagapatam:  Fort  flagstaff 

Kalingapatam :  Light-house 

Gopalpur:  Light-house 

Gaujam:  Fort 

Juggernath :  Great  temple 

False  Point :  Light-house 

Balasor  River:  Chandipur  light  .. 

Saugor  Island:  Light-house 

Diamond  Harbor:  Flagstaff 

Calcutta:  Ft.  William  semaphore. 


Chittagong  River:  Light-house 

Akyab:  Oyster  Reef  light 

Old  temple 

Ramree  Island:  S.  pt 

Chedubah  Island:  N W.  peak 

Cape  Negrais:  Extreme 

Bassein  River:  Alguada  Reef  light 

Bassein:  Port  Dalhousie 

Andaman  Is.:  Table  Id.,  Light-house  . 

Port  Cornwallis,  Rock  in 
entrance 

Port  Blair,  Light- house. 

Little  Andaman  Island, 

SE.pt 

Krishna  Shoal:  Light  vessel 

Rangoon  River:  Grove  Pt.  light 

Rangoon :  Great  Dagon  pagoda 

Moulmein :  Docks 

Moulmein  River:  Amherst  Pt.  light. . . 

Double  Island :  Light-house 

Tavoy  River:  Light-house 

Mergui:  Court-house 

Tenasserim 

St.  Matthew  Island:  Hastings  Harbor.. 
Pak  Chan  River:  Light-house 


Tongka    Harbor,   Junkseylon  Island: 
Light-house 

Pulo  Penang:  Fort  Cornwallis 

Dinding  Channel :  Hospital  Rock 

One  Fathom  Bank :  Light-house 

Cape  Rachado :  Light-house 

Malacca;  Stat.  St.  Pauls  Hill 

Singapore  Strait:  Coney  Island  light... 

Singapore:  Fullerton  Battery 

Singapore  Strait:  Pedra  Branca  light . . . 

Summit  Bintang  great 

hill,  1,253  feet 

Rhio  Straits,  Pulo  Sauh:  Light-house  .. 

Terkolei :  Light-house 

Little Garras:  Light-house 

Rhio,  Bintang  Island:  Residency  flag- 
staff   

Pitong  Island :  Peak 

Abang  Besar  Island :  N.  pt 


Linga  Island :  Flagstaff 

Singkep  Island:  Mountain  summit. 
Menali  Island:  N.  pt 


Nicobar  Islands,  Car  Nicobar:  N.  pt  . . . 


l^t.  N. 


13  04  06 
13  05  15 
13  25  15 

13  53  08 

15  47  00 

16  09  45 

16  56  21 

17  41  34 

18  19  00 

19  13  00 
19  22  30 

19  48  17 

20  20  20 

21  27  15 

21  38  40 

22  11  10 
22  33  25 

22  11  00 
20  05  00 
20  08  53 
18  51  00 
18  50  30 
16  01  30 

15  42  14 

16  01  30 

14  12  30 

13  18  40 

11  40  40 

10  27  00 

15  37  26 

16  30  01 
16  46  00 
16  26  00 
16  04  45 
15  52  00 
13  36  40 

12  26  15 
12  06  00 
10  05  05 

9  58  00 


50  00 
24  45 
13  05 
52  10 
24  08 
11  30 
1  09  57 
1  17  11 
1  19  57 

1  04  20 
1  03  13 
0  57  10 
0  44  30 


0  55  50 
0  36  52 
0  36  30 
Lat.  S. 
0  12  34 
0  26  13 
0  57  51 
Lat.  N. 
9  15  40 


Lun.  Int. 


Long.  E. 


H.W. 


80  14  51 
80  17  00 
80  19  12 
80  12  30 

80  59  00 

81  11  00 

82  15  05 

83  17  42 

84  07  30 

84  52  06 

85  03  29 

85  49  09 

86  44  00 

87  02  20 

88  02  00 
88  11  07 
88  20  12 

91  49  00 

92  39  00 

92  52  40 

93  56  30 

93  31  00 

94  13  16 
94  12  00 

94  23  00 
93  22  30 

92  57  10 
92  45  15 

92  31  10 

95  37  32 

96  23  00 

96  07  30 

97  38  00 
97  33  05 

97  35  00 

98  13  00 

98  35  59 

99  03  00 
98  10  15 
97  35  00 


98  25  30 
100  21  44 
100  34  15 

100  59  12 

101  51  02 

102  15  00 

103  44  47 

103  51  15 

104  24  08 

104  27  21 
104  10  30 
104  19  52 
104  21  19 

104  25  43 
104  04  42 
104  11  31 

104  36  14 

104  30  15 

105  38  20 

92  48  00 


h.    m. 


8  41 


8  42 
8  48 


9  21 


1  25 
1  02 


9  40 


3  05 


9  50 
9  40 


4  26 
3  07 
2  12 


10  50 
10  40 


11  50 


5  50 


7  20 


10  18 


9  40 


L.  W. 


h,    tn. 


Range. 


Spg.    Neap. 


ft. 


2  26   3. 1 


2  36 
2  34 


4.5 
4.4 


3  00  I  6.  8 


9  06  11.2 


7  56 


3  28 


9  55 


3  37 

3  27 


11  15 

10  49 

8  49 


4  20 
4  10 


5  40 


12  00 

"I'os 

"'4'62 


3  14 


6  00  1  12  13 


13.1 


18.7 


6.3 


16.9 
11.7 
19.2 


15.6 
18.0 


14.4 


10.5 
"7.*6" 


7.1 


11.6 


ft. 
'{'.2 


1.9 
1.8 


2.6 


4.4 
5.6 
"3.'6' 


2.9 
2.1 


7.0 
5.0 
7.4 


3.8 


6.2 
"4.' 5 
"3.'2 


3.1 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
SOUTH  COAST  OF  ASIA— Continued. 


[Page  239 


Place. 


Nicobar    Islands,    Nancowrv    Harbor: 
Naval  Pt 

Great  Nicobar:  AV. 
pt.  Galathea  Bay . . 

Acheen  (Acheh)  Head:  Pulo  Bras  light 

N.  extreme 

Diamond  Point:  Light-house 


Point  Baru  or  Datu:  Extreme 

Point  Bon  or  Djabon :  Extreme 

Moeara-Kompehi :  Fort 

Djambi:  Flagstaff  of  fort 

Palembang:  Residency  flagstaff 

Lam  pong  Bay:  Telok  Betong  light 

Blimbing  Bay 

Kroe:  V'^illage 

Engano  Island:  Barioe  anchorage 

Bintoean:  River  mouth  

Mega  Island :  N.  pt 

Benkulen :  Light-house 

Bantal :  Village 

Indrapura  Point:  Extreme 

Pisang:  Light-house 

Padang:  Light-house 

Siberaet  Island :  Sigeb  Pt 

Katiagam :  Village 

Batoe  Islands:  N.  point  of  Simoe  Islet. 
Summit  of  Tello 


Lat.  N. 


8  02  10 

6  46  20 

5  45  00 
5  34  40 

5  15  58 

Lat.  S. 
0  00  32 


Ayer  Bangis:  Fort  flagstaff 

Natal:  Fort  flagstaff. 

Nias  Island :  Lagoendi  Bay 

Sitoli 

Lapan 

Siboga:  Flagstaff 

Singkel :  Post-office 

Bangkaru  Islands:  Bay 

Simaloe  Island:  NW.  pt 

Tampat  Toewon;  Flagstaff 

Analaboe 

Batve  Toetong:  Landing  place. 


00  55 

23  13 

35  33 

59  26 

27  00 

55  02 

11  24 

18  50 

48  35 

59  25 

47  22 

44  54 

10  35 

0  59  56 

0  57  53 

0  53  58 

0  07  41 

0  03  13 

0  02  56 


Lat.  N. 
0  11  41 
0  33  11 
0  34  47 


17  36 
24  16 
44  24 
16  47 
02  32 
51  30 
14  59 
08  14 
38  21 


Long.  E. 


93  29  42 

93  49  20 

95  04  33 
95  19  00 

97  30  11 

103  47  58 

104  21  30 
103  59  14 

103  36  41 

104  45  34 

105  15  58 
104  32  36 
103  55  42 

102  07  28 

103  20  18 

101  00  58 

102  14  50 
101  17  25 
100  50  06 
100  19  28 
100  20  19 

98  53  58 

99  45  20 
98  05  55 

98  16  43 

99  22  09 
99  06  33 
97  43  43 
97  36  46 

97  12  28 

98  46  08 
97  45  06 
97  06  53 

95  56  02 
97  10  13 

96  07  23 
95  34  29 


Lun.  Int. 


Range. 


H.  W. 


h.   m. 
9  05 


10  00 

11  50 


5  50 


5  35 


5  29 


L.  W. 


Spg. 


Neap. 


h.   TO. 
2  52 


ft- 
8.3 


ft. 
2.8 


3  44 

5  34 


5.2 

8.7 


2.3 
3.7 


5  40   11  52 


2.6 


0.7 


12  03 


4.0 


1.1 


11  48 


5.5 


1.4 


11  42   2.8 


0.7 


EAST  COAST  OF  ASIA. 


Java  Head :  First  Pt.  light 

Sunda  Strait:  Krakatoa  I.  peak 

North  Watcher  Island:  Light-house. . . 

Lucipara  I. :  Beacon 

Banka  Island:  Tobol  Ali  Fort . . . . 

Berikat,  summit 

Nanka  I. :  Light-house 

Banka  Island:  Mintok  light 

Blinyu 

Crassok  Pt 

Shoal  water  Island :  Light-house 

Pulo  Lepar:  Light-house 

Pulo  Jelaka:  Light-house 

Billiton  Island:  Tandjong  Pandanflag 

staff 

Langkuas  I.  light 

'  Caspar  Island:  Peak 


Lat.  S. 
6  44  30 
6  08  46 
5  12  17 
3  13  05 
3  00  48 
2  34  18 
•2  23  20 

2  04  03 
1  38  26 

1  29  00 

3  19  10 

2  56  52 
2  52  05 

2  44  40 
2  32  12 
2  24  30 


105  11  48 

105  26  58 

106  27  33 
106  13  02 
106  27  22 
106  50  36 
105  44  30 
105  09  45 

105  46  28 

106  57  30 

107  12  42 

106  54  38 

107  00  43 

107  38  46 
107  37  15 
107  03  33 


5  30 

6  50 


[9  05] 


[6  50] 


[2  08] 


[3  17] 


11  42 
0  37 


2.5 

3.8 


[2  52]  [10. 1] 


[0  38] 


[9.3] 


[8  21]  [5.  6] 


[9  29]  [6. 6] 


0.7 
1.1 


Page  240] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Continued. 


Place. 


Carimata  Island :  Sharp  peak 

Pulo  Eu:  Center? 

Pulo  Aor:  S.  peak,  1,805  feet 

St.  Barbe  Island:  Center  of  W.  side 

Direction  Island:  S.  pt 

Dato  Island:  Summit 

St.  Julian  Island:  Summit 

Tambelan  Island:  S.  pt 

Tamban  I.  obs.  station 

Victory  Island :  S.  pt 

Anamba  Islands:  White  rock 

Pulo  Repon 

Pulo  Domar 

St.  Pierre  Rock:  S.  pt. 

Natuna  Islands:  Pyramidal  rocks 

Semione  I 

Pulo  Varella:  Center 

Pulo  Brala:  Center 

Tringano  River:  N.  pt 

Great  Redang  Harbor:  Bukit  Maria  I . . 

Kalantan:  Entrance  small  river 

Cape  Patani:  NE.  pt 

Singora:  SW.  pt.  of  Ticos  I 

Koh  Krah  Islet:  SE.pt 

Bangkok:  Old  British  factory 

Cape  Liant:  NW.  rock  of  Koh  Mesan . . 

Chentabun  River:  Entrance,  Bar  I 

Koh  Chang:  Small  island  on  W.  side  .. 

Koh  Kong:  S.  pt.  of  river  entrance 

Kusrovie  Rock:  Center 

Koh  Tang  Rocks:  SW.  rock  of  group  . . 
Panjang  Island :  NW.  corner  of  SW.  bay. 

Obi  Islands:  Light-house 

Saigon :  Observatory 

Mitho:  S.  gate  of  citadel 

Cape  St.  James :  Light-house 

Cape  Padaran:  Extreme 

Cape  Varella:  Extreme 

Quin  Hon :  Battery  flagstaff 

Condore  Islands:  Light-house 

Safatu  Island :  Summit 

Ceicer  de  Mer  Island :  SW.  hill 

Natuna  Islands:  Murundum  I.,  SE.  pt. . 
Low  I 

Canton  Pulo:  Light-house 

Cham-Callao  Islet:  Watering  place 

Tourane  Bay:  Light-house 

Hon-Me:  Sunmiit 

Nam-Dinh :  Citadel  tower 

Hon  Dau  Island:  Light-house 

Hai-Fong:  Observation  pagoda 

Hai-Duong:  Citadel  tower 

Ha-Noi:  Citadel  tower 

Pak-Hoi :  Custom-house  flagstaff 

Hainan  Island :  Cape  Bastion,  extreme  . 
Gaalong  Bay,  E.  Brother 


Lat.  S. 


1  33  24 

2  07  00 
2  26  30 

Lat.  N. 
0  07  26 
0  14  19 
0  06  37 
0  55  00 
0  56  52 


00  27 
34  41 
18  10 
25  00 
44  31 
51  42 
03  00 
31  00 


3  17  00 

4  53  00 

5  21  40 

5  44  21 

6  11  53 

6  58  01 

7  13  54 

8  24  47 
13  44  20 
12  35  08 

12  27  43 
12  01  20 
11  33  00 
11  06  25 
10  21  20 

9  18  14 
8  25  20 

10  46  47 
10  21  16 

10  19  51 

11  21  00 

12  53  40 

13  45  23 

8  40  06 

9  58  23 
10  32  36 

2  02  55 

3  00  00 

15  23  34 

15  57  10 

16  07  00 

19  22  14 

20  25  30 
20  40  03 

20  51  44 

20  56  29 

21  01  57 
21  29  00 
18  09  00 
18  11  30 


Long.  K. 

Lun. 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

0     1          II 

108  55  13 

h.     m. 

h.     m. 

ft. 

ft. 

104  17  00 



104  34  06 

1 

107  13  00 

108  01  47 

108  37  05 

106  45  00 

107  32  57 

106  24  10 

106  18  27 

105  35  58 

105  52  00 

105  22  57 

108  38  55 

107  21  40 

107  42  30 

103  40  00 

103  38  00 

103  08  00 
103  01  37 

8  00 

1  48 

5.8 

2.5 

102  20  47 

101  18  39 

100  36  12 
100  45  27 

8  20 

2  08 

2.8 

L2 

100  28  42 
100  56  47 

8  00 

2  00 

7.3 

3.1 

102  04  19 
102  15  47 

10  00 

3  50 

4.5 

2.1 

102  57  14 

102  47  49 

102  56  34 

103  29  14 

104  48  30 

106  42  10 
106  20  38 

5  00 

11  20 

9.8 

4.2 

107  04  55 

108  58  00 

109  23  42 

109  14  52 

106  41  42 

109  06  00 

108  56  27 

109  06  10 

107  48  00 

109  05  35 

108  32  47 

108  11  30 

105  55  22 

106  08  41 

106  47  10 
106  41  08 

9  00 

2  48 

4.3 

2.1 

106  17  56 

105  48  40 

109  06  00 
109  35  00 

5  00 

11  12 

14.0 

6.6 

109  41  30 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued, 


[Page  241 


Place. 


Hainan  Island :  Light-house 

Paracel  Islands :  Triton  I 

Observation  bank  . . . 

Lincoln  I 

Woody  I 

Pratas  Island :  NE.  part 

Ty-f ung-kyoh  Island :  Center 

Tien-pak  Harbor:  Pauk  Pyah  Islet  ... 

Song-yui  Point:  Extreme 

Hui-lang-san  Harbor:  Mamechow  Islet 

Mandarins  Cap:  Summit,  200  ft 

Macao ;  Fort  Guia  light 

Fort  San  Francisco 

Canton :  Dutch  Folly  light 

Raleigh  Rock :  Center 

Gap  Rock:  Light-house 

Hongkong:  Cathedral 

Wellington  Battery 

Lema  Island :  Lema  Head 

Nine-pin  Rock :  Center 

Tuni-ang  Island :  Summit 

Single  Island :  E.  summit 

Mendoza  Island :  Summit 

Pank  Piah  Rock:  Summit 

Pedra  Blanca  Rock:  Summit,  130  ft... 

Chino  Bav:  Obs.  spot 

Cupchi  Point:  Hill 

Breaker  Point:  Light-house 

Cape  of  Good  Hope:  Light-house 

Swatau :  British  consulate 

Lamock  Island :  Light-house 

Brothers  Islets:  SE.  Islet 

Tong-sang  Harbor:  Fall  Peak 

Chapel  Island :  Light-house 

Amov :  Taitan  I.  light 

Dodd  Island :  Light-house 

Chinchin  Harbor:  Pisai  Islet 

Pyramid  Point:  Extreme 

Ockseu  Island :  Light-house 

Sorrel  Rock:  Summit 

Lamyit  Island :  High  Cone  Peak 

Hungwha  Channel :  Sentry  I 

Turnabout  Island :  Light-house 

East  Dog  Island :  Light-house 

Min  River:  Pagoda,  Losing  I 

TemplePt 

Alligator  Island :  Summit 

Tung-yung  Islands:  Peak,  N.  end 

Coney  Island:  Summit 

Double  Peak  Island :  Highest  peak  . . . 

Pih-seang  Island :  Town  I 

Dangerous  Rock:  Summit 

Tae  Islands:  Summit 

Nam-<juan  Harbor:  Bate  I 

Ping-fong  Island :  Summit 

Pih-quan  Peak:  Summit 

Port  Namki :  E.  horn 

Pih-ki-shan  Island:  Summit 

Pe-shan  Islands:  Summit,  SW.  end... 

Tung-chuh  Island:  Summit 

Kweshan  Islands;  Patahecock 

Nimrod  Sound :  IVIiddle  islet 

Tong-ting  Islet:  Summit 

Chin-hai:  Citadel 

Ning-po:  Square  I.  light 

Chusan  Islands:  Ting-hai  Harbor 


Lat.  N. 


20  01  15 

15  46  30 

16  36  00 
16  40  07 
16  49  55 

20  42  03 

21  22  30 
21  24  15 
21  31  00 
21  34  00 

21  28  00 

22  11  40 

22  11  24 

23  06  35 
22  02  00 

21  48  50 

22  16  52 
22  16  23 
22  03  40 
22  15  45 
22  27  06 
22  24  06 
22  30  42 
22  32  54 
22  18  30 
22  48  14 
22  48  07 

22  56  24 

23  14  00 
23  20  43 
23  15  43 
23  32  30 

23  47  15 

24  09  49 
24  23  16 
24  25  44 
24  49  13 
24  52  12 

24  59  36 

25  02  18 
25  12  00 
25  16  30 
25  26  10 
25  58  10 

25  59  00 

26  08  26 
26  09  29 
26  22  37 
26  30  00 
26  36  06 
26  42  30 
26  51  25 

26  58  52 

27  09  20 
27  09  42 
27  19  18 
27  26  18 

27  37  36 

28  05  07 

28  43  45 

29  22  45 
29  34  20 
29  51  53 
29  57  08 

29  59  21 

30  04  30 


Long.  E. 


110  16 

111  14 

111  40 

112  43 
112  20 
116  43 
111  10 
111  15 
111  38 

111  46 

112  21 

113  34 
113  33 
113  16 
113  47 

113  56 

114  09 
114  10 
114  19 
114  22 
114  36 
114  39 

114  50 

115  01 
115  06 

115  47 

116  04 
116  29 
116  47 

116  40 

117  17 
117  42 

117  36 

118  13 
118  10 
118  30. 
118  41 

118  58 

119  27 
119  10 
119  35 
119  45 
119  56 
119  59 
119  27 

119  37 

120  24 
120  29 
120  10 
120  11 
120  22 
120  32 
120  42 
120  25 
120  32 

120  27 

121  06 
121  12 
121  30 

121  55 

122  13 

121  43 

122  35 
121  43 

121  45 

122  03 


Lun.  Int. 


H.  W. 


L.  W. 


h.    in. 


h.    m. 


11  50    5  37 


9  50    3  38 
'2'66T"8'66' 


Range. 


Spg. 


8.2 


6.3 
"5."i" 


Neap. 


9  20    2  52   4. 4    2. 0 


0  30    7  00 
9  45  ,   3  33 


ft. 


3.8 


3.0 
2.' 4 


1 

1            1 

1 

2  50 

9  00 

7.5 

3.5 

11  20 

5  08 

12.0 

7.6 

0  05 

6  13 

15.6 

9.9 

\ 



19. 3   12. 2 
19. 0   12. 0 


50  I   3  38  !  17.  2  i  10. 9 


1  00 


7  12   8. 


4.6 


22489—03- 


-16 


Page  242] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Continued. 


Place. 


Video  Island:  Summit 

West  Volcano  Island:  Light-house 
Chapu:  Battery 

Gutzlaff  Island:  Light-house 

Saddle  Islands:  N.  Saddle  light... 

West  Barren  Island:  Summit 

Shanghai:  Kng.  consulate  flagstaff 

Wusung:  Light-house 

Shaweishan  Island:  Light-house.. 


Lat.  N. 


30  08  04 
30  20  50 
30  36  00 
30  48  37 
30  51  41 

30  44  07 

31  14  42 
31  23  18 
31  25  27 


Pescadores  Islands: 


Fisher  I.  light 23  32  53 

Second  pt. on  N. side  I 
Makung Harbor..    23  32  54 


South  Cape :  Light-house 

Takau:  Saracen  Head 

Port  Heongsan 

Tam-sui  Harbor:  White  Fort 

Kelung  Harbor:  Light-house 

Soo  (Sauo)  Bay:  Beach  near  village.. 
Botel  Tobago  Sima:  S.  extreme 


Tanjong  Datu 

Sardwak  River:  Po  Pt.  light 

Sardwak:  Fort 

Cape  Sirik :  Light-house 

Tanjong  Barram 

Bruni  River:  Light-house 

Labuan  I. ,  Victoria  Hbr. :  Light-house. 

Sandakhan  Harbor:  Light-house 

Unsang:  Anchorage 

Cape  Kaniongan:  E.  pt.  of  Borneo 


Pamaroongl. :  E.  pt.  delta  River  Koetei. 

Pulo  Laut:  S.  pt.  Koengit  Islet 

Selatan  Point:  Extreme  of  Sita  Pt 

Bandjermasin:  Residency  flagstaff 

Sampit  Bay :  Bandaran  Pt 

Kottaringin  Bay :  Samadra  I 

Succadana:  Town 

Padang  Tikar:  Point 


Port  Laykan:  SW.  pt.  of  Celebes 

Macassar:  Fort  light 

Palos  Bay:  Village  at  head 


Cape  Rivers:  NE.  Cape,  Slime  Islet... 

Gorontalo:  Light-house 

Manado  Bay :  Light-house 

Bajuren  Island :  Summit 

Tagulanda  Island :  Peak 

Seao  Island :  Conical  peak 

Sauguir  Island :  S.  pt.  Cape  Palumbatu. 
Taluat  Island:  Kabruang  I.,  SE.  pt... 
Cape  Flesko:  Extreme 


21  55  00 

22  36  14 

24  46  00 

25  10  24 
25  09  12 
24  35  28 
22  01  40 


05  15 
43  50 
33  55 
45  20 
36  15 
02  00 

15  25 
50  10 

16  30 
04  00 


Lat.  S. 
0  45  00 


05  42 
10  40 
18  55 
16  00 
54  00 
14  00 


0  40  00 

5  36  00 
5  08  09 

0  57  00 

Lat.  N. 

1  20  00 
0  29  41 


Cape  Talabo:  E.  end.. 
Wowoni  Island:  N.  pt 
Bouton  Island:  N.  pt . 

E.  pt  . 

Fort.. 
Cape  Lassa:  Extreme . 
Salayar  Island :  N.  pt . 

S.  pt  . 


31  00 
07  00 
22  00 
44  00 
21  00 
3  49  00 
0  27  00 


Lat.  S. 
0  46  00 

3  58  00 

4  23  30 

5  15  00 
5  29  15 
5  35  00 
5  47  00 


6  26  00 


Long.  E. 


Lun.  Int. 


Range. 


H.  W. 


122  45  48 
121  51  25 

121  03  00 

122  10  12 

122  40  17 

123  08  27 
121  28  55 

121  29  36 

122  14  12 

119  28  05 

119  30  12 

120  51  00 
120  15  54 

120  55  00 

121  25  00 
121  44  28 
121  49  20 

121  39  45 

109  39  07 

110  30  30 
109  20  40 

111  21  20 

113  58  57 
115  03  00 

115  16  05 

118  07  20 

119  16  00 

118  56  00 

117  37  00 

116  01  40 

114  42  18 
114  34  56 
113  08  00 
111  24  00 
109  58  00 
109  16  00 

119  26  00 
119  23  55 

119  47  30 

120  43  30 

123  03  08 

124  50  00 

125  22  00 
125  24  30 
125  26  00 
125  39  00 
127  02  30 
124  26  00 

123  27  00 
123  00  00 
123  04  00 
123  16  00 

122  36  41 
120  29  00 
120  30  00 
120  28  30 


h.  TO. 


L.  W. 


Spg.   Neap. 


0  12 


9  45 


10  00 

10  15 

6  00 


4  00 

5  20 


9  35 

12  00 


[7  45] 


7  00 


4  40 


6  00 


h.  m. 


St. 


06 


).l 


3  32 


4.0 


3  47 

4  03 
12  13 


8.0 
3.0 
5.8 


10  12 

11  35 


9.0 
14.1 


3  23 
5  50 


5.5 
5.2 


[1  33]  [7.0] 


0  47 


7.2 


10  55 


3.9 


12  15 


4.3 


4.8 


1.7 


3.4 
1.3 
2.5 


3.9 
6.1 


2.4 
2.2 


3.1 


2.9 


3.1 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 


[Page  243 


Place. 


light 


Anjer:  Fourth  pt.  light 

Bantam :  Flagstaff 

Batavia:  Observatory 

Buitenzorg:  Palace  tower  .. 
Boompjeo  Island:  Racket  I. 

Cheribon :  Light-house 

Tegal:  Flagstaff 

Pekalongan:  Light  W.  of  entrance. 

Samarang:  Light-house 

Rembang:  Residency  flagstaff 

Surabaya:  Time-ball  station .'. 

Paauruan :  Light-house 

Madura  Island:  Light-house 

Soemenep  flagstaff 

Besuki :  Light-house 

Cape  Sedano:  NE.  pt.  of  Java 

Banju wangi :  Fort 

Bantenan:  S.  pt.  of  Java 

Barung  Island:  S.  pt 

Kambangan  Island:  Light-house  .. 
Cape  Anjoe:  Extreme 


Lat.  s. 


Karimon  Djawa  Island:  Flagstaff 

Rawean  Island :  Sangkapura  flagstaff 

Great  Solombo  Island:  N W.  pt 

Arentes  Island :  S.  pt 

Bali  Island:  Bliling  light-house 

Peak,  11,326  ft 

Badong  Bav,  Kotta  village. 

Lombok  Island:  Peak  12,379  ft 

Ampenam  light 

Sumbawa  I. :  Sumbawa  village 

Tambora  Volcano,  sum- 
mit E.  side  of  crater 

Bima,  flagstaff 

Postilion  Islands:  N.  island 

Maria  Reigersbergen  I 

Ardassier  Islands:  S.  id 

Brill  Reef:  Light-house 

Hegadis  Island 

Token  Bessi  I. :  Wangi-Wingi,  NW.  pt. 

Binongko,  S.  pt 

Gunong  Api :  Volcano 

Lucipari  Islands:  N.  islet 

Flores  Island :  Reo  village 

Ende  village 

Flores  Head,  extreme 

Komba  Island:  Peak,  S.  part 

Adenara Island:  Summit,  Mount  Woka. 

Lombata  Island:  Mount  Lamararap 

Pantar  Island :  S.  peak  of  saddle  on  S.  pt 

Ornbay  Island :  Dololo  anchorage 

Timor  Island:  Deli,  custom-house 

Atapopa  

Koupang,  Fort  Concor- 
dia   

Rotti  Island:  W.  pt 

Saru  Island:  Seba  Bay,  on  NW.  side 

Sandalwood  Island :  Nangamessie 

Wetta  Island :  Ilwaki  road 

Roma  Island:  W.  pt 


6  04  15 
6  01  20 
6  07  40 
6  35  45 

5  56  15 

6  43  00 
6  51  09 
6  51  29 
6  57  09 

6  42  18 

7  12  10 
7  37  30 
7  02  00 
7  02  30 
7  43  25 

7  49  00 

8  12  30 
8  47  00 
8  32  00 
7  46  30 

7  25  00 

5  52  57 
5  51  18 
5  32  28 

5  05  46 

8  05  30 
8  21  00 
8  42  30 
8  23  00 
8  34  15 
8  32  00 

8  12  30 

8  27  00 

6  31  00 

7  30  00 

7  35  00 
6  05  50 
6  07  00 

5  15  00 

6  17  00 

6  43  00 
5  28  30 

8  16  15 
8  50  55 
8  04  45 

7  48  00 

8  20  30 
8  33  00 
8  34  00 
8  12  00 

8  34  00 

9  00  00 

10  09  54 

10  46  00 

10  29  00 

9  35  03 

7  53  00 
7  38  00 


Long.  E. 


105  53 

106  08 
106  48 
106  49 
108  22 

108  34 

109  08 

109  41 

110  25 

111  20 

112  43 
112  55 

112  41 

113  53 

113  41 

114  26 
114  22 
114  25 
113  15 
109  02 
106  24 


Lun.  Int. 


Range. 


H.  W. 


110  25  29 
112  39  10 
114  23  42 

114  35  00 

115  03  48 
115  28  00 

115  08  47 

116  27  30 

116  04  09 

117  20  33 

117  57  00 

118  43  55 
118  43  00 
117  56  00 

117  22  00 

118  56  50 

122  40  00 

123  32  00 
123  59  00 

126  43  30 

127  30  00 

120  29  55 

121  38  40 

122  52  00 

123  31  00 
123  15  00 

123  22  00 

124  06  00 

124  23  00 

125  33  57 
124  52  00 

123  33  57 
122  52  00 
121  46  00 
120  14  30 

126  22  00 

127  19  00 


7  11 


[11  58] 


[6  00] 


12  07 
11  44 


10  00 


8  33 


10  50 


7  50 


0  00 


L.  W. 


Spg. 


Neap. 


h.    m. 
0  58 


ft- 
2.4 


ft. 
0.7 


[5  46] 


[3.0] 


[12  13]  [4.0] 


5  54 
5  31 


3  45 


2  21 


4  38 


1  37 


6  12 


0  45 


10  50 


6  58 


4  37 


11  20 


4.9 
6.2 


7.8 


i.7 


5.8 


5.7 


5.7 


8.5 


1.7 
2.3 


2.6 


5.2  I   1.8 


3.0 


2.0 


2.0 


2.0 


2.9 


5  07 


16.5 


5.6 


Page  244] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Continued. 


Lun.  Int. 


Place. 


Moa  Island:  Bu^alo  Peak,  4,100  ft 

Sermalta  Island :  NE.  pt 

Damma  Island :  Kulewatta  Harbor,  N.pt. 

Nila  Island :  Center. 

Mano  or  Bird  Island:  NW.  extremity.. 
Timor  Laut  Island:  Olilet,  on  E.  coast.. 

Vordate  Island :  S.  pt 

Mulu  Island :  N.  pt 

Arm  Islands:  S.  island 

N.pt 

Great  Ki  Island :  S.  pt 

Tello  Islands:  S.  island,  summit 

Tehor  Island:  NE.  pt 

Matabella  Islands:  Kukur 

Goram  Islands:  Goram  Mosque 

Banda  Island:  Mole 

Bouro  Island,  Kajeli :  Fort  Defense 

Ceram  Island :  Kawa 

Amboina  Island:  Light-house 

Xulla  Islands,  Taliabo  Island:  NW.  pt. . 

Mangola  Island:  E.  pt  .. 

Besi  Island:  E.  pt 

Oby  Major  Island :  W.  pt 

Popa  Island:  Outer  Extremity  Bay 

Mysole  Island :  Ef be  Harbor 

Gebey  Islands:  NW.  pt 

Gillolo  Island:  Cape  Tabo:  E.  extreme . 
Cape  Salawag:  NE.  pt . . 
Derrick    Point:  N.   ex- 
treme   

Molucca  Is. ,  Makkian  I. :  Fort  Reeburgh . 
Ternate  Island:  Residency 
flagstaff 

Batian  Island :  Church 


Meiaco-Sima  Is.,  Kumi  I:  N.  Beach  ... 
Broughton  Bay:  Land- 
ing place  

Port  Haddington: 

Hamilton  pt 

Tai-pin-san:  Hirara, 

Karimata  Anch 

Raleigh  Rock:  Summit,  270  ft. 

Ti-ao-usu  Island:  Summit,  600  ft 

Hoa-pin-su  Island :  N.  face 

Loo  Choo  Islands,   Great  Loo  Choo: 

Nafa-Kiang 

Yori-sima,  413  ft. . 
Yerabu-sima  peak, 

687  ft 

Kakirouma:  Sum- 
mit, 2,207  ft 

Iwo-sima:   Volca- 
no, 541  ft 

Oho-sima:   N.  ex- 
treme   

Kikai-jima:  Sum- 
mit, 867  ft 


Lat.  S. 


Range. 


8  12 
8  14 
7  03 

6  44 

5  32 

7  55 
7  04 

6  35 


10 
20 
56 
20 
44 
33 
03 
31 
3  22 
2  55 
41 
44 
48 
28 
30 
11 
04 


Lat.  N. 
0  02  02 

0  11  00 

1  26  00 

2  12  00 
0  24  00 

0  47  13 

Lat.  S. 
0  38  03 

Lat.  X. 
24  26  00 

24  21  30 

24  25  00 

24  48  18 

25  55  00 
25  58  30 

25  47  07 

26  12  25 

27  02  00 

27  21  00 
27  44  00 

27  53  00 

28  31  40 
28  18  00 


Long.  K. 


128 
129 

128 


00  I  129 
50  1.30 


131 
131 
131 
134 
134 
132 
131 
131 
131 
131 
129 
127 
128 
128 
122 
126 
126 
127 
129 
130 


01  00 

00  00 

28  00 

29  00 

17  44 

23  30 
55  00 
40  00 

24  00 
40  00 

54  00 
58  00 
47  00 
50  00 

25  23 
53  18 

06  18 

07  04 
10  00 

20  00 

21  19 

01  00 

18  00 

55  48 
12  00 


122  56  00 
124  17  40 

124  06  40 

125  17  57 
124  .35  00 

123  40  00 
123  30  31 

127  40  10 

128  25  24 

128  33  10 
128  59  00 

128  14  30 

129  42  30 
129  59  00 


H.  W. 


L.  W. 


Spg. 

ft. 


Neap. 


7  57 
7  32 


9.0 
4.2 


6.6 
3.1 


2  20 


8  32 


7.5 


5.5 


129  17  30 
128  52  00 
128  37  00 

128  03  30 

127  21  00 


127  22  39  j   5  00 
127  28  21 


11  10 


3.9 


7  27 


1  14 


4.9 


2.1 


6  30 


0  15 


5.8 


2.5 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 

LPage  245 

1 

Place. 

Lat.  N. 

Long.  E. 

Lun 

Int. 

Range. 

H.W. 

L.W. 

Spg.         Neap. 

1 

• 

M 

e 

a 

a 

3 

■a 
S 

Baliibac  Island,  Cape  Melville:  Light- 
house   - 

O          /         If 

7  49  25 

8  20  25 

9  22  30 

9  43  43 
10  50  00 

10  29  19 

11  26  25 

10  51  26 

11  09  09 
11  25  47 

11  53  53 

12  02  09 
12  39  46 

11  54  28 

12  06  45 

12  20  03 

12  50  15 

13  28  40 
13  31  35 
13  06  05 

12  17  15 

13  49  30 
13  45  22 

13  56  17 

14  12  20 
14  21  48 

14  22  27 
14  29  50 
14  35  49 
14  35  31 
14  52  36 

14  55  33 

15  19  30 
15  34  48 

15  45  43 

16  04  06 
16  27  15 

16  37  15 

17  11  43 

17  16  55 
17  33  56 

17  47  17 

18  01  09 

18  31  08 
18  39  02 
18  21  43 

18  28  32 
18  32  02 
18  50  26 

18  52  54 

19  03  03 
19  22  00 
19  80  00 

O            /         II 

117  00  00 

117  09  35 

118  17  30 

118  43  03 

119  31  10 
119  05  36 

119  29  55 
121  00  25 

120  56  26 
120  45  38 
120  00  48 
120  12  56 

120  27  18 

121  30  24 
121  20  10 

121  03  33 
120  44  42 
120  22  33 

120  59  17 

121  29  20 
121  01  53 

120  09  58 

121  02  56 
120  43  37 

120  38  10 
120  36  40 

120  33  48 
120  54  40 
120  57  19 
120  58  06 
120  13  52 
120  00  15 
119  57  11 
119  54  16 

119  54  00 

120  06  01 

119  56  10 

120  18  25 
120  26  14 

120  25  07 
120  22  51 

120  25  04 
120  28  44 

120  35  35 

120  50  53 

121  37  27 

122  04  14 
122  05  49 
121  48  26 
121  15  42 
121  11  28 
121  32  00 
121  52  00 

h.     m. 

h.     m. 

Si. 

ft. 

Paldwan  Island,  Cape  Bovliluyan:   S. 
extreme 

Victoria  Peak,  5,680  ft. 
Port   Royalist:     Tide 

Pole  Pt.  Light 

Taytay  Fort 

Port  Barton :  Bubon  Pt. 
Kabuli  I. :  Summit,  N. 

extreme 

[11  30] 

[5  20] 

[6.5] 

Cuyo  Island :  Obs.  spot 

Agutaya  Islet:  Summit  of  Mt.  Aguade. . 
Quiniluban  Islet:  Summit 

• 

Culion  Island:  Fort l 

Busuanga  Island:  Mt.  Tundalara 

Apo  Islet:  Summit 

Caluya  Island :  Summit 



Semerara  Island :  N.  extremity 

tremity 

Sablayan  Pt.,Vantay. 

Monte  Calavite 

Escarceo  Pt 

j 

Pt.  Dumaly 

Ylin  Island 

Lubang  Island,  Port 

Tulig 

Luzon  Island,  Batangas:  Ast.  station... 

Balayan:  Plaza  Rizal 

Loro  Peak :  Summit,  3, 985 
feet 

[11  07] 

[4  50] 

[4.9] 

Caballo  I.:  Light-house  . 
Corregidor Island:  Light- 
house   

[10  22] 

[3  56] 

[4.4] 

Cavite:  SangleyPt.  light. 
Manila:  Pasig  light-house 

Manila:  Cathedral 

Subig:  Town 

10  44 

[4  10] 

[4.6] 

[9  42] 

[4  33] 

[3.8] 

CaponesIslet:Light-house 

Iba:  Ast.  station 

Port  Masinloc:  Bani  Pt.. 

Santa  Cruz:  Plaza 

Sual:  Army  Hospital 

Silaqui  Islet:  Summit  . . . 
Port      San      Fernando: 
Main  street 

[10  20] 
;iO  21] 

[9  40] 



[3  33] 
[3  44] 

[3  29] 

[2.4] 
[2.  3] 

[2.6] 

Candon:  Ast.  station 

Port  Santiago:  Remark- 
able tree  S.  of  port 

Vigan :  Race  track 

Salomague  Island:  Port 
Salomague  flagstaff 

Currimao:  Town >.. 

Capa    Bojeador:    Light- 
house   

Mairaira  Pt. :  Semaphore 
Aparri :  Plaza 

5  43 

-0  02 

3.2 

1.9 

,  Port    San    Vicente:  San 
Vicente  Islet 

CapeEngano:  Rona  Islet 

Camiguin  I. :  Summit 

Fuga  Island:  W.  summit. 
Dalupiri  Island :  Peak . . . 
Calayan  Island :  NE.  pt 

6  00 

-0  12 

5.0 

2.7 





Babayan  Claro  Island :  W.  pt 



Page  246] 


APPENDIX  IV. 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 


Place. 


Lat.  N. 


Balingtang  Islands 

Batan  Island :  Morfnt  Irada 

Ibayat  Island :  Mount  Santa  Rosa 

Yami  Island:  Islet  off  SW.  part 

Luzon  Island,  Port  Dimasalasan:  En- 

f  1*3.11  OP 

Polillo  I.V  PoVt'PoliYlo' '. 
Tabaco:  Church  belfry  . 
Cautanduanco   Islands: 

N.  islet 

Cautanduanco  Islands: 

S.  extreme 

Point  Calaan :  S.  extreme' 
Port  Sorsogon,  Tinacos 

Islet 

Masbate  Island,  Palanog:  Pier 

Bugui  Pt.  light-house.. 
Camasusu  I.:  Summit . 
Tintolo Point:  Extreme 

Burias  Island :  Busainga 

Marinduque  I. :  Summitof  MountCatala. 
Maestro  de  Campo  Island,  Port  Con- 

cepcion:  Point  Fernandez 

Ban  ton  Island :  Ban  ton  Mountain 

Tablas  Island :  Tablas  Head 

Sanguilan  Pt 

Carabao  Island:  W.  pt 

Romblon  Island:  Sabang  Pt.  light 

Summit  over  port 

Sibuyan  Island :  Summit 

Samar  Island,  Guiuan :  Pier 

Catbalogan :  Fort 

Maripipi  Island:  Summit ^ . . 

Leyte,  Tacloban 

Ormoc:  Ast.  station 

Palompon :  Church 

Maasin 

Bohol  I.,  Lapiniu  I. :  Mount  Basiao 

Cebu  Island,  Cebu :  Plaza 

Siquiquor  Island,  Port  Canoan:  S.  pt.  of 

entrance  

Negros  Island,  Port  Bunbonon:  E.  pt. 

of  entrance 

Dumaguete :  Town 

Volcano  of  Malaspina, 

8,192  ft 

Bacalod:  Town 

Guimaras  I.,  Inampulugan  I.,  SW.  pt .. 

Panay  Island,  Iloilo:  Fort 

San  Jos^ 

Pan  de  Azucar 

Batbatan Island:  Summit 
Pucio  Point:  Extreme... 

Port  Batan:  Village 

Capiz:  Town 

Siargao  Island,  Port  Sapao:  Semaphore. 

Gibdo  Island :  Semaphore 

Bucas  Island:  E.  pt.  of  Port  Sibanga . . . 

Mindanao  Island:  Surigao 

Cape  St.  Augustin . . . 

Mindanao  Island,  Davao:  Mole 

Saranguni  Islets:  W. 

islet 

Basianang    Bay:  N. 
pt.  of  Donauang  I. 
Polloc:     Small    hill 
back  of  town 


19  58  30 

20  28  30 

20  48  00 

21  04  56 

17  20  17 
14  51  00 

13  21  33 

14  09  00 

13  28  30 
12  31  20 

12  52  20 
12  22  10 
12  36  00 

12  10  03 

11  56  09 

13  07  40 
13  18  10 

12  54  03 
12  56  56 
12  38  42 
12  33  44 
12  03  15 
12  36  00 
12  35  33 
12  24  55 
11  01  30 
11  46  44 
11  47  30 
11  15  08 
11  00  17 
11  02  37 
10  07  39 
10  03  22 
10  17  30 

9  15  17 

9  03  37 
9  18  25 

10  24  35 
10  40  21 
10  26  38 
10  41  27 

10  44  08 

11  16  47 
11  28  20 
11  45  30 
11  35  40 
11  35  06 
10  11  26 

9  53  00 
9  41  34 
9  47  53 

6  14  30 

7  01  22 

5  22  30 

6  28  50 

7  21  15 


Long.  £. 


122  14  00 
122  01  20 
121  52  30 

121  58  24 

122  19  20 
121  54  48 

123  43  53 

124  06  48 

124  04  48 
124  04  18 

123  49  22 
123  35  58 
123  14  36 
123  12  47 
123  07  34 

123  02  45 
121  54  33 

121  43  08 

122  04  48 
122  08  38 
121  58  32 

121  53  53 

122  17  08 
122  16  26 

122  33  23 
126  43  14 

124  51  37 
124  18  15 
124  59  56 
124  36  20 
124  22  07 
124  50  15 

124  32  35 

123  54  18 

123  34  26 

123  06  09 
123  18  43 

123  07  05 
122  55  42 
122  40  20 
122  34  26 

121  54  27 

122  09  09 
121  52  36 

121  58  59 

122  28  50 

122  45  03 
126  02  53 

125  31  17 
125  58  22 
125  28  30 
125  47  48 
125  34  35 

125  13  48 

123  57  37 

124  11  42 


Lun.  Int. 


Range. 


H.  W. 


L.  W. 


Spg. 


Neap. 


h.    m. 


h.    TO. 


ft- 


ft- 


6  08 


0  00 


5.2 


2.8 


[4  30] 


[10  20] 


[5.5] 


6  53    1  25 


1.5 


1.1 


11  47 


4  50 


2.8 


2.0 


11  06 


5  22 


4.2 


1.9 


[11  40] 


[6  15] 


[6.5] 


6  00 


-0  13 


6.9 


5.1 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  A  RIA— Continued. 

[Page  247 

o 

i 

g 

• 

» 

e 

a. 
a. 

a 

i 
2 

i 

£ 

e 

Place. 

Lat.  N. 

Long.  E. 

Lun. 

Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

Mindanao  Island,  Santa  Cruz  Islands: 
SE  islet 

o        /         // 

6  52  15 

6  54  03 

7  18  05 

7  45  41 

8  40  15 

8  08  29 

9  10  19 
10  43  00 
10  27  00 

9  35  30 

7  43  00 

7  00  38 
4  54  10 
4  49  30 

4  55  30 

5  50  00 
5  00  30 
5  13  00 
5  25  15 
5  27  10 
5  32  40 
5  41  30 
5  44  30 

5  54  45 

6  02  30 
6  03  40 

5  52  30 

6  15  15 
6  42  43 

35  39  00 

36  02  50 

36  45  29 

37  24  00 
37  27  41 
37  34  10 

37  36  00 

38  23  37 

38  58  16 

39  09  00 

38  56  00 

40  35  00 

39  30  46 
39  16  00 
38  43  17 
38  47  50 

38  52  38 

38  40  00 

39  04  00 

38  27  00 
37  58  00 
37  27  40 
36  26  45 
36  24  30 
36  07  00 

O             1         II 

122  04  00 
122  04  52 

122  03  18 

122  04  58 

123  23  13 

123  50  44 

124  42  50 
121  33  00 
121  03  00 

121  23  30 

118  27  00 

118  26  06 

119  22  45 
119  48  00 
119  46  45 

118  11  00 

119  44  15 

120  40  45 
120  35  00 
120  11  30 
120  48  25 
120  49  45 

120  55  00 

121  00  40 

121  18  20 
120  58  40 

119  55  55 

120  29  30 

121  56  50 

119  51  30 

120  17  30 

122  16  48 
122  42  00 
122  15  05 

121  31  09 

121  26  21 

120  55  00 
117  42  48 

117  11  44 

118  31  00 

122  00  00 

121  18  03 
121  35  59 
121  08  26 
121  15  54 

121  51  59 

122  11  30 

123  10  34 

124  34  40 
124  34  30 
126  36  27 
126  28  00 
126  24  00 
126  01  09 

h.  m. 

h.  TO. 

ft. 

/t. 

Zamboanga:  Fort... 
Sibuco  Bay:  Hill  S. 
of  beach 

6  50 

0  42 

3.8 

2.8 

Port     Sta.      Maria: 
Fort 

Dapitan:  Village 

Misamis:  Fort 

Camiguin  Island:  Mount  Camiguin 

Sombrero  Rock :  Center       

1 

[10  48] 

[4  50]!  [5.1] 

1 

Piedra  Blanca :  Center         .... 

Cagayanes    Islands:  Rocky    islet     be- 
tween two  larger  islands  . . 

San  Miguel  Isles:  E.  pt.  of  Manuk  Ma- 
nukan 

Cagayan  Jolo   Island:   Middle  of  W. 
coast                        .... 

Omapui  Island:  NW.  extreme 

Sibutu  Island:  Hill  on  E.  coast 

Simonor  Island:  NW.  pt                

1 

Bahaltolis  Island:  Sandakan  Harbor... 
Bongao  Island :  S.  pt 

1 

Keenapoussan  Island :  Center . 

Bubuan  Island :  Lagoon  entrance 

Cuad  Basang  Island:  SW.  pt 

1 

i 

Siassi:  Town 

5  54 

-0  18 

8.6 

6.4 

Bulipongpong  Island :  Center  hill 

Tapul  Island:  Center  hill,  1,676  ft 

Jolo  Islands:  Maimbun  Anchorage,  dry 
bank 

i 

Dalrymple  Harbor,  Tul- 
yan  Islet    

Jolo  light-house 

[9  38] 

[3  10] 

[5.0] 

Doc  Can  Islet:  W.  extreme  . . 

Pangituran  Island:  SW.  pt.   ..     .... 

j  _ 

Basilan  Island :  La  Isabela 

W^ang-kia-tia  Bay:  Langwang  temple  .. 

Kyauchau  Bay :  Yunuisan  light 

Staunton  Island:  Landing  place,  N.  side. 

Shantung  Promontory:  Light-house 

Weihaiwei:  Light,  S.  side  harbor 

Chifu:  Light-house 

4  50 

11  03 

11.4 

6.0 

4  00 

9  20 

10  25 

10  12 

3  08 

4  13 

6.8 
9.0 

8.1 

5.0 
6.6 
6.0 

Fort 

Miautao  Island:  Peak  of  N.  Island 

Pei-ho:  S.  Taku  Fort,  S.  Cavalier 

Tientsin:  Shore  opp.  NE.  angle  of  wall. . 

Shaluitien  Island:  Light-house 

Niuchwang:  Lightship 

6  50 

1  00 

4.5 

3.3 

4  30 

10  50 

11.7 

8.7 

Hulu-shan  Bav:  N.  side 

1 

Liao-ti-shan  Promontory:  SW.  pt.  light 
Port  Arthur:  Obs.  spot 

1 

10  05 

3  53 

7.5 

5.5 

Ta-lien-wan  Bay:    Isthmus  on  S.  San- 
shan  I 

Round  Island :  Summit 

Thornton  Haven,  Hai-yun-tan  Island: 
Beach  opposite  Temple  Point 

Choda  Island:  S.  pt 

Sir  James  Hall  Islands:  N.  island 

Chemulpo :  So  W^olmi 

4  19 

10  31 

28.8 

11.6 

Marjoribanks  Harbor:  Manzoc  Islet 

Tas  de  foin  Islet:  Center 

Guerin  Island:  Summit,  969  ft..   .. 

1 

Page  248] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

EAST  COAST  OF  ASIA— Continued. 


Place. 


Lat.  N. 


Kokoun-tan  Islands:  Camp  Islet 

Barren  Island :  Center,  600  ft 

Sea  Rock:  Center,  160  ft 

Modeste  Island:  N.  peak,  1,228  ft 

Ross  Island:  Peak,  1,920  ft 

Kuper  Harbor:  NE.  extreme  of  Josling  I . 
Port  Hamilton:  W.  pt.  of  Obs.  Island.. 

Bate  Islands:  Summit  Thornton  Islet 

Montravel  Island:  Center,  1,041  feet 

Quelpart  Island:  Beaufort   I.,  middle 

of  W.  side 

Observation  Island:  Point  of  W.  arm... 

Sentinel  Island:  Summit,  400  feet 

Broughton  Head :  Extreme 

Tsau-liang-hai  Harbor:  Light-house 

Tsu  Sima :  Observation  rock 

Iki  Sima:  Summit,  S.  end  of  island 

Oro  No  Sima:  Summit,  277  ft 

Kosime  No  Osima:  Summit  Wilson  I. . . 

Yeboshi  Sima:  Light-house 

Yobuko  Harbor:  Bluff  opposite  Nicoya. 

Hirado  No  Seto:  Taske  light 

Goto  Island :  Ose  Saki  light 

Pallas  Rocks:  S.  rock 

Meiaco  Sima:  Ears  Peak 

Nagasaki :  Transit  Venus  Station 

Kuchinotsu :  Light-house 

Kagoshima:  Breakwater  light 

.Tsukarase  Rocks:  Summit,  96  ft 

Uji  Shima:  High  peak,  1,097  ft 

Yamagawa  Harbor:  Spit  N.  of  town 

Satano  Misaki :  Light-house 


Kusakaki  Jima:  Ingersoll  Rocks,  530  ft. 

Kuro  Sima:  2, 160  ft 

Iwo  Shima:  Peak,  2,469  ft 

Yakuno Shima:  Mount Matomi,6,252 ft. 

Firase  Rocks:  Highest,  92  ft 

Kuchino  Shima:  Summit,  2,230  ft 

Guaja  Shima:  Summit,  1,687  ft 

Naka  no  Shima:  Peak,  3,400  ft 

Suwanose  Jima:  Volcano,  2,706  ft 

Tokara  Jima:  Summit,  860  ft 

Yoko  Shima:  Summit,  1,700  ft 


Shimonoseki  Strait:  Meji  Zaki,  extreme. 

Rokuren  Island :  Light-house 

Shirasu  Reef:  Light-house 

Susaki:  SW.  battery 

Tomo  Roads:  Tamatsu  Sima 

Port  Okayama:  Take  Sima  temple 

Wusimado  Pt. :  Wusimado  Peak,  548  ft. 

Akashi-no-seto:  Maico  Fort 

Hiogo:  Wada  Misaki  light 

Kobe:  Light-house 

Osaka:  Fort  Temposan  light 

Sakai:  Pier-head  light 

Osaki  Bay :  Tree  Islet,  S.  pt 

Yura  No  Uchi:  Pier 

Tanabe  Bay:-  Fossil  pt 

Oo-sima  Hbr. :  Kashinosaki  light,  E.  pt. 

Uragami  Harbor:  Village  pt 

0\va.shi  Bay:  Hikimoto 

Mura  Harbor:  Osima  Islet 


35  48  08 
35  21  00 
34  42  00 
34  42  30 
34  06  00 
34  17  20 
34  01  23 
33  57  00 
33  59  00 

33  29  40 

34  39  00 
34  33  00 

34  48  00 

35  07  15 

34  18  55 
33  44  30 
33  52  10 
33  53  50 
33  41  30 
33  32  30 
33  23  31 
32  36  45 
32  13  12 
32  03  00 
32  43  21 

32  36  05 
31  35  39 
31  20  00 
31  12  00 
31  12  43 
30  59  30 

30  51  00 
30  50  00 
30  47  00 
30  17  00 
30  05  00 
29  59  00 
29  54  00 
29  52  00 
29  38  00 
29  08  00 
28  47  30 

33  57  46 

33  58  53 
33  59  11 

33  23  19 

34  22  37 
34  35  58 
34  37  27 
34  38  05 
.34  39  20 
34  41  18 
34  39  45 
34  35  12 
34  07  42 
33  57  34 
33  41  14 
33  28  15 

33  33  37 

34  06  10 
34  13  ^ 


Lun.  Int. 


Long.  E. 


Range. 


H.W. 


126  31  00 

125  58  00 

126  19  45 
125  16  00 

125  07  00 

126  35  28 

127  18  34 
126  18  00 
126  55  00 

126  58  25 

128  14  00 
128  40  00 

128  44  00 

129  02  10 

129  13  06 

129  42  30 

130  02  00 
130  25  20 
129  58  50 
129  52  43 
129  33  21 
128  36  10 
128  04  39 

128  25  00 

129  52  25 

130  13  40 
130  33  49 
129  46  20 

129  29  00 

130  37  00 
130  39  30 

129  28  00 

129  55  30 

130  18  00 
130  32  00 
130  03  00 
129  56  00 
129  33  00 
129  52  30 
129  42  00 
129  13  30 

129  01  30 

130  57  50 
130  52  07 
130  47  36 
133  17  00 
133  23  23 

133  59  24 

134  09  21 

135  01  51 
135  10  56 
135  11  34 
135  26  00 
135  27  44 
135  08  19 
135  07  21 
135  23  04 
135  51  59 

135  54  25 

136  14  35 
136  48  61 


9  06 


7  36 

8  56 


L.  W. 


9  23 


7  54 


6  40 


7  20 


30 


5  55 
11  16 


h.    111. 


2  52 


10.5 


1  23 

2  44 


7.0 


3  10 


6.4 


1  41 


1  00 


8.4 

ib'.h' 


1   08 


9.5 


2  20 


6.7 


12  08 
5  04 


6.0 
10.2 


7  30 


6  23 


1  26 


4.7 


0  10 


4.7 


Neap. 


ft. 


4.2 


3.0 
2.4 


2.5 


3.5 
*4."4 


3.9 


2.4 


2.0 

4.5 


2.0 


2.0 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 


[Page  249 


Place. 


Matoya  Harbor:  Anori-saki  light 

Oinoi  Saki:  Light-house 

Shimizu  Bay :  Mound  on  pt 

Mikomoto  Island :  Light-house 

Simoda  Harbor:  Center  I 

Yokosuka  Harbor:  Eyi  Yama  pt 

Yokohama:  P^nglish  Hatoba  light 

Tokio:  Naval  Observatory 

No  Sima  Saki:  Light- house 

Vries  Island  (O  Sima)  Volcano:  Sum- 
mit, 2,512  ft 

Kozu  Shima  V^olcano:  Summit,  2,000  ft. 

Mikake  Jima:  Summit,  2,690  ft 

Redfield  Rocks:  S.  rock 

Mikura  Jima:  Summit 

Broughton  Rock:  Summit,  60  ft 

Fatsizio  Island :  Observation  spot 

Aoga  Shima:  Center 

Bayonnaise  Island:  Summit,  26  ft 

Smith  Island :  Summit,  250  ft 

Ponafidin  Island:  Summit,  1,328  ft 

Lots  Wife  Rock:  Summit,  300  ft 

Inaboye  Saki :  Light-house 

Kinkwosan  Island:  Light-house 

Kamaishi  Harbor:  SE.  end  of  village  . . 

Yamada  Harbor:  Ko  Sima,  90  ft 

Siriya  Saki:  Light-house 

Toriwi  Saki:  Center  of  Low  Islet  off  . . . 

Awomori:  Light-house 

Tatsupi  Saki:  N.  side 

Bittern  Rocks:  SW.  rock 

Tobi  Shima:  Takamori  Yama 

Awa  Sima:  NE.  extreme 

Sado  Island:  Ya  Saki 

Fushiki  Harbor:  Light-house 

Cape  Roigen :  Extreme 

Niigata:  Buddhist  temple 

Mana  Sima:  Summit,  200  ft 

Manao  Harbor:  Sorenjo  Pt 

Tsuruga:  Town 

Oki  Islands:  N.  pt 

Taka  Yama  (Cape  Louisa) :  Extreme. . . 

Ai  Sima:  Summit,  300  ft 

Mino  Sima:  Summit,  492  ft 

Kado  Sima:  Tsuno  Shima  light 

Hakodate:  Light-ship 

Endermo  Harbor:  Bluff  on  E.  side 

Okishi  Bay:  Light-house 

Noshiaf  Saki :  Light-house 

Nemuro:  Benten  Sima  light 

Notsuke  Anchorage:  Village 

Noshiaf  Misaki :  Light-house 

Risiri  Islet:  Peak,  5,713  ft 


Lat.  N. 


Kunashir  Island:  St.  Anthonys  Peak . 

Iturup  Island :  NE.  pt 

Urup  Island:  Cape  Vanderlind 

Broughton  Island :  Summit. . .  y. 

Simusir  Island:  Prevost  Peak 

Ketoy  Island:  S.  pt 

Matana  Island:  Peak 

Shiash-Kotan  Island :  Center 

Kharim-Kotan  Island :  Peak 

Oune-Kotan  Island :  SW.  pt 

Moukon  rushi  Island :  Center 

Poro  musir  Island:  Fool's  Peak 

Soumshu  Island :  Center 


Lun.  Int. 


34  21  57 

34  35  52 

35  00  51 
34  34  25 

34  39  49 

35  17  30 
35  26  52 
35  39  18 
34  54  17 

34  43  30 
34  13  15 

34  05  00 
33  56  50 
33  52  00 
33  39  00 

33  04  24 
32  29  00 
32  00  40 
31  27  00 
30  28  26 
29  46  28 

35  42  13  I 

38  16  57  1 

39  16  30  I 

39  27  17 
41  25  58 
41  33  34 

40  50  00 

41  16  17 

40  31  00 
39  12  02  I 
38  29  23  ' 
38  19  55  I 

36  47  47  I 

37  28  00 
37  55  14 
37  35  00 
37  02  37 

35  40  24 

36  30  00 

34  40  00 
34  32  00 
34  48  00 
34  21  12 

41  47  36 

42  19  54 

42  56  52 

43  22  56 
43  20  22 

43  33  11 
45  26  30 
45  11  00 

44  20  00 

45  38  30 

45  37  00 

46  42  30 

47  02  50 

47  17  30 

48  06  00 

48  52  00 

49  08  00 
49  19  00 

49  51  00 

50  15  36 
50  46  00 


Long.  E. 


Range. 


H.  W. 


136  54  09 
138  13  49 
138  31  19 
138  56  30 

138  57  30 

139  39  43 
139  38  41 
139  44  30 
139  53  24 


139  23 
139  08 
139  31 

138  48 

139  34 
139  17 
139  50 

139  43 

140  00 
140  02 
140  14 
140  19 

140  52 

141  35 
141  52 
141  59 
141  27 
140  56 
140  44 
140  22 
139  31 
139  32 
139  15 

138  27 
137  03 
137  22 

139  03 
136  54 
136  58 
136  01 
133  23 
131  36 
131  18 
131  09 
130  50 

140  41 

140  59 

144  52 

145  49 
145  34 
145  18 

141  38 
141  19 


146  15  00 
149  14  00 

149  34  00 

150  28  30 

151  52  50 

152  24  00 

153  12  30 

154  08  00 
154  39  00 
154  44  00 
154  32  00 
156  15  20 
156  26  00 


5  52 


5  52 


5  25 


5  04 


L.  w. 


Spg. 


Neap. 


4  30 


2  30 


11  41 


3  40 
3  32 
3  41 
3  48 

3  33 

4  50 


12  04 


12  04 


11  30 


11  17 


10  45 


8  42 


5  28 


10  00 
9  45 
9  53 

10  00 
9  46 

11  05 


4.3 


3.9 


4.9 


3.7 


3.4 


0.6 


1.1 


3.0 
3.5 
3.0 
3.1 
2.1 
3.7 


ft. 
1.7 


1.6 


1.9 


1.4 


1.3 


0.4 


0.5 


1.8 


^''    Or-  the' 
l^NIVERSITY 


^^' 


Page  250]                                       APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
EAST  COAST  OF  ASIA— Continued. 

*s 

Place. 

Lat.  N.            Long.  E. 

Lun.  Int. 

Range.         1 

H.  W. 

L.  W. 

Spg. 

Neap. 

t 

0 

i 

t 

9 
P 

Cape  Clonard :  E^reme 

O          >          t>                  O            1           II 

36  05  45  !  129  33  30 

36  36  00  1  129  20  00 

37  09  30  1  131  55  00 
37  30  00  '  130  53  00 

39  19  12     127  32  48 

42  14  30  !  137  17  00 
42  38  05  1  130  48  45 

42  33  40  1  131  10  00 

43  05  13     131  53  56 

42  41  00     133  02  00 

43  22  00     135  15  00 

43  53  40  j  135  27  19 

44  30  00     136  02  00 
44  43  45      136  22  30 

44  46  15  !  136  27  15 

45  05  00      136  44  00 

h.    m. 

h.    m. 

ft. 

ft. 

Ping-hai  Harbor 

Liancourt  Rocks:  Summit,  410  ft 

Matu  Sima:  Peak,  4,000  ft 

i 

■  1 

1 

Port  Lazaref:  S.  IJ  miles  from  the  S. 
end  of  Bontenef  I 

i 

Wawoda  Rock :  Summit,  12  ft 

Expedition  Bay :  Light-house 

Port  Novogorod :  Light-house 

Vladivostok :  Cape  Galdobin  light 

Caj>e  Povorotnyi :  Light-house 

2  45 

9  00 

1.9 

0.8 

Port  Olga:  Light-house 

St.  Vladimir  Bay:  Orekhera  Pt 

Shelter  Bay 

Sybillo  Bay 

Pique  Bay 

Bullock  Bav                                  

Luk^  Point:  Extreme 

45  19  30 
45  41  30 

47  20  00 

48  59  30 
51  28  00 

45  53  10 

46  01  20 
i4  24  30 
53  08  05 

55  11  00 

56  25  28 
56  22  30 
59  19  45 

51  02  00 

52  52  37 

53  04  30 

54  56  00 
54  32  24 
56  10  00 

58  26  00 

59  55  00 

62  14  30 

60  18  00 

63  12  00 

64  16  00 
64  25  55 
64  24  30 
64  46  00 

137  10  15 

137  38  15 

138  58  00 
140  23  40 
140  48  00 

142  04  51 

143  26  30 

142  46  30 
140  42  58 

137  40  00 

138  25  50 

143  15  45 
143  07  14 
156  46  00 

158  46  42 
160  04  00 
166  43  00 
168  09  00 
163  24  00 
163  34  00 
170  22  00 
179  04  30 

Long.  W. 

172  04  00 

159  50  00 

173  10  00 
173  07  15 
172  12  30 
172  07  00 

Cape  Disappointment:  Extreme 

Cape  Suff ren :  Extreme 

Cape  St.  Nikolaia:  Light-house 

De  Kastri :  Light-house * 

9  50 

10  45 

3  40 

4  40 

2.7 
6.3 

1.1 
2.6 

Sakhalin  I.,  Cape  Notoro:  Light-house. 

Cape  Siretoku:  Extreme  .. 

Cape  Elizabeth:  N.  pt 

Nikolaevsk:  Cathedral 

11  20 

5  08 

4.2 

1.7 

Great  Shantar  Island  :N.  pt   

Port  Aian:  Cape  Vneshni 

0  10 

7  30 

8.4 

3.4 

St.  Jona  Island:  Summit,  1,200  ft 

Okhotsk:  Battery 

::: i : 

Cape  Lopatka:  Extreme 

3  55 
3  30 

10  08  !     4.  6 

1.9 
2.1 

Petropavlovsk :  Rakof  light 

9  45 

5.1 

Cape  Shipunski :  Extreme 

Bering  Island:  Cape  Khitroff 

Mednoi,  or  Copper  Island :  SE.  extreme. 
Cape  Kamchatka:  Extreme 

Karajinski  Island :  S.  pt 

Cape  Oliutorski:  Extreme,  2,480  ft 

Cape  Navarin:  Extreme,  2,512  ft 

St. Matthew  Island:  Cape  Upright,  SE.  pt 
St  Lawrence  Island:  N  pt 

6  00 

12  15 

4.5 

1.8 

1 

Cape  Tchoukotskoi'  Extreme 

Port  Providence:  Emma  Harbor 

Cape  Indian :  Extreme                  

Arakam  Island :  Cape  Kiguinin 

Anadir  River*  Mouth 

1 

Long.  E. 

64  50  00     178  40  00 

Long.  W. 

65  00  30  [  175  54  00 

66  02  00     169  32  30 

1 

Cape  Bering'  Extreme               ' 

East  Cape :  Extreme ...  .... ... 

1 

1 

ISLANDS  OF  THE  PACIFIC. 

m 
0 
Si 

i 

Malpelo  Island:  Summit,  1,200  ft 

Cocos  Island:  Head  of  Chatham  Bay... 

Redondo  Rock*  Summit  85  ft 

4  03  00 

5  32  57 

0  13  30 
0  20  00 
0  18  50 
0  34  25 

81  36  00 
86  69  17 

9l'  03  00 

89  58  43 

90  30  08 
90  44  9.^ 

Towel's  Island:  W.  cliff 

Bindloe  Island:  S.  summit 

Abingdon  Island :  Summit,  1,950  ft 

AVenman  Island:  Summit,  550  ft 

d 

1  22  55        91   49  4.3 

:::;::::::::  i 

tf 

1 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 


[Page  261 


Place. 


Albemarle  Island :  Iguana  Cove 

Marlborough  Island:  Cape  Hammond.. 

James  Island:  Sugarloaf,  1,200  ft 

Jervis  Island :  Summit 

Duncan  Island :  Center  hill 

Indefatigable  Island :  N\V.  bay 

Barrington  Island:  W.  summit,  900  ft.. 

Charles  Island:  Summit,  1 ,780  ft 

Fatu  Huku  or  Hood  Island :  E.  summit, 

640  ft 

Chatham  Island:  Mount  Pitt,  800  ft 

Christmas  Island:  N.  pt.  of  Cook  Islet.. 
Fanning  Island:  Flagstaff,  entrance  to 

English  Hbr 

Washington  Island 

Palmyra  Island 

Baker  Islet:  Center 

Howland  Islands:  Center  island 

Arorai  or  Hurds  Island:  S.  pt 

Tamana  Island :  Center 

Onoatoa  Island :  Center 

Taputeuea  or Drummond Island:  SE.  pt. 

Nukunau  or  Byron  Island:  SH  pt 

Peru  or  Francis  Island:  NW.  pt 

Nonuti  or  Sydenham  Island 

Aranuka  or  Henderville  Island:  W.  pt. 

of  W.  island 

Apamama  or  Hoppers  Island:  Entrance 

islet 

Maiana  Island:  S.  pt 

Tarawa  Island :  NE.  pt 

Apaiang  Island:  S.  pt 

Maraki  Island:  N.  pt 

Taritari  Island:  S.  pt 

Ebon  Atoll:  Rul:)e  Pt 

Jaluit  or  Bonham  Islands:  Jarbor  Pier. 

Burrh  Island:  Port  Rhin,  N.  pt.  of  en- 
trance   

Majuro  or  Arrowsmith  Islands:  An- 
chorage Djarrit  I 

Arno  Atoll:  NE.  pt 

Odia  Islands:  S.  islet 

Namu  Island :  S.  pt 

Jabwat  Island :  Center 

Aurh  or  Ibbetson  Island:  NE.  end,  an- 
chorage   

Maloclab  Islands:  NW.  end  Karen  Islet. 

Wotje  or  Romanzov  Islands:  Christmas 
Harbor 

Litkieh  Island:  NW.  pt 

Ailuk  Islands:  Capenmr  Islet 

Bigar  Islet :  Center 

Kongelab  or  Pescadores  Islands:  Center 
of  group 

Rongerik  or  Radakala  Islands:  Obser- 
vation spot 

Ailinginae  Island:  Easternmost  Islet... 

Bikini  or  Eschholtz  Islands:  W.  ex- 
treme   

Wottho  or  Schanz  Island :  Center 

Eniwetok  Islands:  North  or  Engibil.. 

Ujelang  or  Providence  Island:  Center 
of  atoll 


Lat.  S. 

Long.  W. 

Lun. 

Int. 

Range. 

H.  W. 

L.  W. 

Spg. 

Neap. 

O    /    tl 

0  59  00 
0  31  00 
0  15  20 
0  25  00 
0  36  30 
0  33  25 

0  50  30 

1  19  00 

1  25  00 

0  44  15 
Lat.  N. 

1  57  17 

3  51  26 

4  41  10 

91  29  12 
91  36  00 
90  52  53 
90  43  30 
90  41  00 
90  33  58 
90  06  13 
90  28  13 

89  40  08 
89  16  58 

157  27  45 

159  21  50 

160  24  30 
162  05  00 
176  32  39 

176  43  09 
LonR.  E. 

177  01  13 
176  07  00 
175  39  00 

175  12  20 

176  31  33 
175  57  09 
174  24  00 

173  32  40 

173  51  14 
173  03  30 
173  03  00 
173  07  00 
173  25  30 
172  45  40 

168  41  31 

169  39  31 

171  46  00 

171  24  30 
171  55  51 
168  46  00 
168  03  00 

168  26  00 

171  09  00 

170  49  00 

170  16  05 

169  01  57 

169  59  20 

170  07  00 

167  24  57 

167  35  00 
166  35  00 

166  24  25 
166  04  00 
162  15  00 

161  08  30 

h.   m. 
2  00 

h.  m. 
8  13 

ft. 
6.2 

ft. 
3.1 

2  45 

8  58 

5.2 

2.6 

:::::::::::::::: 

2  00 

8  13 



6.2 

3.1 

2  10 

8  23 

6.0 

3.0 

2  20 
4  25 
6  00 

8  33 
10  38 
12  15 

6.5 
2.4 
2.4 

3.3 
1.4 
1.4 

5  52  15 
0  13  30 

5  25 

11  40 

1.5 

0.9 

0  49  00 
Lat.  S. 
2  40  54 

7  10 

1  00 

6.2 

3.6 

2  35  00 
1  50  00 
1  29  14 
1  23  42 
1  17  14 
0  36  00 
Lat.  N. 

0  11  10 

0  20  54 

0  51  30 

1  38  45 

' 

1 

i 

1 

' 

4  30 

10  45 

4.7 

2.7 

1  44  15 

2  03  00 

4  45 

11  00 

4.7 

2.7 

3  01  30 

4  35  25 

5  55  07 

6  14  00 

7  05  30 
7  09  17 

7  15  00 

8  14  00' 
8  27  00 

8  19  00 

8  54  21 

9  28  09 
10  03  40 

10  17  25 

11  48  00 

11  19  21 

4  45 

11  00 

4.7 

2.7 

5  00 

11  15 

5.0 

2.8 

4  50 

11  00 

6.2 

3.6 

1 

11  24  00 

[ 

11  07  00 

11  40  00 

10  05  00 

11  40  00 

9  39  00 

i     j 



i 

Page252J                                        APPENDIX   IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 

*j 

Place. 

Lat.  X. 

Long.  E. 

Liin.  Int.           1           Range.          1 

H.W.I 

L.  W. 

Spg. 

Neap. 

• 

a 
* 

m 
m 
« 

d 

2 
3 

i 

•9 
n 
« 
* 

« 

■ 
« 

M 

1 

h 
0_ 

4> 
fl 

2 

■d 
« 

Greenwich  Island:  Northern  islet 

• 

Matelotas  group:  Easternmost  of    the 
S.  islands 

0  /          If 

1  04  00 

8  18  30 

9  29  00 
9  52  30 

0        /      n 

154  47  55 

137  33  30 

138  04  00 

139  42  00 

h.    m. 

h.    m. 

ft. 

ft. 

Yap  Island:  Light  in  Tomil  Bay 

Eau  Island :  Center 

7  15 

1  00 

3.4 

1.9 

Uluthi  or  Mackenzie  Islands:  Mogmog 
Islet ; 

10  06  00     139  46  00 

Feys  or  Tromelin  Island:  E.  extreme  .. 

9  46  00 

140  35  00 
140  52  00 
143  11  00 

143  57  30 

144  31  00 

144  36  00 
146  50  00 

145  55  45 

Sorol  or  Philip  Island :  Center 1     8  06  00 

Eauripik  or  Kama  Islands:  E.  islet '     6  40  00 

Oleai  group:  Raur  Islet,  N.  pt 

Ifalik  or  Wilson  Islets:  N.  end 

Faraulep  Island :  S.  end 

7  21  45 

7  15  00 

8  35  00 
8  03  00 
7  43  30 

W.  Faiu  Islet:  Center 

Oliniarao  Islet:  Center 

Toass  Island:  Center 

7  29  30     146  24  30 

7  22  00     147  06  48 

8  09  00     147  42  00 

Satawal  Island :  Center 

Coquille  or  Pikelot  Island:  Center 

Suk  or  Polusuk  Island :  S.  end 

6  40  00 

7  38  00 

8  59  45 
8  25  30 

7  18  30 
5  55  00 

5  29  18 

3  51  00 
7  39  00 

5  48  00 
7  00  35 

6  41  45 

6  14  00 

5  20  06 

6  53  55 

7  02  00 
7  08  00 

7  19  00 

7  40  30 

8  08  00 

4  20  00 
3  02  00 

5  20  00 

13  25  48 

14  07  30 

14  59  22 

15  08  30 

15  17  10 

16  20  00 

16  41  00 

17  17  00 

17  36  00 

18  04  00 

18  46  20 

19  45  00 

20  00  00 
20  32  54 

149  21  00 

Los  Martires:  Ollap  Islet,  N.  pt 

Namonuito  Islands:  Magur  Islet 

Hall  Island:  Namuine  Islet 

149  27  30 

150  14  30 

151  49  15 

151  56  30 
153  13  30 

153  58  00 
155  00  54 
155  05  00 

157  31  30 

158  12  21 

159  50  00 

160  38  43 
163  00  45 

134  05  24 

Hogolu   (Hogulu)    Group:    N.  end   of 
Tsis  Islet. .'. 

Namoluk  Islands:  NW.  islet 

Mortlock  Islands:  Lukanor,  Port  Cha- 
misso 

Nukuor  or  Monteverde  Islands:  E.  pt. . 
Oraluk  or  Bordelaise  Island:  Center  . . . 
Ngatik  or  Valientes Islands:  E.  extreme. 

MokilorDuperrey Islands:  Aoura,  NE.pt 
Pingelasp  or  MacAskill  Islands:  E.  end 
of  island 

4  00 

10  15 

4.3 



2.4 

Ualan  or  Strong  Island:  Chabrol  Harbor. 
Angaur  Island:  SW.  pt 

6  00 

12  15 

3.5 

2.0 

Pililu  Island:  S.  pt 

133  18  03 

134  27  00 

134  32  30 
134  39  30 
134  17  00 

132  21  00 

131  11  00 

132  16  00 

144  39  30 

145  13  04 

Earakong or  Akamokan  Island:  Center. 
Korror  Islands:   Korror  Harbor,  Mal- 
akal  pier . 

Baubeltaub  Island :  Cape  Artingal 

Kyangle  Islets:  Center  of  largest 

Warren  Hastings  Island:  Center 

Nevil  or  Lord  North  Island:  Center 

Sonserol  Island :  Approx       

Guam  Island:  Fort  Sta.  Cruz,  San  Luis 
d' Apra. 

7  20 

1  20 

2.6 

1.5 

Rota  Island'  Summit 

Tinian  Island :  Sunharon  village 

Saipan  Island:  Magicienne  Bay,  land- 
ine 

145  36  20 

145  43  55 
145  42  50 
145  39  00 

Tanapag  Hbr. ,  Garapag . 
Anataxan  Island:  Center 

7  00 

0  50 

2.0 

1.1 

Sariguan  Island:  Center 

145  47  00 
145  57  00 
145  55  00 
145  52  00 
145  41  45 
145  30  00 
145  21  00 
144  54  00 

Guguan  Island:  Center 

Alamaguan  Island  ■  Center 

.   .   . 

Pagan  Island:  SW.  pt 

Agrigan  Island :  SE.  pt                  

Asuncion  Island :  Crater,  2,600  ft 

Urracas  Islands  ■  Lai^est  islet 

Farralon  de  Pajaro.«:  S.  end 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 


[Page  253 


Place. 


Lat.  N. 


Lun.  Int. 


Long.  E. 


H.  W. 


L.  W. 


Range. 


Spg.        Neap. 


Wake  Island:  Center ;  19  10  54 

Gaspar  Rico  Reef:  N.  clump  of  rocks. ..    14  41  00 


Johnston  or  Comwallis  Islands: 

staff  on  W.  island 

Clipperton  Island :  Center 


Flag- 


Hawaii  Island:  Hilo,  Kanaha  Pt.  light. 

Kawaihae  light 

Kealakeakua  Bay  light. 
Kailua,  stone  church... 

Kahoolawe  Island:  Summit 

Maui  Island:  Kanahena  Pt.  light 

Lahaina  light 

Molokai  Island:  Light-house 

Oahu  Island:  E.  pt.  Makapuu  station  .. 

Diamond  Head 

Honolulu,  Tr.  of  V.  Obs  . 

Honolulu,  Reef  light 

Kauai  Island:  Hanalei,  Black  Head 

Waimea,  stone  church  . .  I 

Bird  Island:  Center 

Necker  Island :  Center 

French  Frigate  Shoal:  Islet  (120  ft.) ... 

Gardiner  Island :  Center 

Maro  Reef:  NW.  pt 

Laysan  Island :  Light-house 

Lisiansky  Island:  Light- house 

Pearl  and  Hermes  Reef:  NE.  extreme.. i 

Midway  Islands:  N.  end  Sand  Islet 

Ocean  Island:  Sand  Islet ' 


Marcus  Island:  Center 

Bonin  Is. ,  Parrys  Group:  N.  rock 

Kater  Island:  N,  rock 

Peel  Island:  Port  Lloyd,  ob- 
servatory   

Volcano  Is.,  San  Alessandro  or  North 

Island:  Center 

Sulphur  Island 

San  Augustine   Island: 

Center , 

Rosario  Island :  Center,  148  ft 

Douglass  Rocks:  Center 

Borodino  Islands:  Center  of  N.  island.. 

Center  of  S.  island  . . 

Rasa  Island :  Center 


Fatu  Hiva  Island :  S.  pt 

Motane  Island:  SSE.  pt 

Tahuata  Island:  Port  Resolution,  wa- 
tering place  

Hiva-Oa  Island :  C.  Balguerie 

Fatu  Huku  Island:  Center 

Roa  Poua  Island :  Obelisk  Islet 

Nuka-Hiva  Island :  Port  Tai-o-hae  light. 

Hiaou  Island:  S.  pt 

Motu-ili  Island :  Summit,  130  ft 

Ua-Huka  or  Ua-L^na  Island:  N.  pt 

Fetouhouhou  Island :  NE.  pt 


Caroline  Islands:  Solar  Eclipse  Transit 

Pier 

Vostok  Island :  Center 

Flint  Island :  S.  extremity 


16  44  48 
10  17  00 

19  46  14 

20  03  00 
19  28  00 

19  38  26 

20  33  39 
20  36  00 

20  52  00 

21  06  17 
21  18  16 
21  15  08 
21  17  57 

21  17  55 

22  12  51 
21  57  17 

23  05  50 
23  35  18 

23  46  00 
25  00  40 
25  31  00 

25  48  00 

26  00  00 

27  56  30 

28  13  15 
28  24  45 

24  14  00 
27  45  00 
27  31  00 

27  05  37 

25  14  00 
24  48  00 

24  14  00 
27  15  32 
20  30  00 

25  59  38 
25  52  45 
24  27  00 

Lat.  S. 
10  32  00 
10  01  40 

9  56  00 
9  45  00 
9  27  30 
9  29  30 
8  55  13 
8  03  30 
8  44  00 
8  54  00 
7  55  00 


10  00  01 

10  06  00 

11  25  23 


166  31  30 

168  54  28 

Long.  W. 

169  32  24 
109  13  00 

155  05  31 
155  48  00 

155  55  00 

156  00  15 
156  35  04 
156  26  00 

156  35  00 

157  18  32 
157  39  07 
157  48  44 
157  51  34 
157  51  54 
159  30  47 
159  40  08 

161  58  17 
164  40  47 
166  17  57 
168  00  52 

170  39  20 

171  44  00 
173  57  00 
175  46  00 

177  21  30 

178  27  45 
Long.  E. 

153  58  00 
142  06  53 
142  11  53 

142  11  23 

141  11  00 
141  13  00 

141  20  00 
140  50  28 
136  10  00 
131  19  30 
131  12  17 
131  01  50 
Long.  W. 
138  39  20 

138  48  30 

139  09  00 
138  47  40 

138  55  10 

140  04  45 
140  04  00 
140  44  00 
140  38  30 

139  33  30 

140  34  40 


150  14  30 
152  23  00 

151  48  34 


h.    m. 


h.    m. 


ft- 


3  09 


9  06 


2.3 


1.3 


2  20 


8  10 


0,9 


3  32 

2  38 


9  58 
8  56 


2.2 

2.1 


1.2 
1.1 


3  46  j   9  59 
'4"66'  "i6"26 


1.5 


0.8 


2.0 


1.1 


3  30 


6  10 


9  45 


1.1 


0.6 


0  00 


2.4 


1.4 


2  30 


8  45 


3.1 


1.9 


3  50   10  05 


4  00 


3.5 


2.1 


10  14  I  1. 1 


0.7 


Page  254] 


APPENDIX  IV. 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 


Place. 


Maiden  Island:  Flagstaff,  W.  side 

Starbuck  Island:  l^lagstaff,  W.  side 

Penrhyn  or  Tongarewa  Island :  NNW.  pt. 

Jarvis  Island:  Center 

Reirson  Island :  Church 

Humphrey  Island:  N.  pt 

Union  or  Tokelau  Islands:  Spot  N.  of 

Fakaofu  or  Bowditch  Islet , 

Union  or  Tokelau  Islands:  Nuku-nono, 

or  SE.  island,  Duke  of  Clarence  I 

Union  or  Tokelau  Islands:  Clump  on 

S.  island,  Oatafu  or  Duke  of  York  I. . . 

Canton  or  Mary  Island:  N.  pt 

Enderbury  Island:  W.  pt , 

Pho'nix  Island,  N.  pt 

Birneys  Island :  S.  pt 

Gardners  Island :  Center 

McKean  Island:  Center 

Hulls  Island:  W.  pt 

Mukulaelae  or  Mitchells  Island:  S.  pt. . , 

Funafuti  or  EUice  Island :  E.  pt 

Nukufetau  or  De  Peysters  Island:  S.  pt 

Vaitupu  Island :  S.  end 

Nui  or  Netherland  Island:  S.  pt 

Nauomaga  Island :  Center 

Niutao  Island :  Church 

Nanomea  Island:  Center 

Ocean  or  Paanopa  Island :  Center  (appx ) 

Pleasant  Island :  Center 

Indispensable  Reefs:  S.  pt.  of  S.  reef.. 

Rennel  Island:  SE.  extreme 

AV.end 

San  Christoval  Island:  Point  Wanga- 
laha 

Guadalcanar  Island:    Wanderer  Bay, 

mouth  of  Boyd  Creek 

Florida  Island:  Mboli  Harbor,  Tree  Islet 
Malaita  Island:  Village,  Mary  I.,  Port 

Adam 

Stewart  Islands:  Largest  islet 

Isabel  Island:    N.  side  of  Cockatoo  Islet 
Gizo  or  Shark  Island:  N.  point  village. 
Choiseul    Island:     Choiseul    Bay    en- 
trance   

Traisury  Islands:  Observation  Islet 

Bougainville  Island:   Hiisker  Pt.,  Ga- 
zelle Harbor 

Buka  Island :  Cape  North 

Lord  Howe  Group:  Center,  small  SW. 

islet  

Center,  small  NE. 

islet 

NW.  pt.  of  Ham- 
mond I 

New  Britain,  Blanche  Bay:  Matupi  I. 

N.  pt 

Duke  of  York  Island:  Makada  Har- 
bor, Spit  Pt 


Lat.  S. 


4  03  00 

5  37  00 

8  55  15 
0  22  33 

10  02  00 

10  20  30 

9  23  02 
9  13  06 

8  39  40 

2  44  25 

3  08  30 
3  42  28 
3  34  15 

,  4  37  42 

3  35  10 

4  30  95 

9  18  00 
8  25  19 
8  04  02 
7  32  00 
7  15  45 

6  12  00 
6  06  00 

5  39  00 

0  52  00 

0  25  00 

12  50  15 

11  52  15 
11  33  45 


10  17  32 

9  41  47 
9  01  30 

9  30  00 
8  23  00 
8  30  50 
8  05  40 

6  42  40 

7  24  30 

6  35  00 
5  00  00 

5  38  00 

5  18  00 

5  18  00 

4  14  12 
4  06  25 


Long.  W. 


155  01  00 
155  56  00 

158  07  00 

159  54  11 
161  05  30 
161  01  12 

171  14  46 

171  44  40 

172  28  10 

171  45  29 
171  10  00 

170  42  37 

171  32  07 
174  40  18 
174  17  26 

172  13  28 
Long.  E. 

179  50  00 
179  07  25 
178  28  51 
178  41  01 
177  16  50 

176  16  30 

177  20  01 
176  06  15 

169  35  00 
167  05  00 

160  26  00 
160  40  15 
159  55  00 


161  33  30 

159  39  30 

160  27  20 

161  27  40 

162  58  15 
159  38  20 
156  50  15 

156  23  16 
155  34  00 

155  05  00 
154  35  00 

159  21  00 

159  34  00 

159  17  00 

152  11  35 
152  06  15 


Lun.  Int. 


Range. 


H,  W. 


L.  W. 


Spg.    Neap. 


ft.     m. 


ft. 


ft. 


6  00 


12  15 


1.5 


0.9 


6  00   12  13 


2.4 


1.4 


5  00 


11  15   4.6 


2.7 


6  45 


0  33 


3.3    2.0 


5  00 


11  15 


3. 5    2. 1 


12  00 


5  47  I  2.  7 


1.6 


9  00 


2  45  i  2. 1 


1.3 


APPENDIX  IV.                                       [Page  265 
MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 

u 

Place. 

Lat.  S. 

Long.  E. 

Lun.  Int. 

Range.          1 

H.  W. 

L.W. 

Spg. 

Neap. 

i 

g 

s 

■0 

m 
« 

S 
e 

a 

a 

M 

© 

i 

« 

2 

a 
» 

m 

N 

B 
b 
» 

New  Ireland:  Carteret  Harbor,  Cocoa- 
nut  I 

0  /         // 

4  41  26 
3  11  00 
2  47  30 

2  33  43 

2  26  30 

1  35  00 

1  55  10 

2  25  40 
2  22  00 

0  45  00 

0  53  15 

1  28  00 

2  51  00 

1  25  40 

2  44  00 

3  47  00 
8  22  00 

8  41  00 

9  25  30 
10  14  30 
10  43  35 
10  37  00 

6  43  00 

8  24  00 

9  03  30 

9  38  00 
9  41  00 

9  43  53 
10  42  00 

10  52  40 

11  23  25 
11  29  10 

16  50  00 

16  55  50 

17  43  00 
17  07  20 
17  24  39 
19  08  00 
19  14  00 

22  10  30 

23  15  02 

9  48  00 

10  21  00 
10  23  30 

10  40  00 

11  17  30 
11  40  24 

o             /          // 

152  42  25 
151  35  30 
150  57  35 

150  04  33 

149  55  36 

149  37  00 

146  40  56 

147  28  .35 
147  55  00 

145  17  00 
145  33  04 

145  08  00 

146  15  00 

135  28  12 
132  04  00 
134  06  00 
137  40  00 
143  36  04 

147  07  04 

148  30  30 

150  14  20 

150  40  34 
147  53  20 

151  01  24 

152  47  00 

150  30  00 
150  58  00 

150  44  43 
152  42  04 
152  47  12 
154  08  00 

154  25  14 

149  58  00 

149  11  54 

150  42  04 
152  06  20 

155  52  24 

158  40  00 

159  00  00 
155  28  24 
155  33  04 

166  53  15 

166  17  15 

165  47  30 

166  00  30 

166  32  14 
166  57  45 

h.    m. 

ft.    m. 

ft. 

ft. 

Katharine  Haven 

Holz  Haven,  E.  side 

New  Hanover  Island:    Water  Haven, 
creek  mouth. 
North     Haven 

anchorage 

St.  Matthias  Island:  SW.  extreme 

Admiralty  Island:  Nares  Harbor,  obs. 
islet 

2  50 

9  03 

2.4 

1.4 

2  30 

8  43 

2.4 

1.4 

St.  Andrew  Island:  Violet  Islet,  60  ft .. 
Jesus  Maria  Island :  SE.  pt 

Commerson  Island:  Center  of  largest 
islet 



Anchorite  Island :  N.  pt 

Hermit  or  Loaf  Island:  Pem6  Islet 

Purdy  Island:  Mole  Islet 

Point  d'  Urville :  extreme 

Drei  Cap  Peninsula:  Wass  Islet 

Triton  Bay:  Fort  Dubus,  Dubus  Haven. 
Cape  Walsche:  Extreme 

6  55 

7  08 

7.3 

4.3 

Fly  River:  Free  Islet,  S.  pt 

Port  Moresby:  N.  end  of  Jane  I 

Cape  Rodney :  Extreme 

8  50 

2  38 

8.0 

4.8 

South  Cape:  S.  pt.  Su  Au  I 

9  15 
8  25 

3  00 
2  12 

8.1 
5.8 

4.8 
3.4 

Hayter  Island :  VV^.  end 

Cape  Cretin :  Cretin  Islets 

Trobriand  Islands:  NE.  pt.  Cape  Denis. 
Woodlark  Islands:  N.  pt 

4  45 
7  05 

10  58 
0  53 

.... 

3.0 
4.2 

1.8 
2.5 

D'Entrecasteaux  Is. :  Ferguson  I.,  SW. 

extreme 

Well  Island,  E.  pt. 

Normanbyl.,  obs. 

islet 

St.  Aignan  Island :  Summit 

1 



Rossel  Island :  E.  pt 

Adele  Island :  S.  extreme 

Coringa  Islands:  Chilcott  Islet 

Herald  Cays:  NE.  Cay 

j 

Tregosse  Islands;  S.  islet 

i 

Lhou  Reef:  Observation  Cay 

1 

. 

Bampton  Island 

1 

Renard  Island :  Center 

1 

Wreck  Reef:  Bird  Islet 

1 

Cato  Island :  Center 

1 

Duff  or  Wilson  Group:  N.  island 

Matema  or  Swallow  Group:  Nimanu 
Islet 



Tinakula  Island:  Summit,  2,200  ft 

Nitendi  Island:  NE.  pt..  Cape  Byron  .. 

Tapua  Island:  Basilisk  Harbor,  S.  pt.  of 

entrance 

Vanikoro:  Ocili  village 

4  50 

11  05 

3.8 

2.3 

Page  256]                                       APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 

i 
•9 

5 

a 

M 

a 

V 

t 

9 

8 

« 

•9 
S 
« 

Place. 

Lat.  8. 

Long.  E. 

Lun. 

Int. 

Range.          1 

H.  W. 

L.  W. 

Spg. 

Neap. 

Torres  or  Ababa  Island:  Hayter  Bay, 
Middle  I..... 

O          '          II 

13  15  00 

13  48  00 

14  11  00 
14  58  00 

16  26  00 

17  44  58 

18  47  30 

0          /          II 

166  33  00 
.167  30  31 

167  30  00 

168  02  00 

167  47  15 

168  18  50 

168  58  00 

169  27  30 

170  11  15 

169  44  45 

171  20  30 

172  05  15 
168  56  45 

170  10  00 

177  07  15 

178  32  15 

177  57  09 

178  10  24 

177  38  00 

178  49  00 

177  09  00 

178  24  40 

178  06  53 

179  44  27 
179  56  25 
179  14  08 
178  59  29 

178  57  46 

179  20  44 
178  54  15 

178  48  32 

179  16  08 
Long.  W. 

179  58  46 
179  51  00 
179  54  26 
179  17  00 
179  32  17 
179  10  00 
179  05  45 
179  10  33 
179  19  49 

178  50  27 

179  04  00 
178  52  00 
178  27  04 
178  30  54 
178  44  00 

h.     m. 

h.     m. 

ft. 

ft. 

Vanua  Lava  Island:    Port  Patterson, 
Nusa  Pt 

6  40 

0  30 

3.8 

2.3 

Santa  Maria  Island:  Lasolara  Anchor- 
ase 

Aurora  Island :  Laka-rere 

MallicoUo  Island:  Port  Sandwich,  pt. 
on  E.  side 

4  38 

5  15 

10  50 

11  27 

3.8 
3.0 

1.9 
1.8 

Vate  or  Sandwich  Island:  Havannah 
Harbor,  Matapou  Bay  flagstaff 

Erromango  Island:    Dillon    Bay,    Pt. 
Williams 

Tanna  Island:  Port  Resolution,  Mission. 

19  31  17 

Erronan  or  Futuna  Island:  NW.  pt 19  31  20 

Aneitvum  Island:  Port  Anatom,  Sand 
Islet 

• 
20  15  17 

5  10 

11  23 

3.1 

1.9 

Matthew  Island:  Peak,  465  feet 

Hunter  Island:  Peak,  974  feet 

22  20  12 
22  24  02 
22  38  07 

Walpole  Island:  S.  pt 

Mitre  Island:  Center 11  55  00 

Rotumah  Island:  Epipigi  Peak 12  30  10 

Kandavu  Island:  N.  rock  Astrolabe  Reef  i 

light !  18  38  15 

Mt.   Washington,   N. 
peak 19  07  09 

. 

6  15 

0  00 

4.2 

2.5 

N'galoa  Harbor,  outer 
beacon 

19  05  30 

6  40 

0  25 

4.0 

2.4 

Vatu  Lele  Island :  S.  pt 

18  36  00 
17  40  45 

Ovalau  Island :  Levuka  light-house 

Yiti  Levu  Island;  Summit  of  Malolo 

Islet 17  44  45 

Suva   Harbor,   low 
light 

18  06  50 

6  30 

0  15 

3.  6         2.  2    1 

Mbega  or  Mbengha  Island:  Swan  Har- 
bor, Leaven  Pt  

18  22  00 

19  09  38 
18  32  49 
17  59  32 
17  37  11 
17  27  14 
17  15  21 
16  42  01 

16  57  53 

16  49  19 

16  08  00 
16  46  00 

Matuku  Island:  N.  side  of  Matuku  en- 
trance  

Moala  Island:  Rocks  off  N.  pt 

Ngau  Island:  Herald  Bay,  E.  side 

Wakaya  Island :  Rocky  Peak 

Makongai  Island:  Dilliendreti  Peak 

Goro  Island:  NW.  pt 

V^anua  Levu  Island :  Mount  Dana 

Nandi,  observation 
islet 

:::::;:::::  i 

Savu  Savu  Pt. ;  ex- 
treme   

6  00 

12  13 

4.3 

2.6 

NE.  Pt 

Taoiuni  Island:  Somu-Somu  town 

Thikombia  Island:  E.  hummock \  15  44  45 

Naitamba  Island :  Center 17  03  00 

Vatu  Vara  Island:  N.  end,  summit i  17  25  33 

Kanathea  Island:  S.  pt |  17  17  20 

Vanua  Mbalavu  Island:  NW.  pt 17  10  00 

Mango  Island:  Pier  end 1  17  25  26 

Thithia  Island:  Highest  peak 17  44  12 

Tuvutha  Island:  Peak 17  39  33 

Naian  Island:  Summit,  580  ft i  17  59  00 

Lakemba  Island:  Kendi  Pt i  18  14  10 

6  10 

0  00 

3.1 

1.9 

Oneata  Island :  Summit  of  Loa  I 

Mothe  Island:  Summit 

18  25  46 
18  38  56 
18  46  00 

Mamuka  Island :  Center,  260  feet 

1 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 


[Page  257 


Place. 


Kambara  Island :  Highest  peak 

Totoya  Island :  Black  Rock  Bay,  W.  side 

Fulanga  Island:  W.  bluff 

Ongea  Leva  Island :  Center 

Vatoa  or  Turtle  Island:  Hummock 

Ono  Islands:  Peak 

Michaeloff  Island :  Center 

Simonoff  Island :  Center 

Fatuna  or  Home  Island:  Mt.  Schouten. 
Uea  or  Wallis  Island:  Fenua-fu  Islet... 
Niua-fu  or  Good   Hope  Island:  NW. 

extreme 

Keppel  Island :  Center 

Boscawen  Island:  Center 

Savaii  Island :  Paluale  village 

Upulo  Is. :  Apia  Harbor,  obs.  spot 

Tutuila  Island :  Pago-Pago,  obs.  pt 

Manua  Island:  Village,  NW.  side 

Rose  Island:  Center 

Iniue  or  Sarage  Island :  S.  pt 

Danger,  or  Bernardo,  Is. :  Middle  rock  . 
Suwarrow  or  Souwaroff  Island:  Cocoa- 
nut  Islet 

Palmerston  Islands:  W.  islet 

Scilly  Islands:  E.  islet 

Bellingshausen  Island :  Center 

Mopelia  (Lord  Howe)  Island:  Center.. 

Maitea  Island:  Summit 

Tahiti  Island :  Light-house 

Tubuai-Manu  or  Maia-iti  I. :  NW.  pass. . 
Eimeo  Island :  Talu  H  br. ,  Vincennes  Pt . 

Huaheine  Island :  Light-house 

Ulietea  Island :  Regent  Pt 

Tahoa  Island:  Center 

Bola-Bola  Island:  Otea-Vanua  village. . 
Tubai  or  Motu-iti  Island:  N.  pt.  of  reef. . 
Marua  or  Maupili  Island:  Center 

Ducie  Island:  NE.  entrance 

Pitcairn  Island:  Village 

Henderson  or  Elizabeth  Island:  Center. 

Oeno  Island :  N.  pt 

Mangareva  or  Gambler  Island :  Flagstaff 
Maruteaor  Lord  Hood  Island:  Center.. 

Maria  or  Moerenhout  Island:  Center 

Vahanga  Island :  W.  pt 

Morane  or  Cadmus  Island :  Center 

Tureia  or  Carysf ort  Island :  E.  pt 

Mururoa  or  Osnabrug  Island:  Obs.  spot. 

Tematangi  or  Bligh  Island:  N.  pt 

Nukutipipi :  SW.pt 

Hereheretue  or  St.  Paul  Island:  Center. 

Vanavana  or  Barrow  Island:  Center 

Nukutavake  or  Queen  Charlotte  I. :  N.  pt 
Reao  or  Clermont  Tonnere  Island:  NW. 

point 

Puka-ruha  or  Series  Island:  NW.  pt 

Vahitahi  Island :  W.  pt 

Ahunui  or  Byam  Martin  Island :  NW.  pt. 

Pinaki  or  Whitsunday  Island:  E.  pt 

Tatakoto  or  Gierke  Island:  Flagstaff  on 

western  coast 


Lat.  S. 


18  56  15 

18  58  57 

19  03  00 
19  04  00 

19  49  11 

20  39  10 

21  00  09 
21  01  39 

14  14  20 
13  23  35 

15  34  00 
15  52  00 

15  58  00 

13  45  00 

13  48  56 

14  18  06 
14  19  00 

14  32  00 

19  10  00 
10  52  47 

13  14  30 

18  05  50 

16  28  00 

15  48  00 

16  52  00 

17  53  00 
17  29  10 
17  36  39 

17  29  23 
16  42  30 
16  50  00 
16  35  00 
16  31  35 
16  11  00 

16  26  00 

24  40  20 

25  03  50 
24  21  20 
24  01  20 
23  07  36 

21  31  30 

22  01  00 
21  20  00 

23  07  50 

20  46  20 

21  50  00 
21  38  00 
20  43  00 

19  53  17 

20  46  07 
19  16  30 

18  29  00 
18  16  00 

18  43  30 

19  37  00 
19  25  00 

17  19  30 


Long.  W. 


178  59  05 

179  52  58 
178  47  25 
178  33  25 
178  13  38 
178  43  27 
178  44  03 
178  49  47 

178  06  45 
176  11  47 

175  40  40 
173  52  00 
173  52  00 

172  17  00 
171  44  56 
170  42  14 
169  32  00 

168  09  00 

169  50  00 
165  51  30 

163  04  10 
163  10  00 
154  30  00 
154  31  00 
154  00  00 

148  05  00 

149  29  00 

150  36  56 
149  50  30 

151  01  28 
151  27  21 
151  35  00 
151  46  00 

151  48  00 

152  12  00 

124  48  00 
130  08  30 
128  19  00 
130  41  00 

134  57  54 

135  33  05 

136  10  15 

136  38  53 

137  06  15 

138  27  45 

138  56  30 
140  38  45 

143  03  15 

144  57  00 

139  08  45 
138  48  30 

136  26  30 

137  03  30 

138  53  15 

140  15  45 
138  40  45 

138  26  26 


Lun.  Int. 


Range. 


H.  W.    L.  W. 


Spg.    Neap. 


h.    m.    1  h.     m. 


ft.  ft. 


6  35  [   0  20 

"6"i6T"6"66' 


3.5 


2.1 


3.1 


1.9 


6  40    0  28 


4.4 


2.7 


25    0  13 


7  00 
6  00 


0  45 
12  13 


3.1 
2.7 
4.6 


1.9 
1.6 

2.7 


3  10  i   9  23 


2.4    1.4 


12  00 


5  48 


LO 


0.6 


12  10    6  00 


1.4 


0.8 


1  50 


03 


2.4    1.4 


22489—03- 


1    Page  268]                                      APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS  OF  THE  PACIFIC— Continued. 

1 

Place. 

Lat.S. 

Long.  W. 

Lun.  Int. 

Range.          1 

H.W. 

L.W. 

Spg. 

Neap. 

e 
I 

s 

9 

s 

s 

m 
■0 

1 

« 

M 

e 

a 
a. 

r 

Hao  or  La  Harpe  Island:  NW.  pass 

Paraoa  or  Gloceater  Island:  Center 

Ravahere  Island:  S.  pt 

O          f          11 

18  05  20 

19  08  45 

18  18  30 
17  49  35 
17  35  28 
17  20  30 
14  49  00 

14  12  00 

15  50  00 

15  44  20 

16  39  10 

16  44  29 

17  20  20 

16  47  49 

17  28  41 
16  26  09 

16  31  00 
15  43  15 
15  30  00 
15  50  00 
14  43  00 

14  29  10 

15  14  30 
15  50  30 
14  53  00 

33  37  36 
33  46  00 
26  18  07 
26  16  00 

26  27  41 

27  10  00 
27  35  46 

27  55  30 
23  55  00 

23  21  45 
22  29  00 

22  45  00 

21  47  00 
21  49  00 
21  11  35 

20  17  00 
20  01  00 

20  04  00 

19  18  00 

18  54  00 

18  39  02 

19  41  35 
19  45  00 

21  08  00 

23  37  06 

28  55  00 

29  15  30 

30  15  00 
30  35  00 

21  44  45 

O         1          II 

140  59  30 

141  41  10 

142  11  31 

143  05  23 
142  35  16 
141  29  43 
138  46  45 

141  15  37 
140  53  35 

142  08  40 

144  14  45 

142  53  34 

145  30  54 

144  17  18 

143  31  17 

143  57  59 

145  22  45 

144  38  34 

145  24  45 

146  02  45 

145  11  00 

146  20  00 

147  11  00 

148  15  00 

148  39  45 

78  50  02 
80  46  00 

79  54  56 

80  06  56 
105  28  00 
109  26  00 
144  17  20 
143  28  21 
147  48  00 

149  35  35 

151  23  41 

152  55  00 

154  51  00 
157  56  00 
159  47  00 
157  23  00 

157  34  00 

158  08  00 

158  54  00 

159  32  00 

174  01  00 

174  59  50 

175  03  00 
175  12  00 

178  55  45 

179  07  45 

177  55  40 

178  31  45 
178  37  00 

Long.  E. 
174  37  45 

h.    m. 
2  40 

h.   TO. 
8  55 

ft- 
2.4 

Jt- 
1.4 

Reitoru  or  Bird  Island:  N.  beach 

Hikueru  or  Melville  Island,  E.  pt 

Tauere  Island:  NW.  pt 

1 

Puka-puka  Island :  E.  pt 

Napuka  Island :  W.  pt 

Angatau  or  Araktcheff  Island:  W.  pt  .. 
Tukume  or  Wolkonsky  Island:  NW  .  pt. 
Tuanske  Island:  N W.  pt 

i 

1 , 

Nihiru  Island  (Tuanake):  SAV.  pt 

Anaa  Island:  Islet  in  N.  pass 

Tepoto  Island:  N.  pt 

! 

Haraiki  or  Crocker  Island:  SW.  pt 

Makemo  or  Phillips  Island:  AV.  pass... 

Fakarana  or  Wittgenstein  Island:  SE. . 

pass 

Taiaro  or  Kings  I. :  Middle  of  W.  shore . 
Aratika  Island:  E.  pt 

Toau  or  Elizabeth  Island:  Amyot  Bay. 
Takapoto  Island:  S.  pt 

Aheu  Island :  Lagoon  Entrance 

Rangiroa  Island:  E.  pt 

4  30 

10  43 

2.1 

1.3 

Makatea  Island:  W.  pt 

Matahiva  Island:  W.  pt 

Juan  Fernandez  Island:  Fort  S.  Juan 
Batista , 

Mas-afuera  Island:  Summit,  4,000  ft  ... 

St.  Ambrose  Island:  N.  part  creek 

St.  Felix  Island :  Center 



Sala  y  Gomez:  NW.  pt 

4  00 
0  40 
0  10 

10  15 
6  53 
6  25 

3.3 

2.8 
2.4 

2.0 
1.7 
1.4 

Easter  Island :  Cooks  Bay,  mission 

Rapa  or  Oparo  Island:  Tauna  Islet 

Bass  Islets  (Morotiri):  SE.  islet,  344  ft . 

Tubuaior  Austral  Is.,  Vavitoa  I. :  Center. 

Tubuai    I.:    Flag 

staff,  N.  side 

Rurutu  I. :  N.  pt . . 
Rimitara  I. :  Cen- 
ter  

Hull  Island:  NW.  pt 

3  00 

9  13 

2.4 

1.4 

Mangara  Island:  Center 

Rarotonga  Island :  N W.  pt 

6  00 

12  15 

2.7 

1.7 

Mauki  or  Parry  Island :  Center 

Mitiero  Island:  Center 

! 

Vatiu  or  Atiu  Island :  Center 

Hervey  Islets:  Center 

Aitutaki  Island:  Center 

Vavau  Island:  Port  Valdes,  Sandy  Pt.. 
Kao  Island :  Summit,  5,000  ft 

6  20 

0  10 

3.8 

2.3 

Tofua  Island :  Summit,  2,800  ft 

Tongatabu  Island:  Light-house 

Minerva  Reefs,  N.  Minerva:  NE.  side.. 
S.   Minerva:  S.  side  of 
entrance 

6  20 

7  50 

0  10 

1  35 

3.8 
5.5 

2.3 
3.3 

Kermadec  Is. ,  Raoul  or  Sunday  I. :  Den- 
ham  B.  flag  staff 

Macauley  I. :  Center 

Curtis  I. :  Center 

Conwav  Reef:  Center 

6  00 

12  13 

3.3 

2.7 

APPENDIX  IV.                                      [Page  269 
MAKITIME  POSITIONS  AND  TIDAL  DATA. 
ISLANDS   OF   THT3   PACIFIC— Continued. 

1 
o 
o 

Place. 

Lat.  S. 

Long.  E. 

Lun.  Int. 

Range.          1 

H.  W.         L.  W. 

Spg. 

Neap. 

Loyalty  Is.,  Uvea  or  Halgan  I.:  Uvea 
Church. 

o        /        // 

20  27  06 

20  46  00 

21  42  00 

21  29  12 

22  00  10 
22  16  22 

O            /          II 

166  36  25 

1 
h.  m.          h.   m. 

! 

ft. 

fl. 

LifuL:  Wreck  Bay,  NW. 
shore 

167  02  30 

168  00  00 

165  58  50 

166  05  00 

6  30  !       0  18 

1 

4.2 

2.5 

Mare  or  Britannia  I. :  S.  pt. 
Port  Kanala:  Observatory 

1 

Port  St.  Vincent:  ^larceau  I 

5  40       11  52 

3.3 
3.1 

2.0 
1.9 

Noumea :  Light-house ..   

166  25  52 

8  25         2  13 

Balari  Pass'  Amedee  I   Ught 

22  28  44     166  28  51 
22  42  30     167  27  55 

Port  Alcmene :  Alcmene  I 

7  55 
7  30 

1  45 

I  17 

3.6 
4.7 

2.2 

3.9 

Norfolk  Island:  Inner  end  of  jetty 

Elizabeth  Reef :  Center 

29  03  45 
29  56  00 

31  31  38 

167  58  06 
159  04  30 

159  05  58 
159  16  10 

Lord  Howe  Island:  S.  end  of  middle 
beach 

8  20 

2  08 

5.4 

.3.3 

Balls  Pyramid-  Summit,  1,816  ft     .   ... 

31   45  10 

Macquarie  Island :  N.  pt 54  19  00 

158  56  00 
166  13  20 
169  08  41 

178  43  05 

179  00  27 

Long.  W. 
176  32  15 

1 

Auckland  Is. :  Port  Ross,  Terror  Cove. . 
Campbell  Island:  S.  harbor.  Shoal  Pt.. 

Antipodes  Island:  Summit,  600  ft 

Bounty  Islands :  Anchorage  N.  I. ,  West 
Group            ..  

50  32  15 
52  33  26 
49  42  00 

47  43  00 

43  57  24 
43  49  03 

11  50 

11  45 

3  20 

5  38 
5  33 
9  30 

3.  2         2.  6 
3.  5         2.  9 
5. 3         4.  3 

Chatham  Island,  Whare-Kauri  Island: 
Port  Waitangi,  Pt.  Hanson 

, 

Chatham  Island,  Whare-Kauri  Island: 
Port  Hutt,  Gordon  Pt 

176  42  00 

5  22 

0  23 

2.5 

2.1 

AUSTRALIA. 

i 
1 

s 
e 

i 

£ 

« 

B 

s 

■ 

Groate  Eylandt:  SE.  pt 

14  16  00 
13  45  00 
12  14  00 
11  53  00 

10  59  00 

11  36  00 
11  57  00 
11  54  00 

10  57  00 

11  22  02 
11  08  00 

11  51  00 

12  13  20 
12  23  20 

12  30  58 

13  59  00 

14  25  50 

15  13  45 

14  42  00 
13  44  00 
13  52  00 

13  57  07 

14  15  00 

13  55  00 

14  14  00 
14  23  00 

14  51  00 

15  16  36 
15  06  00 

14  59  20 

15  13  15 
15  46  00 

Long.  E. 
136  58  00 

136  15  00 

137  00  00 
136  34  00 
136  46  00 
136  07  00 
134  45  00 
134  12  00 
132  36  30 
132  09  18 

130  19  00 

129  58  00 

131  :6  30 

130  37  00 
130  27  00 
129  37  00 
129  20  42 
129  48  14 

128  10  00 
126  57  00 
126  12  00 
125  38  45 
125  39  00 

124  55  00 

125  12  00 
125  00  00 

124  42  00 

125  07  00 
125  01  00 
124  32  11 
124  14  00 
124  04  00 

Bickerton  Island :  Summit 

Cape  Arnheim :  Extreme 

Cape  Wilberforce:  E.  extreme 

8  00 

1  48 

9.8 

5.8 

Cape  W^essel:  Extreme 

Dale  Point:  Extreme 

Cape  Stewart:  Extreme 

Liverpool  River:  W.  pt.  entrance 

Cape  Croker:  Extreme 

6  17 

0  05' 

12.0 

7.1 

Port  Essington:  Government  house 

Melville  Island:  Cape  Van  Diemen 

Bathurst  Island :  Cape  Fourcroy 

Adelaide  River:  E.  entrance  pt' 

Port  Darwin :  Charles  Pt.  light 

5  15 

4  57 
3  50 

5  45 

6  45 

11  27 
11  18 

10  00 

11  58 
0  27 

16.8 
17.0 
16.7 
21.9 
23.0 

9.9 
10.0 

9.9 
12.9 
13.6 

Port  Patterson :  Quail  Islet 

Port  Keats:  Tree  Pt 

Pearce  Point:  Extreme 

Victoria  River:  Water  Vallev 

Cape  Dussejour :  Rock  off  cape 

Cape  Londonderry :  Extreme 

Cape  Bougainville:  Extreme 

Cassini  Island :  S.  pt 

Cape  Voltaire:  Flat  Hill 

Barker  Islets:  Center 

Montalivet  Islands:  W.  islet 

Maret  Islets:  N.  islet 



Colbert  Islet:  Center 

Prince  Regent  River:  Mount  Trafalgar  . 
Port  Nelson:  Careening  beach 

De  Freycinet  Islets:  Beacon  on  summit. 
Red  Islet:  Center. 

Cockell  Islet:  W.  pt 

Page  260] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

AUSTRALIA— Continued. 


Place. 


MacLeay  Islets:  Rock  off  N.  end 

PortUsbome:  S*pt 

Fitz  Roy  River:  Escape  Pt 

Cape  L'  Ev^que:  Extreme 

Lacepede  Island :  N  W .  islet 

Cape  Baskerville:  Extreme 

Cape  Latouche  Tr^ville :  Extreme 

Turtle  Isles:  Center  of  N.  isle 

Cape  Lambert:  Extreme 

Legendre  Island:  NW.  extreme 

Rosemary  Island :  W.  summit 

Enderby  Island:  Rocky  Head 

Montebello  Island:  N.  extreme  of  reef. 

Barrow  Island:  N.  pt 

Northwest  Cape:  Extreme 

Cape  Cuvier:  Extreme 

Cape  Inscription :  Extreme 

Houtman  Rocks:  N.  islet 

Port  Gregory 

Cape  Leschenault:  Extreme 

Rottnest  Island:  Light-house 

Perth  (Fremantle) :  Arthur  Head  light 

Peel :  Robert  Pt 

Cape  Naturaliste:  Extreme 

Cape  Leeuwin :  Light-house 

D' Entrecasteaux  Point:  Extreme 

Nuyts  Point:  Extreme 

West  Cajie  Howe:  Extreme , 

Eclipse  Islets:  Summit  of  largest 

King     George    Sound:    Commissariat 

house  near  Albany  jetty 

Bald  Isle :  Center 

Hood  Point :  Doubtful  Isles 

Recherche    Archipelago:  Termination 

Isle 

Culver  Point:  Extreme 

Dover  Point:  Extreme 

Fowler  Point :  Extreme 

Streaker  Bay :  Port  Blanche 

Coffin  Bay :  Mount  Dutton 

Cape  Catastrophe:  W.  pt 

Neptune  Isles:  SE.  islet 

Port  Lincoln :  English  Church 

Franklin  Harbor:  Observation  spot 

Port  Augusta:  Flagstaff 

Port  Victoria:  Wardang  Island  hut 

Cape  Spencer:  S.  pt 

Investigator  Strait:  Troubridge  light. . 

Port  Wakefield:  Light-house 

Port  Adelaide:  Wonga  Shoal  light 

Cape  Jervis :  Light-house 

Cape  Borda:  Light-house 

Cape  Willoughby:  Light-house 

Port  Victor:  Flagstaff. 

Cape  Jaffa :  Margaret  Brock  light-house 
Cape  Northumberland:  Light-house  ... 

Cape  Nelson :  S.  extreme 

Portland  Bay :  Lawrence  Rock 

Port  Fairy:  Griffith  Island  summit 

Cape  Otway :  Light-house 

King  Island:  Cape  Wickham  light 

Port  Phillip:  Point  Lonsdale  light 

Geelong:  Custom-house 

Mell)ourne :  Observatorv 


Lat.  S. 

Long.  E. 

Lun 

Int. 

ki 

inge. 

H.  W. 

L.  W. 

Spg. 

Neap. 

O    /     It 

15  52  00 

O    /    n 

123  45  00 
123  36  27 

123  39  47 
122  55  45 
122  05  30 
122  15  00 
121  54  00 
118  48  00 
117  11  00 
116  45  00 
116  30  00 
116  23  00 
115  22  00 
115  27  45 
114  10  08 
113  21  00 

112  57  09 

113  35  33 

114  14  30 

115  30  00 
115  30  12 
115  44  23 
115  44  00 
115  00  15 

115  08  00 

116  01  00 

116  38  00 

117  40  00 
117  53  45 

117  54  04 

118  27  00 

119  34  00 

121  58  00 

124  39  00 

125  30  00 

132  33  00 

134  13  40 

135  24  56 

135  56  09 

136  06  24 

135  51  03 

136  57  22 

137  45  24 
137  22  21 

136  53  30 

137  49  39 

138  09  00 
138  26  58 
138  05  29 
136  34  39 
138  07  45 

138  37  09 

139  39  39 

140  39  40 

141  32  39 

141  40  02 

142  14  37 

143  30  39 

h.    in. 

h.  m. 

ft. 

ft. 

15  39  25 

17  24  25 

16  23  00 

16  50  00 

17  09  00 

18  29  00 

19  54  00 

20  36  00 
20  19  00 

11  30 

5  10 

17.6 

10.4 

20  27  00 

20  35  00 

20  16  45 

20  40  40 

21  46  41 

24  00  00 

25  29  19 

28  18  05 

28  12  00 

31  18  00 

32  00  20 

32  03  12 
32  27  00 

[10  16] 

[3  43] 

[2.1] 

33  31  45 

34  21  55 

34  52  00 

35  05  00 

35  09  00 

35  11  54 

35  02  20 
34  55  00 

[10  53] 

[4  40] 

[2.6] 

34  24  00 

34  30  00 

32  57  00 

32  34  00 

32  01  30 
32  48  00 

11  50 

9  35 

5.1 

0.3 

34  29  29 

35  00  15 

0  35 

6  55 

5.5 

0.3 

35  20  15 

34  43  22 

33  44  08 

32  29  42 

34  28  25 

8  20 

2  15 

11.4 

0.7 

35  18  21 

35  07  31 

34  12  00 

34  50  25 

35  36  45 

4  31 
4  04 

10  45 
10  22 

10.2 
6.3 

0.6 
0.9 

35  45  30 

35  51  00 
35  34  06 

4  00 

10  15 

5.8 

0.3 

36  57  00 

38  04  18 
38  26  00 

11  52 

5  40 

4.2 

0.2 

38  24  39 
38  23  47 

0  20 

6  35 

2.7 

2.1 

38  51  45 

39  35  38 

143  57  03 

144  37  00 
144  21  47 
144  58  35 

38  18  00 
38  08  52 
37  49  53 

10  43 
2  02 
2  19 

4  30 
8  20 
8  41 

2.5 
3.0 
1.9 

1.9 
2.3 
1.5 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
AUSTRALIA— Continued. 


[Page  261 


Place. 


Cape  Schanck :  Light-house 

Port  Western :  Extreme  of  W.  head 

Wilson  PromontoiV:  Light,  SE.  pt 

Kent  Island:  Deal  Island  light 

Flinders  Is. :  Strzelecki  Peaks,  SE.  peak 

Goose  Island:  Light  on  S.  end 

Banks  Strait:  Swan  Island  light 

Port  Albert:  Light-house 

Gabo  Island :  Light-house 

Cape  Howe  (east):  Extreme 


Cape  Green :  SE.  pt 

Twofold  Bay:  Lookout  Pt.  light 

Dromedary  Mountain:  Summit 

Montagu  Island :  Light-house 

Bateman  Bay :  Observation  head 

Ulladulla:  Inner  end  of  pier 

Jervis  Bay :  Light-house 

Kiama  Harbor :  Outer  extreme  of  S.  head 

WoUongong:  Summit  of  head 

Sydney :  Observatory 

Port  Jackson:  Outer  S.  head  light  ... 

Broken  Bay:  Baranjo  Head  light 

Newcastle:  Nobby  Head  light 

Port  Stephens:  Light-house 

Sugar  Loaf  Point:  Light-house 

Port  Macquarie :  Entrance 

Solitary  Islands:  S.  Isle  light 

Clarence  River:  S.  Headlight 


Lat.  S. 


Richmond  River:  N.  Head  light 

Brisbane :  Signal  station 

Lookout  Point:  Extreme 

Cape  Moreton :  Light-house 

Double  Island  Point:  Light-house 

Indian  Head :  Extreme 

Sandy  Cape:  Light-house 

Burnett  River:  S.  Head  light 

Lady  Elliot  Islet:  Light-house 

Bustard  Head :  Light-house 

Rodd  Bay :  Spit  end 

Port  Curtis:  Gatcombe  Head  light 

Cape  Capricorn :  Light-house 

Port  Bowen:  Observation  rock 

Percy  Isles:  Pine  I.  light 

Northumberland  Isles :  Summit  of  Prud- 

hoe  I 

Cape  Palmerston :  N.  extreme 

Cape  Conway:  SE.  pt 

Port  Molle:  S.  side  of  entrance 

Cumberland    Island:    Whitsunday   I., 

summit  on  W.  side 

Port  Denison:  Obs.  pt.,  W.  side  of  Stone 

Isle 

Gloucester  Island:  Summit  near  N.  end. 

Holborne  Islet:  Center 

Cape  Bowling  Green:  Light-house 

Cape  Cleveland :  Light-house 

Palm  Islands:  SE.  point  of  SE.  island.. 
Rockingham  Bay:  Peak  of  Goold  Isle.. 

Barnard  Island:  Light-house 

Frank  land  Island:  High  islet 

Cape  Tribulation :  Extreme 

Hope  Island:  S.  islet 

Cook  Mountain:  Summit 

Cape  Bedford :  SE.  extreme 


38  29  42 

38  29  15 

39  08  00 

39  29  45 

40  11  45 
40  18  40 
40  43  40 
38  45  06 
37  34  15 
37  30  10 

37  15  40 
37  04  18 
36  18  30 
36  14  30 
35  43  58 
35  21  41 
35  09  15 
34  40  25 
34  25  30 
33  51  41 
33  51  30 
33  35  00 
32  55  15 
32  45  10 
32  26  20 
31  25  30 
30  12  00 
29  25  30 

28  51  30 
27  27  32 
27  26  20 
27  02  10 
25  56  00 
25  00  15 
24  43  20 
24  45  00 
24  07  00 
24  01  20 
24  01  20 
23  53  00 
23  29  30 
22  31  40 
21  39  00 

21  19  16 
21  32  00 
20  32  20 
20  18  50 

20  15  30 

20  00  50 
19  57  30 
19  41  50 
19  19  20 
19  11  25 
18  45  .30 
18  09  30 
17  40  40 
17  09  45 
16  04  20 
15  45  00 
15  29  45 
15  16  30 


Long.  E. 


144  52  51 

145  01  34 

146  25  16 

147  18  39 

148  04  00 

147  47  39 

148  07  24 

146  37  43 

149  55  10 

149  58  39 

150  03  04 

149  54  45 

150  01  34 
150  13  34 
150  12  34 
150  29  29 
150  46  26 
150  52  19 

150  55  14 

151  12  23 
151  18  15 
151  20  30 

151  48  19 

152  13  20 
152  33  40 

152  55  19 

153  17  00 
153  23  10 

153  35  55 
153  01  48 
153  33  50 
153  28  04 
153  13  00 
153  23  00 
153  13  40 
152  25  00 
152  45  15 
151  41  04 
151  37  15 
151  23  50 
151  14  04 
150  45  44 
150  14  00. 

149  43  .30 
149  31  04 
148  58  00 

148  53  15 

149  00  00 

148  16  54 
148  27  34 
148  23  00 

147  27  40 
147  01  10 
146  42  50 
146  11  04 
146  11  00  . 
146  02  30 
145  29  34 
145  28  30 
145  17  30 
145  23  15 


Lnn.  Int. 


H.W. 


L.W. 


Range. 
Spg.    Neap. 


10  38 


8  40 


8  05 


20 
"26' 


8  40 


8  35 
8  15 


9  00 


10  45 


10  05 


8  55 


h.    m.    \     ft.      i  ft. 


4  25 
"2'27' 


1  52 
"2"67' 
'2"67' 


2  27 


2  23 
2  00 


2  46 

"2"66' 


2  43 


4.5 


5.2 


5.3 


4.2 


4.7 
5.8 


4.1 
"4.'6' 


4  30   6.  4 


6.2 


3.4 


3.1 


3.2 
'3."  3 


2.5 


2.8 
3.6 


2.4 
"2."  4 


3.9 


3  53   9. 0    5. 4 


7.5  I   4.5 


Page  262]                                       APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
AUSTRALIA— Continued. 

Place. 

Lat.  s. 

Long.  E. 

Lun.  Int.           1          Range.          1 

H.W. 

L.W.         Spg. 

Neap. 

e 

i 

c 
(3 

« 

s 
9 

Murdock  Point  ^Extreme  , 

O          /          II 

14  37  15 
14  10  00 

O             '          II 

144  57  30 
144  32  34 
144  15  19 
143  42  15 
143  36  19 
143  34  00 
143  15  15 

143  29  00 
143  06  00 
142  56  19 

II.    TO. 

h.  TO.        ft. 

ft. 

Cape  Melville:  NE.  extreme 

1 

Flinders  Island:  N.  extreme  of  N.  island. 

14  07  45 

Claremont  Point:  Extreme 14  00  30 

Cape  Sidmouth:  Extreme 13  24  45 

Cape  Direction:  NE.  extreme i  12  51  00 

Cape  Grenville:  Extreme 11  58  15 

Sir  Charles  Hardv  Island:  N.  extreme  , 

of  SE.  isle ' '  11  55  00 

Bird  Island:  NW.  isle 11  46  30 

9  00 

2  47  1    9. 6 

5.8 

Hannibal  Isles:  E.  isle 

11  36  30 
10  41  30 
10  37  45 
10  22  00 

10  46  00 
10  36  05 
17  36  40 
17  35  10 
17  06  50 

Cape  York :  Sextant  Rock 

142  32  24 
142  39  20 
142  21  19 

142  10  50 
141  53  49 
140  37  06 
139  45  56 
139  38  36 

1  00 

7  10       8.0 

4.7 

Mount  Adolphus:  Summit 

Travers  Isles :  Center 

Prince  of  Wales  Island:  Cape  Cornwall, 
extreme 

Booby  Island :  Center 

4  20 

10  30 

7.8 

4.7 

Flinders  River:  Entrance 

Albert  River:  Kangaroo  Pt 

Sweers  Island :  Inscription  Pt 

TASMANIA. 

Cape  Portland:  NW.  pt 

40  44  15 

41  03  25 
41  07  05 
41  10  00 
41  08  30 
41  02  50 
40  23  40 
40  40  10 

40  22  00 

41  04  00 

41  41  00 

42  11  37 

42  11  00 

43  19  00 
43  33  30 
43  44  30 
43  29  40 
43  21  00 

42  53  25 

43  14  00 
42  52  00 
42  13  00 
41  34  00 
40  59  40 

147  56  09 
146  47  54 
146  33  30 
146  24  30 
146  12  00 
145  56  39 
144  47  45 
144  39  44 
144  39  19 
144  44  00 

144  57  00 

145  12  34 
145  10  30 

145  53  00 

146  01  04 

146  22  04 

147  08  49 
147  23  40 

147  20  07 

148  02  00 
148  00  00 
148  18  04 
148  19  30 
148  20  50 

Port  Dalrymple:  Low  Head  light 

Port  Sorrell:  NW.  entrance  head 

Port  Frederick :  Entrance 

Leven  River:  W.  entrance  head 

Emu  Bay :  Blackman  Pt  . 

11  10 

5  00 

9.0 

6.9 

Hunter  Island :  N.  pt 

Cape  Grim:  Outer  Doughboy  Islet 

Albatross  Islet:  N.  pt 

Arthur  River:  Entrance 

Pieman  River:  Rocks  close  to  entrance. 

Macquarie  Harbor:  Entrance  Islet 

Cape  Sorrell :  Light-house            .     

7  20 

1  07 

2.7 

2.1 

Port  Davey :  Pollard  Head 

Southwest  Cape:  Extreme  pt. 

Mewstone  Rock:  Center 

Cape  Bninj'^:  Light-house  . 

Bruny  Island :  Penguin  Islet               

Hobart  Town:  Transit  of  Venus  station. 
Cape  Pillar*  Tasman Islet                  ... 

8  05 

1  52 

4.2 

3.2 

Cape  Frederik  Hendrik:  Extreme 

Freycinet  Peninsula:  Summit  . 

St.  Patrick  Head:  N.  pt.... 

Eddystone  Point :  Extreme 

NEW  ZEAIiAND. 

0 

If. 

Three  Kings  Islands:   NE.  extreme  of 
NE.  island 

34  m  20 
34  25  07 

34  31  00 

35  00  20 
35  01  44 
35  17  00 

172  08  49 

173  03  34 
173  00  54 
173  32  39 

173  45  48 

174  06  06 

North  Cape :  Cape  Islet 

Parenga-renga  Harbor:  Kohan  Pt 

Maunganui  Harbor:  White  Pt 

Wangaroa  Harbor:  Peach  Islet 

Bay  of  Islands:  Motu  Mea  Islet 

7  40 
7  26 

1  30 
1  55 

6.4 

5.9 

4.5 

4.2 

APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

NEW  ZEAIiAND— Continued. 


[Page  263 


Place. 


Wangaruru  Harbor:  Grove  Pt 

Wangari  Harbor:  Loot  Pt 

Great  Barrier  Island:  Needles  Pt 

Auckland  Harbor:  Light-house 

Coromandel  Harbor:  Tuhnia  I 

Cape  Colville:  N.  pt 

Cuvier  Island:  Light-house 

Tauranga  Harbor:  Mount  Maunganui, 
860  ft 

AVhite  Island:  Summit,  863  ft 

Cape  Runaway :  Extreme 

East  Cape:  Islet,  420  ft 

Tolaga  Bay :  Matu-heka  Islet 

Mahia  Peninsula:  S.  extreme  of  Port- 
land I 

Ahuriri  Harbor:  Light-house 

Kidnappers  Cape:  Extreme 

Cape  Palliser:  Light-house 

Port  Nicholson:  Pencarrow light 

Wellington:  Queen's  Wharf  light 

Mana-watu  River:  Light-house 

Wanganui  River:  N.  head 

Egmont  Mountain:  Summit,  8,270  ft... 

New  Plymouth:  Flag-staff 

Kawhia  Harbor:  S.  head 

Aotea  Harbor:  S.  head 

Whaingaroa  Harbor:  S.  entrance  pt 

Manukau  Harbor:  Paratutai  flag-staff.. 

Kaipara  Harbor :  Light-house 

Hokianga  River:  Flag-staff  at  entrance. 

Cape  Campbell :  Light-house 

Port  Cooper:  Lyttleton  custom-house  .. 

Akaroa  Island:  Light-house 

Ashburton  River:  N.  entrance  pt 

Waitangi  River:  N.  entrance  head 

Otago  Harbor:  Taivoa  Head  light 

Molyneux  Bay :  Landing  place , 

Nugget  Point:  Light-house 

Bluff  Harbor:  Light-house 

Tewaewae  Bay:  Pahia  Pt 

Solander  Islands:  Summit,  1,100  ft 

Preservation  Inlet:  Light-house 

West  Cape :  Extreme 

Queenstown:  U.  S,  Tr.  of  Venus  station 

Milford  Sound:  Freshwater  Basin 

Cascade  Point:  N.  extreme 

Grey  River:  Entrance 

Hokitika:  Entrance  light , 

Cape  Foul  wind :  Light-house 

Cape  Farewell :  Extreme 

Nelson:  Bowlder  Bank  light 

D'  Urville  Island :  Port  Hardy 

Port  Gore:  Head  of  Melville  Cove 

Port  Underwood;  Flag  Pt 


Port  William:  Howell's  House 

Paterson  Inlet:  Glory  Cove 

Port  Adventure:  White  Beach,  S.  end.. 
Port  Pegasus:    Cove  abreast  Anchor- 
age I 

Codfish  Island :  N W.  extreme 


Snares  Islands:  SW.  islet. 


Lat.  s. 


35  23  48 

35  51  09 

36  01  15 
36  50  06 
36  48  35 
36  28  20 

36  26  20 

37  36  25 
37  30  00 
37  30  45 

37  40  00 

38  20  50 

39  18  00 
39  28  30 

39  38  00 
41  36  45 
41  21  40 

41  17  17 

40  27  10 
39  57  00 
39  18  00 

39  03  35 
38  04  50 
37  59  35 
37  46  22 
37  03  00 
36  23  00 
35  32  05 

41  44  00 
43  46  40 

43  54  00 

44  04  50 

44  54  50 

45  46  55 

46  24  05 
46  27  10 
46  37  00 
46  20  40 
46  36  00 
46  10  00 
45  54  50 

45  02  07 
44  40  20 
44  00  30 

42  26  20 

42  42  20 
41  45  40 

40  29  50 

41  16  05 

40  46  35 

41  01  55 
41  20  28 

46  50  30 

46  58  30 

47  03  52 

47  11  40 
46  45  45 

48  06  43 


Long.  E. 


174  21  24 

174  31  14 

175  25  34 

174  51  00 

175  24  34 
175  21  04 

175  49  00 

176  10  14 

177  10  49 

177  59  34 

178  35  09 
178  20  14 

177  53  15 

176  54  14 

177  06  44 
175  18  45 
174  51  04 

174  47  25 

175  14  40 
174  59  44 
174  03  59 
174  04  35 
174  48  04 
174  50  04 
174  52  19 
174  31  14 
174  08  00 

173  21  59 

174  17  14 

172  44  17 

173  00  20 
171  48  34 
171  11  14 

170  44  02 
169  47  53 

169  50  04 
168  23  00 

167  42  19 
166  54  04 
166  38  15 

166  25  49 

168  40  06 

167  54  45 

168  21  34 

171  11  54 

170  59  30 

171  27  44 

172  41  04 

173  17  30 

173  54  04 

174  11  22 
174  08  24 

168  05  34 
168  09  54 
168  10  57 

167  40  51 
167  36  49 


Lun.  Int. 


H.  W. 


166 


44 


h.  m. 
7  15 
7  05 


7  20 
7  05 


L.  W. 


h.  m. 
1  05 
0  55 


1  10 
0  55 


7  05 


0  55 


8  10 
8  00 


2  00 
1  50 


05  !  12  15 


4  40 

'4'52' 
9  40 


10  50 

"i6'54 
3  30 


Range. 


Spg.   Neap. 


ft. 

6.5 

6.7 


10.8 
10.7 


6.6 

6.8 


3.5 


5.7 


3.6 
6.3 


9  15 
9  10 


3  05 
3  00 


11.6 
11.9 


9  08 
9  05 
9  00 
8  40 

4  45 
3  45 


2  55 
2  .50 
2  50 
2  30 

11  00 
10  00 


12.3 

12.6 

10.0 

9.2 

7.5 
7.4 


3  31 


1  05 

ii'io' 


9  39 


5.6 


7  15 

"s'oo' 


7.8 
'7."5' 


10  10 
10  20 


4  00 
4  10 


9.8 
9.5 


9  55 
9  45 


6  00 


1  00 
11  45 


3  45 
3  35 


12.0 
11.6 


12  15  I  7.6 


9  15 


7.8 


5  40 


7.9 


4.6 

4.8 


7.7 
7.6 


4.4 


4.7 

5.8 


3.0 
4.9 


3.1 
5.4 


8.2 
8.5 


8.7 
9.0 
7.1 
6.5 

6.5 

5.8 


4.4 
"6.'2 
"5.'9 


7.7 
7.5 


9.4 
9.2 


6.6 


6.2 


Page  264] 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 

THE  ARCTIC  REGIONS. 


Place. 


Cape  Waleingham^  Extreme 

Mile  Island:  N.  p* 

Marble  Island :  E.  end 

Cape  Kendall:  Extreme 

Iglooik  Island:  E.  pt 

Victoria  Harbor:  N.  shore 

Elizabeth  Harbor:  Entrance 

Magnetic  Pole,  1831 

Port  Neill:  N.  pt.  of  entrance 

Port  Bowen:  N.  cove 

Batty  Bay :  S.  pt.  of  entrance 

Port  Leopold:  Whaler  Pt 

Careys  Islands 

Discovery  Harbor 

Alert' s  Winter  Quarters 

Cape  Joseph  Henry :  N.  extreme 

Cape  Hecla:  N.  extreme 

Cape  Columbia:  Extreme 

Melville  Island:  Winter  Harbor 

North  Cape 

Liakhov  Islands:  E.  pt.  of  New  Siberia 

Cape  Tscheljuskin :  E.  pt 

Nova  Zembla:  Vaigats  I. ,  N.  pt 

Cape  Costin  (Kostina)  . 

NE.  pt.,  Cape  Desire... 

Franz  Josef  Land :  Wilczek  I 

Mezen:  Epiphany  Church 

Morjovetz  Island :  Light-house 

Archangel :  Trinity  Church 

Jighinsk  Island :  Light-house 

Onega:  St.  Michael's  Church 

Salovetski :  Light-house 

Cape  Sviatoi  Nos:  Light-house 

Bear  Island 

Spitzbergen  Island :  S.  cape 

Cloven  Cliff 

Danes  I.,  Robbe 
Bay 

Thank  God  Harbor 

Cape  York :  Extreme 

Upernivik:  Flagstaff 

Proven:  Village 

Omenak  Island:  Village 

Godhavn:  Village 

Jacobshavn :  Village 

Claushavn :  Village 

Christianshaab:  Village 

Egedesmunde :  Village 

Whalefish  Island:  Boat  Inlet 

Holsteinberg:  Village 

Kangamint 

Ny  Sukkertop:  Village 

Godthaab:  Flagstaff 

Sermelik  Fjord :  Kasuk  Peak 

Fiskernaes:  Village 

Jensen  Nunatak:  Peak 

Ravn  Storo:  Peak 

Frederikshaab:  Church 

Kangarssuk  Havn :  Village 

Arsuk:  Pingo  Beacon 

Kajartalik  Island :  Summit 

Ivigtuk:  House 

Bangs  Havn :  Anchorage 

Aurora  Harbor 


Lat.N. 


00  00 

04  00 
33  00 
42  00 
21  00 
09  17 
38  14 

05  00 
09  13 
13  39 
13  00 
50  05 
49  00 
04  40 
27  00 
40  00 

54  00 
07  00 
47  10 

55  00 


75  10  00 
77  41  00 
70  25  00 
70  55  00 

76  58  00 
79  55  00 

65  50  18 

66  45  50 

64  32  06 

65  12  17 
63  53  36 
65  07  00 
68  08  51 
74  30  00 
76  35  00 
79  50  00 

79  42  00 


38  00 
55  00 

47  48 
20  42 
40  00 
14  04 
13  12 
07  30 

49  06 
42  30 

58  30 
55  54 

48  42 
24  30 
10  36 
29  12 
05  12 

50  00 
42  36 

59  36 
28  20 
10  24 
09  42 
12  12 

47  30 

48  36 


Long.  W. 


28  00 
50  00 
06  00 
15  00 
31  00 
30  33 
10  56 

47  00 
00  54 
54  48 
08  00 
12  00 
10  00 
45  00 
18  00 
38  00 
45  00 
20  00 

48  15 
57  00 


91 

87 

81 

91 

92 

96 

89 

88 

91 

90 

73 

64 

61 

63 

64 

70 
110 
179 

Long.  E. 
150  30  00 
104  01  00 

59  10  00 

53  01  50 

65  40  00 

58  45  00 

44  17  00 

42  30  00 

40  33  30 

36  51  30 

38  08  30 
35  37  00 

39  48  54 
20  00  00 
17  23  00 
11  40  30 

11  07  00 
Long.  W. 
61  44  00 
65  30  00 
55  53  42 
55  20  00 
51  59  00 
53  24  07 
50  56  30 

50  55  30 

51  00  00 

52  46  00 

53  27  00 
63  40  18 
53  23  00 
52  54  00 
51  45  48 
51  10  48 
50  43  36 

48  57  00 
50  20  48 

49  44  00 
48  51  00 
48  26  00 
48  30  42 
48  10  30 
47  52  00 
47  46  48 


Lun.  Int. 


Range. 


H.W. 


4  00 


6  50 


11  38 


10  35 


1  20 


10  00 


7  18 
5  05 
9  02 


L.W. 


h.    m. 


ft. 


10  15 

"'olo' 


12.0 
"8."6' 


5  29 


4  20 


7  40 


3.8 


3  50 


7.0 


2  00 
11'30 

3  10 


2.2 
3.8 
9.1 


9  05    2  55 


0  14 
12  14 
"i6"56' 


8  05 
6  20 


13.9 


6  25 
5  58 


5.3 
5.4 


4  38 


8.0 


1  52 

0  07 


7.5 
10.0 


6  40    0  27 


12.5 


6  12  j   0  00 
'6"i5    6  03' 


9.0 
'i2.'6" 


Neap. 


ft. 


5.1 

"4."  2 


5.  5    2. 9 


2.6  I   1.0 


4.0 


1.3 
2.1 
5.2 


3.0 
2.0 


3.0 


3.6 

4.8 


6.0 


3.6 
"4."  8 


APPENDIX  IV. 

MARITIME  POSITIONS  AND  TIDAL  DATA. 
THE  ARCTIC  REGIONS— Continued. 


[Page  265 


Julianshaab:  Village 

Neunortalik:  Village 

Frederiksthal :  Village 

Cape  Farewell :  Staten  Huk 

Aleuk  Islands :  Center 

Cape  Tortlenskjold:  Extreme 

Cape  Bille:  Extreme 

Cape  Juul:  Extreme 

Cape  Lo wenorn :  Extreme 

Dannesbrog  Island :  Beacon 

Ingolsfjeld 

Rigny  Mount :  Summit 

Pendulum  Islands 

Cape  Philipp  Broke 

Cape  Bismark:  Extreme 

Jan  Maven   Island:    Mt.    Beerenberg, 

6,870ft 

Youngs  Fore- 
land, or  Cape 

Northeast 

Mary  Muss  Bay.. 

Langanaes  Point. 

Rissnaes  Point 

Grimsey  Norddranger:  Tr.  Station 

Skagataaa  Point 

North  Cape:  Kalfatindr 

Straumness  Point 

Fugle  or  Staabierg  Huk:  Point 

Snaefells  Yokul :  Tr.  Station 

Reykiavik :  Observatory 

Cape  Skagi :  Light-house 

Reykianaes :  Light-house 

Ingolfshofde:  Tr.  Station 

Papev  Island:  Tr.  Station 

Reytnur  Fjeld:  Tr.  Station 

Balatangi :  Light-house 

Dia  Fjeld:  Tr.  Station 


Lat.  N. 


60  43  07 
60  08  12 
60  00  00 

59  49  00 

60  09  00 

61  25  00 

62  01  00 

63  14  00 

64  30  00 

65  18  00 

66  19  02 
69  00  12 
74  40  00 
74  55  00 
76  47  00 


71  04  00 


71  08  00 
71  00  00 


22  45 

32  40 

33  42 

07  30 
27  29 
26  30 
30  15 
48  04 

08  40 
04  09 
48  06 
48  19 
35  42 
55  27 
16  14 
45  00 


Long.  W. 


46  01  00 
45  16  00 
44  40  00 
44  01  42 
42  55  00 
42  15  00 
42  00  00 
40  50  00 
39  30  00 
38  30  00 
35  11  00 
26  10  24 
18  17  00 

17  33  00 

18  40  00 


7  36  00 


7  26  00 

8  28  00 

14  30  46 

16  10  24 

17  57  36 

20  05  26 

22  23  04 

23  08  00 

24  31  26 
23  45  08 

21  55  00 

22  39  04 
22  39  00 
16  36  13 
14  08  31 
13  41  10 

13  32  22 

14  23  35 


Lun.  Int. 


Range. 


H.  W. 


h.  m. 

4  56 

5  33 
2  55 
4  00 


11  05 
11  10 


L.  W. 


Spg. 


Neap. 


h.  m. 
11  09 
11  46 
9  10 
10  13 


4  53 

4  58 


11  21 


5  06 


ft. 

7.0 

8.6 

9.4 

7.5 


ft. 

2.8 

3.4 

3.8 

3.0 


6.7 
3.7 


3.9 
2.1 


3.8 


2.2 


5  10   11  25 


14.5 


Page  266J 


INDEX  TO  APPENDIX  IV. 


Page. 

Admiralty  Islands 255 

Adriatic  Sea 226-228 

Africa,  east  coast 232,  233 

north  coast 230 

west  coa.«t 230-232 

Alabama 196 

Alaska 198,199 

Aleutian  Islands 199 

Algeria 230 

Arabia 236 

Arctic  regions 264, 265 

Argentina 208,  209 

Asia,  east  coast 239-250 

islands  .  243,  244 

south  coast 236-239 

Atlantic  Ocean,  islands.  213-215 

Australia 259-262 

Austria 227,228 

Azores  Islands 213 

Bahama  Islands 203 

Balearic  Islands 226 

Baluchistan  237 

Banka  Strait 239 

Belgium 223 

Belize 197 

Bermuda  Islands 214 

Black  Sea 229,230 

Borneo 242 

Brazil 207,208 

British  Columbia 200 

Burma 238 

California 200,  201 

Canary  Islands . .  214 

Cape  Breton  Island 192, 193 

Verde  Islands 214 

Caroline  Islands 252 

Celebes  Island 242 

Central    America,    east 

coast  . . .  197, 198 

west  coast . . .  202, 203 

Cevlon 237 

Chile 209-212 

China 240-242,  247 

Sea 240 

I^ntrance 240 

Cochin  China 240 

Colombia,  north  coast .  198, 206 

west  coast 213 

Connecticut 194 

Cook  Islands 258 

Coral  Sea  Archipelago 255 

Corsica 226 

Costa  Rica 198 

Crozet  Islands 236 

Cuba 203,204 

Cyprus 230 

Delaware 195 

Denmark 222,223 


REGIONS   AND    COASTS. 

Page. 

Ecuador 213 

Egypt 230 

Ellice  Islands 254 

Europe,  Atlantic  coast.  215-225 

Falkland  Islands 214 

Fiji  Islands 256,257 

Florida 195,196 

Formosa  Island 242 

France,    north     and     west 

coasts 223,224 

France,  south  coast 225,  226 

Galapagos  Islands 250, 251 

Gaspar  Strait 239 

Georgia 195 

Germany 221,222 

Gilbert  Islands 251 

Great  Britain 215-218 

Greece 228,229 

Greenland 264,  265 

Guatemala 197 

Guiana 207 

Haiti 204 

Hawaiian  Islands 253 

Holland 223 

Honduras 197,198 

Iceland 265 

India 237,238 

Indian  Ocean,  islands. .  234-236 
Italy 226,227 

Jamaica 204 

Japan 248,249 

Java 243 

Kerguelen  Islands 236 

Korea..... 247,248,250 

Kuril  Islands 249 

Labrador 191,192 

Laccadive  Islands 234 

Ladrone  Islands 252 

Linschoten  Islands 248 

Louisiade  Archipelago 255 

Louisiana 196 

Lower  California 201, 202 

Madagascar 235 

Madeira  Islands 213 

Magdalen  Islands 192 

Mame 193 

Malaysia 238,239 

Maldive  Islands 234 

Mariana  Islands 252 

Marquesas  Islands 253 

Marshall  Islands 251 

Maryland 195 


Page. 

Massachusetts 194 

Mauritius  Island 234 

Mediterranean  Sea 225-230 

Mexico,  east  coast 196, 197 

west  coast 202 

Mississippi 196 

Morocco 230 

Mosquito  Coast 198 

New  Brunswick 192, 193 

Caledonia 259 

Newfoundland 191,192 

New  Guinea  Island 255 

Hampshire 194 

Hebrides  Islands 256 

Jersey 195 

South  Wales 261 

York 194 

Zealand 262,263 

Nicaragua 198 

North     America,     east 

coast  . . .  191-198 

west  coast . . .  198-203 

Australia 259 

Carolina 195 

Island,      New       Zea- 
land  262,263 

Norway 218-219 

Nova  Scotia 193 

Oregon 200 

Pacific  Ocean,  islands --  250-259 

Pelew  Islands 252 

Persia 236,  237 

Peru 212 

Philippine  Islands 245-247 

Phoenix  Islands 254 

Porto  Rico 205 

Portugal 224,225 

Prince  Edward  Island 192 

Queen  Charlotte  Islands . . .  199 
Queensland 261,262 

Red  Sea 233-234 

Rhode  Island 194 

Russia,  south  coast 229 

west  coast 220 

St.    Lawrence,    River   and 

Gulf 192 

Samoan  Islands 257 

Santa  Cruz  Islands 255 

Sardinia 226 

Siam,  Gulf 240 

Siberia 250 

Society  Islands 257 

Solomon  Islands 254 

South  America,  north  and 
east  coasts 206-209 


INDEX  TO  APPENDIX  IV. 


[Page  267 


Page. 
South  America,  W.  coast  209-213 

Australia 260 

Carolina 195 

Island,  New  Zealand..  263 

Spain,      north     and     west 

coasts 224,225 

south  and  east  coasts. .  225 

Stewart  Island 263 

Sumatra 239 

Sweden 219,220    Uruguay 


REGIONS  AND  COASTS — Continued. 
Page. 

Tasmania 262 

Texas 196 

Tonga  Islands 258 

Trinidad 206 

Tuamotu  Archipelago. .  257,  258 

Tunis 230 

Turkey 228,229,230 


208 


Aalborg 223 

Aarhus 223 

Ababa  Island 256 

Abaco  Island 203 

Abang  Besar  Island 238 

Abbeville 223 

Abd-al-Kuri  Island 233 

Aberdeen 216 

Abervrach 224 

Aberystwith 215 

Abingdon  Island 250 

Abo... 220 

AboukirBay 230 

Abreojos  Point 201 

Abrolhos  Island 207 

Ab.secon  Inlet 195 

Acajutla 202 

Acapulco 202 

Accra 231 

Acheen  Head 239 

Aconcagua  Mountain 21 1 

Acre 230 

Adakh  Island 199 

Adalla 230 

Adams,  Port 247 

Addu  Atoll 234 

Adelaide,  Port 260 

River 259 

Adele  Island 255 

Aden 236 

Adenara  Island 243 

Admiralty  Head 200 

Islands 255 

Adolphus  Mountain 262 

Adventure,  Port 263 

^gina 229 

Aero  Island 222 

Ji^rstenen 218 

Africa  Rock 226 

Agalegas  Island 235 

Agdenes .•.  218 

Agiabampo 202 

Agrigan  Island 252 

Aguadilla  Bay 205 

Aguja  Point 212 

Agulhas.Cape 232 

Agutava  Islet 245 

Aheu  Island 258 

Ahunui  Island 257 

Ahuriri 263 

AiSima 249 

Aian 250 

Aignan,  St.,  Island 255 

Aigues  Mortes 226 

Ailinginae  Islands 251 

Aillick  Harbor 191 

Ailly  Point 223 

Ailuk  Islands 251 


Aitutaki  Island 258 

Aix  Island 224 

Ajaccio 226 

Ajano 230 

Akamokan  Island 252 

Akaroa  Island 263 

Akashi-no-seto 248 

Akpatok  Island 191 

Akyab 238 

Alacran  Reef 197 

Alamaguan  Island 252 

Aland  Island 220 

AlargateReef 198 

Albany 194 

Albatross  Islet 262 

Albemarle  Island 251 

Albert,  Port 261 

River 262 

Alboran  Island 230 

Albuquerque  Bank 198 

Alcatrasses  Island 208 

Alcmene 259 

Alcoba^a 207 

Aldabra  Island  235 

Aldeu 218 

Alderney  Harbor 218 

Alegranza  Island 214 

Alegre,  Porto 207 

Alert's  Winter  Quarters  ...  264 

Alessandro,  San,  Island 253 

Aleuk  Islands 265 

Alexander,  Port 232 

Vancouver 200 

Alexandretta 230 

Alexandria 230 

Alfaciues,  Port 225 

Alfred,  Port 232 

Algeciraa 225 

Algier 230 

Ali-Agha,  Port 230 

Alicante 225 

Alij  OS  Rocks 201 

Alipee 237 

Alligator  Island 241 

Reef 196 

Alraadie  Point 231 

Almeria 225 

Alphonse  Island 235 

Alta  Vela 204 

Altata 202 

Altea 225 

Altona 222 

Alvarado 196 

Amager  Island 222 

Amber,  Cape 235 

Amboina  Island 244 

Ambrose,  St. ,  Island 258 

Amchitka  Island 199 


Page. 

Vancouver  Island 199,  200 

Venezuela 206 

Victoria .». .  260, 261 

Virginia 195 

Washington 200 

Western  Australia 259,  260 

West  India  Islands 203-206 

Yucatan 197 

Amelia  Island 195 

Ameni  Islet 234 

Amherst  Harbor 192 

Amirante  Islands 234 

Amour  Point 192 

Amoy 241 

Amsterdam 223 

Island 236 

Ana,  Sta.,  Lagoon 197 

Anaa  Island 258 

Anacapa  Island 201 

Anadir  River 250 

Analaboe 239 

Anamba  Islands 240 

Anataxan  Island 252 

Anchorite  Island 255 

Ancona 227 

Andaman  Islands 238 

Andenes 218 

Andrava  Bay 235 

Andrea,  St. ,  Rock 228 

Andrew,  St 193 

Cape 235 

Island 255 

Andrews,  St. ,  Island 198 

Andros  Island,  Bahamas...  203 

Grecian  Arch 229 

Anegada 205 

Aneityum  Island 256 

Angatau 258 

Angaur  Island 252 

Angeles  Bay 202 

Los 201 

Port,  Mexico 202 

,  Washington 200 

Anghris  Head 217 

Angosto,  Port 210 

Angoxa  Island 233 

AngradosReis 208 

Pequena 232 

Anguilla 205 

Anhatomirim 208 

Anholt  Island 222 

Animas,  Las 202 

Anjer 243 

Anjoe,  Cape 243 

Ann,  Cape 194 

St.,  Bay 204 

Anna, Sta., Island, N.Brazil.  207 

S.  Brazil ....  208 

Annapolis,  Maryland 195 

Nova  Scotia 193 

Anne,  St.,  Island 210 

Annisquam 194 

Anno  Bon  Island 231 

Anns,  St.,  C.  Breton  1 192 

England 215 

Anowik  Island 199 


Page  268J 


INDEX  TO  APPENDIX  IV. 


Page. 

Antareh,  Ras 233 

Antibes 226 

Anticosti  fcland 192 

Antigua 205 

Antipodes  Island 259 

Antivari 228 

Antofagasta .*...  211 

Antonina 208 

Antonio,  Port 204 

San,  Cape,  Argentina .  208 

Cuba 204 

Mt.  and  Island...  214 

Port,  Argentina. .  209 

Chile 211 

Sierra 209 

Antwerp 223 

AogaShinia 249 

Aor,  Pulo 240 

Aotea 263 

Apaiang  Island 251 

Apalaehicola 196 

Apamama 251 

Aparri 245 

Apenrade 221 

Apo  Islet 245 

Apostle  Rocks 209 

AragoCape 200 

Araish,  El 230 

Arakam  Island 250 

Araktcheff  Island 258 

Aran  Island 217 

Aransas  Pass 196 

Aranuka  Island 251 

Aratika  Island 258 

Arcadius  Islands 204 

Areas  Cays 197 

Archangel 264 

Ardassier  Islands 243 

Ardrossan 216 

Arena  de  la  Ventana 201 

Point,  California 200 

L.  C^alif ornia  ....  201 

Arenas  Cay 197 

Arendal  Inlet 219 

Arentes  Island 243 

Argentina 208 

Argostoli,  Port 228 

Arica 212 

Arichat  Harbor 193 

Arkona 221 

Armeghon 238 

Amheiin,  Cape 259 

Arno  Atoll 251 

Arorai  Island 251 

Arran  Island 217 

Arrowsmith  Islands 251 

Arru  Islands 244 

Arsuk 264 

Artaki  Bay 230 

Arthur  River 262 

Port 247 

Arvoredo  Island 208 

Ascension  Bay 197 

Island 214 

Ashburton  River 263 

Ashrafi  Island 233 

Asia  Rock 212 

Assateague  Island 195 

Assens 222 

Assumption  Island 235 

Astoria 200 


PLACES — continued. 

Page. 
Asuncion  Island,  Ladrones.  252 

L.Calif 201 

Atalaia  Point 207 

Athene 229 

Atico 212 

Atiu  Island 258 

Atka  Island 199 

Atkinson  Point 200 

Attu  Island   199 

Auckland  263 

Islands 259 

Audierne 224 

Augusta 193 

Port,  Australia 260 

Sicily 227 

Augustenberg 221 

Augustin,  St.,  Cape,  Brazil.  207 

Philippines.  246 

Augustine,  San,  Island 253 

St.,  Bay 235 

Harbor 195 

Aurh  Island 251 

Aurora  Harbor 264 

Island 256 

Austral  Islands 258 

Avarena  Point 204 

Aves  Island 205 

Aviles 224 

Avlona 228 

Axim  Bay 231 

Awa  Sima 249 

Awomori 249 

Ayamonte 225 

Ayer  Bangis 239 

Ayr 215 

Baago  Island 222 

Babayan  Claro  Island 245 

Baccalieu  Island 191 

Baganiovo 233 

Bahal tolls  Island 247 

Bahama  Island 203 

Bahia,Brazil 207 

Colombia 206 

de  Cadiz  Cay 204 

Honda,  C.  America 202 

Bahrain  Harbor 236 

Bajo  Nuevo 197 

Bajuren  Island 242 

Baker  Islet 251 

Bakers  Island 193 

Baklar 229 

Balabac  Island 245 

Balaklava  Bay 229 

Balari  Pass 259 

Balasor  River 238 

Balatangi 265 

Balayan 245 

Bald  Isle 260 

Balfour  Rock 236 

Bali  Island 243 

Balingtang  Islands 246 

Ballena  Bay 202 

Balls  Pyramid 259 

Ballum 22i 

Ballycottin 218 

Balstrum 222 

Balta  Island 216 

Baltic  Port 220 

Baltimore 195 

Bampton  Island 255 


Page. 

Banda  Island 244 

Banderburum 236 

Band jerinasin 242 

Bangkaru  Islands 239 

Bangkok 240 

Bangor 193 

Bangs  Havn 264 

Banjuwangi 243 

Banka  Island 239 

Strait 239 

Bankot 237 

Banks  Strait 261 

Bantal 239 

Bantam 243 

Bantenan 243 

Banton  Island 246 

Bantry  Bay 216 

Baracoa 203 

Barataria  Bay 196 

Baratoube  Bay 235 

Barbados  Island 205 

Barbara,  Santa,  California  .  201 

Island 201 

Mexico 202 

Port 210 

Barbe,  St. ,  Island 240 

Barbuda 205 

Barcelo  Bay 210 

Barcelona,  Spain . .  225 

Venezuela 206 

Bardsey  Island 215 

Barfleur,  Cape 223 

Bari 227 

Barker  Islets 259 

Barnard  Island 261 

Barnegat  Inlet 195 

Barneveldt  Islands 209 

Barnstable 194 

Barra  Head 216 

Sao  Joao 208 

da 207 

Barren  Island 248 

West 242 

Barrier,  Great,  Island 263 

Barrington  Island 251 

Barrow  Island,  Australia  . .  260 

Tuamotu  Arch . . .  257 

Point 198 

Bartholomew,  St 205 

Cape 209 

Bartolom^,  San 201 

Barton,  Port 245 

Baru,.Point 239 

Barung  Island 243 

Bas,  De,  Island 224 

Basdorf 221 

Basianang  Bay 246 

Bilsiduh 237 

Basilan  Island 247 

Baskerville,  Cape 260 

Basrah 236 

Bass  Islets 258 

Bassa,  Grand 231 

Bassas  Rocks 237 

da  India 235 

Bassein,  Burma 238 

India 237 

River 238 

Basseterre 205 

Bastia 226 

Bastion,  Cape 240 


INDEX  TO  APPENDIX  IV. 


[Page  269 


Page. 
Basto 219 

Batalden  Island 218 

Batan  Island 246 

Port 246 

Batangas 245 

Batavia 243 

Batbatan  Island 246 

Bate  Islands 248 

Bateman  Bay 261 

Bath 193 

Bathurst 231 

Island 259 

Batian  Island 244 

Batoe  Islands 239 

Batoura 229 

Batticaloa 237 

Battle  Islands 191 

Batty  Bay 264 

Batve  Toetong 239 

Baubeltaub  Island 252 

Bauld  Cape 191 

Baxo  Nuevo 204 

Bay  of  Islands 262 

Baynes  Sound 200 

Bayonnaise  Island 249 

Bayonne 224 

Bazaruto  Island 232 

BeachyHead 215 

BealeCape 199 

Bear  Island 264 

Cape 225 

Beata  Island 204 

Beaufort,  N.  Carolina. .....  195 

S.Carolina 195 

Port 232 

Beaver  Harbor 200 

Beaver-tail  Light 194 

Bee  du  Raz 224 

Beda'a,Al 236 

Bedford,  Ca]ie 261 

Bees,  St 215 

Beeves  Eocks 216 

Beirut 230 

Bel  Air 235 

Belfast 193 

Bay 217 

Belgrano 208 

Belize 197 

Bell  Island 191 

Rock,  Scotland 216 

Bellavista  Cape 226 

Belle  Isle,  France 224 

Labrador 191 

Bellingshausen  Island 257 

Bellone,  Cape 235 

BenGhazi 230 

Benbane  Head 217 

Bender  Erekli 230 

Benedicto,  San,  Island 202 

Benevente 207 

Benguela 232 

Benicia 200 

Benidonne 225 

Benin  River 231 

Benito,  San,  Island 201 

Benkulen 239 

Bento,  San,  River 231 

Benzert 230 

Bequia  Island 205 

Berbera 233 

Berdiansk 229 


PLACES — continued. 

Page. 

Bergen,  Germany 221 

Norwav 218 

Berikat '. 239 

Bering,  Cape 250 

Island 250 

Berlanga  Island 225 

Berlin 222 

Benneja  Head 209 

Bermudas 214 

Bernal  Chico 196 

Bernardo  Islands 257 

Berwick 216 

Besuki 243 

Betrapar  Islet 234 

Beverly 194 

Beyt 237 

Bhaunagar 237 

Blanche  Point 227 

Biarritz 224 

Bickerton  I.«land 259 

Bideford 215 

Bidstone 215 

Bierneborg 220 

Bigar  Islet.. 251 

Bikini  Islands 251 

Bilbao 224 

Bille,  Cape 265 

Billiton  Island 239 

Bindloe  Island 250 

Bintang  Hill 238 

Bintoean 239 

Bird  Island,  Australia 262 

Bahamas 203 

BandaSea 244 

N.  Pacific 253 

Seychelle Islands.  234 

Tuamotu  Arch. . .  258 

W.  Africa 231 

Islands,  Magdalen  Is. .  232 

Birneys  Island 254 

Bismark,  Cape 265 

Bittern  Rocks 249 

Bjuroklubb 220 

Blaabjerg 223 

Black  Head 191 

Point  Bay 232 

Stairs  Mountain 217 

Blackness 216 

Blacksod  Point 217 

Blair,  Port 238 

Blaize,  St 232 

Blanco  Cape,  N.,  Africa 231 

Oregon 200 

Peru 212 

S. ,  Africa 231 

Peak 198 

Blankenberghe 223 

Bias,  San,  Argentina 209 

Cape,  Florida 196 

Mexico 202 

Blasket  Islands 216 

Bligh  Island 257 

Blighs  Cape 236 

Blimbing  Bav 239 

Blinyu ' 239 

Block  Island 194 

Bloody  Foreland 217 

Blueflelds 198 

BluffHarbor 263 

Boar  Islands 191 

Boavista  Island 214 


Page. 

BobaraRock 228 

Bodie  Island 195 

Bogense 222 

Bogsher 220 

Bohol  Island 246 

Bojador,  Cape 231 

Bojeador,  Cape 245 

Bola-Bola  Island 257 

Bom  Abrigo  Islet 208 

Bombay 237 

Bon,  Cape 230 

Point 239 

Bona 230 

Bonacca  Island 197 

Bonaive  Island 206 

Bona  venture  Head 191 

Island 192 

Bonavista  Cape 191 

Bongao  Island 247 

Bonham  Islands 251 

Bonifacio 226 

Bonin  Islands i .  253 

Boobjerg 223 

Booby  Island,  Leeward  Is. .  205 

Queensland 262 

Boompjeo  Island 243 

Boon  Island 193 

Borda,  Cape 260 

Bordeaux 224 

Bordelaise  Island 252 

Borja  Bay 210 

Bornholm 222 

Borodino  Islands 253 

Boscawen  Island 257 

Bosphorus 229 

Boston 194 

.Botel  Tobago  Sima 242 

Bougainville,  Cape 259 

Island 254 

Bougaroni,  Cape 230 

Boulogne 223 

Bounty  Islands 259 

Bourbon,  Cape 236 

Bouro  Island 244 

Bouton  Island 242 

Bouvets  Island 215 

Bovlilu van,  Cape 245 

Bowditch  Islet 254 

Bowen,  Port,  Australia 261 

BaffinsBay 264 

Bowling  Green,  Cape 261 

Boyanna  Bay 235 

Bradore  Bay 192 

Brala,  Pulo 240 

Brangmans  Bluff 198 

Bras,  Pulo 239 

Brass  River 231 

Brava  Island,  C.Verde  Is..  214 

E.  Africa 233 

Brazos  Santiago 196 

Bray  Head 217 

Breaker  Point 241 

Bremerhaven 222 

Bremerton 200 

Brest 224 

Brewers  Lagoon 198 

Bridgeport 194 

Brielle 223 

Brill  Reef 243 

Brindisi 227 

Brisbane 261 


Page  270j 


INDEX  TO  APPENDIX  IV. 


Page. 

Bristol,  England 215 

Rhode  Island 194 

Britannia  Island 259 

Broadhaven 217 

Broken  Bay 261 

Bronnosnnd 218 

Brothers  Island,  Red  Sea  . .  233 

Islets,  China 241 

Broughton  Bay 244 

Head 248 

Island 249 

Rock 249 

Brunet  Island 191 

Bruni  River 242 

Brunswick,  Georgia 1 95 

Maine 193 

Bruny,  Cape 262 

Island 262 

Brussels 223 

Brusterort 221 

Bryer  Island 193 

Bubn^n  Island 247 

Bucas  Island 246 

Buchanness 216 

Buddonness 216 

Budrum 230 

Budua 228 

Buenaventura 213 

San 201 

Buenos  Avres 208 

Bugui  Point 246 

Buitenzorg 243 

Buka  Island 254 

Bulipongpong  Island 247 

Biilk 221 

Bull  Harbor 200 

Rock 216 

Bullock  Bay 250 

Burg 221 

Burghaz 229 

Burias  Island 246 

Burin  Harbor 191 

Burnett  River 261 

Burntcoat  Head 193 

Burrh  Island 251 

Busios 208 

Islets 208 

Bustard  Head 261 

Busuanga  Island 245 

Busum 222 

Butt  of  Lewis 216 

Button  Islands 191 

Byam  Martin  Island 257 

Byron  Island 251 

Caballo  Island 245 

Cabeceira,  Cape 233 

Cabeza  de  Vaca 211 

Cabrera  Island 226 

Cabron  Cape 204 

Cabrut  Islet 234 

Cadaques 225 

Cadiz 225 

C'admus  Island 257 

Caen "...  223 

Cagayan  Jolo  Island 247 

Cagayanes  Islands 247 

Cagliari 226 

Caigara 207 

Caicos  Island 203 

West,  Cay 203 


PLACES — continued. 

Pivge. 

Calaan,  Point 246 

Calais,  France 223 

Maine 193 

Calavite,  Monte 245 

Calavan  Island 245 

Calbuco 211 

Calcasieu  Pass 196 

Calcutta • 238 

Caldera 211 

Caldy  Island 215 

Calebar  River,  New 231 

Old 231 

Caledonia 206 

Calf  of  Man 215 

Calicut - 237 

Calimere  Point 237 

Callao 212 

Calpe 225 

Caluya  Island 245 

Calvi 226 

Caniamu 207 

Camaron  Cape 198 

Camasusu  Island 246 

Cam  bay 237 

Cambria 208 

Cambridge,  England 215 

United  States 194 

Camiguin  Island,  Luzon  . . .  245 

Mindanao 247 

Cammin 221 

Campbell,  Cape 263 

Island 259 

Campeche 197 

Campobello  Island 193 

Canaria,  Gran,  Island 214 

Canaveral  Cape 195 

Cancun  Island 197 

Candia  Island 228 

Candon 245 

Cannes 226 

Cannonier  Point 234 

Canoas  Point 201 

Canso,  Cape 193 

North 193 

Canton 241 

Island 254 

Pulo 240 

Cantyre 216 

Cape  Town 232 

Cape  Verde  Islands 214 

Capel  Island 218 

Cape  d'Istria 246 

Capones  Islet 245 

Capraia  Island 226 

Caprera  Island 226 

Capri  Island 226 

Capricorn,  Cape 261 

CarNicobar 238 

Carabane 231 

Carabao  Island 246 

Caraques  Bay 213 

Carataska  Lagoon 198 

Caravellas., 207 

Carbon,  Cape 230 

Carbonera  Cape 226 

Cardamum  Islet 234 

Cardiff 215 

Careys  Islands 264 

Cargados  Carajos 234' 

Caribana  Point 206 

Carimare  Mountain 207 


Page. 

Carimata  Island 240 

Carl  ingford  Lough 217 

Carlobago 227 

Carlos,  San,  deAncud 211 

Point 201 

Carmen  Island 197 

Caroline  Islands,  N.  Pacific.  252 

S.Pacific 253 

Carousel  Island 192 

Carreta  Mountain 212 

Point 198 

Carreto,  Port 206 

'^^arrizal.  Port 211 

Cartagena,  Colombia 206 

Spain 225 

Cartago  Mountain 198 

Carteret  Cape 224 

Harbor 255 

Cartwright  Harbor 191 

Carupano 206 

Carysfort  Island 257 

Reef 195 

Cascade  Point 263 

Casquets  Rocks 223 

Cassini  Island 259 

Castillos 208 

Castle  Island 203 

Caatlehaven 216 

Castro 210 

Urdiales 224 

Catlsland 196 

Catalina  Harbor 191 

Sta.,  Island 201 

Catania 227 

Catastrophe,  Cape 260 

Catbalogan 246 

Catharine  Point 209 

St 215 

Island 208 

Cato  Island 255 

Catoche  Cape 197 

Cattaro 228 

Cautanduanco  Islands 246 

Cavite 245 

Caxones 198 

Cayenne 207 

Cayeux 223 

Caymans 204 

Cazza  Island 228 

Ceara 207 

Cebu  Island 246 

Cedar  Keys 196 

Cedeira 225 

Ceicer  de  Mer  Island 240 

Celebes 242 

Centinela  Islet 206 

Ceram  Island 244 

Cerros  Island 201 

Cestos 231 

Cette 226 

Ceuta 230 

Ceylon 237 

Chacachacare  Island 206 

Chacopata 206 

Chagos  Arch 234 

Chagres 206 

ChahbarBav 237 

Chala  Point.".... 212 

ChaleurBay 192 

Challenger,  Cape 2.36 

Chama  Bav 231 


INDEX  TO  APPENDIX  IV. 


[Page  271 


Page. 

Cham-Callao  Island 240 

Chame,  Point 213 

Chamisso  Island 198 

Champerico 202 

Chanaral  Bay 211 

Island 211 

Chandeleur  Islands 196 

Chao  Islet 212 

Chapel  Island 241 

Chapu 242 

Charles  Cape 195 

Island,  Chile 210 

Galapagos  Group.  251 

Hudson  Strait 191 

Charleston 195 

Charlottetown 192 

ChateauBay 192 

Chatham  Harbor 194 

Island,     Galapagos 

Group 251 

S.  Pacific 259 

ChatteCape 192 

Chaume,La 224 

Chausey  Islands 224 

Chedubah  Island 238 

Chemulpo 247 

Chentabun  River 240 

Chepillo  Island 213 

Cherbourg 223 

Cheribon 243 

Cherso 227 

Chiachi  Islands 199 

Chicarene  Point 202 

Chidleigh  Cape 191 

Chifu 247 

Chignecto  Cape 193 

ChignikBay 199 

Chilca  Point 212 

ChimbaBay 211 

Chimbote 212 

Chincha  Islands 212 

Chinchin  Harbor 241 

Chinchorro  Bank 197 

Chin-hai 241 

ChinoBay 241 

Chirambiri  Point 213 

Chirikof  Island 199 

Chitlaclslet 234 

Chittagong  River 238 

Choda  Island 247 

Choiseul  Island 254 

Port... 235 

Choros  Islands 211 

Christiana  Islands 229 

Christiania 219 

Christianshaab 264 

Christianso  Island 222 

Christianssand 218 

Christiansted 205 

Christiansund 218 

Christmas  Cove 210 

Harbor 236 

I.,  Indian  Ocean 236 

N.  Pacific 251 

Christopher,  St 205 

Christoval,  San,  Island 254 

Chuapa  River 211 

Chuluwan  Island 232 

Chupat  River 209 

Churriica,  Port 210 

Chusan  Islands 241 


PLACES — continued . 

Page. 

Claris  Island 202 

Cica.  Mount 228 

Cienfuegos 204 

Ciotat 226 

Cispata,  Port 206 

CittaNuova 227 

Civitavecchia 226 

Clara,  Sta 200 

Clare  Island 217 

Claremont  Point 262 

Clarence  Harbor,  Bahamas.  203 

Port,  Alaska 198 

River 261 

Clarion  Island 202 

Claushavn 264 

Clear  Cape 216 

Clearwater  Point 192 

Gierke  Island 257 

Clermont  Tonnere  Island 257 

Cleveland,  Cape 261 

Clew  Bay 217 

ClifdenBay 217 

Clipperton  Island,  Mexico  .   202 

N.Pacific 253 

Clonard,  Cape 250 

Coast  Castle,  Cape 231 

Coatzacoalcos 197 

Cobbler  Rock 198 

Cobija 212 

CobreBay 211 

Cochin 237 

Cockell  Islet 259 

Cockscomb  Mountain 197 

Coconada 238 

Cocos  Island,  C.  America  . .  203 

N.Pacific 250 

Cod,  Cape 194 

CoderaCape 206 

Codfish  Island 263 

Codroy  Island 192 

Coetivy  Island 235 

Coffin  Bay 260 

Island,  Madagascar 235 

Nova  Scotia 193 

Cofre  de  Perote  Mt 196 

Coiba  Island 202 

Colberg 221 

Colbert  Islet 259 

Coles  Point 212 

Colina  Redonda 212 

ColnettBay 201 

Colombo 237 

Colon 206 

Colonia 208 

Colonna,  Cape,  Greece 229 

Italy 227 

Columbia,  Cape 264 

Columbretes  Islands 225 

Columbus  Island 198 

Colville,  Cape 263 

Coman  Inlet 211 

Comandatuba 207 

Commerson  Island 255 

Comorin,  Cape 237 

Comoro  Island 235 

Concei^ao 208 

Conception  Island 203 

Point 201 

Conde 207 

CondorCove 211 

Condore  Islands 240 


Page. 

Conducia 233 

Conejo,  El,  Point 201 

Coney  Island 241 

ConfitesCay 204 

Congo  River 232 

Congrehoy  Peak 197 

Conn^table  Islet 207 

Constantinople 229 

Constitution  Cove 212 

Contas 207 

Conte,  Port 226 

Contoy  Island 197 

Conway,  Cape 261 

Reef 258 

Cook  Cape 199 

Mountain 261 

CookraHill 198 

Cooper,  Port 263 

Copenhagen 222 

Copiapo 211 

Copper  Island 250 

Coquet  Island 216 

Coquille  Island 252 

Coquimbo 211 

Coral  Island 208 

Islet 208 

Corcovado  Volcano 210 

Cordouan,  Point 224 

Corfu 228 

Coringa  Islands 255 

Corinto 202 

Cork,  Ireland 218 

Port,  Staten  Island  ...  209 

Cormorant  Island 200 

Corn  Islands 198 

Corn wal  lis  Islands 253 

Port 238 

Coro,  Vela  de 206 

Coromandel  Harbor 263 

Coronation  Island 215 

Corregidor  Island 245 

Cotrientes,  Cape,  Argentina .  208 

Colombia 213 

Mexico 202 

S.  Africa 232 

Corsarios  Bay 206 

Corseulles,  Port 223 

Corso,  Cape 226 

Mountain 210 

Corti 226 

Coruna 225 

Corvolsland 213 

Coslin 221 

Cosmoledo  Island 235 

Cotinguiba 207 

Cotrone 227 

Coubre,  Point  de  la 224 

Courtown  Cays 198 

Coutances 224 

Cove  Rock 232 

Cow  Head 192 

Coy  Inlet 209 

Cozumel  Island 197 

Cracker  Bav 209 

Crassok  Point 239 

Crescent  City 200 

Cretin,  Cape 255 

Creux,  Cape 225 

Crocker  Island 258 

Croisic 224 

Croker,  Cape 259 


Page  272] 


INDEX  TO  APPENDIX  IV. 


Page. 

Crooked  Island 203 

Crozet  Islands 236 

Cruz  Cape 204 

Sta.,  Brazil 207 

California 201 

Island 201 

Islands,      Philijv 

pines 247 

S.  Pacific ...  255 

Leeward  Islands .  205 

Luzon 245 

Port 209 

Cuad  Basang  Island 247 

Cuba 203,204 

Culebra 202 

Culebrita  Island 205 

Culion  Island 245 

Cullera,  Cape 225 

Culver  Point 260 

Cumana 206 

Cumberland  Island 261 

Cumshewa  Harbor 199 

Cupchi  Point 241 

Cupica  Bay 213 

Cura^-ao  Island 206 

Little 206 

Currimao 245 

Currituck  Beach 195 

Curtis  Island 258 

Port 261 

Curzola  Island 228 

Cuttyhunk  Light 194 

Cuvier,  Cape 260 

Island 263 

Cuxhaven 222 

Cuyo  Island 245 

Cyprus 230 

Dfedalus  Shoal 233 

Dago  Island 220 

Dakar,  Port 231 

Dalcahue 211 

Dale  Point 259 

Dalrymple  Harbor 247 

Port 262 

Dalupiri  Island 245 

Damghot 236 

Dam  ma  Island 244 

Danger  Islands 257 

Dangerous  Rock 241 

Dannesbrog  Island 265 

Danube  River 229 

Danzig 221 

Dapitan 247 

Dardanelles 229 

Dar  el  Beida,  Cape 230 

Dar-es-Salaam 233 

Darien,  Colombia 213 

Georgia,  U.S 195 

Darsserort 221 

Darwin,  Port 259 

Dato  Island 240 

Datu,  Point 239 

Dauphin,  Fort 235 

Davao 246 

Davey,  Port 262 

Davids,  8t. ,  Island 214 

De  Kastri  250 

De  Pevsters  Island 254 

Deadman  Rock 192 


PLACHS — continued . 

Page. 

Deception  Island 215 

Deimaniveh 236 

Delagoa  Bay 232 

Delgada  Point 209 

Delgado,  Cape 233 

Point 209 

Demerara 207 

Denia 225 

Denis,St 235 

Denison,  Port 261 

D'Entrecasteaux  Islands 255 

Point 260 

Deseado  Cape 209 

Desert,  Mt.,  Rock 193 

Desertas 213 

Desirade 205 

Desire,  Port 209 

Desolation  Cape 209 

DiaFjeld 265 

Diamond  Harbor 238 

Point 239 

Diedrichshagen 221 

Diego  Garcia 234 

•  Ramirez  Island 209 

San 201 

Cape 209 

Dieppe 223 

Digges  Islands 191 

Dimasalasan,  Port 246 

Dinding  Channel 238 

Dingle  Bay 216 

Diomede  Island 198 

Direction,  Cape 262 

Island 240 

Disappointment,  Cape,  Sib.  250 

Washington 200 

Discovery  Harbor 264 

Disei  Island 233 

DiuHead 237 

DixCove 231 

Djabon,  Point 239 

Djambi 239 

Djursten 219 

Dnieper  Bay 229 

Doc  Can  Islet 247 

Dodd  Island 241 

Dog  Island 205 

Domar,  Pulo 240 

Domesnes 220 

Domingo,  San,  Point 201 

St.,  Cay 203 

City 204 

Dominica ^  205 

Donaghadee 217 

Dondra  Head 237 

Donegal  Bay 217 

Double  Island 238 

Point 261 

Peak  Island 241 

Douglass  Rocks 253 

Dounpatrick  Head 217 

Douvres  Rocks 224 

Dover  Point 260 

Drei  Cap  Peninsula 255 

Drepano,  Port 228 

Drobak 219 

Drogheda 217 

Dromedary  Mountain 261 

Dnimmond  Island 251 

Dublin 217 

Ducie  Island 257 


Page. 

Duff  Islands 255 

Duke  of  Clarence  Island  . . .  254 

York  I., N.Britain.  254 

S.  Pac...  254 

Dulce  Gulf 197 

River 197 

Dulcigno 228 

Dumaguete 246 

Dumaly  Point 245 

Dumf ord  Point 232 

Duncan  Island 251 

Dundee,  Rock  of 210 

Dundrum  Bay 217 

Dungarvan 218 

Dungeness 215 

New 200 

Point 209 

Dunkerque 223 

Dunnet  Head 216 

Duperrey  Islands 252 

Duppel .' 221 

Durazzo 228 

Durnford,  Port 233 

D'  Urville  Island 263 

Point 255 

Dussejour,  Cape 259 

Dwarka 237 

Eagle  Island 217 

Earakong  Island 252 

East  Cape,  Madagascar 235 

New  Zealand 263 

Siberia 250 

Dog  Island 241 

Island,  Crozet  Is 236 

Magdalen  Is 192 

Easter  Island 258 

Eastport 193 

Eau  Island 252 

Eauripik  Islands 252 

Ebon  Atoll 251 

Eckemforde 221 

Eclipse  Harbor 191 

Islands 260 

Eddvstone 215 

'Point 262 

Eden  Harbor 210 

Edenshaw  Cajje 199 

Edenton 195 

Edinburgh 216 

Eeragh  Island 217 

Egedesmunde 264 

Eggegrund  Islet 219 

Egmont  Mountain 263 

Port 214 

Eimeo  Island 257 

Ekholm  Islet 220 

Elba  Island 226 

p]lbing 221 

Elena,  St.,  Port 209 

Sta.,  Point 213 

Elephant  Bav- 232 

Eleuthera  Island 203 

Elias,  St. ,  Mount 199 

Elizabeth  Bav 232 

Cape  ..." 193 

City 195 

Harbor 264 

Island,  Chile 210 

Tuamotu  Arch  257, 258 

Port 232 


INDEX  TO  APPENDIX  IV. 


[Page  273 


I  "age. 

Elizabeth  Eeef 259 

Ellice  Islands 254 

Emden 222 

Emma,  Great,  Island 203 

Emu  Bay 262 

Enanger 219 

Endelave  Island 222 

Enderbury  Island 254 

Enderby  Island 260 

Endermo 249 

Enfant  Perdu  Islan<l 207 

Engano,  Cape 245 

Engano  Island 239 

Engelholm 219 

English  Cay 197 

Eniwetok  Islands 251 

Enrag6Cape 193 

Ensenada 201 

Entry  Island 192 

Erroniango  Island 256 

Erronan  Island 256 

Escarceo  Point 245 

Escarseo  Point 206 

Eschholtz  Islands 251 

Escudo  de  Veragua 1 98 

Escumenac  Point 192 

Esdu  Island 234 

Esmeralda  Islet 206 

River 213 

Espada  Point,  Colombia  . . .  206 

Hayti 204 

Espenberg,  Cape 198 

Esperanza  Inlet 1 99 

Espiritu  Santo  Bay 207 

Cape 209 

Esquimau 200 

Essington,  Port 259 

Estaca  Point 224 

Estangues  Point 206 

Estevan  Point 199 

Etches,  Port 199 

Eten  Head 212 

Eu,  Pulo 240 

Eureka 200 

Euripo  Strait 229 

Europa  Island 235 

Eustatius,  St 205 

Evangelistas  Islantl 210 

Evaristo,  San 201 

Expedition  Bay 250 

Faero  Islands 213 

Fair  Isle  Skroo 216 

Fairy,  Port 260 

Faiu,  W.,  Islet 252 

Fakaofu  Islet 254 

Fakarana  Island 258 

Falkenberg 219 

Falkland  Islands 214 

Falmouth,  England 215 

Jamaica 204 

False  Cape  Horn 209 

Point 238 

Falster  Island 222 

Falsterbo 219 

Famagusta 230 

Famine,  Port 210 

Fanad  Point 217 

Fanning  Island 251 

Fano  Island,  Adriatic 228 

Denmark 223 


I'LACES — continued. 

Page. 

Farallon  Islet 200 

Faraulep  Island 252 

Farewell,  Cape,  Greenland.  265 

New  Zealand 263 

Farina,  Cape 230 

Farisan  Island 234 

Farn  Island 216 

Faro  Island,  Sweden 219 

of  Messina 226 

Farquhar  Islands 235 

Farrall  Rock 198 

Farralon  de  Pajaros 252 

Fartak,  Ras 236 

Fastnet  Rock 216 

Father  Point 192 

Fatsizio  Island 249 

Fatu  Hiva  Island 253 

Huku  Island, Galapagos  251 

Marquesas . .  253 

Fatuna  Island 257 

Fayal  Channel 213 

Island 213 

Fecamp 223 

Fehpe,  San,  Cavs 204 

Point' 202 

Felix,*St.,  Island,  Chile  ...  211 

S.  Pacific  ...  25S 

Fenerive  Point 235 

Fermin  Point 201 

Fernandina 195 

Fernando  Noronha 214 

Po  Island 231 

San,  River 196 

Port 245 

Trinidad 206 

Ferolle  Point 192 

Ferro  Island 214 

Ferrol 225 

Fetouhouhou  Island 253 

Feys  Island 252 

Fidonisi  Island 229 

Figari  Cape 226 

Filzand  Island 220 

Finisterre,  Cape 225 

Firase  Rocks 248 

Fire  Island 1 94 

Firmin,  San 202 

Fischausen 221 

Fish,  Great,  Bav 232 

Little,  Bay 232 

Fiskernaes 26^ 

Fitz  Roy  River 260 

Fiume 227 

Five  Fathom  Bank 195 

Flamborough 216 

Flamenco 211 

Island 213 

Flat  Island 234 

Flattery,  Cape 200 

Flensberg 221 

Flesko,  Cape 242 

Flinders  Island 262 

Islands 261 

River 262 

Flint  Island 253 

Florence 226 

Flores  Island,  Azores 213 

Indian  Arch 243 

Uruguay 208 

Florida  Island 254 

Flower  Cove 192 


Page. 

Flushing 223 

Fly  River 255 

Foerder  Islet 219 

Fogo  Island 214 

Fohr 222 

Foreland,  North 215 

South 215 

Formigas  Islands 213 

Shoal 204 

Formosa  Island 242 

Fornws 223 

Forsmark 21.9 

Forsyth  Point 199 

Forth  Mountain 217 

Fortune  Island.. -1 203 

Foulwind,  Cape 263 

Four,  Le,  Rock 224 

Fowey  Rocks 195 

Fowler  Point 260 

Francis  Island 251 

St.,  Cape,  C.  Colon V. . .  232 

N^wf'dl'd  . .  191 

Francisco,  San 200 

Cape 213 

Head 212 

River 207 

Sao 208 

Frankland  Island : 261 

Franklin  Harbor 260 

Franz  Josef  Land 264 

Eraser  River 200 

FrayleRock 204 

Fravles  Point 212 

Frederick,  Port 262 

Frederik  Hendrik,  Cape. . .  262 

Frederikshaab 264 

Frederiksthal 265 

Frederiksvaern 219 

Fredriksten 219 

Freels  Cape 191 

Frehel,  Cape 224 

Freikallen 218 

Fremantle 260 

French  Cav 203 

Frigate  Shoal 253 

Freycinet,  De,  Islets 259 

Peninsula 262 

Frio,  Cai)e,  Brazil 208 

W.  Africa 232 

Port 208 

Froward  Cape 210 

Fruholm 218 

Frying  Pan  Shoals 195 

Fuenterrabia 224 

Fuerta  Ventura  Island 214 

Fuerte  Island 206 

Fuga  Island 245 

Fugle  Huk 265 

Fulanga  Island 257 

Fulehuk 219 

Funafuti  Island 254 

Funk  Island 191 

Funkenhageh 221 

Furen  Islet 218 

Fushiki 249 

Futuna  Island 256 

GaalongBay 240 

Gabo  Island 261 

Gabriel  Mountain 216 

Gaeta 226 


22489—03- 


-18 


Page  274] 


INDEX  TO  APPENDIX  IV. 


Page. 

Gafor  Island 234 

Galapagos  Islands 250, 251 

Galera  Point,  Ecuador 213 

Trinidad 206 

Galgenl>erg 222 

Galiola  Rock 227 

Galita  Island .♦ 230 

Gallant,  Port 210 

Galle,  Point  de 237 

Gallegos  River 209 

Galley  Head 218 

Gallinas  River 231 

Gallipoli,  Italy 227 

Turkey  , 229 

Galloway,  iVliill  of 215 

Galveston 196 

Galway 217 

Gambler  Island 257 

Gange 220 

Gannet,  Outer,  Island 191 

Rock 193 

Gap  Rock 241 

Garcia  d' Avila 207 

Gardiner  Island 253 

Gardners  I.,  I^ong  Island  . .  194 

S.  Pacific 254 

Garra^,  Little 238 

Gaspar,  Island  and  Strait . .  239 

Rico  Reef 253 

Gasparilla  Island 196 

Gaspe  Cape 192 

Gata,  Cape,  Cyprus 230 

de,  Spain 225 

Gaujam 238 

Gay  Head 194 

Gebey  Islands 244 

Geelong 260 

Gefle 219 

Genoa 226 

Geoi^e,  Fort,  Cay 203 

St.,  Cape,  Florida 196 

Newfdl'd  . .  192 

Nova  Scotia.  193 

Island,  Alaska . .-.  199 

Azores 213 

Georges  Island 202 

St.,  Cay 197 

Georgetown 195 

Georgia,  South,  Island 214 

Geronimo,  San,  Island 201 

Geyser  Reef 235 

Gharib,  Has 233 

Ghir,Cape 231 

Gilxlo  Island 246 

Gibraltar 225 

Giglio  Island 226 

Gijon 224 

Gilbert  Islands 251 

Gillolo  Island 244 

Ginger  Cay 203 

Girgenti 227 

Gizau 234 

Gizo  Island 254 

Glas  Island 216 

Glasgow 216 

Glashedy  Island ^21 7 

Glenan  Islands 224 

Glocester  Island 258 

Glorioso  Islands 235 

Gloucester  Island,  Aus 261 

Massachusetts 194 


PLACES — continued. 

Page. 

Glover  Reef 197 

Gnarp 220 

Goa 237 

Godhavn 264 

Godthaab 264 

Goedereede 223 

Golam  Head 217 

Gomenitza 228 

Gomera  Island 214 

Gonaives 204 

Gonave  Island 204 

Good  Hope,  Cape,  Africa..  232 

China 241 

>• Island 257 

Success  Bay 209 

Goose  Island 261 

Gopalpur 238 

Goram  Islands 244 

GordaCay 198 

Point 212 

Gore,  Port 263 

Goree  Island 231 

Road 209 

Gorgona  Island 213 

Goro  Island 256 

Goroiitalo 242 

Goto  Island 248 

Gottenburg 219 

Gottland  Island 219 

Gough  Island 214 

Gozier  Islet 205 

Gozo  Island 227 

Gracias  a  Dios  Cape 198 

Graciosa  Island 213 

Grado 227 

Grand  Manan  Island 193 

Port 234 

Riband  Island 226 

Grande  Point 211 

Grange  Point 204 

Granitz 221 

Granville 224 

Grappler,  Port 210 

Grave,  Point  de 224 

Gravelines 223 

Gready  Harbor 191 

GreatBirdRock 192 

Rock  Head 198 

Green,  Cape 261 

Island,  Labrador 191 

Newfoundland. . .  192 

Nova  Scotia 193 

Greenly  Island 192 

Greenspond  Island 191 

Greenwich 215 

Island 252 

Gregory,  Cape 209 

Port 260 

Grenada 205 

Grenville,  Cape 262 

Grey  River 263 

Greytown 198 

Griefswald 221 

Grief swalder  Die 221 

Grim,  Cape 262 

Grimsey  Nordd  ranger 265 

Grip 218 

GrisNezCape 223 

Groate  Eylandt 259 

Groix,  Island  de 224 

Gross-Horst 221 


Page. 

Grouin  du  Cou,  Point  de 224 

Gruizza  Rock 227 

Gryto 218 

Guadalcanar  Island ,  254 

Guadeloupe,  L.  California. .  201 

West  Indies 205 

Guaineco  Islands 210 

Guaira,  La 206 

Guaja  Shima 248 

Guam  Island 252 

Guana,  Little,  Cay 203 

Guanape  Islands 212 

Guanica 205 

Guantanamo 204 

Guarapiri  Islets 207 

Gnaratiba  Cape 208 

Guardafui,  Cape 233 

Guascama  Point 213 

Guatulco,  Port 202 

Guayaquil 213 

Guaymas 202 

Guerande 224 

Guerin  Island 247 

Guguan  Island 252 

Guimaras  Island 246 

Guiuan 246 

Guldager 223 

Gull  Island,  Little 194 

Gullan,  San,  Island 212 

Gun  Cay 203 

Gunong  Api  Island 243 

Gutzlaff  Island 242 

Gwadar  Bay 237 

Gwatar  Bay 237 

Habana 204 

Habibas  Island 230 

Hacha,  Rio  de  la 206 

Haddington,  Port 244 

Haedic  Island 224 

Hafun,  Ras 233 

Hagenmeister  Island 198 

Hague,  Cape  la 223 

The 223 

Hai-Duong 240 

Hai-Fong 240 

Haifa 230 

Hainan  Island 240,  241 

Haitien,  Cape » 204 

Hai-vun-tan  Island 247 

Hakodate 249 

Half  Port  Bay 210 

Half-Moon  Cay,  Belize 197 

Nicaragua 198 

Halgan  Island 259 

Halifax 193 

Haliguen,  Port 224 

Hall  Island 252 

Islands,  Sir  James 247 

Halmstad 219 

Hals 223 

Halt  Bay 210 

Halten  Island 218 

Hamberg 219 

Hamilton  Island 214 

Mountain 200 

Port 248 

Hammamet  Bay 230 

Hammerfest 218 

Hampton.. 194 

Hamrange 219 


INDEX  TO  APPENDIX  IV. 


[Page  275 


Page. 

Hanalei 253 

Hanfelah  Bay 233 

Hangklip,  Cape 232 

Hannibal  Isles 262 

Hano  Island 219 

Ha-Noi 240 

Hao  Island 258 

Haradsskar  Islet 219 

Haraiki  Island 258 

Harbor  Grace 191 

Harburg 222 

Hardy,  Sir  C,  Island 262 

Harpe,  La,  Island 258 

Harrison  Cape 191 

Hartlepool 216 

Harvey,  Port 200 

Harwich 216 

Hatteras  Cape 195 

Haujani  Islet 237 

Haustholni 223 

Haute  Island 193 

Havre 223 

Cape  le 193 

Hawaii 253 

Hayter  Island 255 

Heard  Island 236 

Hearts  Content 191 

HeaudeBrehat 224 

Heawandu  Island 234 

Hecate  Bay 199 

Cove 200 

Hecla,  Cape 264 

Hed,  Rasal 236 

Hee-tah-doo  Island 234 

Hegadis  Island 243 

Heiligen  Creutz 221 

Hekkingen 218 

Hela 221 

Helena,  St.,  Island 214 

Helgoland 222 

Heliers,  St 218 

Hellevoetsluis 223 

Helliso 218 

Hellyer  Rocks -...  210 

Helsinborg 219 

Helsingfors 220 

Helvick  Head 218 

Henderson  Island 257 

Henderville  Island 251 

Henlopen  Cape 195 

Henrv  Cape 195 

Port 210 

Heongsan,  Port 242 

Herald  Cays 255 

Hereheretue  Island 257 

Hermes,  Cape 232 

Hermit  Island 255 

Hermite  Island 209 

Herradura  de  Carrizal 211 

Hervey  Islets 258 

Hesquiat  Harbor 199 

Hesselu  Island 222 

Hessenstein 221 

Hestskjaer 218 

Heve,  Cape  la 223 

Hiaou  Island 253 

Hikueru  Island 258 

Hillswickness 216 

Hilo 253 

Himmittee  Island 234 

Hiniiwar 237 


PLACES — continued. 

Page. 

Hiogo 248 

Hirado  No  Seto 248 

Hirtshals 223 

Hi va-Oa  Island 253 

Hjelm  Islet 223 

Hjertholm 218 

Hjoerringa  Mountain 218 

Hoa-pin-su  Island 244 

Hobart  Town 262 

Hodeidah  Road 234 

Hog  Island,  Indian  Ocean. .  235 

Virginia.. 195 

Islands 197 

Hogland  Island 220 

Hogolu  Islands 252 

Hogsty  Reef 203 

Hogulu  Islands 252 

HoheWeg 222 

Hohenschonberg 221 

Hokianga  River 263 

Hokitika 263 

Holborne  Islet 261 

Hole-in-the-Wall 232 

Hollo  Island 219 

Holmestrand 219 

Holmogadd 220 

Holsteinberg 264 

Holvhead 215 

HoiiDau  Island 240 

Hondeklip  Bav 232 

Honfleur  .....' 223 

Hongkong 241 

Hon-M6 240 

Honolulu 253 

Hood  Island 251 

Lord,  Island 257 

Point,  Australia 260 

Port,  Cape  Breton  Id . .  193 

Hope  Island 261 

Hopedale  Harbor 191 

Hopes  Advance,  Cape 191 

Hoppers  Island 251 

Horn,  Cape 209 

Head 217 

Island 196 

Home  Island 257 

Hornelen  Mountain 218 

Horsens 222 

Horten 219 

Hospital  Bight 197 

Hougue,  Cape  La 223 

Houtman  Rocks 260 

Howaivuh 236 

Howe,  Cape,  East 261 

West 260 

Lord,  Island 257,  259 

Islands 254 

Sound 200 

Howland  Islands 251 

Howth  Peninsula 217 

Huafo  Island 210 

Huaheine  Island 257 

Huanchaco  Point 212 

Huarmey 212 

Huasco 211 

Hudiksvalls 220 

Huelva 225 

Hiigeberg 221 

Hui-lang-san 241 

Hull  Island..... 258 

Hulls  Island 254 


Page. 

Hulu-shanBay.. 247 

Humber  River 216 

Humboldt 200 

Humphrey  Island 254 

Hungwha  Channel 241 

Hunter  Island,  N.  Hebrides.  256 

Tasmania 262 

Hurds  Island 251 

Hurst  Castle 215 

Husum 222 

Hvidingso 218 

Iba 245 

Ibayat  Island 246 

Ibbetson  Island 251 

Ibiza,  Port 226 

Icacos  Point,  Belize 197 

Trinidad 206 

Ichabo  Island 232 

Icy  Cape 198 

leraka 229 

Ifalik  Islands 252 

Iglooik  Island 264 

Ignacio,  San,  Point 201 

Iguape 208 

IkiSima 248 

Ildefonso  Islands 209 

Ilha  Grande 208 

Ilheos 207 

Ho 212 

Iloilo 246 

Inaboye  Saki 249 

Inaccessible  Island 214 

Inagua  Islands 203 

Inch  Keith  Rocks 216 

Indefatigable  Island 251 

Indian,  Cape 250 

Harbor : 191 

Head 261 

Tickle 191 

Indianola 196 

Indio  Point 208 

Indispensable  Reefs 254 

Indrapura  Point 239 

Ingolfshofde 265 

Ingolsfjeld 265 

Inishboffin 217 

Inishowen  Head 217 

Inishrahull 217 

Inishturk  Island 217 

Iniue  Island 257 

Innamban  Bay 232 

Inscription,  Cape 260 

Investigator  Strait 260 

Ipswich 194 

Iquique 212 

Ireland  Island 214 

Isaac,  Great,  Cay 203 

Isabel  Cape 210 

Island 254 

Point 196 

Isene 229 

Isidro,  San,  Cape 210 

Isla  Grande 202 

Island  Harbor 199 

Islav 212 

Isle'of  Man 215 

Isola 227 

Isolette,  Cape 236 

Istria,  Caped' 227 


Page  276] 


INDEX  TO  APPENDIX  IV 


Page. 

Itacolomi  Islet 208 

Point 207 

Itapacaroya  Point 208 

Itaparica 207 

Itapemirim 207 

Itnrup  Island 249 

Ivigtuk f 2()4 

IwoShima 248 

Iwo-sima 244 

Jabwat  Island 251 

Jackson,  Port 261 

Jacksonville 1 95 

Jacinel 204 

Jacobshavn 264 

Jaffa,  Cape 260 

Jago,  St.,  Island 214 

Jaguaribe  River 207 

Jaluit  Island 251 

Jamaica 204 

James  Island 251 

St.,  Cape,  C.  China...  240 

Vancouver  1 .   199 

Jan  May  en  Island 265 

Jara  Head 211 

Jarea... 225 

Jarvis  Island 254 

Jashak  Bay 237 

Java 243 

Head 239 

Jean,  St. ,  de  Luz 224 

Jebel  Zukur  Island 234 

Jelaka,  Pulo 239 

Jelalil 234 

Jensen  Nunatak 264 

Jeremie 204 

Jershoft 221 

Jervis  Bav 261 

Cape 260 

Island 251 

J  esus  Maria  Island 255 

Jibara 203 

Jiddah 234 

Jighinsk  Island 264 

Joao,  San,  da  Barra 207 

Johanna  Island 235 

John,  St.,  Cape,  Newfdl'd.  191 

Staten  Island  209 

Island ^205 

Johns,  St.,  Island,  Red  Sea.  233 

N.  Brunswick  . . .  193 

Newfoundland. . .  191 

River 195 

Johnston  Islands 253 

Jolo  Islands 247 

Jomf ruland 219 

Jona,  St. ,  Island 250 

Jos6,  San,  California 200 

de  Guatemala 202 

del  Cabo 201 

Port 209 

Joseph  Henry,  Cape 264 

Juan  Fernandez  Island 258 

San 205 

Cape 205 

delSur 202 

Point 197 

Port,  Peru 212 

Vancouver  1 .  200 

St., Bay...- 206 

Juanico,  San,  Point 201 


PLACES — continued . 

Page. 

Jubv,  Cape 231 

Judith  Point 194 

Juggernath 238 

Juist 222 

Julian,  San,  Port 209 

St., Island 240 

Julianshaab 265 

Juneau 199 

Jupiter  Inlet 195 

Jura  Island 229 

Juul,  Cape 265 

Kabenda  Bay 232 

Kabuli  Island 245 

Kado  Sima 249 

Kagoshima 248 

Kahoolawe  Island 253 

Kaipara  Harbor 263 

Kais  Islet 236 

Kajartalik  Island 264 

Kakirouma 244 

Kal  Farun  Islet 233 

Kalama 200 

Kalantan 240 

Kalboden  Island 220 

Kalibia 230 

Kalingapatam 238 

Kallundborg 222 

Kalpeni  Islet 234 

Kama  Islands 252 

Kamaishi 249 

Kamardn  Bay 234 

Kambangan  Island 243 

Kambara  Island 257 

Kamchatka,  Cape 250 

Kanala,  Port 259 

Kanathea  Island 256 

Kandavu 256 

Kandeliusa  Island 229 

Kangamint 264 

Kangarssuk  Havn 264 

Kaniongan  Point 242 

Kannanur 237 

Kao  Island 258 

Kappeln 221 

Kara  Burnu,  Cape 229 

Karachi 237 

Karajinski  Island 250 

Karimon  Djawa  Island 243 

Karlshamn 219 

Karlskrona 219 

Ka^ke 220 

Kasm 237 

KatakoloBay 228 

Kater  Island 253 

Katiagam 239 

Katie  Rock 228 

Kauai  Island 253 

Kawhia  Harbor 263 

Keats,  Port 259 

Kee-lah  Island 234 

Keeling  Islands 236 

Keenapoussan  Island 247 

Keitum 222 

Kelung 242 

Kendall,  Cape 264 

Kent  Island 261 

Keppel  Island 257 

Kermadec  Islands 258 

Kertch 229 

Ketoy  Island 249 


Page. 

Key  West 196 

Khurig  Islet 236 

Kharim-Kotan  Island 249 

Khaur  Fakan  Bav 236 

Kheli '. 229 

Khor  Nohud 234 

Xowarat 233 

Ki  Islands 244 

Kiama  Harbor 261 

Kidnappers  Cape 263 

Kiefali,  Cape 228 

Kiel  221 

Kikai-jima 244 

Killiney  Hill 217 

Killybegs 217 

Kilwa  Kisiwani 233 

Kimbeedso  Island 234 

King  George  Sound 260 

Island,  Alaska 198 

Australia 260 

Kings  Island 258 

Kingston 204 

Kingstown 217 

Kink wosan  Island 249 

Kinnsund 218 

Kino  Point 202 

Kinsale 218 

Kirkwall 216 

Kisimayu  Bay 233 

Kiska  Island '. 199 

Kistna 238 

Kiswere 233 

Kittan  Islet 234 

Kjorge 222 

Knocklane 217 

Knockmealdown Mountain.  218 

Knocknarea 217 

Knox  Bay 2OO 

Cape 199 

Knysna 232 

Kobe 248 

Kodiak  Island 199 

Koh  Chang 240 

Kong 240 

Krah  Islet 240 

Tang  Rocks 240 

Kokoun-tan  Islands  . . . 248 

Koksher : 220 

Kolding 222 

Komba  Island 243 

Kompas  Mountain 218 

Kongelab  Islands 251 

Konigsberg 221 

Koniushi  Island 199 

Koppem 21 8 

Koprino  Harbor 200 

Koroni  Anchorage 228 

Korror  Islands 252 

Kos 229 

Kosair,  Arabia 236 

Red  Sea 233 

Kosime  No  Osima . . : 248 

Koster 219 

Kottaringin  Bay 242 

Kovra  Rythi  Point 235 

Kozu  Shima  Mountain 249 

Krakatoa  Island 239 

Krishna  Shoal 238 

Kroe 239 

Kronberg 222 

Kronstadt 220 


INDEX  TO  APPENDIX  IV. 


[Page  277 


Page. 

Krusenstern  Cape 198 

Kub  Kalat 237 

Kuchino  Shima 248 

Kuchinotsu 248 

Kuino 220 

Kullen  Point 219 

Kumi  Island 244 

Kunipta 237 

Kunashir  Island 249 

Kundapur 237 

Kuntidah 234 

Kuper  Harbor 248 

Port 199 

Kiiria  Maria  Islands 236 

KuroSima 248 

Kusakaki  Jima 248 

Kusrovie  Rock 240 

Kusterjeh 229 

Kutpur 237 

Kuweit 236 

Kweshan  Islands 241 

Kyangle  Islets 252 

Kyauchau  Bay . .   247 

Kyuquot  Sound 1^'9 

Labuan  Island 242 

Labyrinth  Head 209 

Laccadive  Islands 234 

Lacepede  Island 260 

Lady  Elliot  Island 261 

Frances,  Port 235 

Lagartos 197 

Laghi,  Cape 228 

Lagoon  Head 201 

Lagos 225 

River 231 

Lagosta  Island 228 

Lagostini  Island 228 

Lakemba  Island 256 

Laniaka 230 

Lambayeque 212 

Lambert,  Cape 260 

Lamo  Bay 233 

Lamock  Island 241 

Lampedusa  Island 227 

Lam  pong  Bay 239 

Lamyit  Island 241 

Landfall  Island 209 

Lands  End 215 

Landskrona 219 

Landsort 219 

Langanaes  Point 265 

Langeland  Island 222 

Langeoog 222 

Langesund 219 

Langford,  Port 199 

Langkuas  Island 239 

Langotangen 219 

Langwarden 222 

Lanzarote  Island 214 

Laruehuapi  Cove 211 

Lassa,  Cape 242 

Lassau 221 

Latakivah 230 

Latouche  Treville,  Cape  ...  260 

Laun 191 

Laurie  Island 215 

Laut,  Pulo 242 

Lavaca 196 

Lavata 211 


PLACES — continued. 

Page. 
Lawrence,  St. ,  Island ,  Alaska  198 

Siberia 250 

Laykan,  Port 242 

Laysan  Island 253 

Lazaref ,  Port 250 

Lazaro,  San,  Cape 201 

Leander  Shoal 192 

Leba 221 

Lebu  River 211 

Leeuwin,  Cape 260 

Legendre  Island 260 

Leghorn 226 

Lema  Island 241 

Lemnos  Island 229 

Lengua  de  Vaca  Point 211 

Lennox  Cove 209 

Leones  Island 209 

Leopold,  Port 264 

Lepar,  Pulo 239 

I^epreau  Cape 193 

Lernia 197 

Lerwick 216 

Leschenault,  Cape 260 

Lesina  Island 228 

L'  Etang  Harbor 193 

Leven  Island 235 

Port 235 

River 262 

L'  Eveque,  Cape 260 

Lewis,  St.,  Cape 191 

Leyden 223 

Levte  Island 246 

Lhou  Reef 255 

Liakhov  Islands 264 

Liancourt  Rocks 250 

Liant,  Cape 240 

Liao-ti-shan 247 

Libau 220 

Libertad,  C.  America 202 

Mexico 202 

Lifu  Island 259 

Lighthouse  Rocks 199 

Limerick 216 

Limon,  Port 198 

Lincoln  Island 241 

-^—  Port 260 

Lindesnes 218 

Lindi  River 233 

Lindo,  Port 229 

Linga  Island 238 

Linguelta,  Cape 228 

Linosa  Island 227 

Lipari  Island 226 

Lisbon 225 

Lisburne  Cape 198 

Lisian.sk y  Island 253 

Lissa  Island 228 

List 221 

Lister 218 

Lith 234 

Litkieh  Island 251 

Little  Hope  Island 193 

Lituya  Bay 199 

Liverpool 215 

Port 235 

River. : 259 

Livorno 226 

Lizard  Point 215 

Llico 211 

Loa  River 212 


Page. 

Loango  Bay 232 

Lobito  Point 232 

Loboa  Cay,  Bahamas 203 

Mexico 196 

de  Afuera  Island 212 

Tierra 212 

Island,  Canaries 214 

T  Jruguaj^ 208 

Point,  N.  Chile 212 

S.  Chile 212 

Lodingen 218 

Lofoten  Island 218 

Loggerhead  Key 196 

Loheiyah 234 

Loma  Point 201 

Lonias  Point 212 

Lombata  Island 243 

Lombok  Island 243 

London,  East 232 

Londonderry 21 7 

Cape 259 

Long  Island,  Bahamas 203 

United  States 194 

Loo  Choo  Islands 244 

Looke,  Port 235 

Lookout  Cape,  N.  Carolina.  195 

1 Point,  Australia 261 

Maryland 195 

Lopatka,  Cape 250 

Lopez,  Cape 231 

Lorenzo,  San,  Cape 213 

Island 212 

Loreto 201 

Lorient 224 

Loro,  Mount 245 

Lorstakken  Mountain 218 

Los,  Isles  de 231 

Lota 211 

Lots  Wife  Rock 249 

Lough  Larne 217 

Louis,  Port,  Falkland  Is . . .  214 

Guadeloupe 205 

Mauritius  Island.  234 

St 231 

Louisburg 193 

Louisiade  Archipelago 255 

Loune 223 

Low  Island 240 

Port 210 

Lowenorn,  Cape 265 

Lowestoft 216 

Loyalty  Islands 259 

Lubang  Island 245 

Lucar,  San 225 

Lucas,  San 201 

Lucia,  Santa 235 

St 204 

Cape 232 

Id.,  C.  Verde  Is. .  214 

Windward  Is  205 

Lucipara  Is\Jind 239 

Lucipari  Islantk 243 

Lucrecia  Point 203 

Lucrietta  Island 227 

Liiis,  San,  Island 202 

Luke  Point 250 

Lundy  Island 215 

Lunenburg 193 

Lungo 220 

Lupona  Point 201 


Page  278] 


INDEX  TO  APPENDIX  IV 


Page. 

LiirioBay 233 

Lussin  Piccolo 227 

Luzon  Island 245, 246 

Lyo  Island 222 

Maasin a. 246 

Macah6 207 

IVlflORo  241 

MacAskiil" Islands! ........  252 

Macassar 242 

Macauley  Island 258 

Maceio 207 

Machias 193 

Island 193 

Machikora 235 

Mackenzie  Islands 252 

MacLeay  Islets 260 

Macquarie  Harbor 262 

Island 259 

Port 261 

Macquereau  Point 192 

Madagascar 235 

Reef,  Africa 232 

Yucatan 197 

Madame  Island 193 

Madanas  Point 208 

Madeira  Island 213 

Madras 238 

Madryn,  Port 209 

Madura  Island 243 

Maestro  de  Campo  Island. .  246 

Mafamale  Island 233 

Mafia  Island 233 

Magadoxa 233 

Magdalen  Cape 192 

Islands 192 

Magdalena  Bay 201 

River 206 

Magnetic  Pole 264 

Magoari  Cape 207 

Mah  Kundu  Island 234 

Mahanuru 235 

Mah6 237 

Mahia  Peninsula 263 

Mahon,  Port 226 

Maiana  Island 251 

Maiden  Rocks 217 

Mairaira  Point 245 

Mill  t  Island 233 

Maitea  Island 257 

Maitencillo  Cove 211 

Majamba  Bay 235 

Majorca 226 

Majunga 235 

Majuro  Islands 261 

Makalleh  Bay 236 

Makarska 228 

Makatea  Island 258 

Makaua  Island 233 

Makemo  Island 258 

Makers  Ledge,  South 192 

Makkian  Island 244 

Makongai  Island 256 

Makry 229 

Mala  Point 203 

Malabrigo  Bay 212 

Malacca 238 

Malaga 225 

Malaita  Island 254 

Malamocco 227 

Malaspina,  Port 209 


PLACBS — continued . 

Page. 

Maiden  Island 254 

Maldonado,  Mexico 202 

Uruguay 208 

Male  Island  " 234 

MalembaBay 232 

Malin  Head  ". 217 

Mallicollo  Island 256 

Malmi) 219 

Malo,  St 224 

Maloclab  Islands 251 

Maloren 220 

Malpelo  Island,  Galapagos.  250 

Panama 203 

Malta 227 

Marauka  Island 256 

Manaar 237 

Mana  Sima 249 

Manado  Bay 242 

Manao 249 

Mana-watu  River 263 

Manda  Roads 233 

Mandarins  Cap 241 

Mandavi 237 

Manfredonia 227 

Mangalore ,  237 

Mangara  Island 258 

Mangaratiba 208 

Mangareva  Island 257 

Mangarin  Point 245 

Mangarol 237 

Mangles  Point 213 

Mango  Island 256 

Manila 245 

Mano  Island,  Asia 244 

Denmark 223 

Manoel,  Cape 231 

Manta  Bay 213 

Manua  Island 257 

Manukau  Harbor 263 

Manvers,  Port 191 

Manzanilla  Bav 202 

Point ' 204 

Maracaibo 206 

Maraki  Island 251 

Marambaya  Island 208 

Maranhao  Island 207 

Marble  Island 264 

Marblehead 194 

Marcial,  San,  Point 201 

Marcos,  San,  Island 201 

Marcus  Island 253 

Mare  Harbor 214 

Island,  California. ....  200 

S.  Pacific 259 

Maret  Islets 259 

Margaret  Bay 193 

Margate  Head 232 

Maria  Island 257 

INIadre  Island 202 

Port 204 

Sta.,  Cape,  Portugal. . .  225 

Uruguay  . . .  208 

Cove 201 

di  Leuca,  Cape 227 

Island,  Azores 213 

Chile 211 

S.  Pacific . . .  256 

Port 247 

Mariana  Islands 252 

Maricas  Islands 208 

Marie  Galante 205 


Page. 

Marienleuchte 221 

Mariguana  Island 203 

Marinduque  Island 246 

Marion  Island 236 

Maripipi  Island 246 

Maritimo  Island 227 

Marjes  Islets 206 

Marjoribanks 247 

Marks,  St 196 

Marlborough  Island 251 

Marmora  Island 230 

Marmorice 229 

Maro  Reef 253 

,  Maroni  River 207 

Marsala 227 

Marseille 226 

Marshall 231 

Islands 251 

Marstenen  Islet 218 

Marta,  Sta 206 

Martha,  St. ,  Cape 208 

Martin  de  la  Arena,  San 224 

Garcia  Island 208 

San,  Island,  L.  Calif . .  201 

St. ,  I. ,  Leeward  Is 205 

Vaz  Rocks 214 

Martinique 205 

Martires,  Los 252 

Marua  Island 257 

Marutea  Island 257 

Mary  Island 254 

St.,  Bay 232 

Cape,  Madagascar .  235 

Newfound- 
land  191 

Nova  Scotia.  193 

Reefs 192 

Marys,  St. ,  Island 235 

MarzoCape 213 

Mas-af uera  Island 258 

Maabate  Island 246 

Masinloc 245 

Masirah  Island 236 

Maskat 236 

Massaua  Harbor 233 

Masset  Harbor 199 

Masulipatam 238 

Matabella  Islands 244 

Matacong  Island 231 

Matagorda 196 

Matahiva  Island 258 

Matamoras  Cove 211 

Matana  Island 249 

Matanzas  Peak 204 

Matatane 235 

Matelotas  Islands 252 

Matema  Islands 265 

Maternillos  Point 204 

Matinicus  Rock 1 93 

Matoya 249 

Matthew  Island 256 

St.,  Island,  Alaska 198 

Burma 238 

— Siberia 250 

Matthias,  St. ,  Island 256 

Matu  Sima 250 

Matuku  Island 256 

Mauger  Cay 197 

Maui  Island 253 

Mauki  Island 258 

Maunganui  Harbor 262 


INDEX  TO  APPENDIX  IV 


[Page  279 


Maupili  Island 257 

Mauritius 234 

May,  Cape , 195 

Island 216 

Mayaguez 205 

Maye  Mountain 207 

Mayne  Harbor 210 

Mountain 210 

Mayo  Island 214 

Mayotta  Island 235 

Maysi  Cape 203 

Mayumba  Bay 231 

Mazarron 225 

Mazatlan 202 

Mazeraba  River 232 

Mbega  Island 256 

Mchinga  Bay 233 

McKean  Island 254 

Mecate  Mountain 196 

Mecatina  Islands 192 

Mednoi  Island 250 

Mega  Island 239 

Megalo  Kastron 228 

Mehediah 230 

Meiaco  Sima 248 

Meiaco-sima  Islands 244 

Mejia  Island 202 

Mel,  Ilhado 208 

Melbourne 260 

Meleda  Island 228 

Melinda 233 

Melle,  Cape 226 

Mellish  Reef 255 

Melmore  Head 217 

Melo,  Port 209 

Melville,  Cape,  Baliibac  I..  245 

Queensland 262 

Island,  Australia 259 

Barrows  Strait. . .  264 

Tuamotu  Arch 258 

Memel 221 

Memory  Rock 203 

Menali  Island 238 

Menchikof  C'ape 199 

Mendocino  Cape 200 

Mendoza  Island 241 

Merbat 236 

Mercy  Harbor 210 

Mergui 238 

Mesa  de  Dona  Maria 212 

Messina 227 

Mesurado,  Cape 231 

Meurka 233 

Mew  Islands 217 

Mewstone  Rock 262 

Mexican  Boundary 201 

Mexico,  City  of .'. 196 

Mexillon  Bay 212 

Mexillones  Mountain 212 

Mezen 264 

Mugan  Mwania 233 

Miautao  Island 247 

Michael,  St. ,  Fort 198 

Island 213 

Michaeloff  Island 257 

Middleton  Island 199 

Midway  Islands 253 

Miguel,  San,  Island 201 

Islands 247 

Mikake  Jima 249 

Mikindini 233 


PLACES — continued . 

Page. 

Mikomoto  Island 249 

Mikura  Jima 249 

Milagro  Cove 211 

Milazzo 226 

Mile  Island 264 

Milford  Sound 263 

Milo  Island 229 

Min  River 241 

MinaBay,  El 231 

Minchinmadiva  Mountain  .  210 

Mindanao  Island 246,  247 

Mindo»o  Island 245 

Mine  Head 218 

Minerva  Reefs 258 

Minikoi  Island 234 

MinoSima 249 

Minorca 226 

Minots  Ledge 194 

Minow 235 

Minsener  Sand 222 

Mintok 239 

MiramichiBay 192 

Misamis 247 

Miscou  Island 192 

Mississippi  River,  mouth  . .  196 

City 196 

Misteriosa  Bank 197 

Mita  Point 202 

Mitchells  Island 254 

Mitho 240 

Mitiero  Island 258 

Mitre  Island 256 

Mityleni  Island 229 

MizenHill 216 

Moa  Cayo,  Port 203 

Island 244 

Moala  Island 256 

Mobile 196 

Mocha  Island 211 

Mocomoco  Point 206 

Modeste  Island 248 

Moeara  Kompehi 239 

Moen  Island 222 

Moerenhout  Island 257 

Mogador 231 

Mohilla  Island 235 

Mojanga 235 

Mokamba,  Port 233 

Mokatein 236 

Mokha 234 

Mokil  Islands 252 

Molle,  Port 261 

Mollendo,  Port 21 2 

MollerPort 199 

Molloy 236 

Molokai  Island 253 

Molonta  Peninsula 228 

Molucca  Islands 244 

Moluk  Island 234 

Molyneux  Bay 263 

Sound 210 

Mombasa 233 

Mona  Island 205 

Monastir 230 

Mondego,  Cape 225 

Monfalcone 227 

Monhegan  Island 193 

Monomoy  Point 194 

Monrovia 231 

Montagu  Island 261 

Montalivet  Islands 259 


Page. 

Montauk  Point 194 

Monte  Christo  Islet 226 

Montebel  lo  Island 260 

Montego  Bay 204 

Montepio 196 

Monterey 201 

Monteverde  Islands 252 

Montevideo 208 

Montravel  Island 248 

Montreal 192 

Monts,  Point  de 192 

Montserrat 205 

Monze,  Cape 237 

Mopelia  Island 257 

Morane  Island 257 

MorantCays 204 

Point 204 

Moray  va 225 

Morecambe  Bay 215 

Moreno  Mountain 212 

Moresby,  Port 255 

Moreton,  Cape 261 

Morgan,  Cape 232 

Morjovetz  Island 264 

Morlaix 224 

Morotiri  Islands 258 

Morro  Avuca 202 

de  Sao  Paulo 207 

Petatlan 202 

Solar 212 

Mortlock  Islands 252 

Mosquito  Cays 198 

Motane  Island 253 

Mothe  Island 256 

Mothoni 228 

Motu-ili  Island 253 

Motu-iti  Island . . . ; 257 

Moudros 229 

Moukon  rushi  Island 249 

Moulmein 238 

River 238 

Mount,  Cape 231 

Mourondava 235 

Moville 217 

Mozambi<iue .  233 

Msimbati 233 

Mugeres  Island 197 

Muilcalpue  Cove 211 

Mukulaelae  Island 254 

Muleje 201 

Mulu  Island 244 

Mura  Harbor 248 

MuratHill 233 

Murderers  Bay 235 

Murdock  Point 262 

Murundum  Island 240 

Mururoa  Island 257 

Muscat 236 

Musendum,  Ras 236 

Mussel  Bav 210 

Mysole  Island 244 

Nachvack  Bay 191 

Nafa-Kiang 244 

Nagai  Island 199 

Nagasaki 248 

Naian  Island 256 

Nain 191 

Nairn  Cay 203 

Naitamba  Island 256 

Naka  no  Shima 248 


Page  280] 


INDEX  TO  APPENDIX  IV. 


Page. 

Nakkehooed 222 

Nam-Dinh 240 

Namki,  Port 241 

Namoluk  Islands 252 

Nainonuito  Islands 252 

Nam-quan A 241 

Naniu  Island 251 

Nanaimo 200 

Nancowry  Harbor 239 

Nanka  Island 239 

Nanomea  Island 254 

Nanoose  Harbor 200 

Nantes 224 

Nantucket  Island 194 

S.Shoal 194 

Naples 226 

Napuka  Island 258 

Nar  Foree  Island 234 

Naranjo,  Port 203 

Narendri  Bay 235 

Nargen  Island 220 

Narva ,---.220 

Nasca  Point 212 

Nasparti  Inlet 199 

Nassau 203 

Natal,  Brazil 207 

Port,  Africa 232 

Sumatra 239 

Natashquan  Point 192 

Natuna  Islands 240 

Naturaliste,  Cape 260 

Nauoinaga  Island 254 

Navachista 202 

Navalo,  Port 224 

Navarin 228 

Cape 250 

Navassa  Island 204 

Navesink  Highlands 195 

Navidad  Bank 203 

Bav 202 

Navire  Bay 236 

Naxos  Island 229 

Nazaire,  St.,  Port 224 

Necker  Island 253 

Needles  Rocks 215 

Negapatam 237 

Negrais,  Cape 238 

Negro,  Rio 209 

Negros  Island .   246 

Neill,  Port 264 

Nelson 263 

Cape 260 

Port 259 

Nemuro 249 

Neptune  Isles 260 

Nera  Point 227 

Netherland  Island 254 

Neunortalik 265 

Neuwerk 222 

Nevil  Island 252 

Neville,  Port 200 

Nevis 205 

New  Bank 197 

Bedford 194 

Britain 254 

Caledonia 259 

(iuinea 255 

Hanover 255 

Haven 194 

Hebrides 256 

Ireland 255 


PLACES — continued. 

Page. 

New  London 194 

Orleans 196 

Plymouth 263 

South  Orknevs 215 

Shetland 215 

Westminster 200 

York 194 

Newbem 195 

Newburyport 194 

Newcastle 261 

Newfoundland 191,192 

Newport,  Ireland »..  217 

Rhode  Island 194 

Newton  Head,  Great 218 

Ngatik  Islands 252 

Ngau  Island 256 

Nias  Island 239 

Nice 226 

Nicholas,  St. ,  Island 214 

Nicholson,  Port 263 

Nickerie  River 207 

Nicobar,  Great,  Island 239 

Islands 238,  239 

Nicolas  Mole 204 

San,  Island 201 

Nidingen  Islet 219 

Nieuport 223 

NieweDiep 223 

Nihiru  Island 258 

Niigata 249 

Nikalao,  St.,  Island 229 

Nikolaevsk 250 

Nikolaia,  St.,  Cape 250 

Nikolo,  St.,  Port 229 

Nila  Island 244 

Nile  River 230 

Nimrod  Sound 241 

Nine-pin  Rock 241 

Ning-po 241 

Nipe,  Port 203 

Nitendi  Island 255 

Niua-fu 257 

Niuchwang 247 

Niutao  Island 254 

NoSmaSaki 249 

Noir  Island 209 

Noir  Moutier  Island 224 

Nolloth,  Port 232 

Nome  Cape 198 

Nonuti  Island 251 

Nootka  Sound 199 

Nord  Koster  Islands 219 

Norderney 222 

Norfolk 195 

Island 259 

Norman  Cape 192 

Norrkopings  Inlopp 219 

Norrsher  Islet 220 

Norrtelge 219 

North  Cape,  Arctic  Amer. .  264 

Brazil 207 

C.  Breton  1 192 

Iceland 265 

New  Zealand 262 

Norwav.. 218 

Harbor  . . . .' 199 

Island,  Vancouver 199 

Volcano  Islands. .  253 

Lord,  Island 252 

Standing  Creek 197 

Northumberland  Cape 260 


Page. 

Northumberland  Isles 261 

Northwest  Cape 260 

Norwalk  Island 194 

Noshiaf  Misaki 249 

Saki 249 

Nosi  Be 235 

Nostra  Senhora  do  Deserto.  208 

Notch  Cape 210 

Notsuke 249 

Nottingham  Island 191 

Noumea 259 

Noun,  Cape 231 

Nouvelle,  Port 226 

Nova  Zembla 264 

Novogorodj  Port 250 

Nuevitas,  Port 203 

Nuevo,  Port 202 

Nugget  Point 263 

Nui  Island 254 

Nuistad 220 

Nuka-Hivi 253 

Nukufetau  Island 254 

Nukunau  Island 251 

Nuku-nono 254 

Nukuor  Islands 252 

Nukutavake  Island 257 

Nukutipipi  Island 257 

Numba  Island 233 

Nunez  River 231 

Nunivak  Island 198 

Nurse  Channel  Cay 203 

Nuyts  Point 260 

Ny  Sukkertop 264 

Nyborg 222 

Nyk jobing 222 

Oahu 253 

Oatafu  Island 254 

Oban 216 

Obi  Islands 240 

Obispo  Shoal 197 

Obristadbroekke 218 

Observation  Island 248 

Oby  Major  Island 244 

Occasional  Harbor 191 

Ocean  Island,  N.  Pacific  . . .  253 

S.  Pacific 254 

Ockseu  Island 241 

Ocracoke 195 

Oddensby 222 

Odenskholm 220 

Odessa 229 

Odia  Islands 251 

Oeno  Island 257 

Offer  Wadham 191 

Oho-sima 244 

Okayama,  Port 248 

Okhotsk 250 

Oki  Islands 249 

Okishi  Bay 249 

Okso 219 

Oland  Island 219 

Old  Fort  Island 192 

Point  Comfort 195 

Providence 198 

Oleai  Islands 252 

Oleron  Island 224 

Olga,  Port 250 

Olimarao  Islet 252 

Olinda 207 

OlipaRock.- 228 


INDEX  TO  APPENDIX  IV. 


[Page  281 


Page. 

Oliutorski,  Cape 250 

Olivenga 207 

Omapui  Island 247 

Omena':  Island 264 

Omo  Island 222 

Omoa 197 

Oinoi  Saki 249 

One  Fathom  Bank 238 

Oneata  Island 256 

Onef^a 264 

Ongea  Levu  Island 257 

Ono  Islands 257 

Onoatoa  Islands 251 

Oo-Sima  Harbor 248 

Oparo  Island 258 

Opobo  River 231 

Oporto 225 

Oraluk  Island 252 

Oran 230 

Orange  Cape,  Brazil 207 

Magellan  Strait..  209 

Oranienbauni 220 

Orchila  Island 206 

Oregrund 219 

Orfordness 216 

Orizaba  JNIoiintain 196 

Orkney  Islands 216 

Ormarah 237 

Ormoc 246 

Ornbay  Island 243 

Oro  No  Sima 248 

Oropesa  Cape 225 

Orskar  Rock 219 

Oruba  Island 206 

Osaka 248 

Osaki  Bay 248 

Oscarsberg 219 

OscuroHead 211 

Osnabrug 257 

Ostend 223 

Osthammar 219 

Ostro  Point 228 

Otago  Harbor 263 

Otranto,  Cape  and  Port 227 

Otwav,  Cape 260 

Port 210 

Oune-Kotan  Island 249 

Ouro  River 231 

O valau  Island 256 

Owashi  Bay 248 

Oxford 215 

Oxhoft 221 

Paanopa  Island 254 

Pabellon  de  Pica 212 

Pacasmayo 212 

Padang 239 

Tikar 242 

Padaran,  Cape 240 

Padre,  Port 203 

Pagan  Island 252 

Pagonia,  Port 228 

Painiboeuf 224 

Paita 212 

Paix,  Port 204 

Pajaros  Islets 21 1 

Pak  Chan  River 238 

Pak-Hoi  240 

Pakonjidol  Rock 228 

Palamos  Bay 225 

Palanc  )<; 24() 


PLACES — continued. 

Page. 

Palawan  Island 245 

Palenibang 239 

Palenita 202 

Palermo 226 

Port 228 

Pali,  Cape.... 228 

Pallas  Rocks 248 

Palliser,  Cape 263 

Palm  Islands 261 

Palma  Island 214 

Palmas  Bav 208 

Capo  ■- 231 

Point 197 

Palmerston,  Cape 261 

Islands 257 

Palmyra  Island 251 

Palompon 246 

Palos  Bay 242 

Pamaroong  Island 242 

Pampatar  Island 206 

Pan  de  Azucar  Island 211 

Panama 203 

Panay  Island •. 246 

Pangituran 247 

Panjang  Island 240 

Pank  Piah  Rock 241 

Pantar  Island 243 

Papey  Island 265 

Paposo  Road 211 

Para 207 

Paraca  Bay 212 

Paracel  Islands 241 

Parahiba  River  and  Port..  207 

Paramaribo   207 

Paranagua 208 

Paranahiba  River 207 

Paraca  Island 258 

Parati 208 

Paredon  Grande  Cay 204 

Parenga-renga 262 

Parenzo 227 

Parga 228 

Parida 202 

Parinas  Point 212 

Paris 223 

Parker  Cape 210 

Paros  Island 229 

Parry  Island 258 

Parrys  Group 253 

Pasado  Cape 213 

Pa-sages,  Port 224 

Pascagoula,  East 196 

Pasni 237 

Passaro,  Cape 227 

Pasuruan 243 

Patache  Point 212 

Patani,  Cape, 240 

Paternoster  Rocks 219 

Paterson  Inlet 263 

Pato  Island 206 

Patook  River 197 

Patos  Island 202 

Patras .• 228 

Patrick,  St. ,  Head 262 

Patterson,  Port 259 

Paul,  St. ,  de  Loando 232 

Island,  N.  Amer.   192 

'-  Tuamotu  ...  257 

Reunion  Island . .  235 

Rocks 214 

Pauls,  St. ,  Island 236 


Pago. 

Paumben  Pass 237 

Paxo  Island 228 

Paypoton  Mountain 197 

Pa?.,  La 201 

Pearce  Point 259 

Pearl  and  Hermes  Reef 253 

Cays 198 

Pedra  Blanca  Rock 241 

Branca 238 

de  Galha 231 

Pedro  Bank 204 

San 202 

Point 211 

Port 210 

Peel  : 260 

Island 253 

Pegasus,  Port 263 

Pei-ho 247 

Pekalongan   243 

Pelado  Island 212 

Pelagosa  Rock 228 

Peloro,  Cape 227 

Pemba  Bay 233 

Pembroke  Cape 214 

Pena  Point 206 

Penang,  Pulo 238 

Penas  Anchorage 202 

Pendulum  Islands 265 

Penguin  Islands 236 

Penha  Grande 231 

Peniche 225 

Penmarch  Rocks 224 

Penrhyn  Island 254 

Pensacola 196 

Pentland  Skerries 216 

Percy  Isles 261 

Perim  Island,  Africa 233 

India 237 

Pernambuco 207 

Pernau 220 

Peros  Banhos  Islands 234 

Perth 260 

Peru  Island 251 

Perula  Bay 202 

Pescadores  Islands,  Asia,  E. 

coast 242 

N.  Pacific 251 

Peru 212 

Point 212 

Pe-shan  Islands 241 

Petali  Island 229 

Petalidi  Bay •. 228 

Peter,  St.,  Port 224 

Peterhof 220 

Petersburg,  St 220 

Petersdorf 221 

Petit  Manan  Island 193 

Petite  Ri viCre 204 

Terre 205 

Petropavlovsk 250 

Petropolis 208 

Pha-li-du  Island 234 

Philadelphia 195 

Philip  Island 252 

Philipp  Broke,  Cape 265 

Philips  Point 202 

Phillip,  Port 260 

PhiUips  Island 258 

Phoenix  Island 254 

Pi 226 

Pianosa  Island 226 


Page  282] 


INDEX  TO  APPENDIX  IV. 


Page. 

Piohidanque 211 

Pichilinque  Bay 201 

Pico  Island 213 

Pictou  Harbor 193 

Piedra  Blanca 247 

Piedras  Blancas ^ 201 

Cay,  Cuba,  N.  coast. . .  204 

S.  coast 204 

Point. 208 

Pieman  River 262 

Pierre,  St.,  Newf'dl'd 191 

Reunion  1 235 

Rock 240 

Pietro  di  Nembo,  St. ,  Island .  227 

Pigeon  Point 200 

Pih-ki-shan  Island 241 

Pih-quan  I^eak 241 

Pih-seang  Island 241 

Pikelet  Island 252 

Pilier,  Le,  Island 224 

Pililu  Island 252 

Pillau 221 

Pillar,  Cape,  Chile 209 

Tasmania 262 

Pinaki  Island 257 

Pine,  Cape 191 

Pines,  Isle  of 204 

Pingelasp  Islands 252 

Ping-fong  Island 241 

Ping-hai  Harbor 250 

Pinnacle  Islet 198 

Pinos  Point 201 

Pique  Bay 250 

Piraeus - 229 

Pirano 227 

Pisagua 212 

Pisang 2.39 

Pisco 212 

Pitcairn  Island 257 

Pitea 220 

Pitong  Island 238 

Placentia  Harbor 191 

Point 197 

Pladda  Island 216 

Plana  Cay  ..., 203 

PlanierRock... 226 

Plata,  Isle 213 

La 208 

Port 204 

Platte  Island 2,34 

Playa  Colorado 202 

Maria,  La 201 

Parda  Cove 210 

Pleasant  Island 254 

Plettenburg  Bay 232 

Plum  Island 194 

Plymouth,  P^ngland 215 

U.  S 194 

PoileBay 192 

Pola 227 

Sta.,  Bay 225 

Polillo  Island 246 

Pollard  Cove 210 

Polloc 246 

Polusuk  Island 252 

Porno  Rock 228 

Ponafidin  Island 249 

Ponapi  Island 252 

Pond  Mountain 210 

Pondicherri 237 

Ponga  River 23 1 


PLACES — conti  nued . 

Page. 

Ponza  Islet 226 

Poolbeg 217 

Popa  Island 244 

Popof  Island 199 

Porcos  Grande  Islet 208 

Porebander 237 

Porinan 225 

Poro  musir  Island 249 

Poros  Island 229 

Port  au  Prince 204 

of  Spain 206 

Royal,  Jamaica 204 

S.  Carolina 195 

Said.. 230 

Portendik 231 

Porthcurnow 215 

Portland,  Bay 260 

Cape 262 

England 215 

Maine 193 

Porto  Bello 206 

Re 227 

Rico... 205 

Santo 213 

Seguro 207 

Yecchio 226 

Portsmouth,  England 215 

U.  S 194 

Possession,  Cape 209 

Island 236 

Postilion  Islands 243 

Povorotnyi,  Cape 250 

Prado 207 

Pratas  Island 241 

Premeira  I.^lands 233 

Preservation  Inlet 263 

Prestenizza  Point 227 

Prevesa 228 

Pribilof  Island 199 

Prince  Edward  Island 192 

Edwards  Islands 236 

Prince  of  Wales  Cape 198 

Island 262 

Sound 191 

Regent  River 259 

Princes  Island 231 

Proeste 222 

Progreso 197 

Promontore  Point 227 

Proti  Passage 228 

Proven 264 

Providence 1 94 

Island 251 

Port 250 

Psara  Island 229 

Pucio  Point 246 

Puerto  Cabello 206 

Santo  Bay 206 

Puka-puka  Island 258 

Puka-ruha  Island 257 

Pulicat 238 

Pulkowa 220 

Pulpito  Point 201 

Puna 213 

Purdy  Island 255 

Putziger  Heisternest 221 

Pyramid  Point 241 

Pyramidal  Rocks 240 

Quaco,  Cape 193 

Quad,  Cape 210 


Page. 

Quaebo  River 231 

Quebec 192 

Queen  Charlotte  Island 257 

Queenstown,  Ireland 218 

N.Zealand 263 

Quelpart  Island 248 

Quemada  Grande  Island. . .  208 

Quentin,  San,  Port 201 

Querimba  Islands 233 

Queule  Bay 211 

Quilan,  Cape 210 

Quilca 212 

Quillimane 232 

River 232 

Quilon 237 

Quin  Hon 240 

Quiniluban  Islet 245 

Quintero  Point 211 

Quita  Sueno  Bank 198 

Quoddy  Head 193 

Quoin  Great,  Island 236 

Point 232 

Race,  Cape 191 

Island 200 

Rachado,  Cape 238 

Radakala  Islands 251 

Radama  Islands 235 

Port 235 

Ragged  Island 203 

Ragusa  Rocks,  Pettini  di  . .  228 

Rakkin,  Ras 236 

Raleigh  Rock,  China 241 

Formosa 244 

Ramas,  Cape 237 

Rame  Head 232 

Ramree  Island 238 

Rangiroa  Island 258 

Rangoon 238 

River 238 

Ranu  Cove 211 

Raoul  Island 258 

Rapa  Island 258 

Raper  Cape 210 

Raphti,  Port 229 

Rarotonga  Island 258 

Rasa  Island 253 

Rathlin  Island 217 

O'Birne  Island 217 

Ratnagherry 237 

Ravahere  Island 258 

Ravn  Storo 264 

Rawean  Island 243 

Ray  Cape 192 

Raza  Island,  Brazil 208 

C.Verde  Is 214 

L.California 202 

Razzoli  Island 226 

Re  Island 224 

Real  River 207 

Reao  Island 257 

Recherche  Archipelago 260 

Recife  Cape 2.32 

Red  Islet 259 

Redang,  Great,  Harbor 240 

Redfield  Rocks 249 

Redonda  Islet 205 

Redondo  Rock 250 

Refuge  Cove 199 

Reirson  Island 254 

Reitoru 258 


INDEX  TO  APPENDIX  IV. 


[Page  283 


Rembang 243 

Kemedios  Bay 202 

Kenard  Island 255 

Islands 255 

Reiinel  Island 254 

Kensher 220 

Repon,  Pulo 240 

Re-olution  Island 191 

Reunion  Island 235 

Revel 220 

Rev,  Isladel 213 

Reyes  Head 211 

Point 200 

Reykianaes _ 265 

Reykiavik 265 

Revthur  Fjeld 265 

Rhio 238 

Rhodes,  Port 229 

Rhvnns  of  Islay 216 

Ribnitz '..  221 

Rich  Point 192 

Richmond 195 

Harbor 192 

River 261 

Riga 220 

Rigny  Mount 265 

Riniitara  Island 258 

Ringkjobin 223 

Rio  Grande  del  Norte 196 

do  Norte 207 

Sul 208 

Janeiro 208 

Riofrio,  Port 210 

Risiri  Islet 249 

Rissnaes  Point 265 

Rivadeo 224 

Rivad«sella 224 

Rivers,  Cape 242 

Rixhoft 221 

Roa  Poua  Island 253 

Roatan 197 

Roberts  Point 200 

Roca,  Cape 225 

Partida,    Mexico,    E. 

coast 1 96 

AV.  coast 202 

Rocas  Reef 214 

Rochefort 224 

Rochelle 224 

Rockabill 217 

Rockall  Islet 213 

Rockingham  Bay 261 

Rockland 193 

Rodd  Bay 261 

Rodkallen 220 

Rodney,  Cape 255 

Rodoni,  Cape 228 

Rodriguez  Island 234 

Rodsher  Island 220 

Roeskilde 222 

Rogosnizza 227 

Roigen,  Cape 249 

Rokuren  Island 248 

Roma  Island 243 

Romain  Cape 195 

Roman,  San,  Cape 206 

Romanzof  Cape 198 

Romanzov  Islands 251 

Romblon  Island 246 

Rome 226 

Ronaldsav,  North 216 


PLACES — continued. 

Page. 

Roncador  Cay 198 

Rongerik  Islands 251 

Roodewal  Bav 232 

Roque,  St. ,  Cape 207 

Roques  Islands 206 

Rosa,  Sta. ,  Island 201 

Rosalia,  Sta. ,  Bay 201 

Ro.salind  Bank 198 

Rosario  Island 253 

Rose  Island 257 

Spit  Point 199 

Rosemary  Island 2H0 

Rosier  Cape 1 92 

Ross  Island 248 

Ros-sel  Island 255 

Rostock 221 

Rota  Island 252 

Rotterdam 223 

Rotti  Island 243 

Rottnest  Island 260 

Rotumah  Island 256 

Round  Island 247 

Roundhill  Island 191 

Rovigno 227 

RoxoCape 196 

Royal  Island 203 

Royalist,  Port 245 

Ruad  Island 230 

Riigenwalde 221 

Rum  Cay 203 

Runaway,  Cape 263 

Runo  Island 220 

Ruixirt  Island 210 

Rurutu  Island 258 

Ryvingea  Island 218 

Saba 205 

Sabine  Pass 196 

Sabioncello  Peninsula 228 

Sablayan  Point 245 

Sable  Cape 193 

Island 193 

Sacatula  River 202 

Sacrificios  Island 196 

Point 202 

Saddle  Group 242 

Island 191 

Sado  Island.. 249 

Safajah  Island 233 

Safatu  Island 240 

Saida 230 

Saigon  240 

Saintes  Islands 205 

Saipan  Island 252 

Sakai 248 

Sakhalin  Island 250 

Sakonnet  Point 194 

SalCav 204 

Island 214 

Sala  y  Gomez 258 

Salado  Bay 211 

Salavar  Island 242 

Saldanha  Bay 232 

Salem 194 

Sali 230 

Salina  Cruz 202 

Salinas  Bay,  C.  America 202 

L.  California 201 

Point 204 

Sali.tfbury  Island 191 

Salomague  Island 245 


Page. 

Salonika 229 

Salovetski 264 

Saltee,  Great 217 

Salut  Islands 207 

Salvador,  San 203 

Salvage  Islands 214 

Salvore  Point 227 

Sama,  Port  and  Peak 203 

Samana 204 

Cay 203 

Samanco  Bay 212 

Samar  Island 246 

Samarang 243 

Sambro  Islands 193 

Samoan  Islands 257 

Samos  Island 229 

Sampit  Bay 242 

Samso  Island 222 

Samsoe  Island 223 

Sand  Island 196 

Key 196 

Sandakhan  Bay 242 

Sandalo,  Cape 226 

Sandalwood  Island 243 

Sandfly  Cay 197 

Sandhammaren 219 

Sandwich  Island 256 

Islands 214 

Sandv  Cape 261 

Hook 195 

Point 210 

Sanguin  River 231 

Sanihel  Island 196 

Sankaty  Head 194 

Sannakh  Island 199 

Santander 224 

River 196 

Santiago  Cape 210 

de  Chile 211 

-Cuba 204 

Port 245 

Santona 224 

Santos 208 

Sapelo  Island 195 

Sarage  Island 257 

Saranguni  Islands 246 

Saniwak 242 

River 242 

Sariguan  Island 252 

Sarstoon  River 197 

Saru  Island 243 

Saseno  Island 228 

Satano  Misaki 248 

Satawal  Island 252 

Saugor  Island 238 

Sauguir  Island 242 

Sauh,  Pulo 238 

Saukhoum 229 

Saunders,  Port 192 

Sauo  Bay 242 

Savaii  Island 257 

Savanilla 206 

Savannah 195 

Savanna-la-Mar 204 

Savbrook 194 

Scalp  Mountain 217 

Scarcies  River 231 

Scatary  Island 193 

Schama  Mountain 212 

Schank,  Cape 261 

Schanz  Island 251 


Page  284J 


INDEX  TO  APPENDIX  IV. 


Page. 

Scharhorn 222 

Scheveningen 223 

Schillighorn 222 

Schleimunde 221 

Schleswig 221 

Schonberg „ 221 

Scilly  Islands,  Englana 215 

■ S.  Pacific 257 

Scott  Cape 200 

Scutari 229 

Sea  Bear  Bay 209 

Rock 248 

Seal  Cays 197 

Island 193 

Seao  Island 242 

Seattle 200 

Sebastian, San, Cape,M'g'sc'r  235 

Spain 224 

St.,  Cape,  S.  Africa...  232 

Island 208 

Sebaatopol 229 

Sebenico 227 

Sedano,  Cape 243 

SedashigarBay 237 

Seguin  Island 193 

Sein,  I.  de 224 

Sejro  Island 222 

Selatan  Point 242 

Seldom-come-by  Harbor 191 

Semeny  River 228 

Semerara  Island 245 

Semiamoo  Bay 200 

Semione  Island 240 

Sentinel  Island 248 

Series  Island 257 

Sermalta  Island 244 

Sermelik  Fjord 264 

Sermo  Island 229 

Serrana  Bank 198 

Serranilla  Bank 198 

Seskar  Islet 220 

Setubal 225 

Seuheli  Par 234 

Seven  Heads 218 

Seychelle  Islands 234 

Sfax 230 

Shag  Rocks 214 

Shahah 236 

Shahr,  Abu 236 

Shaikh  Shu'aib  Islet 236 

Shaluitien  Island 247 

Shanghai ._ 242 

Shannon  River ." 216 

Shantar  Islands 250 

Shantung 247 

Sharjah 236 

Shark  Island 254 

Sharmoh 236 

Shavveishan  Island 242 

Shelburne  HarV>or 193 

Shelter  Bay 250 

Shepherd  Island 198 

Sherbedat,  Ras 236 

Sherbro  Island 231 

River 231 

Sherm  Hassejy 233 

Joobbah 233 

Rabigh 234 

Wej 233 

Yahar  .  233 

Shetland  Islands' '. 216 


PLACES — continued. 

Page. 

Shiash-Kotan  Island 249 

Shields,  North 216 

Shimizu  Ba.v 249 

Shimonoseki  Strait 248 

Shinnecock  Buy 194 

Ship  Island 196 

Shoal 196 

Shipunski,  Cape 250 

Shirasu  Reef 248 

Shoals,  Isles  of 194 

Shoal  water  Cape 200 

Island 239 

Siargao  Island 246 

Siassi 247 

Siberaet  Island 239 

Siboga 239 

Sibuco  Bay 247 

Sibutu  Island 247 

Sibuyan  Island 246 

Sidtnouth,  Cape 262 

Sierra  Leone 231 

Sighajik 230 

Sigri,  Port 229 

Sihuatanejo  Point 202 

Sihut 236 

Silan 197 

Silaqui  Islet 245 

Silver  Bank 203 

Simaloe  Island 239 

Simeonof  Island 199 

Simoda 249 

Simon,  St. ,  Island 195 

Simonoff  Island 257 

Simonor  Island 247 

Simons  Bay 232 

Simusir  Island 249 

Singapore 238 

Singkel  Island 239 

Singkep  Island 238 

Single  Island 241 

Singora 240 

Sinon 231 

Sinope 230 

Siphano  Island 229 

Siquiquor  Island 246 

Sirik,  Cape 242 

SiriyaSaki 249 

Sisal 197 

Sitka 199 

Sittee  Point 197 

Skagataas  Point 265 

Skagi,  Cape 265 

SkagsHead 220 

Skaw,  Cape 223 

Skelligs  Rocks 216 

Skerries  Rocks 215 

Skerry vo re  Rocks 216 

Skiathos  Island 229 

Skidegate  Bay 199 

Skoorgaarde 221 

Skumbi  River 228 

Skyring  Mountain 209 

SligoBay 217 

Slyne  Head 217 

Smalls  Rocks 215 

Smerwick 216 

Smith  Island,  Japan 249 

Washington 200 

Sni  vrna 230 

Snaefells  Yokul 265 

Snares  Islands 2()3 


Page. 

Socorro  Island,  Chile 210 

Mexico 202 

Socotra  Island 233 

SoderSkars 220 

Soderarm 219 

Soderhamm 219 

Sofala 232 

Sohar 236 

Sola  Island 206 

Solander  Islands 263 

Solitary  Islands 261 

Solombo,  Great,  Island 243 

Solomon  Islands 254 

Solta  Island 228 

Sombrero 205 

Key 196 

Rock 247 

Sommer  Island 220 

Song-yui  Point 241 

Sonserol  Island 252 

SooBay 242 

Sooke  Inlet 200 

Sorelle  Rocks 228 

Sorol  Island 252 

Sorrel  Rock 241 

Sorrell,  Cape 262 

Port 262 

Sorsogon,  Port 246 

Soumshu  Island 249 

South  Cape,  Formosa 242 

N.  Guinea 255 

Rock 217 

Water  Cay 197 

Southampton 215 

Southsea  Castle    215 

Southwest  Cape 262 

Reef 196 

Spalato  Passage 228 

Port 228 

Sparo  Vestervik 219 

Spartel,  Cape 230 

Spartivento  Cape,  Italy 227 

Sardinia 226 

Spencer,  Cape 260 

Spezzia 226 

Spikeroog 222 

Spiridione,  St. ,  Port 228 

Spitz bergen 264 

Spodsbjerg 222 

Spurn  Head 216 

Square  Handkerchief  Bank .  203 

Staabierg  Huk 265 

Stack,  South 215 

Stade 222 

Stag  Rocks 218 

Stamp  Harbor 199 

Stampali  Island 229 

Stanley,  Port 214 

Starbuck  Island 254 

Start  Point 215 

Startpoint 216 

Staten  Island 209 

Staunton  Island 247 

Stavanger 218 

Steilacoom 200 

Steinkirchen 222 

Stemshesten 218 

Stensher  Rock 220 

Stephens,  Port 261 

Stettin 221 

Stewart,  Cape 259 


INDEX  TO  APPENDIX  IV. 


[Page  285 


Stewart  Islands 254 

Stirrup  Cavs 203 

Stirsudden 220 

Stockholm 219 

Stonington 19-1 

Stopelmiinde 221 

Stora 230 

Storiiowav 216 

Stot '. 218 

Stralsimd 1:21 

Strati  If^land : 229 

StraumneHS  Point 265 

Streaker  Bav 260 

Streckelsberg 221 

Stro>ionof  Cape 199 

Stroinytad 219 

Stromtaiigen 219 

Strong  Island 252 

Strovathi  Island 228 

Stuart  Island 198 

Suakin 233 

Sual 245 

Subig 245 

Sucoadana 242 

Suda,Port 228 

Sueik 236 

Suez 233 

Suff ren,  Cape 250 

Sugar  Loaf  Point 261 

Sughrah 236 

Suk  Island 252 

Suli)hur  Island 253 

Sunibawa  Island 243 

Sum  burgh  Head 216 

Sunda  Strait 239 

Sunday  Island 258 

Sunderland 216 

Sundsvall 220 

Sunraivani 237 

Sup6/- 212 

Sur 230 

Surabava 243 

Surat.: 237 

River 237 

Surigao 246 

Surop 220 

Susaki 248 

Suvvanose  Jima 248 

Suwarrow  Island 257 

Svalferort  Tzerel 220 

Svartklubben 219 

Svendborg 222 

Svenor 219 

Sviatoi  Nos 264 

Svinoen 218 

Swallow  Bay 210 

Islands 255 

Swan  Islands 197 

Swansea : 215 

Swatau 241 

Sweers  Island 262 

Swinemunde 221 

SybilloBay 250 

Sydenham  Island 251 

Sydney,  Australia 261 

Harbor,  C.  Breton  I . .  192 

Synesvarde  Mountain 218 

Syra 229 

Syracuse 227 

Tabaco 246 

Taljasco  River 197 


PLACES — continued. 

Page. 

Tablas  Island 246 

Point 211 

Table  Bav 232 

Head 191 

Island 238 

Taboga  Island 203 

Tabou  River 231 

Tacloban 246 

Tacoma 200 

TacoradyBay 231 

Tae  Islands 241 

Tagulanda  Island 242 

Tahiti 257 

Tahoa  Islanc  I 257 

Tahuata  Island 253 

Taiaro  Island 258 

Tai-pin-san 244 

Tajer,  Port 227 

Taka  Yama 249 

Takapoto  Island '. .  258 

Takau 242 

Takhkona  Point 220 

Talabo,  Cape 242 

Talcahuano 211 

Ta-lien-wan  Bay 247 

Talinay  Mountain 211 

Taltal,  Port 211 

Taluat  Island 242 

Tamana  Island 251 

Tamandar^ 207 

TamarPort 210 

Tamatave 235 

Tambelan  Island 240 

Tampa  Bay 196 

Tampat  Toe  won  Point 239 

Tampico 196 

Tam-sui  Harbor 242 

Tanabe  Bay 248 

Tancook  Island 193 

Tandjong  Pandan 239 

Tanga  Bay 233 

Tangier 230 

Tanjong  Barram 242 

Datu  242 

Tanna  Island 256 

Tantang,  Port 235 

Taoiunu 256 

Taormi  na  Cape 227 

Tapua  Island 255 

Tapul  Island 247 

Taputeuea 251 

TaraHill 217 

Taranto 227 

Tarawa  Island 251 

Tarbertness 216 

Tarifa 225 

Taritari  Island 251 

Tarpaulin  Cove 194 

Tarragona 225 

Taa  de  Foin  Islet 247 

Tatakoto 257 

Tatsupi  Saki 249 

Tauere  Island 258 

Tauranga  Harbor 263 

Tauzon,  Cape 235 

Tavolara  Cape 226 

Tavov  River 238 

Taytao  Cape 210 

Taytay  Fort 245 

Tchesme 229 

Tchoukotskoi,  Cape 250 

Tegal 243 


Page. 

Tehor  Island 244 

Tellicherri 237 

Tel  lo  Islands 244 

Tematangi  Island 257 

Tenasserim 238 

Tenedos  Island 230 

Teneriffe  Island 214 

Tenez,  Cape 230 

Tepoca  Cape 202 

Tepoto  Island 258 

Tequepa 202 

Terceira  Island 213 

Teresa,  Sta. ,  Bav 201 

Terkolei ' ■  238 

Terminos  Lagoon 197 

Ternate  Island 244 

Terstenik  Rock 227 

Testa,  Cape 226 

Testigos Islets.. _ 206 

Tewaewae  Bav 263 

Thabi,  Abu. .'. 236 

Thank  God  Harbor 264 

Thermia  Island 229 

Thikombia  Island 256 

Thithia  Island 256 

Thomas,  St.,Id.,B.ofBiafra  231 

West  Indies.  205 

Thome,  St. ,  Cape 207 

Three  Kings  Islands 262 

Points  Cape,  Africa  . . .  231 

Argentina  . .  209 

Honduras  ..  197 

Ti-ao-usu  Island 244 

Tiburon  Island 202 

Tiegenort 221 

Tien-pak 241 

Tientsin 247 

Tilly  Bay 210 

Timbalier  Island 196 

Timor  Island 243 

Laut  Island 244 

Tinakula  Island 255 

Tinian  Island 252 

Tintolo  Point 246 

Tirby  Point 198 

Toass  Island 252 

Toau 258 

Tobago 205 

Tobi  Shima 249 

Tobol  Ali 239 

Tocopilla 212 

Todos  Santos 201 

To-du  Island 234 

Tofua  Island 258 

Tokara  Jima 248 

Tokelau  Islands 254 

Token  Bessi  Island 243 

Tokio 249 

Tolaga  Bav 263 

Tolkemit.' 221 

Tomas,  San 201 

Tomo  Roads 248 

Tongarewa  Island 254 

Tongatabu  Island 258 

Tongka  Harbor 238 

Tongoi 211 

Tong-sang  Harbor 241 

Tong-ting  Islet 241 

Tonning 222 

Topolobampo 202 

Tor 233 

Torbjornskjaer 219 


Page  286j 


INDEX  TO  APPENDIX  IV. 


Page. 

Tordenskjokl,  Cape 265 

Torgauten 219 

ToriwiSaki 249 

Tornea 220 

Toro  Point 206 

Torres  Island 256 

Point * 208 

Port 226 

Tortola 205 

Tortosa,  Cape 225 

Tortugas  Island 206 

Tory  Hill 217 

Island 217 

Tosco  Cape 201 

Totoya  Island 257 

Toulinguet  Islands 191 

Toulon 226 

Tourane  Bay 240 

Towers  Island 250 

Townsend,  Port 200 

Trsenen 218 

Trafalgar,  Cape 225 

Tralee  Bay 216 

Trani 227 

Trapani 226 

Travemunde 221 

Travers  Islands 262 

Treasury  Islands 254 

Trebizond 230 

Tregosse  Islands 254 

Trelleborg 219 

Tremiti  Islands 227 

Trepassey  Harbor 191 

Tres  Montes  Cape 210 

Puntas  Cape,  Chile  ...  210 

Venezuela . .  206 

Trevandrum 237 

Trevose  Head 215 

Triangle  Island 200 

Triangles 197 

Tribulation,  Cape 261 

Trichendore 237 

Trieste 227 

Trincomali 237 

Tringano  River 240 

Trinidad  Head 200 

Island 214 

Tripoli,  Africa 230 

Turkey 230 

Tristan  d'  Acunha 214 

Triton  Bay 255 

Island 241 

TriunfoCape 197 

Trobriand  Islands 255 

Tromelin Island, Carolinels.  252 

Indian  Ocean 235 

Troniso 218 

Trondheim 218 

Troon 215 

Truxillo 197 

Tsau-liang-hai 248 

Tscheljuskin,  Cape 264 

Tsmano 235 

TsuSima 248 

Tsukarase  Rocks 248 

Tsuruga 249 

Tuanske  Island 258 

Tubal  Island 257 

Tubuai  Islands 258 

Tubuai-Manu  Island 257 

Tucacas  Island 206 

Tuckers  Beach 195 


PLACES — continued. 

Page. 

Tukume  Island 258 

Tully  Mountain 21 7 

Tumaco 213 

Tuinbez 212 

Tung-chuh  Island 241 

Tung-yung  Islands 241 

Tuni-ang  Island 241 

Tunis 230 

Tuni)  Island 223 

Tupilco  River 197 

Tureia  Island 257 

Turk  Island 203 

Turnabout  Island 241 

Turo  Island 222 

Turtle  Island 257 

Isles 260 

TuskarRock 217 

Tuspan  Reefs 196 

Tuticorin 237 

Tutova 207 

Tutuila  Island 257 

Tuvutha  Island 256 

Tuxtla  Volcano 196 

Twelve  Islands 236 

Twofold  Bay 261 

Tybee  Island 195 

Ty-fung-kyoh  Island 241 

Tynemouth 216 

Ua-Huka  Island 253 

Ualan  Island 252 

Ubatuba 208 

Uea  Island 257 

Ujelang  Island 251 

Uji  Shima 248 

Uleaborg 220 

Ulietea  Island 257 

Ulko  Kalla  Rock 220 

Ulladulla 261 

Ulsire 218 

Uluthi  Islands 252 

Umea 220 

Una 207 

Unalaska  Island 199 

UnareBav 206 

Underut  Islet 234 

Underwood,  Port 263 

Unga  Island 199 

Unie  Island 227 

Union  Bay 209 

Islands 254 

Port  de  la 202 

Unsang 242 

Upernivik 264 

Upright  Port 210 

Upsala 219 

Upulo  Islands 257 

Uragami 248 

Urracas  Islands 252 

Urup  Island 249 

Usborne,  Port 260 

Usedom 221 

Ushant 224 

Ustica  Island 226 

Ute  Islet 220 

Utilla  Island 197 

Utrecht 223 

Uvea  Island 259 

Vache  Island 204 

Vadso 218 

Vahanga  Island 257 


Page. 

Vahitahi  Island 257 

Vaitupu  Island 254 

Valdes  Island 200 

Valdivia 211 

Valencia 225 

Valentia 216 

Valentine  Harbor 210 

St.,  Cape 210 

Valery  en  Caux,  St 223 

Valiente  Peak 198 

Valientes  Islands 252 

Valparaiso 211 

Vanavana  Island 257 

Vancouver 200 

Vanikoro 255 

Vannes 224 

Vanua  Lava  Island 256 

Levu  Island 256 

Mbalavu  Island 256 

Vardo 218 

Varella  Cape 240 

Pulo -. 240 

Varna  Bay 229 

Vate  Island 256 

Vathi,  Port 228 

Vatiu  Island 258 

Vatoa  Island 257 

Vatu  Lele  Island 256 

- —  Vara  Island 256 

Vavau  Island 258 

Vavitoa  Island 258 

Vaza  Barris  River 207 

VegUa 227 

Veiro  Island 222 

Vela,La,Cape 206 

Venangue  Be  Bay 235 

Vendres,  Port 225 

Venice 227 

Ver,  Point  de 223 

Vera  Cruz 196 

Verde  Cape 231 

Cay,  Bahamas 203 

Cuba 204 

Vicente,  San,  Cape 209 

Port 245 

Victor,  Port 260 

Victoria 200 

Harbor 264 

Port,  Australia 260 

Seychelle  Islands.  234 

River 259 

Victory  Cape 210 

Lsland 240 

Vidal,  Cape .• 232 

Video  Island 242 

VieborgBay 220 

Vieques  Island 205 

Vieste 227 

Vigan 245 

Vigo 225 

Villa 218 

Nova  da  Princessa 208 

Villajoyose 225 

Ville  Tranche 226 

Vinaroz 225 

Vincent,  San,  de  la  Barquera  224 

St.,  Cape,  Madagascar.  235 

Portugal 225 

Id.,  C.  Verde  Is..  214 

Windward  Is.  205 

Port,  S.  Pacific...  259 

^"ineyard  Haven 194 


INDEX  TO  APPENDIX  IV. 


[Page  287 


Page. 

Vingorla 23" 

Rocks 237 

Virgin  Gorda 205 

Virgins,  Cape 209 

Viti  Levu 256 

Vizagapatam 238 

Viziadrug 23" 

Vladimir,  St.,  Bav 250 

Vladivostok 250 

Vliko,  Port 228 

Vohemar 235 

Vojazza  River 228 

Volcano  Island,  West 242 

Islands 253 

Volta  River 231 

Voltaire,  Cape 259 

Vordate  Island 244 

Vordingborg 222 

Vostok  Island 253 

Vourlah 230 

Vriea  Island 249 

Wadero  Island 219 

Wadsworth,  Fort 194 

Wahdu  Island 234 

Waimea 253 

Waitangi  River 263 

Wakaya  Island 256 

Wake  Island 253 

Wakefield,  Port 260 

Walfisch  Bay 232 

Walker  Cav 203 

Wallis  Island 257 

Walpole  Island 256 

Walsche,  Cape 255 

Walsingham,  Cape 264 

Wanganui  River 263 

Wangari  Harbor 263 

Wangaroa  Harbor 262 

Wangaruru ,  263 

Wangeroog 222 

Wang-kia-tia  Bay 217 

Warberg 219 

Warnemunde 221 

Warren  Hastings  Island  . . .  252 

Washington 195 

Island 251 

Watch  Hill  Point 194 

Watcher,  North,  Island 239 

Waterfall  Bluff 232 

Waterford 217,  218 


PLACES — continued. 

Page. 

Waterloo  Bav 232 

Watlings  Island 203 

WawodaRock 250 

Wedge  Island 193 

Weggs  Cape 191 

Weichselmunde 221 

Weihai wei 247 

Wellington 263 

Wenman  Island 250 

Wessel,  Cape 259 

AVest  Cape 263 

Western,  Port 261 

Westminster  Hall  Islet 210 

Wetta  Island 243 

Wexford 217 

Whaingaroa  Harbor 263 

Whale  Back 194 

Whalefish  Island 264 

AVhite  Haven 215 

Head  Island 193 

Island 263 

Rock 240 

Whitsunday  Island 257 

Whittle  Cape 192 

Wicklow 217 

Wilberforce,  Cape 259 

Wilhelmshaven 222 

Willemstadt 223 

William,  Port 263 

Willoughby,  Cape 260 

Wilmington 195 

Wilson  Islands 255 

Islets 252 

Promontory 261 

Windau 220 

Winter  Harbor 264 

Wismar 221 

Wittgenstein  Island 258 

Wolgast 221 

Wolkonsky  Island 258 

Wollaston  Island , .  209 

Wollin 221 

Wollongong 261 

Wood  Island,  Labrador 192 

Maine 193 

Woodlark  Islands 255 

Woody  Island 241 

Wostenholme  Cape 191 

Wotje  Islands 251 

Wottho  Island 251 

Wowoni  Island 242 


Page. 

Wrangell 199 

Wrath,  Cape 216 

Wreck  Reef 255 

AVusimado  Point 248 

Wustrow 221 

Wusung 242 

Xulla  Islands 244 

Yakuno  Shima 248 

YakutatBav 199 

Yamada . .  /. 249 

Yamagawa 248 

Yami  Island 246 

Yanez 211 

Yap  Island 252 

Yaquina  Head 200 

Yarmouth 193 

Yeboshi  Sima 248 

Yembo 233 

Yerabu-sima.. 244 

Yen,  Island  de 224 

Ylin  Island 245 

Yobuko 248 

Yoke  Shima 248 

Yokohama 249 

Yoko-shima 244 

Yokosuka 249 

York,  Cape,  Greenland 264 

Queensland 262 

Minster  Rock 209 

Youghal 218 

Ystad 219 

YtapereBav 235 

Point .". 235 

YuiadaRoad 229 

YuraNoUchi 248 

Zafarana 233 

Zafarin  Islands 230 

Zambesi  River 232 

Zamboanga 247 

Zante 228 

Zanzibar 233 

Zapotitlan  Point 197 

Zara 227 

Vecchia 227 

Zempoala  Point 196 

Zengg 227 

Zeyla 233 

Zirona  Grande  Island 227 


288  LUNAB   DISTANCES. 


APPENDIX  V. 

LUNAE  DISTANCES. 


By  reason  of  the  comparative  rapidity  of  motion  of  the  moon  relatively  to  the  earth,  it  occurs  that 
the  angular  distance,  measured  from  the  earth,  between  the  moon  and  a  body  that  occupies  a  fixed,  or 
nearly  fixed,  position  in  the  celestial  sphere,  is  constantly  changing.  If,  therefore,  an  observer  accu- 
rately measures  with  a  sextant  the  angle  between  the  moon  and  one  of  the  various  celestial  bodies  for 
which  the  lunar  distance  is  tabulated  in  the  Nautical  Almanac,  this  observed  distance,  reduced  to  true 
distance,  affords  a  means  for  determining  the  absolute  instant  of  time  at  which  the  observation  was 
taken;  and  from  this  may  be  deduced  the  longitude  and  the  chronometer  error. 

If  it  were  practicable  to  obtain  results  with  a  close  degree  of  accuracy  l)y  this  method,  it  would  be  an 
invaluable  aid  to  the  navigator,  eliminating  all  anxiety  as  to  change  of  rate  of  the  chronometer,  and 
even  rendering  it  possible  to  navigate  a  vessel  without  such  an  instrument.  It  is  unfortunately  the  case, 
however,  that  the  method  does  not  afford  results  that  may  be  regarded  as  reliable  within  small  limits, 
since  a  very  small  error  in  the  observed  angle,  which  it  may  not  be  possible  to  avoid  even  though  every 
care  be  taken,  causes  a  large  error  in  the  deduced  time.  Navigators  of  the  present  day  do  not,  there- 
fore, employ  the  method  of  lunar  distances  except  under  extraordinary  circumstances,  such  as  when  an 
accident  to  the  chronometer  occurs,  or,  on  a  very  long  voyage,  when  there  is  reason  to  suspect  the  cor- 
rectness of  the  chronometer  error  as  brought  forward  by  the  rate. 

In  order  to  facilitate  the  method  of  determining  the  longitude  from  lunar  distances,  there  is  pub- 
lished in  the  Nautical  Almanac,  for  every  third  hour  of  Greenwich  mean  time,  the  angular  distances  of 
the  center  of  .the  moon  from  the  center  of  the  sun,  from  the  brightest  planets  and  from  certain  blight 
fitted  stars  selected  in  tlie  path  of  the  moon.  All  the  distances  that  can  be  observed  on  the  same  day 
are  grouped  together  under  that  date,  and  the  columns  are  read  from  left  to  right  across  both  pages  of 
the  same  opening.  The  letter  W.  or  E.  is  affixed  to  the  name  of  the  sun,  jilanet,  or  star  to  indicate 
that  it  is  on  the  west  or  east  side  of  the  moon.  An  observer  on  the  surface  of  the  earth  having  meas- 
ured a  lunar  distance,  corrected  it  for  instrumental  errors  and  for  the  semidiameters  of  the  objects,  and 
cleared  it  from  the  effects  of  refraction  and  parallax,  finds  the  true  or  geocentric  distance.  With  this 
distance  and  the  distances  in  the  Nautical  Almanac  of  the  same  bodies  on  the  same  day,  the  Greenwich 
mean  time  of  the  observation  can  be  found,  as  will  hereafter  be  described. 

The  unavoidable  errors  to  which  the  observation  of  lunar  distance  is  subject  are  diminished  by 
making  a  number  of  measurements.  Errors  of  the  instrument  may  be  diminished  by  measuring 
distances  on  opposite  sides  of  the  moon,  when  possible,  ana  combining  the  results. 

Before  taking  the  observation,  the  Nautical  Almanac  must  be  examined  to  see  from  what  objects  the 
•distances  are  computed.  If  the  star  or  planet  selected  for  observation  is  not  recognized  from  its  position 
relatively  to  other  bodies  in  the  heavens,  it  can  easily  be  identified  from  the  distance  given  in  the 
Almanac;  for  the  observer  may  set  the  sextant  to  the  distance,  computed  roughly  for  the  estimated  time 
at  the  meridian  of  Greenwich,  and  direct  his  sight  to  the  east  or  west  of  the  moon,  according  as  the 
object  is  marked  E.  or  W.  in  the  Nautical  Almanac,  and,  having  found  the  reflected  image  of  the  moon 
upon  the  horizon  glass,  sweep  the  instrument  to  the  right  or  left,  and  the  image  will  pass  over  the  star  or 
planet  sought,  if  above  the  horizon  and  the  weather  clear;  the  star  or  planet  is  always  one  of  the  brightest, 
and  is  situated  nearly  in  the  arc  passing  through  the  moon's  center,  perpendicular  to  the  line  connecting 
the  two  horns. 

Although  all  the  instruments  used  in  these  observations  ought  to  be  well  adjusted,  yet  particular 
care  should  be  taken  of  the  sextant  used  in  measuring  the  angular  distance  of  the  moon  from  the  sun  or 
star,  since  an  error  of  V  in  this  distance  will  cause  an  error  of  nearly  30''  in  the  longitude  deduced 
therefrom.  When  a  great  angular  distance  is  to  be  measured  it  is  absolutely  necessary  to  use  a  telescope, 
and  its  parallelism  with  respect  to  the  plane  of  the  instrument  must  be  carefully' examine<l;  but  in 
measuring  small  distances  the  use  of  the  telescope  is  not  of  such  great  importance,  and  a  sight  tube  may 
then  l)e  xised,  taking  care,  however,  that  the  eye  and  point  of  contact  of  the  objects  on  the  horizon  glass 
be  equally  distant  from  the  plane  of  the  instrument.  It  is  always  conducive  to  accuracy  to  xise  a 
telescope,  and,  after  a  little  practice,  this  is  easily  done. 

While  one  person  is  observing  the  distance  of  the  objects,  two  others  should  observe  the  altitudes. 
The  chronometer  should  be  under  the  eye  of  a  fourth  person  appointed  to  note  the  time;  the  observer 
who  takes  the  angular  distance  gives  previous  notice  to  the  others  to  be  ready  with  their  altitudes  by 
the  time  he  has  finished  his  observation,  which,  being  done,  the  time,  altitudes,  and  distance  should  be 
carefully  noted;  if  other  sets  of  observations  are  taken  it  must  be  done  within  the  space  of  fifteen 
rdinutes,  and  the  mean  of  all  the  observations  should  be  worked  as  a  single  one. 

When  a  ship  is  rolling  considerably  it  is  difficult  to  measure  the  distance  of  the  objects,  but  when 
steady  there  is  much  less  difficulty,  especially  in  small  distances,  which  are  much  more  easily  measured 
than  large  ones,  and  are  not  so  liable  to  error  from  an  ill  adjustment  of  the  telescope;  an  observer  would 
therefore  do  well  to  choose  those  times  for  observation  when  the  distance  of  the  objects  is  less  than  70° 
or  80°.  But  it  must  be  observed  that  neither  of  the  objects,  if  possible,  ought  to  be  at  a  less  altitude 
than  10°,  on  account  of  the  uncertainty  of  the  refraction  near  the  horizon,  for  the  horizontal  refraction 
varies  from  33''  to  36^  40''  by  an  alteration  of  40°  in  the  thermometer;  this  alteration  might  cause  an 
error  of  2°  in  the  longitude  with  an  observer  who  uses  the  mean  refraction. 


LUNAR   DISTANCES.  289 

In  measuring  the  distance  of  the  moon  from  the  sun  we  must  bring  the  moon's  round  limb  in 
contact  with  the  nearer  Hml^  of  the  sun.  In  measuring  the  distance  of  the  moon  from  a  planet  or  fixed 
star  tlie  round  limb  must  be  brought  in  contact  with  the  center  of  the  star  or  planet,  observing  that,  the 
semidiameter  of  the  planet  being  only  a  few  seconds,  the  center  of  it  can  be  estimated  sufficiently  near 
for  all  the  ])urposes  of  this  observation. 

In  taking  the  altitude  of  the  moon,  the  round  limb,  whether  it  be  the  upper  or  lower,  must  be 
brought  to  the  horizon.  In  misty  weather  it  is  rather  difficult  to  observe  the  altitude  of  the  stars  on 
account  of  their  dimness.  Sometimes  they  are  so  dim  that  they  can  not  be  seen  through  the  telescope 
of  a  sextant,  particularly  if  the  mirrors  are  not  well  silvered.  In  this  case  the  telescope  must  be  laid 
aside  and  the  altitude  taken  with  a  sight  tube. 

It  has  been  assumed  that  there  were  observers  enough  to  measure  the  altitudes  when  the  distance 
was  observed,  but  if  that  is  not  the  case  the  altitudes  may  be  estimated  in  a  manner  to  be  explained 
hereafter. 

The  method  here  given  is  that  of  Professor  Chauvenet,  and  involves  the  use  of  the  tables  in  this 
Appendix.  The  object  of  these  tables  is  to  give  the  true  correction  of  a  lunar  distance  in  all  cases  when, 
with  the  apparent  distance  of  the  moon  from  the  sun,  a  planet,  or  star,  the  apparent  altitudes  of  the 
two  objects  have  also  been  obtained  by  observation.  They  enable  us  readily  to  take  into  account: 
First,  the  parallax  of  the  moon  in  the  latitude  of  the  observer,  allowing  for  the  spheroidal  figure  of  the 
earth;  second,  the  i)arallax  of  the  sun  or  a  planet;  third,  the  true  atmospheric  refraction,  allowing  for 
the  actual  state  of  the  air  as  shown  by  the  barometer  and  thermometer;  and,  fourth,  that  effect  of 
refraction  which  gives  the  apparent  disks  of  the  moon  and  sun  an  oval  or  elliptical  figure. 

The  longitude  deduced  from  a  lunar  observation,  when  no  attention  is  paid  to  the  spheroidal  figure 
of  the  earth,  to  the  barometer  and  thermometer,  or  to  the  elliptical  figure  of  the  disks,  may  in  certain 
cases  be  in  error  a  whole  degree.  It  is  true  these  extreme  cases  are  rare  in  practice,  but  cases  are 
common  in  which  from  such  neglect  the  error  in  the  longitude  is  10^,  15',  or  20',  and  it  is  absolutely 
necessary  to  get  rid  of  such  errors  and  to  leave  no  other  inaccuracy  in  the  result  than  that  which 
unavoidably  follows  from  the  observations. 

The  Observation. — The  record  of  a  complete  observation  embraces: 

1.  The  latitude  and  approximate  longitude  of  the  place  of  observation. 

2.  The  approximate  local  time. 

3.  The  time  of  observation  as  shown  ])y  a  chronometer,  and  the  error  of  the  chronometer,  or  its 
difference  from  mean  Greenwich  time. 

4.  The  apparent  distance  of  the  moon's  bright  limb  from  a  star  or  planet,  or  from  the  nearer  limb 
of  the  sun. 

5.  The  apparent  altitude  of  the  moon's  upper  or  lower  limb  above  the  sea  horizon. 

6.  The  apparent  altitude  of  the  star,  i)lanet,  or  lower  limb  of  the  sun  above  the  sea  horizon. 

7.  The  height  of  the  barometer  and  thermometer. 

8.  The  height  of  the  eye  above  the  level  of  the  sea. 

9.  The  index  correction  of  the  sextant. 

The  index  correction  of  the  sextant  may  be  supposed  to  be  previously  determined;  but,  since  even 
in  the  best  instruments  it  is  not  constant,  its  determination  should  be  considered  a  necessary  part  of  the 
observation. 

The  error  of  the  chronometer  alluded  to  is  that  which  is  obtained  by  applying  the  daily  rate 
(multiplied  by  the  j^rojjer  number  of  days)  to  the  error  found  before  leaving  port.  The  agreement  or 
disagreement  of  the  error  thus  found  with  that  found  by  the  lunar  observation  will  be  the  test  of  the 
accuracv  of  the  chronometer,  subject,  of  course,  to  the  accepted  limits  of  accuracy  of  the  observation 
itself. 

Preparation'  of  the  Data. — Greenwich  Date. — Correct  the  chronometer  time  for  its  error  from 
Greenwich  time  and  deduce  the  Greenwich  date,  i.  e.,  the  Greenwich  day  and  hour  (mean  time),  reck- 
oning the  hours  in  succession  from  0  to  24,  beginning  at  noon. 

Xauticdl  Almanac. — With  the  Greenwich  date  enter  the  Almanac  and  take  out  the  moon's  semi- 
diameter  and  horizontal  parallax;  if  the  sun  is  observed,  take  its  semidiameter;  in  the  case  of  a  planet, 
take  its  horizontal  parallax  only. 

Apparent  Altitude  of  the  Moon. — To  the  altitude  given  by  the  sextant  apply  the  index  correction  of 
the  instrument  and  subtract  the  dip  of  the  horizon  (Table  14).«  If  the  lower  limb  is  observed,  add  the 
semidiameter  and  augmentation  (Table  18) ;  if  the  upper  lindj  is  observed,  subtract  the  augmented  semi- 
diameter.    The  result  is  the  apparent  altitude  of  the  moon's  center,  denoted  "  ([  's  App.  Alt." 

Apparent  Altititde  of  the  Sun,  Planet,  or  Star. — To  the  observed  altitude  apply  the  index  correction  of 
the  sextant,  and  subtract  the  dip  (Table  14) ;  and  if  the  sun  is  used,  add  its  semidiameter  when  the  lower 
limb  is  observed,  or  subtract  it  when  the  upper  limb  is  observed.  The  result  is  the  apparent  altitude 
required,  denoted  by  "Q's  or  jfc's  App.  Alt." 

Apparent  Distance. — First,  when  the  sun  is  used,  to  the  observed  distance  (corrected  for  index  error 
when  necessary)  add  the  moon's  augmented  semidiameter  and  the  sun's  semidiameter;  second,  when  a 
planet  or  star  is  used,  add  the  moon's  augmented  semidiameter  if  its  nearer  limb  is  observed,  but 
subtract  it  if  its  farther  limb  is  observed.     The  result  is  "App.  Dist." 

Moon's  Reduced  Par alkLc  and  Refraction. — Enter  Table  19  with  the  latitude  of  the  place  of  observa- 
tion and  the  moon's  horizontal  parallax,  and  take  out  the  correction,  which  add  to  the  horizontal 
parallax.     Call  the  result  the  moon's  reduced  parallax,  or  "  (['s  Red.  P." 

Enter  Table  I  with  the  moon's  apparent  altitude,  and  take  out  the  mean  reduced  refraction,  and 
apply  to  this  mean  refraction  the  corrections  given  in  Tables  21  and  22,  adding  or  subtracting  these  cor- 
rections according  to  the  directions  in  the  tallies.  The  result  is  the  moon's  reduced  refraction,  or  ''C's 
Red.  R." 


a  The  tables  designated  by  their  numbers  in  Arabic  notation  are  to  be  found  in  Part  II.    The  tables  contained  in  this 
Appendix,  which  are  for  exchisive  use  with  lunar-distance  observations,  are  denoted  by  Roman  numbers. 

22489—03 19 


290  LUNAR    DISTANCES. 

Subtract  the  "(['s  Red.  R."  from  the  "C's  Red.  P."  and  mark  the  result  as  "C's  Red.  P.  and  iJ." 

Reduced  Parallax  and  Refraction  of  Sun,  Planet,  or  Star.c — With  the  apparent  ahitude  of  the  sun, 
planet,  or  star,  take  from  Table  I  the  mean  reduced  refraction,  which  correct  by  Tables  21  and  22.  If 
the  sun  is  observed,  subtract  its  horizontal  parallax  (which  may  always  be  taken  at  8''.5)  from  its  reduced 
refraction,  and  mark  the  result  as  "O's  Red.  P.  and  jK."  If  a  planet  is  observed  subtract  its  horizontal 
parallax,  and  mark  the  result  as  "  >l<:'s  Red.  P.  and  i2."  If  a  star  is  observed,  its  reduced  refraction  is 
at  once  the  required  "  -X-'s  Red.  P.  and  R." 

Computation  of  the  True  Distanx-e. — Take  from  Tables  II,  III,  IV,  and  V  respectively  the  four 
logarithms  A,  B,  C,  'D,f>  and  place  these  logarithms  each  at  the  head  of  a  colunni,  marking  the  columns 
A,  B,  C,  and  D;  then  put  the— 

log  of  (t  s  Red.  P.  and  R.  (Table  IX)  in  columns  A  and  B. 

log  of  O's  or  jfc's  Red.  P.  and  R.  (Table  IX)  in  columns  C  and  D. 

log  sin  a 's  App.  Alt.  (Table  44)  in  columns  A  and  D. 

log  sin  O's  or  sjc's  App.  Alt.  (Table  44)  in  columns  B  and  C. 

log  cot  App.  Dist.  (Table  44)  in  columns  A  and  C. 

log  cosec  App.  Dist.  (Table  44)  in  columns  B  and  D. 

The  sum  of  the  four  logs  in  Col.  A  is  the  log  (Table  IX)  of  the  First  Part  of  (i's  Correction,  which  is 
to  be  marked  +  when  the  app.  dist.  is  less  than  90°,  but  —  when  the  app.  dist.  is  greater  than  90°. 

The  sum  of  the  four  logs  in  Col.  B  is  the  log  (Table  IX)  of  the  Second  Part  of  C's  Correction,  which 
is  always  to  be  marked  — . 

The  sum  of  the  four  logs  in  Col.  C  is  the  log  (Table  IX)  of  the  First  Part  of  the  Q's  or  >\i:'s  Correction, 
which  is  to  be  marked  —  when  the  app.  dist.  is  less  than  90°,  but  +  when  the  ajjp.  dist.  is  greater 
than  90°. 

The  sum  of  the  four  logs  in  Col.  D  is  the  log  (Table  IX)  of  the  Second  part  of  the  Q' s  or  ■}ii' s  Correc- 
tion, which  is  always  to  be  marked  —• 

Combine  the  first  and  second  parts  of  the  (J 's  correction  according  to  the  signs  prefixed;  that  is, 
take  their  sum  if  they  have  the  same  sign,  but  their  difference  if  they  have  different  signs,  and  prefix  the 
sign  of  the  greater  to  the  result,  which  call  "  C's  ivJiole  correction." 

In  the  same  manner  form  the  "O's  or  >|<:'s  vjhole  correction." 

Firiit  Correction  of  Distance. — Combine  the  (i's  whole  corr.  and  the  O'*  or  >|<'s  whole  corr.,  according 
to  their  signs;  the  result  is  the  First  Correction  of  Distance,  which  is  to  be  added  to  or  subtracted  from 
the  apparent  distance,  according  as  its  sign  is  -p  or  — . 

Second  Correction  of  Distance. — Enter  Table  VI  with  the  Apparent  Distance  and  the  First  Correction 
of  Distance,  and  take  out  the  Second  Correction  of  Distance,  which  is  to  be  applied  to  the  distance 
according  to  the  directions  in  the  side  columns  of  the  Table. 

Correction  for  the  Elliptical  Figure  of  the  Moon's  Dish,  or  Contraction  of  the  Ifoon's  Semi-diameter. — Enter 
Table  VII  A  .with  the  C's  App.  Alt.  and  C's  Red.  P.  and  R.,  and  take  out  the  number.  With  this 
number  and  the  (L's  whole  correction  enter  Table  VII  B  and  take  out  the  required  contraction,  which  is 
to  be  added  to  the  app.  dist.  when  the  farther  limb  is  observed,  but  subtracted  when  the  nearer  limb  is 
observed. 

Correction  for  the  Elliptical  Figure  of  the  Sun's  Disk,  or  Contraction  of  the  Sun's  Semi-diameter. — Enter 
Table  VIII  A  with  the  O's  App.  Alt.  and  O's  Red.  P.  and  R.,  and  take  out  the  number.  With  this 
number  and  the  O's  whole  corr.  enter  Table  VIII  B  and  take  out  the  required  contraction,  which  is 
always  to  be  sxibtracted  from  the  distance  (the  nearer  limb  of  the  sun  being  always  observed). 

Correction  for  Compression,  or  for  the  Spheroidal  Figure  of  the  Earth. — Take  from  the  Nautical  Alma- 
nac for  the  Greenwich  date  the  declinations  of  the  bodies  to  the  nearest  whole  degree.  With  the  moon's 
declination  and  apparent  distance,  take  from  Table  XI  A  the  first  part  of  N,  and  mark  it  with  the  sign  , 
in  the  table  if  the  declination  is  North;  but  if  the  declination  is  SoutJi,  change  the  sign  from  +  to  —  or 
from  —  to  -p.  With  the  sun's  or  star's  declination  and  the  apparent  distance,  take  from  Table  XI  B  the 
second  part  of  N,  giving  it  the  same  sign  as  the  declination.  Take  the  sum,  or  difference,  of  the  two  parts, 
according  as  their  signs  are  the  same  or  different,  and  to  the  resulting  number  prefix  the  sign  of  the 
greater.  The  logarithm  of  this  number  of  seconds,  taken  from  Table  IX,  with  its  sign  prefixed,  is  the 
required  log  N.  To  log  N  add  the  log  sine  of  the  latitude  of  the  place  of  observation;  the  sum  is  the  log 
(Table  IX)  of  the  required  correction  for  compression.  In  north  latitude  add  this  correction  if  log  N  is  +, 
or  subtract  it  if  log  N  is  — ;  in  south  latitude  subtract  the  correction  when  log  N  is  +>  and  add  it  when 
log  N  is  — . 

All  these  corrections  being  applied  to  the  Apparent  Distance,  the  result  is  the  True  Distance. 

To  FixD  THE  Greenwich  Time. — Find  in  the  Nautical  Almanac  the  two  distances  between  which  the 
true  distance  falls.  Take  out  the  first  of  these,  together  with  the  Prop.  Log  following  it,  and  the  hours 
of  Greenwich  time  over  it.  Find  the  difference  tetween  the  distance  taken  from  the  Almanac  and  the 
true  distance,  and  to  the  log  of  this  difference  (Table  IX)  add  the  Prop.  Log  from  the  Almanac;  the 
sum  is  the  log  (Table  IX)  of  an  interval  of  time  to  be  added  to  the  hours  of  Greenwich  time  taken  from 
the  Almanac.     The  result  is  the  approximate  Greenwich  time. 

To  correct  this  Greenwich  time,  take  the  difference  between  the  two  Prop.  Logs  in  the  Almanac 
which  stand  against  the  two  distances  between  which  the  true  distance  falls.  With  this  difference  and 
the  interval  of  time  just  found  enter  Table  X  and  take  out  the  seconds,  which  are  to  be  added  to  the 
approximate  Greenwich  time  when  the  Prop.  Logs  are  decreasing,  but  subtracted  when  the  Prop.  Logs 
are  increasing.    The  result  is  the  true  Greenwich  time. 

By  comparing  with  this  the  local  mean  time  the  longitude  will  be  found;  or,  if  testing  the  time 
shown  by  chronometer,  the  difference  between  the  true  Greenwich  time  and  the  time  shown  by  the 
chronometer  is  the  error  of  the  chronometer  as  determined  bv  the  lunar  observation. 


a  The  parallax  of  a  star  being  zero,  its  "reduced  parallax  and  refraction  "  become,  of  course,  merely  its  "  reduced  refrac- 
tion; "  but  as  no  mistake  can  arise  from  marking  it  as  "  3|c'8  Red.  P.  r  nd  R.,"  this  designation  has  been  retained  in  order  to 
give  simplicity  and  uniformity  at  once  to  the  rules  and  the  tables. 

b  No  interpolation  is  necessary  in  taking  out  these  logarithms. 


LUXAR    DISTANCES. 


291 


Degree  of  Dependenxe. — If  the  error  thus  determined  agrees  with  that  deduced  by  means  of  the 
rate  and  original  error,  it  may  be  accepted  as  a  confirmation  of  the  rate  of  the  chronometer;  if  otherwise, 
more  or  less  doubt  is  thrown  upon  the  chronometer,  according  to  the  degree  of  accuracy  of  the  lunar 
observation  itself.  An  error  of  10^^  in  the  measurement  of  the  distance  produces  about  20'  error  in  the 
Greenwich  time;  and  since,  even  with  the  best  observers,  a  single  set  of  distances  is  subject  to  a  possible 
error  of  10'^,  it  may  be  well  to  consider  the  chronometer  as  still  to  be  trusted  so  long  as  it  does  not 
differ  from  the  lunar  by  more  than  20^  Since,  however,  so  much  depends  upon  skill  in  measuring  the 
distance,  the  observer  can  only  form  a  correct  judgment  of  the  degree  of  dependence  to  be  placed  upon 
his  own  observations  by  repeated  trials  and  a  careful  comparison  of  his  several  results. 

Example:  In  Lat.  35°  30^  N.,  Long.  30°  W.,  by  account,  at  the  local  mean  time,  1855,  September  6, 
IS*"  8'"  0%  the  observed  distance  of  Q'a  andC  's  nearer  limbs  was  43°  52^  10^^;  observed  alt.  C,  49°  32^  50^^ 
observed  alt.  0,  5°  27^  10^^;  barometer,  29'".  1;  thermometer,  75°;  height  of  the  eye  above  the  sea,  20" 
I.  C,  0^  00''';  required  the  longitude. 


L.  M.  T.,  Sept.  6, 
Long.,  D.  R., 

G.  31.  T.,  approx., 

Obs.  Alt.  C, 
Dip,  Table  14, 
C's  Aug.  S.  D., 

(T'sApp.  Alt., 

C'sRed.  R.,  Table! 
Bar.  29'".  1,  Table  21 
Ther.  75°,  Table  22, 

C'sRed.  R., 
C'sRed.  P., 

C'sRed.  P.  andR., 


Preparation  of  the  Data. 


18"  OS-" 
+  2  00 

20  08 

49' 

+ 

32^  50^' 

4  23 

15  01 

49 

43 

28 

V 

16^^ 
3 
4 

1 
54 

09 
23 

53 

14 

C'sS.  D., 
Aug.  Table  18, 

C's  Aug.  S.  D, 

Obs.  Alt.  0, 
Dip, 
O'sS.  D., 

O's  App.  Alt, 

O'sRedR.,  Table  I, 
Bar.,  Table  21, 
Ther.,  Table  22, 

0's  Red.  R., 
O's  Par., 

O's  Red.  P.  aiid  R., 


14^  50^^0|C'aPar.,  N.  A., 
11    .2  Aug.,  Table  19, 


C'sRed.  P., 


54^ 


15  01  .2 

5° 

27^ 

10^^ 

— 

4 

23 

+ 

15 

55 

5 

38 

42 

8^ 

57'^ 
16 

— 

28 

8 

13 

8 

+ 


19''^  4 
3   .6 


54     23   .0 


Obs.  Dist.  01    IC,      43°  52^   10^^ 


8     05 


C's  Aug.  S.  D., 
O'sS.  D., 

App.  Dist., 

C'sDec,  N.  A., 
O's  Dec,  N.  A., 


+ 


15    01 
15    55 

44    23     06 

25°  N. 
6°N. 


log  A,  Table  II,  0.  0021 

log  ([  's  Red.  P.  and  R.,  3. 5043 

log  sin  C  's  App.  Alt. ,  9. 8825 

log  cot  App.  Dist. ,  0. 0093 

flog.  Table  IX,  3.  3982 

\lst  Part  C  's  corr.,         +41'  4^' 


B. 


log  B,  Table  III,  9. 9951 

log  (L  's  Red.  P.  and  R.,  3. 5043 

log  sin  O's  App.  Alt.,  8. 9929 

log  cosec  App.  Dist. ,  0. 1552 


/log.  Table  IX,  2.  6475 

\2d  Part  C's  corr.,  -  7'  24'^ 

C 's  whole  corr.,  +34'  18'' 


log N,  Tabs.  XIandIX,  ( - )  0.  845 
log  sin  Lat,  +  35°  30',  (  +  )  9.  764 

riog.  Table  IX,  (-) 0.609 

\Corr.  for  Compression,    —      4" 


Computation  of  the  True  Distance. 

C. 

log  C,  Table  IV,  9.  9949 

log  O's  Red.  P.  and  R.,  2.  6857 

log  sin  O's  App.  Alt,  8.  9929 

log  cot  App.  Dist. ,  0.  0093 


flog.  Table  IX, 
list  I 


Part  O's  corr.. 


1. 6828 
-0'  48" 


D. 

log  D,  Table  V,  9. 9992 
log  O's  Red.  P.  and  R.,    2.  6857 

log  sin  C '  s  App.  Alt ,  9.  8825 

log  cosec  App.  Dist.,  0. 1552 

/log.  Table  IX,  2.  7226 

t2d  Part  O '  s  corr. ,  +8'  48" 

O '  s  whole  corr. ,  +8'  00" 


App.  Dist, 

Ist  Corr., 

2d  Corr.,  Table  VI,  — 

Contraction  of  d's 

S.D.,  Table  VII, 
Contraction  of  O's 

S.D., Table  VIII, 
Corr.  for  Comp. 

True  Distance, 


44°  23'  06" 
+        42  18 
16 


0 
20 


45    04  44 


292 


LUNAR    DISTANCES. 


Extract  from  Nautical  Almanac,  September,  1855. 
GREENWICH  MEAN  TIME:  LUNAR  DISTANCES. 


to 

1                        1 

'                              i    PL 

Star's  name  and     i     Midnitrht            of  ' 

position.           1     Midnight.        ^o^ 

xv. 

p.  L. 
Of 

Diff. 

XVIIIh. 

p.  L. 

Of 
Diff. 

XXI"". 

P.  L. 

of 

Diff. 

6 

Si-N            E.     '48°  46'  55'' 

3422          47°  25'  3"       3427 

46°  3'  17" 

3433 

44°  41'  38" 

3438 

Computation  of  Greemcich  Mean  Time. 


True  Distance, 

Distance,  N.  A.,  at  XVIIl", 

Difference, 

Approximate  interA'al, 
Add— 

Approx.  G.  M.  T., 
Corr.,  Table  X, 

True  G.  M.  T., 
L.  M.  T., 

Longitude, 


45°  04'  44" 
46    03     17 


58 

33 

2'' 

18 

09" 

04^ 

20 

09 

04 
2 

20 
18 

09 

08 

02 
00 

P.  L.,  0.3433 

log,  Table  IX,  3.5457 


log,  Table  IX,  3.8890 


2     01     02   =  30°  15'  30"  W. 


Diff.  P.  logs   +  5 


Example:  In  Lat.  55°  20'  S.,  Long.  120°  25'  W.,  by  account,  on  August  29, 1855,  at  9'>  40"  00'  p.  m., 
local  mean  time,  the  following  distance  and  altitudes  were  found,  being  the  mean  of  six  observations 
corrected  for  index  error.  Observed  distance  of  Fomalhaut  and  moon's  farther  limb,  46°  30'  23"; 
observed  alt.  C,  6°  26'  10";  observed  alt.  Fomalhaut,  52°  34'  40";  barometer,  31'°;  thermometer,  20°; 
height  of  the  eye  above  the  sea,  18". 


L.  M.  T. ,  August  29,       9"  40"'  00^ 
Long,  by  D.  K.,       +8    01    40 


Approx.  G.  M.  T., 

Obs,  alt.  C 

Dip,  - 

C'saug.  S.  D.,        + 

C's  A  pp.  Alt., 

C 's  Red  R.,  Table  I, 
Bar.,  Table  21,         + 
Ther.,  Table  22,       + 

(C'sRedR., 
C'sRetl.  P., 

C'sRed.  P.  andR., 


17 

41 

40 

6° 

26' 

4 

16 

10" 
09 

28 

6 

38 

29 

7' 

48" 

16 

32 

8 
60 

36 
20 

51    44 


Preparation  of  the  Data. 

C'sS.D.,Naut.Al., 
Aug.,  Table  18,      + 


\ 


C's  aug  S.  D., 

Obs.  alt.  >)«, 
Dip, 

:!|!:'s  Ai>p.  Alt., 


*'sRed.R.,TableI, 
Bar.,  Table  21,  -f 
Ther.,  Table  22,     -j 

>|<'s  Red.  R., 
*'s  Red  P., 

*'s  Red.  P.  and  R. 


16'   26".  3 
2  .0 

16 

28 

.3 

52° 

34' 
4 

40" 
09 

52 

30 

31 

1' 

13" 
2 
5 

1 

20 
0 

> 

1 

20 

C'sPar.,  N.  A., 
Aug.,  Table  19, 

C  Red  P., 

Obs.  Dist.  -X-  IC, 
C's  aug.,  S.  D., 

App.  Dist., 


C's  Dec,  N.  A., 
>l<:'s  Dec,  N.  A., 


+ 


60'  11".  8 
8  .3 


60    20 

.1 

46° 

30' 
16 

23" 

28 

46 

13 

55 

4°N. 
30°   S. 


LUNAR    DISTANCES. 


293 


log  A,  Table  II,  0.0274 

log  C  's  Red.  P.  and  R.,  3.4919 

log  sin  C  '  s  App.  Alt. ,  9. 0632 

log  cot  App.  Dist.,  9.9813 


I  log,  Table  IX,  2.5638 

tlst  Part  C's  com,  +     6^  06^^ 

B. 

log  B,  Table  III,  0.0001 

log  C  's  Red.  P.  and  R.,       3.4919 

log  sin  sjc's  App.  Alt.,  9.8995 

log  cosec  App.  Dist. ,  0.1414 

flog,  Table  IX,  3.5329 

\2d  Part  (T's  corr.,  -  56^  51'^ 

C's  whole  corr.,  —  50    45 

log  N,  Tabs.  XI  and  (-)      1.2.30 

IX, 

logsinLat., -55°,  (  — )      9.913 


flog  Table  IX, 
\Corr.  for  Comp., 


;+; 


1.143 
14'' 


Computation  of  the  True  Distance. 

C. 

log  C,  Table  IV,  9.9999 

log  )f:'s  Red.  P.  and  R.,  1.9031 

log  sin  *'s  App.  Alt.,  9.8995 

log  cot  App.  Dist.,  9.9813 


flog.  Table  IX, 
\lst  Part  >)i:'s  corr. 

D. 


1.7838 


log  D,  Table  V,  0.0267 

log  *'s  Red.  P.  and  R.,  1.9031 

log  sin  (L  's  App.  Alt,  9.0632 

log  cosec  App.  Dist.,  0.1414 

flog.  Table  IX,  1.1344 

[2d  Part  >|c's  corr.,         +  0'  14'' 
>|<'s  whole  corr.,  —  0  47 


App.  Dist.,                    46= 

13' 

55" 

1st  corr.,                      — 

51 

32 

2dcorr.,  Table  VI,     — 

22 

Contraction  of  d  's  \  , 
S.D.,  Table  VII,i  + 

17 

Corr.  for  Comp.,       + 

14 

True  Distance,              45 

22 

32 

Extract  from  Nautical  Almanac,  August,  1855. 
GREENWICH  MEAN  TIME:  LUNAR  DISTANCES. 


j3 

Star's  name  and 
position. 

Midnight. 

P.  L.                                   P.  L. 

of               XV  h.             1      of 
Diff.                                '    Diff. 

i 
1 

XVIII  >>. 

P.  L. 

of 

Diff. 

XXI  ^ 

P.  L. 

of 

Diff. 

29 

Fomalhaut  W. 

42°  11' 34" 

2.535     ;  43°  51' 59"     .2527 

i                              1 

45°  32'  35" 

2521 

47°  13'  19" 

2516 

Computation  of  Greenwich  Mean  Time. 


True  Distance, 
Dist.,  N.  A.,  at  XV^ 

Difference, 

Approx.  interval. 
Add— 

Approx.  G.  M.  T., 
Corr.,  Table  X, 

True  G.  M.  T., 
L.  M.  T., 

Long., 


45°  22'  32" 
43   51    59 


1 

30  33 

2'' 
15 

42"' 01' 

17 

+ 

42   01 
01 

17 
9 

42  02 
40  00 

P.  L.,  0.2527 

log,  Table  IX,     3.7350 


Diff.  P.  logs  —  6 


loe,  Table  IX,     3.9877 


+  8    02  02  =  120°  30'  30"  W. 


Method  op  Taking  a  Lunar  Observation  by  One  Observer. — Three  observers  are  required  to 
make  the  necesssary  observations  for  determining  the  longitude — one  to  measure  the  distance  of  the 
bodies,  and  the  others  to  take  the  altitudes.  In  case  of  not  having  a  sufficient  number  of  instruments 
or  observers  to  take  the  altitudes,  the  latter  may  be  calculated,  there  being  given  the  latitude  of  the  place, 
the  time,  the  right  ascensions,  and  the  declinations  of  the  objects.  These  calculations  are  long,  however, 
especially  in  the  case  of  the  moon,  and  a  considerable  degree  of  accuracy  is  required  in  finding  from  the 
Nautical  Almanac  the  moon's  right  ascension  and  declination,  which  must  be  liable  to  some  error  on 
account  of  the  uncertainty  of  the  ship's  longitude.  The  following  method  of  obtaining  those  altitudes 
is  far  more  simple,  and  sufficiently  accurate.  This  method  depends  on  the  supposition  that  the  altitudes 
increase  or  decrease  uniformly. 


294 


LUNAR    DISTANCES. 


Before  measuring  the  distance  of  the  bodies,  take  their  altitudes,  and  note  the  times  by  a  chro- 
nometer; then  measure  the  distance  and  note  the  time  (or  measure  a  number  of  distances,  and  note 
the  corresponding  times,  and  take  the  means);  after  having  measured  the  distances,  again  measure  the 
altitudes,  and  note  the  times;  then,  from  the  two  observed  altitudes  of  either  of  the  objects,  the  required 
altitude  of  that  object  may  be  found  from  the  following  formula,  which  is  based  upon  simple  proportion: 

dXe 

where  x  =  change  of  altitude,  in  minutes,  between  first  altitude  and  time  of  measuring  the  lunar 
distance,  being  positive  or  negative  according  as  body  is  rising  or  falling; 
d  =  difference  between  first  and  second  altitudes,  in  minutes; 
e  =  time,  in  seconds,  between  first  altitude  and  lunar  observations;  and 
/  =  time  in  seconds,  between  first  and  second  altitudes. 
The  change  of  altitude  thus  deduced,  applied  w-ith  proper  sign  to  the  first  altitude,  gives  the 
altitude  at  time  of  observing  the  lunar  distance. 

Example:  Suppose  the  dista,nces  and  altitudes  of  the  sun  and  moon  were  observed,  as  in  the 
following  table;  it  is  required  to  find  the  altitudes  at  the  time  of  measuring  the  mean  distance. 


Times  by  chro- 
nometer. 

2"  03™  20' 
2  04  20 
2    05     50 

Mean,     2    04     30 


Lunar  dis- 
tance. 

40°  00'  00'' 
40    00  30 
40    01   30 

40    00  40 


Times  hy  chro- 
nometer. 


2^  02 
2   06 


"00^ 
10 


'.{ 


Obs.  alt. 
d's  L.  L. 

20°   46' 

21     20 

(/,      34 


For  C- 
Time  of  lunar  obs., 
Time  of  1st  alt.. 


2"  04" 
2    02 


30^ 
00 


,    34  X  150 
"^       250~ 
First  altitude, 

X, 


/  2    30 
\      ISO" 

=  +  20'.4  =  +  20'  24" 

20°  46'  00" 

+        20   24 


10 
250^ 

For  Q. 
Time  of  lunar  obs., 
Time  of  1st  alt., 


Times  by  chro- 
nometer. 

2^  02™  30" 
2    07    00 

/       4     30 
1  270' 


2'>  04" 
2    02 


Ob><.  alt. 
Q's  L.  L. 

40°   20' 
39     12 


<' 


08 


30^ 
30 


«, 


X  120 


270 
First  altitude, 


=  -30'.2 


Required  altitude. 


J  2    00 
\      120' 

=  —  30'  12" 

40°  20'  00" 
30   12 

39    49  48 


Required  altitude,  21    06  24 

To  obtain  the  altitudes  by  calculation  the  following  formulae  may  be  employed: 

tan  A  =  tan  d  sec  t; 

smh=  ^•OB(A-L)sind 
sm  A 

in  which  d  is  the  declination;  t,  the  hour  angle;  L,  the  latitude;  /;,  the  true  altitude  of  the  center  of  the 
object;  A,  an  arc  Avhich  has  the  same  name  or  sign  as  the  declination  and  is  numerically  in  the  same 
quadrant  as  t.     In  the  solution,  strict  regard  must  be  had  for  the  signs. 

Example:  Required  the  apparent  altitude  of  the  sun's  center  on  December  22,  1879,  in  Lat.  48°  23' 
N.,  Long.  60°  W.,  at  10"  01™  14'  a.  m.,  app.  time. 


L.  A.  T.,  December  21,      22"  01™  14» 
Long.,  +   4   00    00 


t, 

O's  Dec. 


1"  58™  46' 
23°  27'  16"  S. 


G.  A.  T.,  December  22,        2   01    14 


t 
d 

A 
L 


29°  41'  30" 
—  23    27    16 

-26    32    20 
+  48    23   00 


sec  0.06113 

tan  (-)  9.63735 


tan  (-)  9.69848 


74    55    20 


h  13    23   58 

ref.— par.  +  3   50 


sin      (-)  9.59991 
cosec(— )  0.34989 

cos      (  +  )  9.41520 
sin      (+)  9.36500 


App.  alt.         13    27  48 


Page  296]           APPENDIX  V:  TABLE  II. 

Log.  A,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App 
alt.  of 
moon. 

Redticed  parallax  and  refraction  of  moon.                         1 

41' 

42' 

48' 

44' 

45' 

46' 

4i' 

48' 

40' 

50' 

51' 

52' 

58' 

54' 

55' 

5°  0^ 
2 
4 
6 
8 

.0288 
.0286 
.0284 
.0282 
.0281 

0295 
0293 
0291 
0289 
0287 

0301 
0299 
0297 

0294 

0308 

0306 

0304 

0302 

0300 

0298 

0296 

0295 

0293 

0291 

0289 

0288 

0286 

0284 

0282 

0281" 

0279 

0277 

0276 

0274 

0315 
0313 
0311 
0309 
0307 
0305 
0303 
0301 
0299 
0297 
0296 
0294 
0292 
0290 
0289 

0321 
0319 
0317 
0315 
0313 
0311 
0309 
0307 
0306 
0304 
0302 
0300 
0298 
0296 
0295 

0328 
0326 
0324 
0322 
0320 
0318 
0316 
0314 
0312 
0310 

0335 
0333 
0330 
0328 
0326 
0324 
0322 
0320 
0318 
0316 

0341 
0339 
0337 
0335 
0333 
0331 
0329 
0327 
0325 
0323 
0321 
0319 
0317 
0315 
0313 

0348 
0346 
0344 
0341 
0339 
0337 
0335 
0333 
0331 
0329 
0327 
0325 
0323 
0321 
0319 

0355 
0352 
0350 
0348 
0346 
0344 
0341 
0339 
0337 
0335 

0361 
0359 
0357 
0354 
0352 

0368 
0366 
0363 
0361 
0359 

5  10 
12 
14 
16 
18 

5  20 
22 
24 
26 
28 

.0279 
.0277 
.0275 
.0274 
.0272 

0285 
0284 
0282 
0280 
0278 

0292 
0290 
0288 
0286 
0285 

0350 
0348 
0346 
0344 
0341 
0339 
0337 
0335 
0333 
0331 
0329 
0327 
0326 
0324 
0322 
0320 
0318 
0316 
0315 
0313 

0356 
0354 
0352 
0350 
0348 
0346' 
0344 
0341 
0339 
0337 
0335 
0334 
0332 
0330 
0328 
0326" 
0324 
0322 
0320 
0319 

.0270 
.0269 
.0267 
.0265 
.0264 

0277 
0275 
0273 
0272 
0270 

0283 
028r 
0280 
0278 
0276 

0308 
0306 
0304 
0303 
0301 

0314 
0313 
0311 
0309 
0307 

0333 
0331 
0329 
0327 
0325 

0346 
0344 

5  30 
32 
34 
36 

38 

.0262 
.0261 
.0259 
.0258 

0268 
0267 
0265 
0264 
0262 
0261 
0259 
0258 
0256 
0255 
0253 
0252 
0251 
0249 
0248 

0275 
0273 
0271 
0270 
0268 
0267 
0265 
0264 
0262 
0261 

0287 
0285 
0283 
0282 
0280 
0279 
0277 
0275 
0274 
0272 

0293 
0291 
0290 
0288 
0286 
0285 
0283 
0281 
0280 
0278 

0299 
0297 
0296 
0294 
0292 
0290 
0289 
0287 
0286 
0284 

0305 
0303 
0302 
0300 
0298 
0296 
0295 
0293 
0291 
0290 
0288 
0287 
0285 
0283 
0282 

0311 
0309 
0308 
0306 
0304 

0317 
0315 
0314 
0312 
0310 

0323 
0321 
0320 
0318 
0316 
0314 
0312 
0311 
0309 
0307 

0342 
0340 
0338 
0336 
0334 
0332 
0330 
0328 
0326 
0324 

5  40 
42 
44 
46 
48 

5  50 
52 
54 
56 
58 

0273 
0271 
0270 
0268 
0267 

0302 
0301 
0299 
0297 
0296 

0308 
0306 
0305 
0303 
0301 

0259 
0258 
0256 
0255 
0254 

0265 
0264 
0262 
0261 
0259 

0271 
0269 
0268 
0266 
0265 

0277 
0275 
0274 
0272 
0271 

0282 
0281 
0279 
0278 
0276 

0294 
0292 
0291 
0289 
0287 

0300 
0298 
0296 
0295 
0293 

0305 
0304 
0302 
0300 
0299 

0311 
0309 
0308 
0306 
0304 
0303" 
0.301 
0299 
0298 
0296 

0317 
0315 
0313 
0312 
0310 
0308 
0307 
0305 
0303 
0302 

0323 
0321 
0319 
0317 
0316 

6  0 
2 
4 
6 
8 

0247 
0245 
0244 
0243 
0241 

0252 
0251 
0249 
0248 
0247 
0246 
0244 
0243 
0242 
0240 

0258 
0256 
0255 
0254 
0252 

0263 
0262 
0261 
0259 
0258 

0269 
0268 
0266 
0265 
0263 

0275 
0273 
0272 
0270 
0269 
0267 
0266 
0265 
0263 
0262 

0280 
0279 
0277 
0276 
0274 
0273 
0271 
0270 
0269 
0267 
"0266 
0264 
0263 
0262 
0260 

0286 
0284 
0283 
0281 
0280 
0278 
0277 
0275 
0274 
0273 

0291 
0290 
0288 
0287 
0285 
0284 
0282 
0281 
0279 
0278 

0297 
0295 
0294 
0292 
0291 
0289 
0288 
0286 
0285 
0283 

0314 
0312 
0310 
0309 
0307 

6  10 
12 
14 
16 

18 



0240 
0239 
0237 
0236 
0235 
0234 
0233 
0231 

0251 
0250 
0248 
0247 
0246 

0256 
0255 
0254 
0252 
0251 

0262 
0261 
0259 
0258 
0257 

0295 
0293 
0292 
0290 
0289 
0287 
0286 
0284 
0283 
0281 

0300 
0299 
0297 
0295 
0294 

0306 
0304 
0302 
0301 
0299 

6  20 
22 
24 
26 

28 

0239 
0238 
0237 
0236 
0234 
0233 
0232 
0231 
0230 
0229 

0245 
0243 
0242 
0241 
0240 
0238 
0237 
0236 
0235 
0234 

0250 
0249 
0247 
0246 
0245 

0255 
0254 
0253 
0251 
0250 

0261 
0259 
0258 
0257 
0255 

0271 
0270 
0268 
0267 
0266 

0276 
0275 
0274 
0272 
0271 

0282 
0280 
0279 
0277 
0276 

0292 
0291 
0289 
0288 
0286 

0298 
0296 
0295 
0293 
0292 

0297 
0295 
0294 
0292 
0291 
0290 

6  30 
32 
34 
36 
38 

0244 
0242 
0241 
0240 
0239 

0249 
0248 
0246 
0245 
0244 

0254 
0253 
0251 
0250 
0249 
0248 
0246 
0245 
0244 
0243 

0259 
0258 
0257 
0255 
0254 
0253 
0252 
0250 
0249 
0248 

0264 
0263 
0262 
0260 
0259 

0270 
0268 
0267 
0266 
0264 

0275 
0273 
0272 
0271 
0269 
0268 
0267 
0265 
0264 
0263 
"0262 
0260 
0259 
0258 
0257 

0280 
0278 
0277 
0276 
0274 

0285 
0284 
0282 
0281 
0279 

0290 
0289 
0287 
0286 
0284 

6  40 
42 
44 
46 

48 

0227 
0226 
0225 
0224 
0223 

0232 
0231 
0230 
0229 
0228 

0238 
0236 
0235 
0234 
0233 
0232 
0231 
0230 
0229 
0227 

0243 
0241 
0240 
0239 
0238 

0258 
0257 
0255 
0254 
0253 
0252 
0250 
0249 
0248 
0247 

0263 
0262 
0260 
0259 
0258 
0257 
0255 
0254 
0253 
0252 

0273 
0272 
0270 
0269 
0268 
"0266' 
0265 
0264 
0263 
0261 

0278 
0277 
0275 
0274 
0273 
0271 
0270 
0269 
0267 
0266 

0283  0288 
0282  !  0287 
0280  0285 
0279  '■  0284 
0278  0283 

6  50 
52 
54 
56 

58 

0222 
0221 
0220 
0219 
0218 

0227 
0226 
0225 
0224 
0223 

0237 
0236 
0235 
0233 
0232 

0242 
0241 
0239 
0238 
0237 

0247 
0246 
0244 
0243 
0242 

0276 
0275 
0274 
0272 
0271 

0281 
0280 
0279 
0277 
0276 

7  0 

0217 

0222 

0226 

0231 

0236 

0241 

0246 

0251 

0255 

0260 

0265 

0270 

0275 

APPENDIX  V:  TABLE  II.            [Page  297 

Log.  A,  for  computing  the  Mrst  Correction  of  the  Lnnar  Distance. 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                        1 

44' 

45' 

46' 

47' 

48'  1  49'    50' 

51' 

62' 

68' 

54' 

55' 

66'  j  67' 

7°  0^ 
3 
6 
9 

12 

.0222 
.0220 
.0218 
.0217 
.0215 

0226 
0225 
0223 
0222 
0220 

0231 
0230 
0228 
0226 
0225 

0236 
0234 
0233 
0231 
0230 

0241 
0239 
0238 
0236 
0234 

0246  0251 
0244  0249 
0242  i  0247 
0241  0245 
0239  0244 

0255 
0254 
0252 
0250 
0248 

0260 
0258 
0257 
0255 
0253 

0265 
0263 
0261 
0260 
0258 

0270 
0268 
0266 
0264 
0262 

0275 
0273 
0271 
0269 
0267 

7  15 
18 
21 
24 

27 

.0214 
.0213 
.0211 
.0210 
.0208 
.0207 
.0206 
.0204 
.0203 
.0202 

0219 
0217 
0216 
0214 
0213 
0211 
0210 
0209 
0207 
0206 
0205 
0203 
0202 
0201 
0200 
0198 
0197 
0196 
0195 
0193 

0223 
0222 
0220 
0219 
0217 

0228 
0226 
0225 
0223 
0222 
0220 
0219 
0218 
0216 
0215 

0233 

0231 

0230 

0228 

0227 

0225^ 

0224 

0222 

0221 

0219 

0237 
0236 
0234 
0233 
0231 
0230 
0228 
0227 
0225 
0224 
0222 
0221 
0219 
0218 
0217 
0215 
0214 
0213 
0211 
0210 

0242 
0240 
0239 
0237 
0236 

0247 
0245 
0243 
0242 
0240 

0251 
0250 
0248 
0246 
0245 

0256 
0254 
0253 
0251 
0249 

0261 
0259 
0257 
0255 
0254 
0252 
0250 
0249 
0247 
0246 

0265 
0263 
0262 
0260 
0258 

7  30 
33 
36 
39 
42 

0216 
0215 
0213 
0212 
0210 
0209 
0208 
0206 
0205 
0204 
0203 
0201 
0200 
0199 
0198 

0234 
0232 
0231 
0229 
0228 
0227' 
0225 
0224 
0222 
0221 

0239 
0237 
0235 
0234 
0232 
0231 
0229 
0228 
0227 
0225 

0243  0248 
0241  0246 
0240  0244 
0238  !  0243 
0237  0241 

0257 
0255 
0253 
0252 
0250 

! 

7  45 
48 
51 
54 
57 

8  0 
3 
6 
9 

12 

.0200 
.0199 
.0198 
.0196 
.0195 
.0194 
.0193 
.0192 

0213  0218 
0212  0216 
0211  0215 
0209  0214 
0208  0212 
0207  0211 
0206  1  0210 
0204  0208 
0203  i  0207 
0202  '  0206 

02a5 
0234 
0232 
0231 
0229 

0240 
0238 
0237 
0235 
0234 
0232 
0231 
0229 
0228 
0227 

0244 
0242 
0241 
0239 
0238 
0236' 
0235 
0233 
0232 
0231 
0229 
0228 
0226 
0225 
0224 

0248 
0247 
0245 
0244 
0242 
0241 
0239 
0238 
0236 
0235 
0233 
0232 
0231 
0229 
0228 
0226 
0225 
0224 
0223 
0221 

0249 
0248 
0246 
8245 
0243 
0242 
0240 
0239 

0219 
0218 
0217 
0215 
0214 

0224 
0222 
0221 
0220 
0218 
0217 
0217 
0214 
0213 
0212 
0211 
0209 
0208 
0207 
0206 

0228 
0227 
0225 
0224 
0222 

8  15 
18 
21 
24 
27 

8  30 
33 
36 
39 
42 

8  45 
48 
51 
54 
57 

0192 
0191 
0190 
0189 
0188 

0196 
0195 
0194 
0193 
0192 
0191 
0190 
0188 
0187 
0186 

0201 
0199 
0198 
0197 
0196 

0205 
0203 
0202 
0201 
0200 

0209 
0207 
0206 
0205 
0204 

0213 
0212 
0210 
0209 
0208 

0221  0225 
0220  0224 
0218  0222 
0217  0221 
0216  0220 

0237 
0236 
0235 
0233 
0232 

0187 
0186 
0184 
0183 
0182 

0195 
0193 
0192 
0191 
0190 

0199 
0197 
0196 
0195 
0194 

0203 
0201 
0200 
0199 
0198 

0207 
0205 
0204 
0203 
0202 

0215 
0213 
0212 
0211 
0210 

0219 
0217 
0216 
0215 
0214 

0223 
0221 
0220 
0219 
0217 
0216 
0215 
0214 
0212 
9211 

0230 
0229 
022S 
0226 
0225 

0181 
0180 
0179 
0178 
0177 

0185  0189 
0184  0188 
0183  '  0187 
0182  1  0186 
0181  0185 

0193 
0192 
0191 
0190 
0189 

0197 
0196 
0195 
0193 
0192 

0201 
0200 
0198 
0197 
0196 

0205 
0203 
0202 
0201 
0200 

0208 
0207 
0206 
0205 
0204 

0212 
0211 
0210 
0209 
0208 

0220  0224 
0219  0223 
0218  0221 
0216  0220 
0215  1  0219 

9  0 
3 

6 

9 

12 

0176 
0175 
0174 
0173 
0172 

0180  0184 
0179  0183 
0178  0182 
0177  0181 
0176  !  0180 

0188 
0186 
0185 
0184 
0183 

0191 
0190 
0189 
0188 
0187 

0195 
0194 
0193 
0192 
0191 

0199 
0198 
0197 
0196 
0194 

0203 
0201 
0200 
0199 
0198 

0206 
0205 
0204 
0203 
0202 

0210 
0209 
0208 
0207 
0206 

0214  0218 
0213  0216 
0211  0215 
0210  1  0214 
0209  1  0213 

• 

9  15 
18 
21 
24 

27 

0171 
0170 
0170 

0175 
0174 
0173 
0172 
0171 

0179 
0178 
0177 
0176 
0175 

0182 
0181 
0180 
0179 
0179 

0186 
0185 
0184 
0183 
0182 

0190 
0189 
0188 
0187 
0186 

0193 
0192 
0191 
0190 
0189 

0197 
0196 
0195 
0194 
0193 

0201 
0200 
0199 
0198 
0196 

0204 
0203 
0202 
0201 
0200 

0208  j  0212 
0207  1  0211 
0206  !  0209 
0205  0208 
0204  0207 

9  30 
33 
36 
39 
42 

9  45 
48 
51 
54 
57 

0170 
0170 
0169 
0168 
0167 

0174 
0173 
0172 
0171 
0170 

0178 
0177 
0176 
0175 
0174 
0173 
0172 
0171 
0170 
0169 

0181 
0180 
0179 
0178 
0177 

0185 
0184 
0183 
0182 
0181 
0180 
0179 
0178 
0177 
0176 

0188  0192 
0187  0191 
0186  0190 
0185  0189 
0184  0188 

0195 
0194 
0193 
0192 
0191 
0190 
0189 
0188 
0187 
0186 

0199 
0198 
0197 
0196 
0195 
0194 
0193 
0192 
0191 
0190 

0203  0206 
0201  !  0205 
0200  i  0204 
0199  0203 
0198  1  0202 

1 

0166 
0165 
0164 
0163 
0163 

0169 
0169 
0168 
0167 
0166 

0176 
0176 
0175 
0174 
0173 

0183 
0182 
0182 
0181 
0180 

0187 
0186 
0185 
0184 
0183 

0197 
0196 
0195 
0194 
0193 

0201 
0200 
0199 
0198 
0197 

0203 
0202 
0201 
0200 

10  0 

0162 

0165 

0169 

0172 

0175 

0179  0182 

0186 

0189 

0192 

0196  0199 

Page  298] 

APPENDIX  V:  TABLE  II. 

Log. 

A,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App. 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                        1 

46' 

47' 

48' 

49' 

50' 

61' 

oS' 

o8' 

54'    55' 

56' 

0196 

57' 

68' 

10°  0' 

.0162 

0165 

0169 

0172 

0175 

0179 

0182 

0186 

0189  '  0192 

0199 

5 

.0160 

0164 

0167 

0171 

0174 

0177 

0181 

0184  ;  0187  0191 

0194  0197 

10 

.0159 

0162 

0166 

0169 

0172 

0176 

0179 

0182  1  0186  0189 

0192  0196 

15 

.0158 

0161 

0164 

0168 

0171 

0174 

0178 

0181  ;  0184  i  0187 

0191  i  0194 

I 

20 

.0156 

0160 

^163 

0166 

0170 

0173 

0176 

0179 

0183  i  0186 

0189 

0192 

25 

.0155 

0158 

0162 
0160 

0165 

0168 

0171 

0175 

0178 

0181 
0180 

0184 

0188 

0191 

10  30 

.0154 

0157 

0164 

0167 

0170 

0173 

0177 

0183 

0186 

0189 

35 

.0153 

0156 

0159 

0162 

0166 

0169 

0172 

0175 

0178  0181 

0185  j  0188 

40 

.0151 

0155 

0158 

0161 

0164 

0167 

0171 

0174 

0177  0180 

0183  i  0186 

45 

.0150 

0153 

0157 

0160 

0163 

0166 

0169 

0172 

0175  0179 

0182  0185 

•  50 

.0149 

0152 

0155 

0158 

0162 

0165 

0168 

0171  i  0174  i  0177 

0180 

0183 

55 

.0148  i  0151 

0154 

0157 

0160 

0163 

0167 

0170  1  0173  i  0176 

0179 
0177 

0182 

11  0 

.0147  1  0150 

0153 

0156 

0159 

0162 

0165 

0168  !  0171 

0174 

0181 

5 

.0146 

0149 

0152 

0155 

0158 

0161 

0164 

0167  1  0170 

0173 

0176 

0179 

10 

0148 

0151 

0154 

0157 

0160 

0163 

0166 

0169 

0172 

0175 

0178 

15 

0146 

0149 

0152 

0155 

0158 

0161 

0164 

0167 

0170 

0173  1  0176 

20 

0145 

0148 

0151 

0154 

0157 

0160 

0163 

0166 

0169 

0172  0175 

25 
11  30 

0144 

0147 

0150 

0153 

0156 

0159 

0162  1  0165 

0168  i  0171  1  0174 

0143 

0146 

0149 

0152 

0155 

0158 

0161  0164 

0167 

0170  1  0172 

35 

0142 

0145 

0148 

0151 

0154 

0157 

0160  1  0162 

0165 

0168  0171 

40 

0141 

0144 

0147 

0150 

0153 

0156 

0158  0161 

0164 

0167  0170 

45 

0140 

0143 

0146 

0149 

0151 

0154 

0157  !  0160 

0163 

0166  0169 

50 

0139 

0142 

0145 

0148 

0150 

0153 

0156  :  0159 

0162 

0165  0167 

55 

12  0 

0138 

0141 

0144 

0146 
0145 

0149 
0148 

0152 

0155  0158 

0161 

0163 
0162' 

0166 

0137 

0140 

0143 

0151 

0154  !  0157 

0159 

0165 

5 

0136 

0139 

0142 

0144 

0147 

0150 

0153  0156 

0158 

0161  0164 

10 

0135 

0138 

0141 

0143 

0146 

0149 

0152 

0154 

0157 

0160  0163 

15 

0134 

0137 

0140 

0142 

0145 

0148 

0151 

0153 

0156 

0159  0162 

20 

0133 

0136 

0139 

0141 

0144 

0147 

0150 

0152 

0155 

0158  1  0160 

25 

0132 

0135 

0138 

0140 

0143 

0146 

0148 

0151 

0154 

0157  0159 

12  30 

0131 

0134 

0137 

0139 

0142 

0145 

0147  !  0150 

0153 

0155  0158 

35 

0130 

0133 

0136 

0138 

0141 

0144 

0146  0149 

0152 

0154  ;  0157 

40 

0129 

0132 

0135 

0137 

0140 

0143 

0145  !  0148 

0151  1  0153  0156 

45 

0129 

0131 

0134 

0136 

0139 

0142 

0144  \  0147 

0150 

0152  0155 

0158 

50 

0128 

0130 

0133 

0136 

0138 

0141 

0143  0146 

0149 

0151  '  0154 

0156 

1 

55 

0127 

0129 
0129 

0132 
0131 

0135 

0137 
0136 

0140 

0142 

0145 

0148 

0150  0153 

0155 

13  0 

0126 

0134 

0139 

0141 

0144 

0147 

0149  0152 

0154 

5 

0125 

0128 

0130 

0133 

0135 

0138 

0141 

0143 

0146 

0148  0151 

0153 

10 

0124 

0127 

0129 

0132 

0135 

0137 

0140 

0142 

0145 

0147  0150 

0152 

15 

0123 

0126 

0129 

0131 

0134 

0136 

0139 

0141 

0144 

0146  0149 

0151 

1 

20 

0123 

0125 

0128 

0130 

0133 

0135 

0138 

0140 

0143 

0145  0148 

0150 

25 

0122 

0124 

0127 

0129 

0132 
0131 

0134 
0133 

0137 
0136 

0139 

0142 

0144  1  0147 
0143  1  0146 

0149 

1 

13  30 

0121 

0124 

0126 

0129 

0138 

0141 

0148 

35 

0120 

0123 

0125 

0128 

0130 

0133 

0135 

0138 

0140 

0142  0145 

0147 

40 

0120 

0122 

0124 

0127 

0129 

0132 

0134  i  0137 

0139 

0142  0144 

0146 

45 

0121 

0124 

0126 

0128 

0131 

0133 

0136 

0138 

0141  1  0143 

0145 

50 

0120 

0123 

0125 

0128 

0130 

0132 

0135 

0137 

0140  ;  0142 

0145 

55 

0120 

0122 

0124 

0127 

0129 

0132 
0131 

0134 
0133 

0136 
0136 

0139  !  0141 

0144 
0143 

14  0 

0119 

0121 

0124 

0126 

0128 

0138  0140 

! 

5 

0118 

0121 

0123 

0125 

0128 

0130 

0132 

0135 

0137  i  0139 

0142 

10 

0117 

0120 

0122 

0124 

0127 

0129 

0132 

0134 

0136  i  0139 

0141 

15 

0117 

0119 

0121 

0124 

0126 

0128 

0131 

0133 

0135 

0138 

0140 

20 

0116 

0118 

0121 

0123 

0125 

0128 

0130 

0132 

0135 

0137 

0139 

25 

0115 

0118 

0120 

0122 

0124 

0127 

0129 

0131 

0134 

0136 

0138 

! 

14  30 

0114 

0117 

0119 

0121 

0124 

0126 

0128 

0131 

0133  0136  i  0137 

i 

35 

0114 

0116 

0118 

0121 

0123 

0125 

0128 

0130 

0132 

0134 

0137 

40 

0113 

0115 

0118 

0120 

0122 

0124 

0127 

0129 

0131 

0134 

0136 

\ 

45 

0112 

0115 

0117 

0119 

0121 

0124 

0126 

0128 

0130 

0133 

0135 

1 

50 

0112 

0114 

0116 

0118 

0121 

0123 

0125 

0127 

0130 

0132 

0134 

1 

55 

0111 

0113 

0116 

0118 

0120 

0122 

0124 

0127 

0129 

0131  0133 

15  0 

0110 

0113 

0115 

0117 

0119 

0121 

0124 

0126 

0128 

0130  ;  0133 

! 

APPENDIX  V:  TABLE  11.            [Page  298 

Log.  A,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                        1 

43' 

49' 

50' 

51' 

52'    58' 

54' 

56' 

56' 

57' 

58' 

59' 

15°  0' 
10 
20 
30 
40 
50 

16  0 
10 
20 
30 

.0110 
.0109 
.0108 
.0107 
.0105 

0113 
0111 
0110 
0109 
0107 
dlO'6 
0105 
0104 
0103 
0102 

0115 
0113 
0112 
0111 
0110 

0117 
0116 
0114 
0113 
0112 

0119  0121 
0118  1  0120 
0116  0119 
0115  '  0117 
0114  '  0116 

0124 
0122 
0121 
0119 
0118 

0126 
0124 
0123 
0121 
0120 

0128 
0127 
0125 
0124 
0122 

0130 
0129 
0127 
0126 
0124 

0133 
0131 
0129 
0128 
0126 



.0104 
.0103 
.0102 
.0101 
.0100 

0108 
0107 
0106 
0105 
0103 

0110 
0109 
0108 
0107 
0105 

0112 
0111 
0110 
0109 
0107 

0115 
0113 
0112 
0111 
0109 

0117 
0115 
0114 
0113 
0111 

0119 
0117 
0116 
0115 
0113 

0121 
0119 
0118 
0117 
0115 

0123 
0121 
0120 
0119 
0117 

0125 
0124 
0122 
0121 
0119 

40 
50 
17  0 
10 
20 

.0098 
.0097 
.0096 
.0095 
.0094 

0100 
0099 
0098 
0097 
0096 

0102 
0101 
0100 
0099 
0098 

0104 
0103 
0102 
0101 
0100 

0106 
0105 
0104 
0103 
0102 

0108 
0107 
0106 
0105 
0104 

0110 
0109 
0108 
0107 
0106 

0112 
0111 
0110 
0109 
0107 

0114 
0113 
0112 
0110 
0109 

0116 
0115 
0114 
0112 
0111 

0118 
0117 
0116 
0114 
0113 

30 
40 
50 
18  0 
10 

0095 
0094 
0093 
0092 
0091 

0097 
0096 
0095 
0094 
0093 

0099 
0098 
0097 
0096 
0095 

0101 
0100 
0099 
0098 
0097 

0103 
0101 
0100 
0099 
0098 

0104 
0103 
0102 
0101 
0100 

0106 
0105 
0104 
0103 
0102 

0108 
0107 
0106 
0105 
0104 

0110 
0109 
0108 
0107 
0105 

0112 
0111 
0109 
0108 
0107 

0109 
0108 
0107 
0106 
0105 
0104 

20 
30 
40 
50 
19  0 
10 
20 
30 
40 
50 

0090 
0089 
0088 
0088 
0087 

0092 
0091 
0090 
0089 
.0088 

0094 
0093 
0092 
0091 
0090 

0096 
0095 
0094 
0093 
0092 

0097 
0096 
0095 
0094 
0093 

0099 
0098 
0097 
0096 
0095 

0101 
0100 
0099 
0098 
0097 

0103 
0102 
0101 
0099 
0098 

0104 
0103 
0102 
0101 
0100 

0106 
0105 
0104 
0103 
0102 

0086  0087 
0085  0087 
0084  0086 
0083  1  0085 
0082  j  0084 

0089 
0088 
0087 
0087 
0086 
0085 
0084 
0083 
0082 
0082 

0091 
0090 
0089 
0088 
0087 

0092 
0092 
0091 
0090 
0089 
0088 
0087 
0086 
0086 
0085 
0084 
0083 
0082 
0082 
0081 

0094  0096 
0093  0095 
0092  :  0094 
0091  0093 
0090  1  0092 

0098 
0097 
0096 
0095 
0094 
0093 
0092 
0091 
0090 
0089 
0088 
0088 
0087 
0086 
0085 

0099 
0098 
0097 
0096 
0095 

0101 
0100 
0099 
0098 
0097 

0103 
0102 
0101 
0100 
0099 
0098 
0097 
0096 
0095 
0094 
0093 
0092 
0091 
0090 
0090 

20  0 
10 
20 
30 

•  40 
50 

21  0 
10 
20 
30 

0082 
0081 
0080 
0079 
0079 
0078 
0077 
0076 
0076 
0075 

0083 
0082 
0082 
0081 
0080 

0086 
0086 
0085 
0084 
0083 

0090 
0089 
0088 
0087 
0086 

0091 
0090 
0089 
0089 
0088 

0094  i  0096 
0093  1  0095 
0093  0094 
0092  '  0093 
0091  0092 

■ 

0079 
0079 
0078 
0077 
0076 

0081 
0080 
0079 
0079 
0078 

0082 
0082 
0081 
0080 
0079 

0085  1  0087 
0085  '  0086 
0084  1  0085 
0083  !  0085 
0082  0084 

0090  0091 
0089  0091 
0088  i  0090 
0087  0089 
0087  i  0088 

40 
50 
22  0 
10 
20 

0074 
0074 
0073 
0072 
0072 

0076 
0075 
0074 
0074 
0073 

0077 
0076 
0076 
0075 
0074 

0079 
0078 
0077 
0076 
0076 
0075 
0074 
0074 
0073 
0072 

0080 
0079 
0079 
0078 
0077 
0076 
0076 
0075 
0074 
0074 

0082 
0081 
0080 
0079 
0079 
0078 
0077 
0076 
0076 
0075 

0083 
0082 
0081 
0081 
0080 

0084 
0084 
0083 
0082 
0081 

0086 
0085 
0084 
0083 
0083 

0087 
0086 
0086 
0085 
0084 

0089 
0088 
0087 
0086 
0086 

30 
40 
50 
23  0 
10 

0071 
0070 
0070 
0069 
0068 

0072 
0072 
0071 
0070 
0070 

0074 
0073 
0072 
0072 
0071 

0079 
0079 
0078 
0077 
0076 

0081 
0080 
0079 
0078 
0078 

0082 
0081 
0081 
0080 
0079 

0083 
0083 
0082 
0081 
0080 

0085 
0084 
0083 
0082 
0082 

1 

20 
30 
40 
50 
24  0 

0068 
0067 
0067 
0066 

0069 
0069 
0068 
0067 
0067 

0070 
0070 
0069 
0069 
0068 

0072 
0071 
0071 
0070 
0069 

0073 
0072 
0072 
0071 
0071 

0074 
0074 
0073 
0073 
0072 

0076 
0075 
0074 
0074 
0073 

0077 
0076 
0076 
0075 
0074 

0078 
0078 
0077 
0076 
0076 

0080 
0079 
0078 
0078 
0077 

0081 
0080 
0080 
0079 
0078 

10 
20 
30 
40 
50 

0066 
0066 
0065 
0065 
0064 

0067 
0067 
0066 
0066 
0065 

0069 
0068 
0068 
0067 
0066 

0070 
0069 
0069 
0068 
0068 

0071 
0071 
0070 
0069 
0069 

0073 
0072 
0071 
0071 
0070 

0074 
0073 
0072 
0072 
0071 

0075 
0074 
0074 
0073 
0072 

0076 
0076 
0075 
0074 
0074 

0078 
0077 
0076 
0076 
0075 

25  0 

0063 

0065 

0066 

0067  j  0068 

0069  1  0071 

0072  1  0073 

0074; 

Page  300] 

APPENDIX  V:  TABLE  11. 

Log.  A,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App. 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                         1 

50' 

51' 

52' 

58'  j  54'  1  56' 

56'    57'  i  58' 

59' 

80' 

1 

25°  0' 

.0063 

0065 

0066  '  0067  0068  0069 

0071  0072  0073 

0074 

1 
1 

20 

.0062 

0064 

0065  0066  I  0067  0068 

0069  0071  0072 

0073 

40 

.0061 

0062 

0064  1  0065  0066  i  0067 

0068  '  0069  0071  i  0072 

26  0 

.0060 

006f 

0063  0064  0065  0066 

0067  0068  0069  :  0071 

1 

20 

.0059 

0060 

0062  1  0063  '  0064  0065 

0066  1  0067 
0065  ;  0066 

0068  0069 



1 

40 

.0058 

0059 

0061  0062  0063  0064 

0067  0068 

1 

27  0 

.0057 

0058 

0060  0061  '  0062  0063 

0064  0065  0066  0067 

20 

.0056 

0057 

0059 

0060  0061  0062 

0063  0064  0065  0066 

40 

.0055 

0057 

0058 

0059  i  0060  0061 

0062  0063  0064  ■  0065 

28  0 

.0055 

0056 

0057 

0058  0059  0060 

0061  0062  j  0063  0064 

20 

.0054 

0055 

0056 

0057  0058  0059 

0060  i  0061  0062  0063 

40 

.0053 

0054 

0055  0056  0057  ■  0058 

0059  i  0060  0061  0062 

j 

29  0 

.0052 

0053 

0054  0055  0056  0057 

0058  0059  0060  0061 

1 

20 

.0051 

0052 

0053  i  0054  0055  0056 

0057  0058  1  0059  0060 

40 

.0050 

0051 

0052  1  0053  0054  0055 

0056  0057  0058  0059 

30  0 

.0050 

0051 

0051  0052  j  0053  0054  ;  0055  0056  0057  i  0058 

1 

20 

.0049 

0050 

0051  1  0052  1  0052  0053 

0054  0055  0056  0057 

40 

.0048 

0049 

0050  i  0051  0052  0053 

0053  0054  0055  0056 

31  0 

.0047 

0048 

0049  0050  0051  0052 

0053  0053 

0054  0055 

20 

.0047 

0047 

0048  0049  0050  0051 

0052  0053 

0054  0054 

0055 

40 

.0046 

0047 

0048  ^  0048  0049  0050 

0051  :  0052 

0053  i  0054 

0054 

32  0 

.0045 

0046 

0047  1  0048  1  0048  0049 

0050  !  0051 

0052 

0053 

0054 

20 

.0044 

0045 

0046  '  0047  0048  0049  0049  0050  I   0051 

0052 

0053 

1 

40 

.0044 

0045 

0045  ;  0046  0047  0048  0049  0049  |  0050 

0051 

0052 

1 

33  0 

.0043 

0044 

0045  1  0045  0046  0047  !  0048  0049 
0044  i  0045  0046  0046  ,  0047  !  0048 

0049 

0050 

0051 

20 

.0042 

0043 

0049  i  0050 

0050 

1           1 

40 

.0042 

0043 

0043  0044  0045  i  0045  '  0046  '  0047  i  0048  !  0049 

0050 

34  0 

.0041 

0042 

0043  0043  1  0044  0045  0046  |  0046  !  0047  -  0048 

0049 

20 

.0040 

0041 

0042  0043  i  0043  0044  0045  i  0046  0047  0047 

0048 

40 

.0040 
.0039 

0041 
0040 

0041  j  0042  0043  0044  \   0044  |  0045 
0041  1  0041  0042  0043  1  0044  j  0044 

0046 

0047 

0047 

35  0 

0045 

0046 

0047 

20 

.0039 

0039 

0040  0041  0042  0042  j  0043  0044 

0044 

0045 

0046 

40 

.0038 

0039 

0039  i  0040  0041  0042  0042  0043  i  0044 

0044 

0045 

36  0 

.0037 

0038 

0039  0040  .  0040  0041  0042  0042  \   0043 

0044  0044 

20 

.0037 

0038 

0038  0039  0040 

0040 
0040 

0041  0042  0042  |  0043 

0044 
0043 

40 

.0036 

0037 

0038  1  0038  0039 

0040 

0041  i  0042  0042 

1 
1 

37  0 

.0036 

0036 

0037  '  0038  0038  0039  |  0040 

0040  0041  0042  !  0042 

20 

.0035 

0036 

0037  0037  0038 

0039  0039 

0040  !  0040  0041 

0042 

40 

.0035 

0035 

0036  0037  0037 

0038  0039 

0039  0040  0040 

0041 

38  0 

.0034 

0035 

0035  i  0036  i  0037 

0037  0038 

0039  0039  0040 

0040 

20 

.0034 

0034 

0035 

0036  1  0036 

0037  1  0037 

0038  0039  1  0039  0040 

40 

.0033 

0034 

0034 

0035  0036 

0036  0037 

0037  0038  0039  0039 

39  0 

0033 

0034 

0034  0035  0036  \   0036 

0037  !  0037  0038  '  0039 

20 

0033 

0033 

0034  i  0035  i  0035 

0036 

0036 

0037  0037  1  0038 

40 
40  0 

0032 

0033 

0033  '  0034 

0035 

0035 

0036 

0036  1  0037  '  0037 

0032 

0032 

0033  0033 

0034  i  0035 

0035  0036  0036  0037 

20 

0031 

0032 

0032  0033  0034  0034 

0035  0035  0036  0036 

40 

0031 

0031 

0032  ;  0032  0033  i  0034 

0034  0035  0035  0036 

41  0 

0030 

0031 

0031  1  0032  ;  0033  1  0033 

0034  1  0034  1  0035  0035 

20 

0030 

0030 

0031 

0031 

0032 

0033 

0033 

0034  I  0034  i 
0033  1  0034  ; 

0035 

40 

0029 

0030 

0030 

0031 

0032 

0032 

0033 

0034 

42  0 

1 

0029  1 

0029 

0030 

0031 

0031 

0032 

0032  0033  1  0033  j  0034 

20 

0029 

0029 

0030 

0030 

0031 

0031 

0032  0032  !  0033  0033 

40 

0028 

0029 

0029 

0030  0030  1 

0031 

0031 

0032  0032  0033 

43  0 

1 

0028 
0027 

0028 
0028 

0029 
0028 

0029 
0029 

0030 
0029 

0030 

0031 

0031  0032  !  0032 

20 

0030 

0030 

0031 

0031  0032 

40 

0027 

0027 

0028 

0028 

0029 

0029 

0030 

0030 

0031  0031 

44  0 

0026 

0027 

0027. 

0028 

0028 

0029 

0029 

0030 

0030  0031 

20 

1 

0026 

0026 

0027 

0027 

0028 

0028 

0029 

0029 

0030  '  0030 

40 

0026  ; 

0026 

0026 

0027 

0027 
0027 

0028 

0028 

0029 

0029  j  0030 

45  0 

1  0025  j 

0026 

0026 

0027 

0027 

0028 

0028 

0029  ,  0029 

APPENDIX  V:  TABLP]  II.          [Page  301. 

Log.  A,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                         1 

51' 

52' 

53' 

54' 

55' 

56' 

57' 

58' 

69' 

60' 

45°  0^ 
30 

40,     0 
30 

47  0 
30 

48  0 
30 

49  0 
30 

.0025 
.  0025 
.0024 
.0023 
.0023 
.0022 
.0022 
.0021 
.0021 
.0020 

0026 
0025 
0024 
0024 
0023 

0026 
0025 
0025 
0024 
0024 

0027 
0026 
0025 
0025 
0024 
0024 
0023 
0022 
0022 
0021 

0027 
0026 
0026 
0025 
0025 
0024 
0023 
0023 
0022 
0022 

0027 
0027 
0026 
0026 
0025 

0028 
0027 
0027 
0026 
0025 

0028 
0028 
0027 
0026 
0026 

0029 
0028 
0027 
0027 
0026 
0025' 
0025 
0024 
0024 
0023 

0029 
0028 
0028 
0027 
0026 

0023 
0022 
0022 
0021 
0021 

0023 
0023 
0022 
0022 
0021 

0024 
0024 
0023 
0023 
0022 

0025 
0024 
0024 
0023 
0022 
0022 
0021 
0021 
0020 
0020 

0025 

0024 

0024 

0023 

0023 

0022 

0022 

0021 

0021 

0020 

0020 

0019 

0019 

0018 

0018 

0017" 

0017 

0016 

0016 

0015 

0026 
0025 
0025 
0024 
0023 

50  0 
30 

51  0 
30 

52  0 
30 

53  0 
30 

54  0 
30 

.0020 
.0019 
.0019 
.0018 
.0018 

0020 
0020 
0019 
0019 
0018 
0018 
0017 
0017 
0016 
0016 
"0016 
0015 
0015 
0014 
0014 

0020 
0020 
0020 
0019 
0019 
0018 
0018 
0017 
0017 
0016 
0016 
0015 
0015 
0015 
0014 

0021 
0020 
0020 
0019 
0019 
0018 
0018 
0017 
0017 
0017 

0021 
0021 
0020 
0020 
0019 

0022 
0021 
0020 
0020 
0019 

0023 
0022 
0021 
0021 
0020 
0020 
0019 
0019 
0018 
0018 
0017 
0017 
0017 
0016 
0016 

0023 
0022 
0022 
0021 
0021 
0020 
0020 
0019 
0019 
0018 

.0018 
.0017 
.0017 
.0016 
.0016 

0019 
0018 
0018 
0017 
0017 

0019 
0018 
0018 
0018 
0017 

0019 
0019 
0018 
0018 
0017 
0017 
0016 
0016 
0016 
0015 

1 

55  0 
30 

56  0 
30 

57  0 

.0015 
.  0015 
.  0015 
.0014 
.0014 

0016 
0016 
0015 
0015 
0015 

0016 
0016 
0016 
0015 
0015 

0017 
0016 
0016 
0015 
0015 

0018 
0017 
0017 
0016 
0016 

1 
i 

30 

58  0 
30 

59  0 
30 

.0014 
.  0013 
.0013 
.0012 
.0012 

0014 
0013 
0013 
0013 
0012 

0014 
0014 
0013 
0013 
0012 

0014 
0014 
0013 
0013 
0013 

0014 
0014 
0014 
0013 
0013 

0015 
0014 
0014 
0013 
0013 

0015 
0014 
0014 
0014 
0013 

0015 
0015 
0014 
0014 
0013 

0015 
0015 
0014 
0014 
0014 

0015 
0015 
0015 
0014 
0014 

60 
61 
62 
63 
64 

.0012 
.0011 
.0011 
.0010 
.0009 
.0009 
.0008 
.0008 
.  0007 
.0007 

0012 
0011 
0011 
0010 
0010 
0009 
0008 
0008 
0007 
0007 
0007 
0006 
0006 
0005 
0005 
000b 
0005 
0004 
0004 
0004 

0012 
0011 
0011 
0010 
0010 
0009 
0009 
0008 
0008 
0007 

0012 
0012 
0011 
0010 
0010 
0009 
0009 
0008 
0008 
0007 

0013 
0012 
0011 
0011 
0010 
0009 
0009 
0008 
0008 
0007 
0007 
0006 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 

0013 
0012 
0011 
0011 
0010 

0013 
0012 
0011 
0011 
0010 

0013 
0012 
0012 
0011 
0010 
0010 
0009 
0009 
0008 
0008 

0013 
0012 
0012 
0011 
0010 
0010 
0009 
0009 
0008 
0008 
0007 
0007 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 
0004 
0003 
0003 
0003 
0003 

0013 

0013 

0012 

0011 

0011 

0010' 

0009 

0009 

0008 

0008 

65 
66 

67 
6S 
69 

0009 
0009 
0008 
0008 
0007 
0007 
0006 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 

0010 
0009 
0008 
0008 
0007 
0007 
0007 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 
0004 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 

i 

70 
71 
72 
73 
74 

.0007 
.0006 
.  0006 
.0005 
.  0005  ^ 

0007 
0006 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 

0007 
0006 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 
0004 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003" 

0007 
0007 
0006 
0006 
0005 
0005 
0005 
0004 
0004 
0004 
0004 
0003 
0003 
0003 
0003 

0007 
0007 
0006 
0006 
0006 

75 

76 
77 
78 
79 

.  0005 
.0004 
.0004 
.0004 
.0004 
.0004 
.  0003 
.0003 
.  0003 
.0003 
.0003 
.0003 
.0003 
.  0003 
.0003 

0005 
0005 
0004 
0004 
0004 

80 
81 

82 
83 
84 

0004 
0003 
0003 
0003 
0003 

0004 
0003 
0003 
0003 
0003 

0004 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 

0004 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 
0003 

0004 
0003 
'0003 
0003 
0003 

85 
86 
87 
88 
89 

0003 
0003 
0003 
0003 
0003 

0003 
0003 
0003 
0003 
0003 

0003 
0003 
0003 
0003 
0003 

0003 
0003 
0003 
0003 
0003 

0003 
0003 
0003 
0003 
0003 

90 

.  0003  0003 

0003 

0003 

0003 

0003 

0003 

0003  0003 

Page  302J            APPENDIX  V:  TABLE  III. 

Log.  B,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App.  alt. 
of  sun 
or  star. 

Reduced  refraction  and  parallax  of  sun  or  star. 

0'  0" 

0'  80" 

V  0" 

1'  30" 

2'  0" 

2'  80"  1  8'  0"  1  8'  80" 

4'  0" 

4'  80" 

5'  0" 

5'  80" 

5°  0' 
10 
20 
30 
40 

• 

50 

6  0 
20 
40 

7  0 

9. 9976 
9. 9977' 

9. 9978 

9. 9979 

9. 9980 

9. 9981 
'9.  9982 
9. 9983 

9. 9983 

9. 9984 

9. 9986 

9. 9987 

9. 9989 

9. 9990 

9. 9991 

9. 9970 
9.  9972 

9. 9974 

9. 9975 

9. 9976 

9. 9977 

9. 9978 

9. 9979 
9.99M 

9. 9981 

9. 9982 
9. 9982 
9. 9984 

"9.  9986 
9. 9987 

20 
40 
8  0 
20 
40 

9. 9981 

9. 9982 

9. 9982 

9. 9983 
9.9984 
9. 9985 

9. 9985 

9. 9986 

9. 9987 

9. 9989 

9. 9990 

9. 9991 

9. 9992 

9. 9993 

9  0 
20 
40 

10 

11 

9. 9992 

9. 9993 

9. 9994 

9. 9994 

9. 9995 

9. 9995 

9. 9996 

9. 9997 

9. 9998 

9. 9999 

9. 9989 
9.  9991 

9. 9986 

9. 9986 

9. 9987 
9.  9988 
9. 9989 

12 
13 
14 
15 
16 

9. 9997 
9. 9997 

9.  9995 

9. 9995 

9. 9996 
9. 9996 

9. 9992 

9. 9992 

9. 9993 

9. 9994 

9. 9994 

9. 9995 

9. 9996 
9. 9998 

9. 9990 

9. 9991 

9. 9992 

9. 9993 
9. 9993 

18 
20 
25 
30 
50 

0.0001 

0.0001 
0.0001 

0.0000 
0. 0000 
0. 0001 
0. 0001 

9. 9999 
9. 9999 
0. 0000 
0. 0000 
0. 0001 

9.9998 

9. 9998 

9. 9999 
0. 0000 
0. 0001 

9. 9997 

9. 9998 

9. 9999 
0. 0000 
0.0001 

9. 9995 

9. 9996 

90 

0.0001 

0.0002 

0.  0002  1  0.  0002 

1 

App.  alt. 
of  sun 
or  star. 

Reduced  refraction  and  parallax  of  sun  or  star.                        1 

6'  0" 

6'  80" 

7'  0"  1  7'  30" 

8'  0" 

8'  30" 

0'  0" 

0'  80" 

10'  0" 

10'  80"  i  11'  0"   11'  80"  1 

5°  0' 
10 
20 
30 
40 
50 

6  0 
20 
40 

7  0 

9. 9959 

9. 9960 

9. 9962 

9. 9963 
9. 9965 

9. 9967 

9. 9968 

9. 9970 

9. 9971 
9.  9973 
9.  9974 
9.  9975 

9. 9976 

9. 9977 

9. 9978 
9.  9979 
9.  9981 

9. 9951 

9. 9953 

9. 9954 

9. 9956 

9. 9957 

9. 9947 
9.  9949 

9. 9951 

9. 9952 
9. 9954 

9.  9944 
9. 9946 

9. 9948 

9. 9949 

9. 9951 

9. 9952 
9. 9954 
9. 9956 
9. 9959 
9. 9961 
9. 9963 

9. 9965 

9. 9966 
9. 9968 

9. 9940 
9. 9942 
9.  9944. 
9.  9946 

9. 9948 

9. 9949 
9. 9951 
9. 9954 
9. 9956 
9. 9958 
9. 9960 
9. 9962 
9. 9964 

9. 9937 
9. 9939 
9. 9941 

9. 9943 

9. 9944 
'9. 9946 
9. 9948 
9. 9951 
9. 9953 
9. 9956 

9. 9933 
9. 9935 
9. 9937 
9. 9939 
9. 9941 
9.9943 
9. 9945 
9. 9948 
9. 9951 
9.  9953 

9. 9929 
9. 9932 
9. 9934 
9. 9936 
9. 9938 

9. 9926 
9. 9928 
9. 9931 
9. 9933 
9. 9935 

9. 9922 
9. 9925 
9. 9927 
9. 9929 
9. 9932 

9.  9919 
9. 9921 
9. 9924 

9. 9965 

9. 9966 
9. 9968 
9.  9969 
9. 9971 

9. 9958 
9. 9960 
9. 9962 
9. 9964 
9. 9966 
9.9968 
9. 9969 

9. 9971 

9. 9972 

9. 9973 

9. 9974 

9. 9975 

9. 9976 

9. 9977 

9. 9955 
9. 9957 
9. 9959 
9. 9961 
9. 9963 

9. 9940 
9. 9942 
9. 9945 
9. 9948 

9. 9937 
9. 9939 

20 
40 
8  0 
20 
40 

9. 9972 

9. 9974 

9. 9975 

9. 9976 

9. 9977 

9. 9965 

9. 9967 

9. 9968 

9. 9970 

9. 9971 
9.9972 

9. 9958 

9  0 
20 
40 

10 

11 

9. 9978 

9. 9979 

9. 9980 

9. 9981 
9. 9983 

12 
13 
14 
15 
16 

9. 9985 

18 
20 
25 
30 
50 

-^ 

90 

APPENDIX  V:  TABLE  IV.            [Page  303 

Log.  C,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App.  alt. 
of  sun 
or  star. 

Reduced  refraction  and  parallax  of  sun  or  star.                        1 

O'O" 

0'30" 

I'O"  i  1'30" 

1 

2'0" 

2'  30"    3'  0" 

3'  80"    4'  0" 

4'  80" 

5'0" 

5'  30" 

5°  0' 
20 
40 

6  0 
20 

9. 9969 

40 

7 

8 

9 

10 

9. 9988 

9.  9984 
9. 9986 

9. 9980 
9. 9982 
9. 9984 

9. 9986 

9. 9987 

9. 9988 

9. 9989 

9. 9990 

9. 9990 

9. 9991 

9. 9974 
9. 9978 
9. 9980 
9. 9982 
9.  9984 
9. 9985 

9. 9987 

9. 9988 

9. 9989 

9. 9970 
9. 9972 
9. 9975 
9. 9978 
9. 9981 

11 
12 
13 
14 
15 

9.  9995 

9. 9993 
9.  9994 
9.  9994 

9. 9990 

9. 9991 
9.  9992 
9. 9993 

9. 9993 

9. 9994 
9. 9994 

9. 9994 

9. 9995 
9.  9996 

9. 9989 

9. 9990 

9. 9991 

9. 9991 

9. 9992 

9. 9987 

9. 9988 

9. 9989 

9. 9990 
9.  9991 

9. 9982 

9. 9984 

9. 9985 

16 

17 
18 
20 
25 

9. 9998 
9.  9999 
9.  9999 
9.  9999 
0. 0000 
0.  0000 

9. 9997 

9. 9998 

9. 9998 
'9.  9999 

9. 9999 
9. 9999 
0. 0000 

9.  9996 
9.  9996 
9.  9996 
9.  9997 
9. 9998 

9. 9998 

9. 9999 
9. 9999 

9. 9995 
9. 9995 

9. 9995 

9. 9996 

9. 9997 

9.  9993  i  9.  9992 

9. 9993  9. 9992 

9. 9994  9. 9993 
9.9994  9.9993 
9. 9996 

30 
40 
50 
90 

0. 0000 
0. 0000 

0.  0000 
0.  0000 
0.  0000 
0.  0000 

9. 9998 

9. 9999 

9. 9997 

\ 

' 

App.  alt. 
of  sun 
or  star. 

Reduced  refraction  and  parallax  of  sun  or  star.                        1 

6'0" 

6'  30" 

7'0" 

7'  30" 

8'0" 

8' 80" 

O'O"   9' 80" 

10'  0" 

10'  80" 

11' 0" 

11'  30" 

5°  0^ 
20 
40 

6  0 
20 

.  40 

7 

8 

9 
10 

9. 9962 
9. 9964 
9. 9966 
"9.  9968 
9.  9969 
9.9973 
9.  9976 
9.  9979 

9. 9956 
9. 9959 
9. 9961 
9. 9963 

9.  9949 
9. 9953 
9. 9955 
9. 9958 
9.  9960 
9.  9962 
9.  9964 
9.  9969 
9. 9972 
9. 9975 

9. 9946 
9. 9949 
9. 9952 
9. 9955 
9. 9957 
9. 9960 
9. 9962 
9. 9966 
9. 9970 

9. 9942 
9.  9946 
9. 9949 
9. 9952 
9. 9955 
9. 9957 
9. 9959 
9. 9964 
9. 9968 

9. 9938 
9. 9942 
9.  9946 
9.  9949 
9. 9952 
9. 9954" 
9. 9956 
9. 9962 

9. 9935  '  9. 9931 
9. 9939  9. 9936 
9. 9943  9. 9939 
9. 9946  9. 9943 
9.  9949  i  9.  9946 

9.  9927 
9. 9932 
9. 9936 
9. 9940 
9. 9943 
9. 9946 

9.  9924 
9. 9929 
9. 9933 
9. 9937 

9. 9920 
9. 9925 
9. 9930 

9. 9916 
9. 9922 

9. 9965 
9. 9967 
9. 9971 
9. 9974 
9. 9977 

9. 9951 
9. 9954 
9. 9960 

9. 9949 
9. 9951 

11 
12 
13 
14 
15 

9.  9981 
9.  9983 

9. 9979 

16 
17 
18 
20 
25 

30 
40 
50 
90 

APPENDIX  V:  TABLE  V. 

[Page  305 

Log.  D,  for  computing 

tlie  First  Correction  of  the  Lunar  Distance. 

A  pp. 
alt.  ot 
moon. 

Reduced  parallax  and  refraction  of  moon.                        1 

45' 

46' 

47' 

48' 

49' 

60'  !  51' 

52'  i  68' 

54' 

55' 

56' 

67' 

58' 

8°  0' 

.0192 

0196 

0200 

0204 

0208 

0212  !  0217  0221  0225 

0229 

0233 

0237 

5 

.0190 

0194 

0198 

0202 

0206 

0210  0214  0218  0222 

0227  '  0231 

0235 

10 

.0188 

0192 

0196 

0200 

0204 

0208  '  0212 

0216  0220 

0224  !  0228 

0232 

15 

.0186 

0190 

0194 

0198 

0202 

0206  :  0210 

0214  0218 

0222  0226 

0230 

20 

.0184 
.  0182' 

0188 
0186 

0192 
0190 

0196 
0194 

0200 
0197 

0204  0207 
020r  0205' 

0211  0215 
0209  0213 

0219  1  0223 

0227 

25 

0217  ;  0221 

0225 

8  30 

.0180 

0184 

0188 

0192 

0195 

0199  0203 

0207  0211 

0215  1  0219 

0223 

35 

.0178 

0182 

0186 

0190 

0193 

0197  0201  1  0205  i  0209 

0213  0216 

0220 

40 

.0176 

0180 

0184 

0188 

0191 

0195  0199  !  0203  {  0207 

0210  0214  0218 

45 

50 

.0174 
.0173 

0178 
0176 

0182 
0180 

0186 
0184 

0189 

0193 

0197  I  0201  !  0205 
0195  1  0199'  0202 

0208  '  0212 
0206  0210 

0216 
0214 

0188 

0191 

55 

.0171 

0175 

0178 

0182 

0186 

0189  1  0193  1  0197  0200 

0204  0208 

0212 

9  0 

.  0169 

0173 

0177 

0180 

0184 

0188  0191  0195  0198 

0202  0206 

0209 

5 

.0167 

0171 

0175 

0178 

0182 

0186  0189  I  0193  0197 

0200  1  0204 

0207 

10 
15 

.0166 

0169 
0168 

0173 
0171 

0177 

0180 

0184 

0187  1  0191  0195  1  0198 
0186  0189  0193  0196 

0202 

0205 

.  0164 

0175 

0179 

0182 

0200 

0203 

20 

.  0163 

0166 

0170 

0173 

0177 

OIHO  0184  0187  0191  '  0194 

0198 

0201 

25 

.0161 

0165 

0168 

0172 

0175 

0179  0182 

0186  0189  0193 

0196 

0199 

9  30 

0163 

0166 

0170 

0173 

0177  ,  0180 

0184  ,  0187  0191 

0194 

0198 

35 

0161 
0160 

0165 

0168 
0167 

0172 
0170 

0175  1  0179  '  0182  0185 

0189 

0192  0196 

40 

0174  1  0177  j  0180  t  0184 

0187  0191  '  0194 

45 

0158 

0162 

0165 

0169 

0172  i  0175  0179  •  0182 

0185  i  0189  0192 

0195 

50 

0157 

0160 

0164 

0167 

0170  ;  0174  '  0177  0180 

0184  !  0187  0190 

0194 

55 

0156 

0159 

0162 

0165 

0169  ;  0172  j  0175  0179 

0182  1  0185  0189 

0192 

10  0 
5 

0154 
0153 

0157 
0156 

0161 
0159 

0164 
0162 

0167  i  0171  1  0174  i  0177 
0166  j  0169  1  0172  0175 

0180  i  0184  0187 
0179  0182'  0185 

0190 

0188 

1 

10 

0151 

0155 

0158 

0161 

0164  '  0167  0171  0174 

0177  '  0180  '  0183 

0187 

15 

0150 

0153 

0156 

0160 

0163  0166  0169  1  0172 

0175 

0179  0182 

0185 

20 

0149 

0152 

0155 

0158 

0161  i  0164  0168  0171 

0174 

0177  !  0180 

0183 

25 
10  30 

0147 
0146 

0150 
0149 

0154 
0152 

0157 
0155 

0160  1  0163  0166  0169 

0172 

0175  1  0179 

0182 

0J58 

0162  1  0165 

0168 

0171  1  0174 

0177 

0180 

35 

0145 

0148 

0151 

0154 

0157 

0160  0163 

0166 

0169  i  0172  1  0175 

0179 

40 

0143 

0147 

0150 

0153 

0156 

0159  0162 

0165 

0168 

0171  1  0174 

0177 

.  -l-^ 

0142 

0145 

0148 

0151 

0154 

0157  ;  0160 

0163 

0166 

0169 

0172 

0175 

50 
55 

0141 

0144 

0147 

0150 
0149 

0153 

0156  !  0159 

0162 
0161 

0166 

0168 

0171 

0174 
0172 

0140 

0143 

0146 

0152  0155  0158 

0164  1  0167  i  0170 

11  0 

0139 

0142 

0145 

0147 

0150  0153  0156 

0159 

0162  ■  0165  1  0168 

0171 

0 

0137 

0140 

0143 

0146 

0149  1  0152  0155 

0158 

0161  !  0164  1  0167 

0170 

10 

0139 

0142 

0145 

0148  0151  0154 

0157  0159  i  0162  0165 

0168 

15 

0138 
0137 

0141 
0140 

0144 
0143 

0147  0150  0152  i  0155  0158  i  0161  0164 

0167 

20 

0145  1  0148  0151 

0154  0157 

0160  0163 

0165 

25 

0136 

0139 

0141 

0144  '  0147  0150 

0153  0156 

0158  !  0161 

0164 

11  30 

0135 

0137 

0140 

0143  0146  0149 

0151  0154 

0157  :  0160 

0163 

35 

0133 

0136 

0139 

0142  0145  0147 

0150  0153 

0156  1  0159 

0161 

40 
45 

0132 

0135 

0138 
0137 

0141  0143  0146 
0140  0142  0145 

0149  0152 

0154  1  0157 

0160 
0159 

"- 

0131 

0134 

0148  0150  0153  i  0156 

50 

0130 

0133 

0136 

0138  0141  0144 

0147  0149 

0152  i  0155 

0157 

55 

0129 

0132 

0135 

0137  0140  0143 

0145  0148 

0151  !  0153 

0156 

12  0 

0128 

0131 

0134 

0136  0139  0142 

0144  0147  0150  '  0152 

0155 

5 
10 

0127 
0126 

0130 

0132 

0135 

0138  0140 
0137  0139 

0143  0146 
0142  0145 

0148  0151 

0154 



0129 

0131 

0134 

0147  0150 

0152 

15 

0125 

0128 

0130 

0133  0136  0138 

0141  0143  0146  0149 

0151 

20 

0124 

0127 

0129 

0132  0135  0137 

0140  0142  0145 

0147 

0150 

25 

0123 

0126 

0128 

0131  0133  i  0136 

0139  1  0141  0144 

0146 

0149 

12  30 
35 

0122 

0125 

0127 

0130 

0132  !  0135 
0131  1  0134 

0138  i  0140  1  0143 

0145 
0144 

0148 
0147 



0121 

0124 

0126 

0129 

0136  i  0139 

0141 

40 

0120 

0123 

0125 

0128  0130 

0133 

0135  0138 

0140 

0143 

0145 

45 

0119 

0122 

0124 

0127  0129 

0132 

0134  0137 

0139 

0142 

0144 

0147 

50 

0118 

0121 

0123 

0126  0128 

0131 

0133 

0136 

0138 

0141 

0143 

0146 

55 

0118 

0120 

0123 

0125  0127 

0130 

0132 

0135 

0137 

0140 

0142 

0145 

13  0 

0117 

0119 

0122 

0124  0126 

0129 

0131 

0134  0136 

0139 

0141 

0143 

22489—03- 


-20 


Page  306]            APPENDIX  V:  TABLE  V. 

Log.  D,  for  computing  the  First  Correction  of  the  Lunar  Distance. 

App. 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon. 

47' 

48' 

40' 

60' 

51' 

62' 

68' 

84' 

66' 

66' 

67' 

58' 

59' 

13°  0' 
10 
20 
30 
40 

.0117 
.0115 
.0113 
.0112 

0119 
0117 
0116 
0114 
0112 

0122  0124 
':   0120  0122 
0118  0120 
0116  0119 
0114  !  0117 

0126 
0125 
0123 
0121 
0119 

0129 
0127 
0125 
0123 
0121 

0131 
0129 
0127 
0125 
0124 

0134 
0132 
0130 
0128 
0126 

0136 
0134 
0132 
0130 
0128 

0139 
0137 
0134 
0132 
0131 

0141 
0139 
0137 
0135 
0133 

0143 
0141 
0139 
0137 
0135 
0133 
0131 
0129 
0127 
0126 

50 
14  0 
10 
20 
30 

0111 
0109 
0107 
0106 
0104 

0113 
0111 
0110 
0108 
0106 

0115 
0113 
0112 
OHO 
0109 

0117 
0116 
0114 
0112 
0111 

0120 
0118 
0116 
0114 
0113 

0122 
0120 
0118 
0117 
0115 

0124 
0122 
0121 
0119 
0117 
0115 
0114 
0112 
0111 
0109 

0126 
0125 
0123 
0121 
0119 
0118 
0116 
0114 
0113 
0111 
0110 
0108 
0107 
0105 
0104 
0102 
0101 
0100 
0098 
0097 

0129  0131 
0127  0129 
0125  0127 
0123  !  0125 
0121  1  0123 

40 
50 
15  0 
10 
20 

0103 
0101 
0100 
0099 
0097 

0105 
0103 
0102 
0101 
0099 
0098 
0096 
0095 
0094 
0093 

0107 
0106 
0104 
0103 
0101 

0109 
0108 
0106 
0105 
0103 

0111 
0110 
0108 
0107 
0105 

0113 
0112 
0110 
0109 
0107 

0120 
0118 
0116 
0115 
0113 
0112' 
0110 
0108 
0107 
0106 

0122  !  0124 
0120  i  0122 
0118  0120 
0117  0119 
0115  0117 
"0113  "0115" 
0112  0114 
0110  0112 
0109  0111 
0107  0109 

30 
40 
50 
16  0 
10 

0096 
0094 
0093 
0092 
0091 

0100 
0098 
0097 
0096 
0094 

0102 
0100 
0099 
0098 
0096 

0104 
0102 
0101 
0099 
0098 

0106  0108 
0104  0106 
0103  0105 
0101  0103 
0100  0102 

20 
30 
40 
50 
17  0 

0089 
0088 
0087 
0086 
0085 

0091 
0090 
0089 
0088 
0087 

0093  i  0095 
0092  1  0094 
0091  0092 
0089  0091 
0088  0090 

0097 
0096 
0094 
0093 
0092 

0099 
0097 
0096 
0095 
0093 

0100 
0099 
0098 
0096 
0095 

0104 
0103 
0101 
0100 
0099 
0097 
0096 
0095 
0094 
0092 

0106  0108 
0105  0106 
0103  0105 
0102  !  0104 
0100  i  0102 

10 
20 
30 
40 
50 

0084 
0083 

0085 
0084 
0083 
0082 
0081 

0087 
0086 
0085 
0084 
0083 

0089 
0088 
0086 
0085 
0084 

0091 
0089 
0088 
0087 
0086 

0092 
0091 
0090 
0089 
0087 

0094 
0093 
0091 
0090 
0089 

0096 
0094 
0093 
0092 
0091 
0090 
0087 
0085 
0083 
0081 
0079 
0077 
0075 
0073 
0071 

0099 
0098 
0096 
0095 
0094 

0101 
0099 
0098 
0097 
0096 

18  0 
20 
40 

19  0 
20 

0080 
0078 
0076 
0074 
0072 

0082  0083 
0079  0081 
0077  0079 
0075  0077 
0073  ;  0075 

0085 
0083 
0080 
0078 
0076 

0086  0088 
0084  0086 
0082  0083 
0080  0081 
0078  0079 

0091 
0089 
0087 
0084 
0082 

0093 
0090 
0088 
0086 
0084 

0094 
0092 
0090 
0087 
0085 
0083 
0081 
0079 
0077 
0075 

0093 
0091 
0089 
0086 

40 

20  0 
20 
40 

21  0 

0070 
0068 
0067 
0065 
0063 

0072 
0070 
0068 
0066 
0065 

0073 
0071 
0069 
0068 
0066 

0074 
0073 
0071 
0069 
0067 

0076  0077 
0074  0075 
0072  0073 
0070  0072 
0068  0070 

0080 
0078 
0076 
0074 
0072 

0081 
0079 
0077 
0075 
0074 

0084 
0082 
0080 
0078 
0076 
0074 
0072 
0070 
0069 
0067 
0065 
0064 
0062 
0060 
0059 

20 
40 
22  0 
20 
40 

0062  0063 
0060  0061 
0059  0060 
0057  0058 
0056  0057 

0064 
0063 
0061 
0059 
0058 

0065 
0064 
0062 
0061 
0059 

0067 
0065 
0063 
0062 
0060 

0068 
0066 
0065 
0063 
0061 
0060 
0058 
0057 
0055 
0054 

0069 
0067 
0066 
0064 
0062 
0061 
0059 
0058 
0056 
0055 

0070 
0069 
0067 
0065 
0064 
"0062 
0060 
0059 
0057 
0056 

0072 
0070 
0068 
0066 
0065 

0073 
0071 
0069 
0068 
0066 
0064 
0063 
0061 
0059 
0058 

23  0 
20 
40 

24  0 
20 

0054 
0053 
0052 
0050 

0055 
0054 
0053 
0051 
0050 

0057 
0055 
0054 
0052 
0051 

0058 
0056 
0055 
0053 
0052 

0059 
0057 
0056 
0054 
0053 

0063 
0061 
0060 
0058 
0057 

40 

25  0 
20 
40 

26  0 

0049 
0047 
0046 
0045 
0044 

0050 
0048 
0047 
0046 
0045 

0051 
0049 
0048 
0047 
0046 
0044 
0043 
0042 
0041 
0040 
0039 

0052 

0050 

0049 

0048 

0046 

0045 

0044 

0043 

0042 

0040  . 

0039 

0053 
0051 
0050 
0049 
0047 
0046 
0045 
0044 
0042 
0041 
0040 

0053 
0052 
0051 
0049 
0048 

0054 
0053 
0052 
0050 
0049 

0055 
0054 
0053 
0051 
0050 
0048 
0047 
0046 
0045 
0043 
0042; 

0056 
0055 
0053 
0052 
0051 
0049 
0048 
0047 
0045 
0044 
0043' 

0057 
0056 
0054 
0053 
0052 
0"05"0 
0049 
0047 
0046 
0045 
0044 

20 
40 
27  0 
20 
40 

0043 
0041 
0040 
0039 
0038 

0043 
0042 
0041 
0040 
0039 

0047 
0046 
0044 
0043 
0042 

0048 
0046 
0045 
0044 
0043 
0042' 

28  0 

0037  0038 

0041 

APPENDIX  V:  TABLE  V.           [Page  307 

Log.  D,  for  computing  tiie  First  Correction  of  the  Lunar  Distance. 

App 
alt.  of 
moon. 

Reduced  parallax  and  refraction  of  moon.                         1 

50' 

51'   1   52' 

58' 

54' 

55'   1   56' 

67'   I   58' 

59' 

60' 

28°  0^ 

0. 0037 

0. 0038 

0.  0039 

0. 0039 

0. 0040 

0. 0041  0. 0042 

0. 0042  0.  0043 

0.0044 

30 

0. 0036 

0. 0036 

0.  0037 

0. 0038 

0.  0038 

0. 0039  0.  0040 

0.  0040  1  0.  0041 

0. 0042 

29  0 

0. 0034 

0. 0035 

0. 0035 

0. 0036 

0. 0037 

0.0037  0.0038 

0.  0039  1  0.  0039 

0. 0040 

30 

0. 0033 

0. 0033 

0.0034 

0. 0035 

0. 0035 

0.  0036  0.  0036 

0.  0837  0.  0038 

0. 0038 

30  0 
30 

0.  0031 
0. 0030 

0. 0032 
0. 0030 

0. 0032 
0. 0031 

0. 0033 
0. 0031 

0. 0034 
0. 0032 

0. 0034  0.  0035 
0.  0033 1 0. 0033 

0.0035  0.0036 
a  6034  0.0034 

0. 0037 
"0.0035 

31  0 

0. 0028 

0. 0029 

0. 0029 

0. 0030 

0. 0031 

0. 0031  0. 0032 

0. 0032  0.  0033 

0. 0033 

30 

0.  0027 

0. 0028 

0. 0028 

0.  0029 

0.  0029 

0. 0030  0. 0030 

0. 0031  0. 0031 

0. 0032 

0. 0032 

32  0 

0. 0026 

0. 0026 

0.  0027 

0.  0027  1  0.  0028 

0.  0028  i  0.  0029 

0.  0029  1  0. 0030 

0. 0030 

0.  0031 

30 

0. 0024 

0. 0025 
0. 0024 

0.  0025 

0.  0026 

0.  002(i 

0. 0027  0. 0027 
0.  0025  0.  0026 

0.  0028  1  0.  0028 
0.  0026  !  0.  0027 

0. 0029  0.  0029 
0.0027  0.0028 

33  0 

0. 0023 

0. 0024 

0. 0025 

0. 0025 

30 

0. 0022 

0. 0022 

0. 0023 

0. 0023 

0.  0024 

0.  0024  0.  0025 

0.  0025  !  0.  0025 

0.0026  0.0026 

34  0 

0. 0021 

0. 0021 

0. 0022 

0. 0022 

0.  0022 

0. 0023  0.  0023 

0.  0024 

0. 0024 

0.0024  0.0025 

30 

0.  0020 

0. 0020 

0. 0020 

0. 0021 

0. 0021 

0.  0022  0.  0022 

0. 0022 

0. 0023 

0.0023  0.0023 

35  0 

0.0018 

0. 0019 

0.  0019 

0. 0020 
0.0018 

0. 0020 
0. 0019 

0.  0020 
0. 0019 

0. 0021 
0.0019 

0.0021 
"0.  0020 

0. 0021 
0. 0020 

0.0022  0.0022 
0.0020  0.0021 

30 

0.  0017 

0.  0018 

0.  0018 

3(5  0 

0.  0016 

0.0017 

0.0017 

0.0017 

0. 0018 

0. 0018 

0.  0018 

0.0019 

0. 0019 

0.0019  0.0019 

30 

0.0015 

0.0016  0.0016 

0.0016 

0. 0016 

0. 0017 

0.  0017 

0.  0017 

0.0018 

0.0018  0.0018 

37  0 

0.  0014 

0.0014 

0.0015 

0.  0015 

0.  0015 

0. 0016 

0.  0016 

0.  0016 

0.  0016 

0.0017  0.0017 

30 

0.  0013 

0.  0013 
0.0012 

0.0014 
0. 0013 

0.0014 

0.  0014 
0.0013 

0. 0014 
0. 0013 

0.0015 
0.  0014 

0.  0015 
6.  0014 

0.  0015 
0.  0014 

0.0015  0.0016 
0.0014  0.0014 

38  0 

0.  0012 

0.  0013 

30 

0.0011 

0.0011 

0.  0012 

0.0012 

0.0012 

0. 0012 

0.  0012 

0.  0013 

0.  0013 

0. 0013  0. 0013 

39  0 

0.  0010 

0.  0010 

0.  0011 

0.  0011 

0.  0011 

0. 0011 

0.0011 

0.0012 

0.0012 

0.0012  0.0012 

30 

0.0009 

0.  0010 

0.0010 

0.  0010 

0. 0010 

0.  0010 

0.0010 

0.0011 

0.0011  0.0011 

40 

0.0008 

0.0009 

0. 0009 

0.  0009 
0.  0007 

0. 0009 
0. 0007 

0. 0009 
0. 0007 

0. 0009 

0.  0010 
070607 

0.  0010 
0. 0008 

0. 0010 

41 

0.0007 

0.0007 

0. 0007 

0. 0007 

0. 0008 1    1 

42 

0. 0005 

0.  0005 

0. 0005 

0. 0005 

0. 0005 

0. 0005 

0.  0005 

0.  0005 

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Page  308J 

APPENDIX  V: 

lABLE 

VI. 

Second  Correction  of  the  Lunar  Distance. 

Appar- 
ent dis- 
tance. 

First  correction  of  distance. 

Appar- 

3' 

V 

10 

12' 

14' 

16' 

18'       20' 

21' 

22' 

28' 

24' 

26' 

26' 

27' 

28' 

ent  dis- 
tance. 

Sub. 

II 

II 

II 

II 

// 

II 

//          II 

II 

It 

II 

// 

II 

II 

II 

II 

Add. 

15°  (y 

0 

2 

3 

5 

6 

8 

11       13 

14 

16  i     17 

19 

20 

22 

24 

26 

30 

0 

2 

3 

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6 

8 

10       13 

14 

15  1     17 

18 

20 

21 

23 

25 

16    0 

0 

3 

\ 

6 

8 

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13 

15 

16 

18 

19 

21 

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24 

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0 

3 

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14 

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17 

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20 

21 

23 

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0 
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3 
3 

4 
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6 
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7 

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14 

15 

16 

18 

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16 

17 

19 

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13 

14 

15 

16 

18 

19 

20 

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0 

3 

4 

5 

6 

8 

10 

11 

12 

13 

15 

16 

17 

18 

20 

30 

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2 

4 

5 
5 

6 
6 

8 

10 

11 

12 

13 

14 

15 

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10 

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23 

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3 

4 

5 

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8 

9 

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11 

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13 

14 

15 

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3 
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2 
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2 

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2 

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4 

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2 

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3 

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2 

2 

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3 

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3 

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0 

2 

2 

2 

2 

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3 

3 

3 

4 

4 

62 

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2 

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3 

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3 

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118 

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2 

3 

3 

3 

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116 

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2 

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2 

2 

2 

2 

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2 

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2 

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110 

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0 

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0 

1         1 

1 

1 

1 

2 

2 

2 

2 

106 

78 

0       0 

0 

0 

0 

0 

1         1 

1 

1 

1 

1 

1 

1 

1 

102 

82 

0       0 

0 

0 

0 

0 

0 

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1 

1 

1 

1 

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1 

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0 
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0 
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Appar- 
ent dis- 
tance. 

3' 

14' 

16' 

18' 

20' 

21' 

22' 

28' 

24' 

25' 

26' 

27' 

28' 

Appar- 
ent dis- 
tan<'c. 

First  correction  ol 

distance. 

APPENDIX  V:  TABLE  VI.                             [Page  309 
Second  Correction  of  the  Lxinar  Distance. 

Appar- 
ent dis- 
tance. 

First  correction  of  distance. 

Appar- 
ent dis- 
tance. 

29' 

80' 

81' 

II 

31 

30 

29 

28 

27 

27" 

26 

25 

24 

24 

23 

22 

21 

20 

19 

18 

17 

16 

16 

15 

14 

14 

13 

13 

12 

82' 

II 

33 
32 
31 
30 
29 
28 
28 
27 
26 
25 
25 
23 
22 
21 
20 
19 
18 
18 
17 
16 
15 
15 
14 
14 
13 

88' 

84' 

85' 

86' 

37' 

88' 

89' 

40' 

41' 

42' 

48' 

44' 

Sub. 
15°  0' 
30 

16  0 
30 

17  0 

27 
26 
26 
25 
24 
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23 
22 
21 
21 
20 
19 
18 
17 
16 
16 
15 
14 
14 
13 
13 
12 
12 
11 
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29 

28 

27 

27 

26 

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24 

23 

23 

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22 

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19 

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16 

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14 

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13 

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35 

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30 

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28 

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38 

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35 

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33 

32 

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29 

28 

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40 

39 

37 

36 

35 

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33 

32 

31 

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42 

41 

39 

38 

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45 

43 

42 

40 

39 

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47 

45 

44 

43 

41 

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50 

48 

46 

45 

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52 

50 

49 

47 

46 

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55 
53 
51 
50 

48 

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57 
56 
54 
52 
50 

II 

60 

58 

56 

54 

53 

63 
61 
59 
57 
55 

Add. 

30 

18  0 
30 

19  0 
30 

36 
35 
34 
33 
32 

38 
37 
36 
35 
34 

40 
39 
38 
37 
36 

42 
41 
40 
39 
37 
36 
35 
33 
31 
30 

44 

43 

42 

41 

39 

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36 

35 

33 

31 

47 
45 
44 
43 
41 

49 
47 
46 
45 
43 

51 
50 
48 
47 
46 

54 
52 
50 
49 
48 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 

26 
25 
24 
22 
21 
20 
19 
19 
18 
17 
16 
16 
15 
15 
14 

28 
26 
25 
24 
23 

29 
28 
26 
25 
24 

31 
29 
28 
27 
25 
24 
23 
22 
21 
20 

33 
31 
30 

28 
27 

35 
33 
31 
30 

28 

40 
38 
36 
35 
33 

42 
40 
38 
36 
35 

44 
42 
40 
38 
36 

46 
44 
42 
40 

38 

22 
21 
20 
19 
18 

23 
22 

21 
20 
19 

26 
25 
23 
22 
22 

27 
26 
25 
24 
23 

28 
27 
26 
25 
24 

30 
29 
27 
26 
25 
24 
23 
22 
22 
21 

31 
30 
29 
28 
26 

33 
32 
30 
29 
28 

35 
33 
32 
30 
29 

36 
35 
33 
32 
30 

17 
17 
16 
16 
15 

19 
18 
17 
16 
16 

20 
19 
18 
17 
17 

21 
20 
19 
18 
18 

22 
21 
20 
19 
19 

23 
22 
21 
20 
20 

25 
24 
23 
23 
22 

27 
26 
25 
24 
23 

28 
27 
26 
25 
24 

29 
28 
27 
26 
25 

35 
36 
37 

38 
39 

10 
10 
10 
9 
9 
9 
8 
8 
7 
7 
6 
6 
5 
5 
5 
4 
4 
4 
3 
3 
3 
2 
2 

i 

1 

11 
11 
10 
10 
10 
9 
9 
8 
8 
7 
7 
6 
6 
5 
5 
5 
4 
4 
4 
3 
3 
2 
2 
1 
1 
0 

12 

12 

11 

11 

10 

10 

9 

9 

8 

8 

7 

7 

6 

6 

5 

13 

12 

12 

11 

11 

11 

10 

9 

9 

8 

8 

7 

6 

6 

6 

14 
13 
13 
12 
12 

14 
14 
13 
13 
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15 
15 
14 
14 
13 

16 
16 
15 
14 
14 

17 
16 
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15 
15 

18 
17 
17 
16 
16 

19 
18 
18 
17 
16 

20 
19 
19 
18 
17 

21 
20 
19 
19 
18 

22 
21 
20 
20 
19 

23 
22 
21 
.21 
20 

24 
23 
22 
22 
21 

140° 
138 
136 
134 
,  132 

40 
42 
4-f 
46 
48 

11 
11 
10 
9 
9 
8 
7 
7 
6 
6 

12 
11 
10 
10 
9 

13 
12 
11 
10 
10 

13 
13 
12 
11 
10 

14 
13 
12 
12 
11 

15 
14 
13 
12 
11 

16 
15 
14 
13 
12 

17 
16 
14 
13 
13 

17 
16 
15 
14 
13 

18 
17 
16 
15 
14 

19 
18 
17 
16 
15 

-20 
19 
17 
16 
15 

50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
74 
78 
82 
86 

8 

8 

7. 
7 
6 

9 

8 
8 
7 

7 

9 
9 

8 
8 
7 

10 
9 
9 
8 
7 

11 

10 

9 

9 

8 

11 

10 

10 

9 

8 

10 
9 
9 

12 

11 

11 

10 

9 

13 
12 
11 
10 
10 

14  1     14 
13       13 
12       12 
11       11 
10       11 

130 
128 
126 
124 
122 

5 

4 
4 
4 
3 

5 
5 
4 
4 
4 

5 
5 
5 

\ 

6 
6 
5 
4 
4 

6 
6 
5 
5 
4 

7 
6 
6 
5 
5 

6 

6 
5 
5 

7 
7 
6 
6 
5 

8  i      8 
7  1      7 
6         7 
6         6 
5         6 

8 
8 
7 
7 
6 

9 

8 
8 
7 
6 

9 
9 

8 
7 

7 

10 
9 

8 

8 

7 

120 
118 
116 
114 
112 

3 
2 
2 

1 
1 

3 
3 
2 

1 

1 

3 
3 
2 

1 
1 

4 
3 
2 

1 
1 

4 
3 
2 

2 

1 

4 
3 
2 
2 

1 

4 

3 
3 

9 

5 
4 
3 
2 

1 

5 
4 
3 
2 
1 

5 
4 
3 
2 

1 

5 
4 
3 
2 

1 

6 
4 
3 
2 
1 

6 
5 
3 
2 
1 

6 
5 
4 
2 

1 
0 

110 

106 

102 

98 

94 

90° 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

90° 

Appar- 
ent dis- 
tance. 

29' 

30 

81' 

82' 

33' 

84' 

86' 

86' 

87' 

38' 

89' 

40' 

41' 

42' 

48' 

44' 

Appar- 
ent dis- 
tance. 

First  correction  of  distance. 

Page  310] 

APPENDIX  V:  TABLP:  YI. 

Second  Correction  of  the  Lunar  Distance 

Appar- 
ent dis- 
tance. 

First  correction  of  distance. 

Appar- 
ent dis- 
tance. 

45' 

46' 

47'  1  48' 

49' 

50' 

51' 

52' 

68' 

64' 

55' 

56' 

57' 

68' 

69' 

60' 

Sub. 
15°  0' 

66 

II 
69 

// 
72 

II 

75 

78 

II 
81 

II 
85 

II 
88 

91 

II 
95 

99 

II 
102 

II 
106 

110 

113 

II 
117 

Add. 

30 

64 

67 

70 

72 

76 

79 

82 

85 

88 

92 

95 

99 

102 

106 

110 

113 

16  0 

62 

64 

67  L  70 
65  '68 

73 

76 

79 

82 

85 

89 

92 

95 

99 

102 

106 

110 

30 

60 

62 

71 

74 

77 

80 

83 

86 

89 

92 

96 

99 

103 

106 

17  0 

58  !  60 
56  59 

63 
61 

66 

69 

71 
69 

74 

77 

80 

83 

86 

90 

93 

96 

99 

103 
100 

30 

64 

66 

72 

75 

78 

81 

84 

87 

90 

93 

96 

18  0 

54  57 

59  1  62 

64 

67 

70 

73 

75 

78 

81 

84 

87 

90 

94 

97 

30 

53  55 

58  ;  60 

63 

65 

68 

71 

73 

76 

79 

82 

85 

88 

91 

94 

19  0 

51  54 

56  1  58 

61 

63 

66 

69 

71 

74 

77 

79 

82 

85 

88 

91 

30 

50  ,  52 
49  51 

54  57 
53  55 

59 

62 

64 
62 

67 
65 

69 

72 

75 

77 

80 

83 

86 
83 

89 
86 

20 

58 

60 

67 

70 

73 

75 

78 

81 

21 

46  48 

50  52 

55 

57 

59 

61 

64 

66 

69 

71 

74 

76 

79 

82 

22 

44  ;  46 

48  j  50 

52 

54 

56 

58 

61 

63 

65 

68 

70 

73 

75 

78 

23 

42  44 

45 

47 

49 

51 

53 

56 

58 

60 

62 

64 

67 

69 

72 

74 

24 

40  41 
38  40 

43 
41 

45 
43 

47 
45^ 

49 
47 

51 
49 

53 

55 

57 

59 

61 
59 

64 
61 

66 
63 

68 
65 

71 
67 

25 

51 

53 

55 

57 

26 

36  38 

40 

41 

43 

45 

47 

48 

50 

52 

54 

56 

58 

60 

62 

64 

27 

35  36 

38 

39 

41 

43 

45 

46 

48 

50 

52 

54 

56 

58 

60 

62 

28 

33  35 

36  j  38 

39 

41 

43 

44 

46 

48 

50 

51 

53 

55 

57 

59 

29 

32  33 
31  32 

35  36 

33  i  35 

38 

39 

41 

43 

44  1  46 

48 

49 

51 

53 

55 
53 

57 

30 

36 

38 

39 

41 

42   44 

46 

47 

49 

51 

54 

31 

29  31 

32  '   33 

35 

36 

38 

39 

41   42 

44 

46 

47 

49 

51 

52 

32 

28  30 

31  1  32 

34 

35 

36 

38 

39  1  41 

42 

44 

45 

47 

49 

50 

33 

27  28 

30  31 

32 

34 

35 

36 

38 

39 

41 

42 

44 

45 

47 

48 

34 

26 

27 
26 

29  1  30 

28  29 

31 
30 

32 

34 

35 

36 

38 

39 

41 

42 

44 

45 
43 

47 
45 

35 

25 

31 

32 

34 

35 

36 

38 

39 

40 

42 

36 

24  25 

27  28 

29 

30 

31 

32 

34   35 

36 

38 

39 

40 

42 

43 

37 

23  25 

26  27 

28 

29 

30 

31 

33 

34 

35 

36 

38 

39 

40 

42 

38 

23  24 

25 

26 

27 

28 

29 

30 

31 

33 

34 

35 

36 

38 

39 

40 

39 

22  1  23 

24 

25 

26 

27 
26 

28 

29 

30 

31 

33 

34 

35 

36 

38 

39 
37 

40 

21  22 

23 

24 

25 

27 

28 

29 

30 

31 

33 

34 

35 

36 

140° 

42 

20  21 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

33 

34 

35 

138 

44 

18 

19 

20 

21 

22 

23 

24 

24 

25   26 

27 

28 

29 

30 

31 

33 

136 

46 

17 

18 

19 

19 

20 

21 

22 

23 

24 

25 

26 

26 

27 

28 

29 

30 

134 

48 

16 
15 

17 
16 

17 
16 

18 
17 

19 

20 

20 

21 

22 

23 

24 

25 

26 

26 

27 

28 

132 

50  ' 

18 

18 

19 

20 

21 

21 

22 

23 

24 

25 

25 

26 

130 

52 

14 

14 

15 

16 

16 

17 

18 

18 

19 

20 

21 

21 

22 

23 

24 

25 

128 

54 

13 

13 

14 

15 

15 

16 

16 

17 

18 

18 

19 

20 

21 

21 

22 

23 

126 

56 

12 

12 

13 

14 

14 

15 

15 

16 

17 

17 

18 

18 

19 

20 

20 

21 

124 

58 

11 
10 

12 
11 

12 
11 

13 
12 

13 

14 

14 

15 

15 

16 

16 

17 

18 

18 

19 

20 

122 

60 

12 

13 

13 

14 

14 

15 

15 

16 

16 

17 

18 

18 

120 

62 

9 

10 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

15 

16 

16 

17 

118 

64 

9 

9 

9 

10 

10 

11 

11 

12 

12 

12 

13 

13 

14 

14 

15 

15 

116 

66 

8 

8 

9 

9 

9 

10 

10 

11 

11 

11 

12 

12 

13 

13 

14 

14 

114 

68 

7 
.  6 

7 

7 

8 

8 

8 

9 

9 

10 

10 

10 
9 

11 

11 

11 

12 

12 

13 

112 

70 

7 

7 

8 

8 

8 

9 

9 

10 

10 

10 

11 

11 

11 

110 

74 

5 

5 

6 

6 

6 

6 

7 

7 

7 

•  7 

8 

8 

8 

8 

9 

9 

106 

78 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

7 

102 

82 

2 

3 

3 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4 

98 

86 

1 
0 

45' 

1 
0 

46' 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

94 
90° 

90° 

Appar- 
ent dis- 
tance. 

0 

47' 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

48' 

49' 

50' 

61' 

62' 

68' 

64' 

65' 

56' 

57' 

68' 

59' 

60' 

Appar- 
ent dis- 
tance. 

First 

correc 

tion  of  distan 

ce. 

APPENDIX  V:  TABLE  VII. 

[Page  311 

For  finding  the  Correction  of  the  Lunar  Distance  for  the  Contraction  of  the  Moon 

'9  Semidiameter.    1 

TABLE  VII  A.— GIVING  THE  ARGUMENT  FOR  TABLE  VII  B. 

Red. 
P.  and 

R.  of 
moon. 

Apparent  altitude  of  moon. 

6° 

5i° 

6° 

64° 

7° 

7i°    8= 

8i' 

9° 

|9ic 

ic 

'  11<: 

12 

'  18' 

»  14°|  15<= 

10° 

17° 

18° 

20° 

25° 

80° 

40° 

60° 

iV 

65 

56 

[ 

42 

63 

54 

47 

41 

43 

62 

53 

46 

40 

35 

44 

60 

51 

45 

39 

34 

30 

27 

45 

58 

50 

43 
42 

38 
37 

33 
33 

30 
29 

26 
26 

24 
23 

21 
21 

20 
19 

17 

l5 





1  1 



0 

46 

57  149 

47 

56 

48 

41 

36 

32 

28 

25 

23 

20 

19 

17 

14 

12 

10 

48 

54 

46 

40 

35 

31 

28 

25 

22 

20 

;i8 

17 

14 

12 

10 

9 

8 

7 

6 

49 

53 

45 

39 

35 

30 

27 

24 

22 

19 

18 

16 

14 

12 

10 

9 

8 

7 

6 

6 

5 

3 

50 

52 

44138 

34 

30 

26 

24 

21 

19 

il7 

16 

13 

11 

10 

9 

8 

7 

6 

5 

5 

3 

3 

2 

51 

50 

43   38 

33 

29 

26 

23 

21 

19 

17 

15   13 

11    10 

8 

7 

7 

6 

5 

5 

3 

2 

2 

2 

52 

49 

42   37 

32 

28 

25 

23 

20 

18 

17 

15   13 

11      9 

8!      7 

7 

6 

5 

4 

3 

2 

2 

2 

53 

48 

41:36 

32 

28 

25 

22 

20 

18 

16 

15   12 

11 

9 

8-      7 

6 

6 

5 

4 

3 

2 

2 

2 

54 

47 

41135 

31 

27 

24 

22 

19 

18 

16 

15   12 

10 

9 

8;      7 

6 

6 

5 

4 

3 

2 

2 

2 

55 

35 

30 

27 
26 

24 
23 

21 
21 

19 
19 

17 
17 

16 
15 

14   12 

10 
10 

9 
9 

81      7 

6 

6i 

6 

5 

5 

5 

4 
4 

3 
3 

2 
2 

2 
2 

2 
2 

56 

1 

14 

12 

8 

7 

57 

18 

17 

15 

14 

12 

10 

9 

7 

7 

6 

5 

5 

4 

3 

2 

2 

2 

58 

13111 

10 

8 

7 

7 

6 

5 

5 

4 

3 

2 

2 

2 

59 

8 

7 

6 

6 

5 

5 

4 

3 

2 

2 

2 

60 

1 

\ 

4 

3 

2 

2 

2 

1 

AB 

LE 

VII  B.— CONTRACTION  OF  MOON'S  SEMI-DIAMETER. 

<u  O  c 

I'll 

Argument,  number  from  Table  VII  A. 

"1 

tj6 

i 

8  i 
// 

10 

12 
ir 

16 

II 

18 
II 

20 

22 

II 

24 

II 

26 

II 

28 
II 

SO 

II 

32 

// 

34! 

i_ 

II 

36 

II 

38 

II 

40 

n 

44 

II 

48 
II 

52 

II 

56 

II 

60      64 

II    1    // 

, 

0 

0  ( 

)  0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

01 

0 

0!  0 

•  5 

0   ( 

)  0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

10 

0  ( 

)'0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

15 

0  ( 

)  0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

11 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

3 

3 

3 

20 

0  ( 
0  ( 

)!0 
)  1 

y 

1 
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1 

1 

1 
1 

1 

2 

1 

2 

2 
2 

2 
2 

2 
2 

2 
3 

2 
3 

2 
3 

3 
3 

3 
3! 

3 
3 

3 
4 

3 
4 

4 
4 

4 
5 

4 
5 

4 
5 

5 
6 

5 
6 

22 

24 

0  Oil 

1 

1 

2 

2 

2 

2 

3 

3 

3 

3 

3 

4 

41 

4 

4 

5 

6 

6 

6 

6 

7 

7 

26 

0 

L   1 

1 

2 

2 

2 

2 

3 

3 

3 

4 

4 

4 

4 

5! 

5 

5 

5 

6 

6 

7 

8 

8 

9 

28 

0 

I   1 

2 

2 

2 

3 

3 

3 

3 

4 

4 

4 

5 

5 

5i 

6 

6 

6 

7 

8 

8 

9 

9 

10 

30 

0 

I    1 
I    1 

1  1 
2 

2 
2 

2 

2 

3 
3 

3 
3 

3 

4 

4 
4 

4 
5 

4 
5 

5 

5 

5 

6 

5 
6 

6 

7 

6 

1 : 

6 

7 

7 
8 

7 
8 

8 
9 

9 
10 

9 
11 

10 
11 

11 
12 

12 
13 

32 

34 

0 

I   1 

2 

2 

3 

3 

4 

4 

5 

5 

6 

6 

6 

7 

7 

8 

8 

9 

9 

10 

11 

12 

13 

14 

15 

36 

I    2 

2 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

10 

10 

11 

12 

13 

15 

16 

17 

38 

1    2 

21 

3i 

3 

4 

5 

5 

6 

6 

7 

8 

8 

9 

9 

10 

10 

11 

12 

13 

14 

15 

16 

17 

18 

40 

I    2 

3 

31 

4 

4 

5 

6 

6 

7 

8 

8 

9 

9 

10 

11 

12 

12 

13 

14 

15 

17 

,18 

19 

20 

42 

I    2 

3 

41 

4 

5 

6 

6 

7 

8 

8 

9 

10 

11 

11 

12 

13 

13 

14 

16 

17 

18 

20 

21 

23 

44 

2   2 

3 

4 

5 

5 

6 

7 

8 

9 

9 

10 

11 

12 

12 

13 

14 

15 

15 

17 

19 

20 

22 

23 

45 

2   2 

3 

4 

5 

6 

6     7 

8 

9 

10  11 

11 

12 

13 

14 

15 

15 

16'    18 

19 

21 

23 

24 

46 

2   3 

3 

4i 

5 

6 

7     7 

8 

9 

10   11 

12 

13 

14 

14 

15 

16 

17!    19 

20 

22 

24 

47 

2   3 

4 

4 

5 

6 

7 

8 

9 

10 

11    11 

12 

13 

14 

15 

16 

17 

18  i    19 

21 

23 

25 

48 

2   3 

4 

5 

6 

6 

7 

8 

9 

10 

11    12 

13 

14 

15 

16 

17 

18 

18 

20 

22 

24 

26 

49 

2   3 

4 

5! 

6 

7 

8 

9 

10 

11 

12   12 

13 

14 

15 

16 

17 

18 

19 

21 

23 

25 

- 

50 

2   3 

4 

5 

6 

7 

8     9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

22 

24 

26 

51 

2   3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1-1  i 

15 

16 

17 

18 

19 

20 

21 

23 

25 

27 

52 

2  3 

4 

5 

6 

8 

9 

10 

11 

12 

13 

14! 

15 

16 

17 

18 

19 

21 

22 

24 

26 

53 

2   3 

4 

6 

7 

8 

9 

10 

11 

12 

13 

15 

16 

17 

18 

19 

20 

21 

22 

25 

27 

54 

2   3 

5 

6 

7 

8 

9 

10 

12 

13 

14 

15 

16 

17 

19 

20 

21 

22 

23 

26 

55 

2   4 

5 

6 

7 

8 

10 

11 

12 

13 

15 

16 

17 

18 

19 

21 

22 

56 

i  4 

5 

6 

8 

9 

10 

11 

13 

14 

15 

16 

57 

4 

5 

7 

1 

When  the  nearer  limb  is  obser\-ed,  suhstract  this  correction;  when  ihe  farther,  add. 


Page  312j                          APPENDIX  V:  TABLE  VIII. 

For  finding  the  Correction  of  the  Lunar  Distance  for  the  Contraction  of  the  Sun's  Semidiameter. 
TABLE  VIII  A.— GIVING  THE  ARGUMENT  FOR  TABLE  VIII  B. 

Red.  P. 
and  R. 
of  sun. 

Apparent  altitude  of  sun.                                                                          1 

5°  I  5i° 

6° 

6i° 

JO 

7i° 

8° 

8i° 

»" 

9*° 

10° 

11° 

12° 

18° 

14° 

15° 

16° 

17° 

18° 

20° 

25° 

80° 

40° 

50° 

V   (/' 
30 

2  0 
30 

3  0 
30 

4  0 
30 

5  0 
30 

55 
59 
62 
66 
69 
73 

51 
55 
59 

50 
54 
58 
62 

49" 

53 

58 
62 
66 
70 
74 
79 

47 

52 
56 
61 
65 
70 

50 

47 
52 

50 
55 
60 

65 
70 
75 

47 
52 
57 
63 

68 

74 

• 

49 
54 
60 
66 
71 

45 

51 
57 
62 
68 
74 

49 
55 
61 
67 
74 

I5" 
52 
59 
66 
72 

- 

48 
55 
63 
70 

44 
51" 
59 
66 
74 

46 
54 
62 
70 

40 
49 
57 
65 

42 
51 
60 
68 

35 

44 

•53 

62 

37 

47 
57 
67 

30 
42 
53 

34 
46 
59 

22 
24 
46 

18 
29 



6  0 
30 

7  0 
30 

8  0 

55;  57 
59  62 
64   67 
69   72 
73   77 

30 

9    0 

30 

10    0 

30 

63  66 
66!  70 
70I74 
74   78 

771 

74   78 
79 

i 

11     0 
30 

76 

80 

81 

i 

TABLE  VIII  B.— CONTRACTION  OF  SUN'S  SEMIDIAMETER. 

Whole 

correction 

of  sun. 

Argument,  number  from  Table  VIII  A. 

20 

24 

28 

82 

36 

40 

44  1  46  1  48  j  50    52 

54 

56 

58    60 

62 

64 

66 

68 

70 

72 

0 
0 

1 

2 
2 
3 
4 

5 
5 
6 

7 

8 

9 

10 

11 

74 

II 
0 
0 

1 

2 

2 

3 

4 

5 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

16 

17 

18 

20 

21 

23 

24 

26 

28 

76 

0 
0 

1 
1 

2 
3 

4 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

18 

19 

21 

22 

24 

25 

27 

29 

78 

0 
0 

1 
1 
2 

3 
4 
4 
5 
6 
7 
t 

8 
9 
10 
11 
12 
14 
15 
16 
17 
19 
20 
22 
23 
25 
26 
28 
30 

0  0 

1  0 

2  0 
\   30 

3  0 

0 
1 

0 

1 

0 

1 

2 

0 

1 

2 

0 
1 
2 
3 

0 
0 
2 
3 
4 

//   j   /> 

01    0 
0     0 
2;    2 
3!    2 
4     4 

• 

ff  ]  It 

Oi   0 
0:   0 

2!   1 
2     2 
3;    3 

0 
0 
1 
2 
3 

n 

0 
0 

1 

2 
3 
4 

5 
6 

7 
8 
9 
11 
12 
13 
15 

0 
0 

1 

2 
3 
4 
5 

? 

8 
9 
10 
12 
13 
14 

It 

0 
0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

14 

// 

0 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

0 
0 

1 

2 

3 

4 

5 

5 

6 

7 

8 

9 

10 

12 

13 

0 
0 

1 

2 
3 
3 
5 
5 
6 
7 
8 
9 

10 
11 
13 

II 

0 
0 

1 

2 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 

0 
0 
1 
2 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

II 
0 
0 

1 

2 
2 
3 

4 
5 
6 
6 

7 

8 

9 

10 

11 

30 

4  0 
20 
40 

5  0 

— 

— 

— 

— 

5 

7 

5 
6 

7 

9 

10 

5 ;  4 

6  6 

7  7 

8  8 
9(    9 

4 
6 

7 
8 
9 

20 
40 
6    0 
20 
40 

1 

! 

11 
12 

10   10 
]2lll 

13  12 

14  14 
16   15 

7  0 
20 
40 

8  0 
20 

1 
1 

1 

18 

17 
19 

16 
18 
20 
21 

16 
17 
19 
21 

15 
17 
18 
20 
22 

15 
16 
18 
19 
21 

14 
16 
17 
19 
20 
22^ 
24 

14 
15 
17 
18 
20 
21 
23 
25 

13 
15 
16 
17 
19 
20 
22 
24 
25 

13 
14 
16 
17 
18 
20 
21 
23 
25 
26 

13 
14 
15 
16 
18 
19 
21 
22 
24 
26 
28 

12 
13 
15 
16 
17 
19 
20 
22 
23 
25 
27 
28 

40 

9    0 

20 

40 

10    0 

j 

! 

23 

23 

20 

40 

11     0 

20 

1 

Subtract  this  correction  from  the  distance. 


APPENDIX  V:  TABLE  IX. 

[Page  313 

Lo 

garithms  of  Smal 

Arcs  in  Space  or  Time. 

Arc. 

0" 

1" 

2" 

3" 

4" 

5" 

6" 

7"   i   8" 

1 

9" 

O    t            II 

0"  0™  0' 

0.0000 

0.  3010 

0.  4771 

0. 6021 

0.6990 

0. 7782 

0.  8451  0.  9031  0.  0542 

0  10 

1.0000 

1.0414 

1.0792 

1.1139 

1. 1461 

1. 1761 

1. 2041 

1.2304  1.2553 

1. 2788 

0  20 

1.  3010 

1. 3222 

1.  3424 

1.3617 

1. 3802 

1.  3979 

1.4150 

1. 4314  1  1. 4472 

1.4624 

0  30 

1.4771 

1. 4914 

1.5051 

1.5185 

1.5315 

1. 5441 

1. 5563 

1.5682 

1.5798 

1.5911 

0  40 

1. 6021 

1.6128 

1.6232 

1. 6335 

1.6435 

1.6532 

1.  6628 

1.6721 

1.6812 

1.6902 

0  50 
0  10 

1.6990 
1. 7782 

1.  7076 
1.  7853 

1. 7160 

1. 7243 

1. 7324 

1. 7404 

1. 7482 
1.8195 

1.  7559 
1.  8261 

1. 7634 
1.8325 

1. 7709 

1. 7924 

1. 7993 

1.8062  1  1.8129 

1. 8388 

1  10 

1. 8451 

1.8513 

1. 8573 

1. 8633 

1.8692  1.8751 

1.8808 

1.  8865 

1. 8921 

1.  8976 

1  20 

1. 9031 

1.9085 

1.9138 

1.9191 

1.9243  1  1.9294 

1. 9345 

1. 9395  1. 9445 

1.9494 

1  30 

1. 9542 

1.9589 

1.9638 

1. 9685 

1.9731  1.9777 

1.  9823 

1.9868  1  1.9912 

1. 9956 

1  40 

2. 0000 

2. 0043 

2. 0086 

2. 0128 

2.0170  2.0212 

2. 0253 

2. 0294  !  2.  0334 

2.  0374 

1  50 

2.  0414 

2. 0453 

2.  0492 

2. 0531 

2. 0569  2. 0607 

2.0645 

2. 0682 

2. 0719 
2. 1072 

2.  0755 

0  2   0 

2.0792  !  2.0828 

2.  0864 

2. 0899 

2.0934  2.0969 

2.1004 

2.  1038 

2.  1106 

2  10 

2.1139  2.1173 

2. 1206 

2. 1239 

2.  1271  2.  1303 

2.  1,335 

2. 1367  2. 1399 

2. 1430 

2  20 

2.  1461   2.  1492 

2. 1523 

2. 1553 

2.1584  2.1614 

2.  1644 

2. 1673  2. 1703 

2. 1732 

2  30 

2.1761   2.1790 

2.  1818 

2. 1847 

2. 1875  1  2. 1903 

2. 1931 

2. 1959  2. 1987 

2. 2014 

2  40 

2.2041  2.2068 

2.  2095 

2.2122 

2. 2148  2. 2175 

2. 2201 

2. 2227  2. 2253 

2. 2279 

2  50 

2. 2304  2. 2330 

2.  2.355 

2.  2380 

2. 2405  2. 2430 

2. 2455 

2.  2480  2.  2504 

2. 2529 

0  3   0 

2. 2553 

2. 2577 

2.  2601 

2. 2625 

2.  2648  1  2. 2672 

2. 2695 

2. 2718  2. 2742 

2. 2765 

3  10 

2.  2788 

2.  2810 

2.  2833 

2.  2856 

2. 2878  2.  2900 

2. 2923 

2. 2945  2. 2967 

2. 2989 

3  20 

2.  3010 

2.  3032 

2. 3054 

2. 3075 

2. 3096  2. 3118 

2. 3139 

2.3160  2.3181 

2. 3201 

3  30 

2.  3222 

2.  3243 

2.  3263 

2.  3284 

2.3304  2.3324 

2. 3345 

2. 3365  :  2. 3385 

2.  3404 

3  40 

2.  3424 

2.  .3444 

2.  3464 

2.  3483 

2.3502  !  2.3522 

2. 3541 

2. 3560  5  2. 3579 

2.  3598 

3  50 
0  4   0 

2.  3617 

2. 3636 

2. 3655 

2.  3674 

2. 3692 
2.  3874 

2.3711 

2. 3729 

2. 3747 

2.  3766 
2. 3945 

2.  3784 
2.  3962 

2.  3802 

2. 3820 

2.  3838 

2.  3856 

2. 3892 

2. 3909 

2. 3927 

4  10 

2.  3979 

2.  3997 

2.  4014 

2.  4031 

2.  ':048  1  2.4065 

2. 4082 

2. 4099  2. 4116 

2.  4a  33 

4  20 

2.  4150 

2.  4166 

2.4183 

2. 4200 

2.4216  '  2.4232 

2. 4249 

2. 4265  2.  4281 

2.  4298 

4  30 

2. 4314 

2.  43.30 

2.  4.346  2.  4362 

2.4378  2.4393 

2. 4409 

2. 4425  2.  4440 

2.  4456 

4  40 

2.  4472 

2. 4487 

2.4502  '  2.4518 

2.4533  2.4548 

2.  4564 

2. 4579  2. 4594 

2.  4609 

4  50 
0  5   0 

2.  4624 

2. 4639 

2.4654  i  2.4669 

2.4683  2.4698 

2.4713 

2.  4728 

2.  4742 
2.  4886 

2.  4757 
2.  4900 

2. 4771 

2. 4786 

2.  4800 

2. 4814 

2.4829  2.4843 

2. 4857 

2. 4871 

5  10 

2. 4914 

2. 4928 

2.  4942 

2. 4955 

2.4969  \   2.4983  '  2.4997 

2.5011 

2. 5024 

2. 5038 

5  20 

2. 5051 

2. 5065 

2. 5079 

2.5092 

2.5105  2.5119  i  2.5132 

2.  5145 

2.5159 

2.5172 

5  30 

2.5185  2.5198 

2.5211 

2.  5224 

2.  5237  2. 5250 

2. 5263 

2. 5276 

2. 5289 

2. 5302 

§  40 

2.5315  2.5328 

2. 5340 

2. 5353 

2. 5366  2. 5378 

2. 5391 

2. 5403 

2.  5416 

2. 5428 

5  50 

2. 5441 

2. 5453 
2.  5575 

2. 5465 
2. 5587 

2. 5478 
2. 5599 

2.  5490 
2.5611 

2. 5502 

2. 5514 

2.  5527 

2. 5539 

2.5551 

0  6   0 

2.  5563 

2.5623  2.5635 

2.  5(547 

2. 5658 

2.  5670 

6  10 

2.5682  1  2.5694 

2. 5705 

2.5717 

2.5729  2.5740  2.5752 

2. 5763 

2. 5775 

2.  5786 

6  20 

2.5798  !  2.5809 

2. 5821 

2. 5832 

2.5843  2.5855  i  2.5866 

2.  5877 

2. 5888 

2. 5899 

6  30 

2.5911   2.5922 

2. 5933 

2.  5944 

2. 5955 

2. 5966 

2.  5977 

2. 5988  !  2. 5999 

2. 6010 

6  40 

2.6021  i  2.6031 

2.  6042 

2.  6053 

2.  6064 

2.  6075 

2. 6085 

2.6096  2.6107 

2.6117 

6  50 
0  7   0 

2.  6128 

2.  6138 

2.  6149 

2.6160 

2.  6170 

2.  6180 

2.6191 

2.6201  2.6212 

2. 6222 

2. 6232 

2. 6243 

2.  6253 

2. 6263 

2.  6274 

2.6284  1  2.6294 

2.  6304  2.  6314 

2. 6325 

7  10 

2.6335  I  2.6345 

2.  6355 

2.  6365 

2.  6375 

2.6385  2.6395 

2. 6405  1  2. 6415 

2. 6425 

7  20 

2.6435  i  2.6444 

2.  6454 

2.  6464 

2.  6474 

2.6484  2.6493 

2.  6.503  1  2.  6513 

2. 6522 

7  30 

2. 6532 

2.  6542 

2.  6551 

2. 6561 

2.  a571 

2.6580  2.6590 

2.  6599  2.  6609 

2. 6618 

7  40 

2. 6628 

2. 6637 

2.6646 

2.  6656 

2. 6665 

2.6675  2.6684 

2. 6693  2. 6702 

2.  6712 

7  50 
0  8   0 

2. 6721 
2. 6812 

2.  6730 
2. 6821 

2. 6739 
2.  6830 

2.  6749 

2.  6758 

2.6767  2.6776 
2.6857  1  2.6866 

2. 6785  1  2. 6794 

2. 6803 

2. 6839 

2. 6848 

2. 6875 

2. 6884 

2. 6893 

8  10 

2. 6902 

2. 6911 

2.  6920 

2.  6928 

2.  6937 

2.6946  !  2.6955 

2.  6964 

2.  6972 

2. 6981 

8  20 

2. 6990 

2.  6998 

2.  7007 

2.  7016 

2.  7024 

2. 7033  !  2. 7042 

2.  7050 

2.  7059 

2.  7067 

8  30 

2.  7076 

2.  7084 

2. 7093 

2.  7101 

2.7110 

2.7118  1  2.7126 

2.  7135 

2.  7143 

2.  7152 

8  40 

2.7160  1  2.7168 

2.7177 

2.  7185 

2. 7193 

2.7202  1  2.7210 

2.  7218 

2.  7226 

2.  7235 

8  50 

2. 7243  2. 7251 

2.  7259 

2. 7267 

2. 7275 

2.7284  2.7292 

2.  7300 

2.  7308 

2.  7316 

0  9   0 

2. 7324  2.  7332 

2.  7340 

2. 7348 

2. 7356 

2. 7364  2.  7372 

2. 7380 

2. 7388 

2.7396 

9  10 

2.  7404  2.  7412 

2. 7419 

2. 7427 

2. 7435 

2.7443  2.7451 

2.  7459 

2. 7466 

2.  7474 

9  20 

2.  7482  2. 7490 

2.  7497 

2. 7505 

2.  7513 

2.7520  2.7528 

2.  7536 

2. 7543 

2.  7551 

9  30 

2.  7559  2.  7566 

2.  7574 

2. 7582 

2.  7589 

2.7597  2.7604 

2.  7612 

2.  7619 

2.  7627 

9  40 

2.7634  1  2.7642 

2.  7649 

2.  7657 

2.  7664 

2.  7672  !  2.  7679 

2.  7686 

2.  7694 

2.  7701 

9  50 

2.7709  2.7716 

2.  7723 

2. 7731 

2. 7738 

2.  7745  1  2.  7752 

2. 7760 

2.  7767 

2.  7774 

Page  314] 

APPENDIX  V:  TABLE  IX. 

\ 

Logarithms  of  Small  Arcs  in 

Space  or 

Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

6" 

6" 

7" 

8" 

9" 

O      ' 

0"  10° 

n 

'  0" 

2.  7782 

2.  7789 

2.  7796 

2.7803 

2.  7810 

2.  7818 

2.  7825 

2. 7832 

2.  7839 

2.  7846 

10 

10 

2.7853 

2.  7860 

2.  7868 

2.7875. 

2.  7882 

2.  7889 

2. 7896 

2. 7903 

2.  7910 

2. 7917 

10 

20 

2. 7924 

2.  7931 

2.  7938 

2. 7945 

2. 7952 

2.  7959 

2. 7966 

2.  7973 

2.  7980 

2.  7987 

10 

30 

2. 7993 

2.8000 

2. 8007 

2.  8014 

2. 8021 

2.  8028 

2.8035 

2.  8041 

2.8048 

2. 8055 

10 

40 

2.80Q2 

2. 8069 

2. 8075 

2.  8082 

2. 8089 

2.8096 

2.  8102 

2.8109 

2.  8116 

2. 8122 

10 

50 

2.  8129 

2.  8136 

2.  8142 

2.  8149 

2. 8156 

2.  8162 

2. 8169 

2.  8176 
2.8241" 

2.  8182 

2.  8189 

0  11 

0 

2.  8195 

2. 8202 

2.  8209 

2. 8215 

2. 8222 

2.  8228 

2.  8235 

2.  8248 

2.  8254 

11 

10 

2.  8261 

2. 8267 

2. 8274 

2.  8280 

2. 8287 

2.  8293 

2.8299 

2. 8306 

2. 8312 

2. 8319 

11 

20 

2. 8325 

2. 8331 

2. 8338 

2. 8344 

2.  8351 

2. 8357 

2. 8363 

2. 8370 

2. 8376 

2. 8382 

11 

30 

2.  8388 

2. 8395 

2. 8401 

2. 8407 

2.  8414 

2.  8420 

2.8426 

2. 8432 

2.  8439 

2.8445 

11 

40 

2. 8451 

2.  8457 

2. 8463 

2. 8470 

2.8476 

2.  8482 

2. 8488 

2. 8494 

2.8500 

2.  8506 

11 

50 

2. 8513 

2.8519 

2.  8525 

2. 8531 

2. 8537 

2.  8543 

2. 8549 

2. 8555 

2.  8561 

2.  8567 

0  12 

0 

2. 8573 

2.  8579 

2.8585 

2. 8591 

2. 8597 

2.  8603 

2. 8609 

2. 8615 

!  2.  8621 

2.  8627 

12 

10 

2.  8633 

2.  8639 

2.8645 

2.  8651 

2. 8657 

2.  8663 

2.  8669 

2.  8675 

2.  8681 

2. 8686 

12 

20 

2. 8692 

2.  8698 

2.8704  2.8710 

2. 8716 

2. 8722 

2. 8727 

2.  8733 

2.  8739 

2. 8745 

12 

30 

2. 8751 

2.  8756 

2. 8762 

2. 8768 

2. 8774 

2. 8779 

2. 8785 

2. 8791 

2.  8797 

2. 8802 

12 

40 

2. 8808 

2.  8814 

2. 8820 

2. 8825 

2. 8831 

2. 8837 

2. 8842 

2.8848 

2.  8854 

2. 8859 

12 

50 

2.8865 

2.  8871 

2.8876  1  2.8882 

2. 8887 

2.  8893 

2.8899 

2.8904 

2.  8910 

2. 8915 

0  13 

0 

2. 8921 

2.  8927 

2. 8932 

2. 8938 

2.  8943 

2.  8949 

2.  8954 

2. 8960 

2. 8965 

2. 8971 

13 

10 

2. 8976 

2. 8982 

2. 8987 

2.  8993 

2. 8998 

2.9004 

2. 9009 

2.  9015 

2.  9020 

2. 9025 

13 

20 

2. 9031 

2. 9036 

2.9042 

2.  9047 

2. 9053 

2. 9058 

2.9063 

2. 9069 

2. 9074 

2. 9079 

13 

30 

2. 9085 

2. 9090 

2. 9096  2. 9101 

2. 9106 

2.9112 

2.9117 

2.9122 

2. 9128 

2. 9133 

13 

40 

2. 9138 

2.  9143 

2. 9149  2.  9154 

2.  9159 

2.  9165 

2.  9170 

2.  9175 

2.  9180 

2. 9186 

13 

50 

2. 9191 

2.  9196 

2.9201  2.9206  i  2.9212 

2.9217 

2. 9222 

2. 9227 

2. 9232  !  2.  9238  | 

0  14 

0 

2. 9243 

2.  9248 

2.9253  2.9258  ;  2.9263 

2.  9269 

2. 9274 

2. 9279 

2.  9284 

2.  9289 

14 

10 

2. 9294 

2.  9299 

2.9304  :  2.9309  2.9315 

2. 9320 

2.  9325 

2.  9330 

2. 9335 

2.  9340 

14 

20 

2.  9345 

2. 9350 

2. 9355 

2.9360  '  2.9365 

2. 9370 

2. 9375 

2.  9380 

2. 9385 

2. 9390 

14 

30 

2.  9.395 

2.  9400 

2.  9405 

2.9410  2.9415 

2. 9420 

2. 9425 

2.  9430 

2.9435 

2. 9440 

14 

40 

2. 9445 

2.  9450 

2. 9455 

2.9460  2.9465 

2.  9469 

2.  9474 

2.  9479 

2. 9484 

2. 9489 

14 

50 

2. 9494 

2.  9499 

2. 9504 

2.9509  2.9513 

2. 9518 

2.  9523 

2.  9528 

2. 9533  !  2. 9538 

0  15 

0 

2.  9542 

2.  9547 

2.  9552 

2.9557  j  2.9562 

2. 9566 

2.  9571 

2. 9576 

2. 9581  2. 9586 

15 

10 

2.  9590 

2.  9595 

2.9600  1  2.9605  i  2.9609 

2. 9614 

2.  9619 

2.  9624 

2. 9628 

2. 9633 

15 

20 

2.  9638 

2.  9643 

2.9647  2.9652  1  2.9657 

2. 9661 

2. 9666 

2. 9671 

2. 9675 

2. 9680 

15 

30 

2. 9685 

2. 9689 

2.9694  2.9699  2.9703 

2. 9708 

2.9713 

2.9717 

2. 9722 

2.  9727 

15 

40 

2. 9731 

2. 9736 

2.  9741  2.  9745  2. 9750 

2.  9754 

2.  9759 

2. 9763 

2. 9768 

2. 9773 

15 

50 

2.  9777 

2. 9823 

2. 9782 

2.  9786 

2.9791   2.9795 

2.  9800 

2.  9805 

2.  9809 

2. 9814 

2.9818 

0  16 

0 

2. 9827 

2. 9832 

2.9836  2.9841 

2.  9845 

2. 9850 

2. 9854 

2. 9859 

2. 9863 

16 

10 

2. 9868 

2. 9872 

2. 9877 

2.9881  2.9886 

2.  9890 

2.  9894 

2.  9899 

2. 9903 

2. 9908 

16 

20 

2. 9912 

2. 9917 

2. 9921 

2.9926  2.9930 

2.  9934 

2.  9939 

2.  9943 

2. 9948 

2. 9952 

16 

30 

2. 9956 

2. 9961 

2. 9965 

2.9969  2.9974 

2.  9978 

2.  9983 

2.  9987 

2. 9991 

2. 9996 

16 

40 

3. 0000 

3.0004 

3. 0009 

3.  0013  3.  0017 

3.  0022 

3. 0026 

3.0030 

3. 0035 

3.0039 

16 

50 

3.0043 

3.0048 

3. 0052 

3. 0056  3.  0060 

3.  0065 

3. 0069 

3.  0073 

3. 0077 

3. 0082 

0  17 

0 

3.  0086 

3. 0090 

3.0095 

3. 0099  3. 0103 

3.  0107 

3.0111 

3.0116 

3.0120 

3.  0124 

17 

10 

3.  0128 

3. 0133 

3.  0137 

3.0141  ,  3.0145 

3.  0149 

3.  0154 

3.0158 

3. 0162 

3.  0166 

17 

20 

3.  0170 

3. 0175 

3.  0179 

3.0183  1  3.0187 

3.  0191 

3.  0195 

3.  0199 

3. 0204 

3. 0208 

17 

30 

3.  0212 

3.  0216 

3.  0220 

3.  0224  3. 0228 

3.  0233 

3. 0237 

3. 0241 

3. 0245 

3. 0249 

17 

40 

3. 0253 

3. 0257 

3. 0261 

3.0265  i  3.0269 

3. 0273 

3. 0278 

3. 0282 

3. 0286 

3.  0290 

17 

50 

3. 0294 

3.  0298 

3. 0302 
3. 0342 

3. 0306 
3. 0346 

3.  0310 

3. 0314 

3. 0318 

3. 0322 

3. 0326 
3. 0366 

3.  0330 

0  18 

0 

3.  0334 

3. 0338 

3. 0350 

3. 0354 

3. 0358 

3. 0362 

3. 0370 

18 

10 

3. 0374 

3.  0378 

3. 0382 

3.0386  i  3.0390 

3. 0394 

3. 0398 

3. 0402 

3. 0406 

3.0410 

18 

20 

3.  0414 

3. 0418 

3. 0422 

3.  0426  3. 0430 

3.  0434 

3. 0438 

3. 0441 

3. 0445 

3.0449 

18 

30 

3.  0453 

3. 0457 

3. 0461 

3.  0465 

3.  0469 

3.  0473 

3. 0477 

3. 0481 

3. 0484 

3. 0488 

18 

40 

3. 0492 

3.  0496 

3. 0500 

3.0504 

3.0508 

3.  0512 

3.  0515 

3. 0519 

3. 0523 

3. 0527 

18 

50 

3.  0531 

3.  0535 

3.  0538 

3. 0542 

3.  0546 

3.  0550 

3.  0554 

3. 0558  3. 0561 

3. 0565 

0  19 

0 

3.  0569 

3.  0573 

3. 0577 

3. 0580 

3. 0584 

3.  0588 

3.  0592 

3.0596  3.0599 

3. 0603 

19 

10 

3.  0607 

3. 0611 

3. 0615 

3. 0618 

3. 0622 

3. 0626 

3.  0630 

3. 0633 

3. 0637 

3. 0641 

19 

20 

3.  0645 

3. 0648 

3. 0652 

3. 0656  3. 0660 

3. 0663 

3. 0667 

3. 0671 

3.0674 

3. 0678 

19 

30 

3. 0682 

3. 0686 

3.  0689 

3. 0693  3. 0697 

3.0700 

3. 0704 

3. 0708 

3. 0711 

3. 0715 

19 

40 

3.0719 

3. 0722 

3. 0726 

3.  0730  3. 0734 

3. 0737 

3. 0741 

3.  0745 

3. 0748 

3.  0752 

19 

50 

3. 0755 

3. 0759 

3. 0763 

3. 0766  3. 0770 

3. 0774 

3. 0777 

3.  0781 

3. 0785 

3. 0788 

APPENDIX  V:  TA.BLE  IX. 

[Page  315 

Logarithms  of  Small  Arcs  in  Space  or 

Time. 

Arc. 

0" 

1" 

2"      8" 

4" 

5" 

6" 

7" 

8" 

9" 

O      ' 

0"  20" 

0' 

3. 0792 

3.  0795 

3.0799  3.0803 

3.0806 

3. 0810 

3. 0813 

3. 0817 

3. 0821 

3. 0824 

20 

10 

3. 0828 

3. 0831 

3.0835  3.0839 

3.0842 

3. 0846 

3.  0849 

3.  0853 

3. 0856 

3. 0860 

20 

20 

3. 0864 

3. 0867 

3.0871  3.0874 

3. 0878 

3. 0881 

3.  0885 

3.  0888 

3. 0892 

3.  0896 

20 

30 

3. 0899 

3.  0903 

3.0906  3.0910 

3.0913  i  3.0917 

3. 0920 

3.  0924 

3. 0927 

3.  0931 

20 

40 

3. 0934 

3.  0938 

3.0941  3.0945 

3.0948  j  3.0952 

3. 0955 

3.  0959 

3. 0962 

3. 0966 

20 

50 

3. 0969 

3.  0973 

3.0976  3.0980 

3.0983  1  3.0986 

3. 0990 

3.  0993 

3. 0997 

3. 1000 

0  21 

0 

3. 1004 

3. 1007 

3.1011  :  3.1014 

3. 1017  3. 1021 

3. 1024 

3. 1028 

3. 1031 

3. 1035 

21 

10 

3. 1038 

3. 1041 

3.1045  '  3.1048 

3. 1052  3. 1055 

3. 1059 

3. 1062 

3. 1065 

3. 1069 

21 

20 

3. 1072 

3. 1075 

3. 1079  ■   3. 1082 

3. 1086  3. 1089 

3. 1092 

3. 1096 

3. 1099 

3. 1103 

21 

30 

3. 1106 

3.1109 

3. 1113 

3.1116 

3. 1119  3. 1123 

3. 1126 

3. 1129 

3. 1133 

3. 1136 

21 

40 

3. 1139 

3. 1143 

3. 1146 

3. 1149 

3. 1153  3. 1156 

3.1159 

3. 1163 

3. 1166 

3. 1169 

21 

50 

3. 1173 

3. 1176 

3. 1179 

3.1183 

3. 1186  1  3. 1189 

3. 1193  . 

3.1196 

3. 1199 

3.  1202 

0  22 

0 

3. 1206 

3. 1209 

3.1212 

3. 1216 

3. 1219  3. 1222 

3. 1225 

3. 1229 

3. 1232 

3. 1235 

22 

10 

3. 1239 

3.1242 

3. 1245 

3. 1248 

3.1252  3.1255 

3. 1258 

3. 1261 

3. 1265 

3. 1268 

22 

20 

3. 1271 

3. 1274 

3. 1278 

3.  1281 

3. 1284 

3. 1287 

3.1290 

3. 1294 

3. 1297 

3.1300 

22 

30 

3. 1303 

3. 1307 

3. 1310 

3.  1313 

3. 1316 

3. 1319 

3. 1323 

3. 1326 

3. 1329 

3. 1332 

22 

40 

3. 1335 

3. 1339 

3. 1342 

3. 1345 

3. 1348 

3. 1351 

3. 1355 

3.1358 

3. 1361 

3. 1364 

22 

50 

3. 1367 

3. 1370 

3. 1374 

3. 1377 

3.1380 

3. 1383 

3. 1.386 

3. 1389 

3. 1392 

3. 1396 

0  23 

0 

3. 1399 

3. 1402 

3. 1405 

3. 1408 

3. 1411 

3.1414 

3.  1418 

3.  1421 

3. 1424 

3. 1427 

23 

10 

3. 1430 

3. 1433 

3. 1436 

3.1440 

3. 1443 

3. 1446 

3. 1449 

3. 1452 

3. 1455 

3. 1458 

23 

20 

3. 1461 

3.1464 

3. 1467 

3. 1471 

3. 1474 

3. 1477 

3. 1480 

3. 1483 

3. 1486 

3. 1489 

23 

30 

3. 1492 

3. 1495 

3. 1498 

3. 1501 

3. 1504 

3. 1508 

3. 1511 

3.1M4 

3. 1517 

3. 1520 

23 

40 

3. 1523 

3. 1526 

3. 1529 

3. 1532 

3. 1535 

3. 1538 

3. 1541 

3. 1544 

3. 1547 

3. 1550 

2a 

50 

3. 1553 

3. 1556 

3. 1559 

3. 1562  3. 1565 

3. 1569 

3. 1572 

3. 1575 

3.1578  3.1581 

0  24 

0 

3. 1584 

3. 1587 

3. 1590 

3.1593  3.1596 

3. 1599 

3. 1602 

3. 1605 

3. 1608  1  3. 1611 

24 

10 

3. 1614 

3.1617 

3. 1620 

3.1623  3.1626 

3. 1629 

3. 1632 

3. 1635 

3. 1638  3. 1641 

24 

20 

3. 1644 

3. 1647  i  3. 1649 

3.1652  1  3.1655 

3. 1658 

3. 1661 

3. 1664 

3. 1667  !  3. 1670 

24 

30 

3. 1673 

3.1676  3.1679 

3. 1682  :  3. 1685 

3. 1688 

3. 1691 

3. 1694 

3. 1697  !  3. 1700 

24 

40 

3. 1703 

3. 1706  i  3. 1708 

3.1711  i  3.1714 

3. 1717 

3. 1720 

3. 1723 

3. 1726  !  3. 1729 

24 

50 

3. 1732 

3.1735  3.1738 

3. 1741 

3. 1744 

3. 1746 

3. 1749 

3. 1752 

3. 17.55 

3. 1758 

0  25 

0 

3.1761 

3. 1764  [  3. 1767 

3. 1770 

3. 1772 

3. 1775 

3. 1778 

3. 1781 

3. 1784 

3. 1787 

25 

10 

3. 1790 

3. 1793  I  3. 1796 

3. 1798 

3. 1801 

3. 1804 

3. 1807 

3. 1810 

3. 1813 

3.1816 

25 

20 

3. 1818 

3.1821  i  3.1824 

3. 1827 

3. 1830 

3. 1833 

3. 1836 

3. 1838 

.3. 1841 

3.1844 

25 

30 

3. 1847 

3. 1850  1  3. 1853 

3. 1855 

3. 1858 

3. 1861 

3.1864 

3. 1867 

3. 1870  1  3. 1872 

25 

40 

3. 1875 

3. 1878 

3. 1881 

3. 1884  3. 1886 

3. 1889 

3. 1892 

3. 1895 

3. 1898  i  3. 1901 

25 

50 

3. 1903 

3.1906 

3. 1909 

3. 1912  3. 1915 

3.1917 

3. 1920 

3. 1923 

3. 1926  !  3. 1928 

0  26 

0 

3. 1931 

3. 1934 

3. 1937 

3.1940  3.1942 

3.1945 

3. 1948 

3. 1951 

3. 19.53  3. 1956 

26 

10 

3. 1959 

3. 1962 

3. 1965 

3.1967  3.1970 

3. 1973 

3. 1976 

3. 1978 

3. 1981 

3. 1984 

26 

20 

3. 1987 

3. 1989 

3. 1992 

3.1995  3.1998 

3. 2000 

3. 2003 

3.  2006 

3. 2009 

3. 2011 

26 

30 

3.  2014 

3.  2017 

3.  2019 

3.2022  3.2025 

3. 2028 

3. 2030 

3.  2033 

3. 2036 

3. 2038 

26 

40 

3. 2041 

3.2044  1  3.2047 

3.2049  3.2052 

3.  2055 

3. 2057 

3.  2060 

3.  2063 

3. 2066 

26 

50 

3.  2068 

3.2071  3.2074 

3.2076  !  3.2079 

3. 2082 

3.  2084 

3.  2087 

3. 2090 

3. 2092 

0  27 

0 

3. 2095 

3.2098  3.2101 

3.2103  j  3.2106 

3. 2109 

3.2111 

3.  2114 

3.2117 

3.2119 

27 

10 

3. 2122 

3.2125  ;  3.2127 

3.2130  1  3.2133 

3.  2135 

3.  2138 

3.  2140 

3.  2143 

3.  2146 

27 

20 

3. 2148 

3.2151  i  3.2154 

3.2156 

3.2159 

3.  2162 

3.2164 

3.  2167 

.3.  2170 

3.  2172 

27 

30 

3. 2175 

3.2177  1  3.2180 

3.2183 

3.  2185 

3. 2188 

.3.  2191 

3.  2193 

3.  2196 

3.  2198 

.  27 

40 

3. 2201 

3.2204  1  3.2206 

3.  2209 

3.  2212 

3.  2214 

3.2217 

3.  2219 

3. 2222 

3.  2225 

27 

50 

3. 2227 

3. 2230 

3.  2232 

3.  2235 

3.  2238 

3.2240 

3. 2243 
3.  2269 

3.  2245 

3. 2248 

3.  2250 

0  28 

0 

3. 2253 

3. 2256 

3. 2258 

3. 2261 

3. 2263 

3. 2266 

3.  2271 

3. 2274 

3.  2276 

28 

10 

3. 2279 

3.  2281 

3.  2284 

3. 2287 

3. 2289 

3. 2292 

3. 2294 

3.  2297 

3. 2299 

3. 2302 

28 

20 

3.2304 

3.  2307 

3.  2310 

3.  2312 

3. 2315 

3.2317 

3. 2320 

3.  2322 

3. 2325 

3. 2327 

28 

30 

3. 2330 

3. 2333 

3.  2335 

3.  2338 

3.2340 

3. 2343 

3. 2345 

3.  2348 

3.  23.50 

3. 2353 

28 

40 

3. 2355 

3. 2358 

3. 2360 

3.  2363 

3. 2365 

3.  2368 

3.  2370 

3. 2373 

3.  2375 

3. 2378 

28 

50 

3. 2380 

3. 2383 

3.  2385 

3.  2388 

3.2390  I  .3.2393 

3. 2395 

3. 2398 

3.  2400 
3.2425 

3. 2403 

0  29 

0 

3. 2405 

3. 2408 

3. 2410 

3.  2413 

3.2415  1  3.2418 

3.  2420 

3. 2423 

3. 2428 

29 

10 

3. 2430 

3. 2433 

3.2435 

3. 2438 

3.  2440 

3.2443 

3.  2445 

3. 2448 

3.  2450 

3. 2453 

29 

20 

3. 2455 

3.  2458 

3.2460 

3. 2463 

3. 2465 

3.  2467 

3.  2470 

3. 2472 

3. 2475 

3. 2477 

29 

30 

3. 2480 

3. 2482 

3. 2485 

3. 2487 

3.  2490 

3.  2492 

3.  2494 

3. 2497 

3. 2499 

3.  2502 

29 

40 

3.2504 

3. 2507 

3. 2509 

3. 2512 

3. 2514 

3. 2516 

3. 2519 

3. 2521 

3.  2524 

3. 2526 

29 

50 

3.  2529 

3. 2531 

3. 2533 

3. 2536 

3.  2538 

3.  2.541 

3.  2.543 

3. 2545 

3.2548 

3. 2550 

Page 

316J 

APPENDIX  V:  TABLE  IX. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

«" 

1" 

2" 

8" 

4" 

5"       6" 

7" 

8"   1   a" 

o   / 

0"  30™ 

II 
0» 

3.2553 

3.2555 

3.2558 

3.2560 

3. 2562 

.3.2565  '  3.2567 

3.  2570 

3. 2572  3. 2574 

30 

10 
20 

3.  2577 

3. 2579 

3. 2582 

3. 2584 

3. 2586 

.3.2589  3.2591 

3.  2594 

3.  2,596  '   3.  2598 

30 

3. 2601 

3. 2603 

3.2605 

3.  2608 

3. 2610 

3.2613  1  3.2615 

3.2617 

3. 2620  3. 2622 

30 

30 

3. 2625 

3.  2627 

3.  2629 

3.  2632 

3. 2634 

3.2636  :  3.2639 

3.  2641 

3. 2643  3. 2646 

30 

40 

3. 2648 < 

3.  2651 

3.  2653 

3.  2655 

3.  2658 

3.2660  ;  3.2662 

3. 2665 

3. 2667  3.  2669 

30 

50 

3. 2672 

3.  2674 

3. 2676 

3. 2679 

3. 2681 

3.2683  ;  3.2686 

3. 2688 

3. 2690  1  3. 2693 

0  31 

0 

3. 2695 

3.  2697 

3.2700 

3.2702 

3. 2704  j  3. 2707 

3.  2709 

3.2711 

3.2714;  3.2716 

31 

10 

3.2718 

3.  2721 

3.  2723 

3.  2725 

3.  2728  3.  27.30 

3.  27.32 

3.  2735 

3.  2737  :  3.  2739 

31 

20 

3.  2742 

3.  2744 

3.  2746 

3.  2749 

3.2751  3.2753 

3.  2755 

3.  2758 

3.  2760 

3. 2762 

31 

30 

3.  2765 

3.  2767 

3. 2769 

3.  2772 

3.2774  3.2776 

3.  2778 

3. 2781 

3. 2783 

3. 2785 

31 

40 

3. 2788 

3.  2790 

3.  2792 

3.  2794 

3.2797  i  3.2799 

3.  2801 

3.  2804 

3. 2806 

3.  2808 

31 

50 

3. 2810 

3. 2813 
3.2835 

3.2815  \   3.2817 
3.2838  ;  3.2840 

3. 2819  1  3. 2822 

3.  2824 

3. 2826 

3.2828  3.2831  | 

0  32 

0 

3. 2833 

3.2842  '  3.2844 

3. 2847 

.3:2849 

3. 2851 

3. 2853 

32 

10 

3. 2856 

3. 2858 

.3.2860  1  3.2862 

3.2865  .3.2867  3.2869 

3. 2871 

3. 2874 

3. 2876 

32 

20  3. 2878 

3. 2880 

3. 2882  3. 2885 

3.2887  1  3.2889 

3. 2891 

3. 2894 

3. 2896 

3. 2898 

32 

30 

3.2900 

3. 2903 

3.  2905  3.  2907 

.3.2909  3.2911 

3. 2914 

3.  2916 

3.  2918 

3.  2920 

32 

40 

3.  2923 

3. 2925 

3. 2927  3. 2929 

3. 2931   3. 2934 

3.  2936 

3. 2938 

3. 2940 

3. 2942 

32 

50 

3.  2945 

3. 2947 

3. 2949  3. 2951 

3. 2953  3. 2956 

3. 2958 

3. 2960 
3. 2982 

3. 2962  \   3. 2964  | 

0  33 

0 

3. 2967" 

3. 2969 

3.2971  !  3.2973 

3.2975  i  3.2978 

3. 2980 

3.2984 

3. 2986 

33 

10 

3.  2989 

3. 2991 

3.2993  j  3.2995 

3. 2997 

3.2999  3.3002 

3. 3004 

3.  3006 

3. 3008 

33 

20 

3. 3010 

3. 3012 

3.3015  3.3017 

3. 3019 

3.3021  1  .3.3023 

3. 3025 

3. 3028 

3.  30,30 

33 

30 

3.3032 

3.  3034 

3.3036  '   3.3038 

3. 3041 

3.3043  '  3.3045 

3. 3047 

3. 3049 

3.  3051 

33 

40 

3. 3054 

3.  3056 

3.3058  3.3060 

3. 3062 

3.3064  3.  .3066 

3. 3069 

3. 3071 

3. 3073 

33 

50 

3. 3075 

3.  3077 

3.3079  '  .3.3081 

3.  3084 

3.3086  3.3088 

3. 3090 

3.3092  3,3094  | 

0  34 

0 

3. 3096 

3. 3098 

3.3101  3.3103 

3. 3105 

3.3107  3.3109 

3.3111 

3.  3113 

3.3115 

34 

10 

3. 3118 

3. 3120 

.3.3122  !  3.3124 

3.3126 

3.3128  3.3130 

3.  3132 

3.  3134 

3.3137 

34 

20 

3. 3139 

3.  3141 

3.3143  1  3.3145 

3.  3147 

.3.3149  3.3151 

.3.31,53 

3.  3156 

3.  31.58 

34 

30 

3. 3160 

3.  3162 

.3.3164  j  3.3166 

.3.  3168  • 

3.3170  3.3172 

3.3174 

.3.3176 

,3.3179 

34 

40 

3.3181 

3.3183 

3.3185  !  3.3187 

3. 3189 

3.  .3191  '   3.3193 

3.  3195 

3.  3197  !  .3.  3199 

34 

50 

3. 3201 

3. 3204 

3.3206  i  3.3208 

3.  3210 
3.  3230 

3. 3212 
3.  3233 

3. 3214 

3.  3216 

3. 3218  !  3. 3220 

0  35 

0 

3".  3222 

3. 3224 

3. 3226 

3.  3228 

3. 3235 

3. 3237 

3.  .3239  !  3.  3241 

35 

10 

3. 3243 

3. 3245 

3. 3247 

3. 3249 

3.  3251 

.3.3253  '  3.3255 

3. 3257 

3. 32,59  3.  3261 

35 

20 

3. 3263 

3. 3265 

3. 3267 

3. 3269 

3.  3272 

3.3274  i  3.3276 

3.  3278 

3.  3280  3. 3282 

35 

30 

3. 3284 

3. 3286  ■ 

3. 3288 

3. 3290 

3.  3292 

3.3294  3.3296 

3. 3298 

3. 3300  !  3.  3302 

35 

40 

3. 3304 

3.  3306 

3. 3308 

3. 3310 

3.3,312  3.3314  \   3.  .331 6 

3.  .3318 

3. 3320  1  3. 3322 

35 

50 

3.  3324 

3. 3326 

3.  3328 

3. 3330 

3. 3332 

3.3334  :  3.3336 
3.3355  3.3357' 

3. 3339 
3.  33,59 

3.3.341  3.  .3343 
3. 3361  3. 3363 

0  36 

0 

3.  3345 

3. 3347 

"3: 3349 

3. 3351 

3.3353' 

36 

10 

3. 3365 

3. 3367 

3.  3.369 

3. 3371 

3. 3373 

3. 3375  3. 3377 

3. 3379 

3. 3381  j  3. 3383 

36 

20 

3. 3385 

3. 3387 

3. 3389 

3. 3391 

3. 3393 

3.3.395  !  3.  .3397 

3.  .3398 

3. 3400  :  3. 3402 

36 

30 

3. 3404 

3. 3406 

3. 3408 

3. 3410 

3.3412  1  .3.3414  |  3.3416 

3.  3418 

3. 3420  I  3. 3422 

36 

40 

3. 3424 

3. 3426 

3. 3428 

3.  34.30 

3.3432  3.  .3434  .3.34.36 

3. 3438 

3. 3440  3. 3442 

36 

50 

3. 3444 

3. 3446 

3.3448 

3.3450  3.3452  '  3.3454  !  3.3456 

3. 3458 

3. 3460  '  3. 3462 

0  37 

0 

3. 3464 

3. 3465 

3.3467 

3. 3469 

3.  .3471  !  3.3473  3.  .3475 

3. 3477 

3. 3479  3.  3481 

37 

10 

3. 3483 

3. 3485 

3. 3487 

3. 3489 

3. 3491 

3. 3493  3. 3495 

3.  M97 

3.  3499  :  3.  3.501 

37 

20 

3.  3502 

3. 3504 

3. 3506 

3. 3508 

3. 3510 

3.  ,3512  3.  3514 

3.  3516 

3.  ,3518  1  3.  3.520 

37 

30 

3. 3522 

3. 3524 

3. 3526 

3. 3528 

3.  35.30 

.3.35.31  3.3.533 

3.  3535 

3.  3.537  1  3.  3.5.39 

37 

40 

3.  3541 

3. 3543 

3. 3545 

3. 3547 

3. 3549 

3.  3.551 

3. 3553 

3.  ,3555 

3. 3556 

3.  3,558 

37 

50 

3. 3560 

3. 3562 

3. 3564 

3.3566 

3. 3568 

3.  3570 

3. 3572 

3. 3574 

3. 3576 

3. 3577 

0  38 

0 

3.  3579 

3.3581 

3. 3583 

3. 3585 

3. 3587 

3.  .3589 

3. 3591 

3. 3593 

3. 3595 

3. 3596 

38 

10 

3. 3598 

3. 3600 

3. 3602 

3.3604 

3. 3606 

3. 3608 

3.  .3610 

3. 3612 

3.  .3614 

3.  .3615 

38 

20 

3. 3617 

3.3619 

3. 3621 

3. 3623 

3.  .3625 

3.  ,3627 

3. 3629 

3. 3630 

3. 3632 

3. 3634 

38 

30 

3. 3636 

3. 3638 

3.  3640 

3. 3642 

3. 3644 

3.  3646 

3. 3647 

3. 3649 

3. 3651 

3. 3653 

38 

40 

3. 3655 

3. 3657 

3.  3659 

3. 3660 

3. 3662 

3.  3664 

3.  .3666 

3.  ,3668 

3.  .3670 

3. 3672 

38 

50 

3. 3674 

3.  3675 

3.  3677 

3. 3679 

3.  3681 

3. 3683 

3.  ,3685 

3.  .3687 
"3.:3705 

3. 3688 

3. 3690 

0  39 

0 

3. 3692 

3.  3694 

3. 3696 

3. 3698 

3. 3700 

3.  3701 

3. 3703 

3. 3707 

3.  3709 

39 

10 

3.3711 

3.  3713 

3. 3714 

3. 3716 

3.  3718 

3.  3720 

3. 3722 

3. 3724 

3.  3725 

3. 3727 

39 

20 

3. 3729 

3.  3731 

3. 3733 

3.  37.35 

3.  3736 

3.  3738 

3. 3740 

3. 3742 

3.3744 

3. 3746 

39 

30 

3. 3747 

3.3749 

3. 3751 

3. 3753 

3.  3755 

3. 3757 

3. 37.58 

3. 3760 

3. 3762 

3. 3764 

39 

40 

3. 3766 

3.  3768 

3. 3769 

3.  3771 

3.  3773 

3.  3775 

3. 3777 

3. 3779 

3. 3780 

3.  3782 

39 

50 

3. 3784 

3. 3786 

3.  3788 

3. 3789 

3.  3791 

3.  3793 

3. 3795 

3. 3797 

3. 3798  ■   3. 3800  1 

APPENDIX 

V:  TABLE  IX. 

[Page  317 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

5"   '    6" 

7" 

8"       S" 

c    / 

Qh  40.T 

II 
0» 

3. 3802 

3. 3804 

3. 3806 

3. 3808 

3. 3809 

3. 3811 

3. 3813 

3.  3815 

j 
3.3817^  3.3818 

40 

10 

3. 3820 

3.  3822 

3. 3824 

3.  3826 

3. 3827 

3. 3829 

3. 3831 

3.  3833 

3. 3835  1  3. 3836 

40 

20 

3. 3838 

3. 3840 

3. 3842 

3. 3844 

3.  3845 

3. 3847 

3. 3849 

3.  3851 

3.3852  3.3854 

40 

30 

3. 3856 

3.  3858 

3.  3860 

3. 3861 

3.  .3863 

3. 3865 

3. 3867 

3.  3869 

3.3870  3.3872 

40 

40 

3. 3874 

3.  3876 

3. 3877 

3. 3879 

3. 3881 

3. 3883 

3.  3885 

3. 3886 

3. 3888  1  3. 3890 

40 

50 

3. 3892 

3.  3893 

3. 3895 

3.  3897 

3. 3899 

3. 3901 

3. 3902 

3.  3904 

3. 3906 

3.  3908 

0  41 

0 

3. 3909 

3.3911 

3.  3913 

3.  3915 

3.  3916 

3.3918  3.3920 

3.  3922 

3. 3923 

3. 3925 

41 

10 

3. 3927 

3.  3929 

3.  3930 

3. 3932 

3.  3934 

3.3936  3.3938 

3. 3939 

3. 3941 

3. 3943 

41 

20 

3. 3945 

3.  3946 

3. 3948 

3. 3950 

3.  3952 

3.3953  3.3955 

3. 3957  3. 3959 

3. 3960 

41 

30 

3. 3962 

3.  3964 

3.  3965 

3. 3967 

3.  3969 

3. 3971 

3.  3972 

3. 3974 

3.  3976 

3. 3978 

41 

40 

3. 3979 

3. 3981 

3. 3983 

3.  3985 

3.  3986 

3. 3988 

3.  3990 

3. 3992 

3.  3993 

3. 3995 

41 

50 

0 

3. 3997 
3.  4014 

3.  3998 
3.  4016 

3.4000 
3.  4017 

3.4002 
3. 4019 

3.  4004 
3.  4021 

3. 4005 
3. 4023 

3.  4007 
3. 4024 

3. 4009 

3.4011 
3. 4028 

3.4012 

0  42 

3. 4026 

3. 4029 

42 

10 

3. 4031 

3.  4033 

3. 4035 

3.4036 

3.4038 

3. 4040 

3.  4041 

3. 4043 

3. 4045  1  3.  4047 

42 

20 

3. 4048 

3. 4050 

3. 4052 

3. 4053 

3. 4055 

3. 4057 

3. 4059 

3. 4060 

3. 4062  1  3. 4064 

42 

30 

3. 4065 

3.  4067 

3. 4069 

3. 4071 

3. 4072 

3. 4074 

3. 4076 

3. 4077 

3. 4079  i  3. 4081 

42 

40 

3. 4082 

3.  4084 

3.  4086 

3.  4087 

3. 4089 

3. 4091 

3. 4093 

3. 4094 

3. 4096  3. 4098 

42 

50 

3. 4099 

3.4101 

3. 4103 

3.  4104 

3. 4106 

3.  4108 

3. 4109 
"3. 4126 

3.4111 

3.4113  3.4115 

0  43 

0 

3.4116 

3.4118 

3.  4120 

3.4121 

3.4123  !  3.4125 

3. 4128 

3.  4130 

3.  4131 

43 

10 

3.  4133 

3.  4135 

3.4136 

3. 4138 

3. 4140  3. 4141 

3. 4143 

3.  4145 

3.  4146 

3.  4148 

43 

20 

3.  4150 

3.  4151 

3.  4153 

3.  4155 

3. 4156  3. 4158 

3.  4160 

3.  4161 

3.  4163 

3.  4165 

43 

30 

3.  4166 

3.  4168 

3. 4170 

3.4171 

3.4173  3.4175 

3.4176 

3.4178 

3.  4180 

3.4181 

43 

40 

3.  4183 

3.  4185 

3.  4186 

3.  4188 

3.4190  3.4191 

3.  4193 

3.  4195 

3.  4196 

3. 4198 

43 

50 

3. 4200 

3.  4201 

3.  4203 

3. 4205 

3. 4206 

3.  4208 
3.  4224 

3. 4209 
3.4226 

3.  4211 
3. 4228 

3.  4213 

3. 4214 

0  44 

0 

3. 4216 

3.4218 

3.4219 

3. 4221 

3. 4223 

3. 4229 

3.  4231 

44 

10 

3. 4232 

3. 4234 

3. 4236 

3. 4237 

3.4239  1  3.4241 

3. 4242 

3. 4244 

3.  4246 

3.  4247 

44 

20 

3. 4249 

3. 4250 

3. 4252 

3. 4254 

3.  4255  3.  4257 

3. 4259 

3. 4260 

3. 4262 

3. 4263 

44 

30 

3.  4265 

3. 4267 

3. 4268 

3. 4270 

3. 4272  3. 4273 

3. 4275 

3. 4276 

3. 4278 

3. 4280 

44 

40 

3. 4281 

3. 4283 

3. 4285 

3. 4286 

3. 4288  3. 4289 

3. 4291 

3. 4293 

3. 4294 

3. 4296 

44 
0  45 

50 
0 

3. 4298 
3.  4314 

3. 4299 
3.  4315 

3. 4301 

3. 4302 
3. 4318 

3. 4304 
3.  4320 

3. 4306 
3.4322 

3. 4307 

3. 4309 

3.  4310 
3.  4326" 

3.4312 
3. 4328 

3.4317 

3. 4323 

3. 4325 

45 

10 

3. 4330 

3. 4331 

3. 4333 

3. 4334 

3. 4336 

3. 4338 

3. 4339 

3. 4341 

3. 4342 

3.  4344 

45 

20 

3. 4346 

3. 4347 

3. 4349 

3.  4350 

3. 4352 

3.  4354 

3. 4355 

3. 4357 

3. 4358 

3.  4360 

45 

30 

3. 4362 

3. 4363 

3.  4365 

3. 4366 

3. 4368 

3. 4370 

3. 4371 

3. 4373 

3. 4374 

3. 4376 

45 

.40 

3. 4378 

3.  4379 

3. 4381 

3. 4382 

3. 4384 

3. 4385 

3. 4387 

3. 4389 

3. 4390 i  .3.  4392  | 

45 
0  46 

50 
0 

3. 4393 

3.  4395 
3.4411 

3. 4396 
3.  4412' 

3. 4398 
3.4414 

3.4400 
3.  4415 

3. 4401  3.  4403 
3.4417  1  3.4419 

3. 4404 

3. 4406 

3. 4408 

3. 4409 

3. 4420 

3.  4422 

3. 4423 

46 

10 

3. 4425 

3.  442(> 

3.4428 

3. 4429 

3. 4431 

3.4433  1  3.4434 

3.4436 

3. 4437 

3. 4439 

46 

20 

3. 4440 

3. 4442 

3.4444 

3.  4445 

3. 4447 

3.4448  i  3.4450 

3. 4451 

3. 4453 

3. 4454 

46 

30 

3.  4456 

3. 4458 

3.  4459 

3. 4461 

3. 4462 

3.4464  .3.4465 

3.4467 

3.  4468 

3. 4470 

46 

40 

3. 4472 

3. 4473 

3.  4475 

3. 4476 

3. 4478 

3.4479  3.4481 

3. 4482 

3. 4484 

3. 4486 

46 

50 

3. 4487 

3.  4489 

3. 4490 

3. 4492 

3. 4493 

3.4495  3.4496 

3. 4498 

3. 4499 

3. 4501 

0  47 

0 

3. 4502 

3.  4504 

3. 4506 

3. 4507 

3. 4509 

3.4510 

3. 4512 

3.4513 

3. 4515 

3. 4516 

47 

10 

3. 4518 

3. 4519 

3.  4521 

3. 4522 

3. 4524 

3. 4526 

3. 4527 

3.  4529 

3. 4530 

3. 45.32 

47 

20 

3. 4533 

3. 4535 

3. 4536 

3. 4538 

3. 4539 

3. 4541 

3. 4542 

3. 4544 

3.4545 

3. 4547 

47 

30 

3. 4548 

3. 4550 

3. 4551 

3. 4553 

3. 4555 

3. 4556 

3. 4558 

3.4559 

3. 4561 

3. 4562 

47 

40 

3. 4564 

3.  4565 

3. 4567 

3. 4568 

3. 4570 

3. 4571 

3.  4573 

3. 4574 

3.4576 

3. 4577 

47 

50 

3.  4579 

3.  4580 

3.  4582 

3. 4583 

3.4585  1  3.4586 

3. 4588 

3. 4589 

3. 4591 

3. 4592 

0  48 

0 

3. 4594 

3.  4595 

3. 4597 

3. 4598 

3. 4600 

3. 4601 

3. 4603 

3. 4604 

3. 4606  i  3. 4607  | 

48 

10 

3. 4609 

3. 4610 

3. 4612 

3. 4613 

3. 4615 

3.4616 

3.  4618 

3.  4619 

3. 4621 

3. 4622 

48 

20 

3. 4624 

3. 4625 

3.  4627 

3.  4628 

3. 4630 

3. 4631 

3. 4633 

3. 4634 

3. 4636 

3.  4637 

48 

30 

3. 4639 

3. 4640 

3.  4642 

3. 4643 

3. 4645 

3.  464(5 

3. 4648 

3.4649 

3. 4651 

3.  4652 

48 

40 

3. 4654 

3. 4655 

3. 4657 

3. 4658 

3. 4660 

3. 4661 

3. 4663 

3.4664 

3.  4666 

3.  4667 

48 

50 

3. 4669 

3. 4670 

3. 4672 

3. 4673 

3. 4675 

3.4676  1  3.4678 

3. 4679 

3. 4681 

3. 4682 

0  49 

0 

3. 4683 

3.  4685 

3. 4686 

3. 4688 

3. 4689 

3. 4691 

3. 4692 

3. 4694 

3.4695 

3. 4697 

49 

10 

3. 4698 

3. 4700 

3.  4701 

3.4703 

3. 4704 

3. 4706 

3. 4707 

3.4709 

3.  4710 

3.4711 

49 

20 

3. 4713 

3. 4714 

3.  4716 

3.4717 

3. 4719 

3. 4720 

3. 4722 

3.  4723 

3.  4725 

3.  4726 

49 

30 

3.  4728 

3. 4729 

3. 4730 

3. 4732 

3.  4733 

3. 4735 

3.  4736 

3. 4738 

3. 4739 

3. 4741 

49 

40 

3.  4742 

3.  4744 

3.  4745 

3. 4747 

3. 4748 

3. 4749 

3. 4751 

3. 4752 

3.  4754 

3. 4755 

49 

50 

3.  4757 

3.  4758 

3. 4760 

3.  4761 

3.  4763 

3. 4764 

3. 4765 

3.  4767 

3.  4768 

3. 4770 

Page  318] 

APPENDIX  V:  TABLE 

IX. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

7" 

Arc. 

0" 

1" 

2"      8"      *" 

5" 

6" 

8" 

9" 

O     1 

0"  50" 

0» 

3. 4771 

3. 4773 

3. 4774 

3. 4776 

3. 4777 

3.  4778 

3.  4780 

1 
3. 4781  '  3. 4783 

3. 4784 

50 

10 

3. 4786 

3. 4787 

3.  4789 

3. 4790 

3.  4791 

3.  4793 

3. 4794 

3.  4796  i  3. 4797 

3. 4799 

50 

20 

3. 4800 

3. 4802 

3. 4803 

3.4804 

3. 4806 

3.  4807 

3.  4809 

3. 4810 

3.  4812 

3. 4813 

50 

30 

3. 4814 

3. 4816 

3.4817 

3.  4819 

3. 4820 

3. 4822 

3. 4823 

3. 4824 

8.  4826 

3. 4827 

50 

40 

3. 4829 

►  3. 4830 

3. 4832 

3. 4833 

3. 4834 

3. 4836 

3. 4837 

3.  4839 

8.  4840 

3. 4842 

50 

50 

3. 4843 

3. 4844 

3. 4846 

3. 4847 

3.4849 

3. 4850 

3. 4852 

3. 4858 

3. 4854 

3.  4856 

0  51 

0 

3.4857 

3.  4859 

3.4860 

3. 4861 

3. 4863 

3. 4864 

3. 4866 

3.  4667 

3. 4869 

8.  4870 

51 

10 

3. 4871 

3.  4873 

3.  4874 

3. 4876 

3. 4877 

3. 4878 

3. 4880 

8.  4881 

3. 4883 

8.  4884 

51 

20 

3. 4886 

3. 4887 

3.  4888 

3.4890 

3.  4891 

3. 4893 

3. 4894 

8. 4895 

3. 4897 

8.  4898 

51 

30 

3. 4900 

3.  4901 

3. 4902 

3. 4904 

3. 4905 

3. 4907 

3. 4908 

8. 4909 

3. 4911 

8. 4912 

51 

40 

3. 4914 

3.  4915 

3. 4916 

3. 4918 

3.4919 

3. 4921 

3.  4922 

3. 4923 

3. 4925 

3. 4926 

51 

50 

3. 4928 

3.  4929 

3. 4930 

3. 4932 

3. 4933 

3. 4935 

3.  4936 

3. 4987 

3. 4939 

3. 4940 

0  52 

0 

3. 4942 

3.  4943 

3. 4944 

3. 4946 

3. 4947 

3. 4949 

3.  4950 

8. 4951 

3. 4953 

8. 4954 

52 

10 

3. 4955 

3.  4957 

3. 4958 

3. 4960 

3. 4961 

3. 4962 

3. 4964 

3. 4965 

3. 4967 

8.4968 

.52 

20 

3. 4969 

3. 4971 

3. 4972 

3. 4973 

3. 4975 

3.  4976 

3. 4978 

3.  4979 

3. 4980 

8. 4982 

52 

30 

3. 4983 

3. 4984 

3.  4986 

3.4987  1  3.4989 

3.  4990 

3. 4991 

3.  4998 

3.  4994 

8.  4995 

52 

40 

3.4997 

3. 4998 

3. 5000 

3.5001  !  3.5002 

3.  5004 

3. 5005 

3.  5006 

3. 5008 

8. 5009 

52 

50 

3.5011 

3.  5012 

3.  5013 

3.  5015 

3. 5016 
3. 5030 

3. 5017 
3.5031 

3. 5019 
3.5032 

3. 5020 
3.5034 

3. 5022 
3.5035 

8. 5023 

0  53 

0 

3. 5024 

3.  5026 

3. 5027 

3. 5028 

8.  5037 

53 

10 

3. 5038 

3.  5039 

3.5041 

3.  5042 

3.  5043 

3. 5045 

3.  5046 

3. 5047 

3.  5049 

8.  5050 

53 

20 

3. 5051 

3.  5053 

3. 5054 

3. 5056 

3. 5057 

3. 5058 

3. 5060 

3.5061  13.5062 

3. 5064 

53 

30 

3. 5065 

3.  5066 

3. 5068 

3. 5069 

3. 5070 

3. 5072 

3. 5073 

3.  5075 

3.  5076 

8.  5077 

53 

40 

3. 5079 

3.  5080 

3.5081 

3.  5083 

3. 5084 

3. 5085 

3. 5087 

3.  5088 

8. 5089 

8. 5091 

53 

50 

3. 5092 

3. 5093 

3. 5095 

3. 5096 

3. 5097 

3. 5099 

3. 5100 

3.  5101 

3.5103 

8. 5104 

0  54 

0 

3.  5105 

3.  5107 

3. 5108 

3.  5109 

3.5111 

3.5112 

3.5113 

3.5115 

5.5116 

8.5117 

54 

10 

3.5119 

3.5120 

3.5122 

3.5123 

3.  5124 

3. 5126 

3.  5127 

3.5128 

8.5180 

8.  5131 

54 

20 

3.  5132 

3.  5134 

3.5135 

3.  5136 

3.  5138 

3. 5139 

3.  5140 

3.5141 

8.5143 

3.  5144 

54 

30 

3.  5145 

3.  5147 

3.5148 

3.  5149 

3.  5151 

3. 5152 

3.  5153 

3.  5155 

3.5156 

8.5157 

54 

40 

3.  5159 

3. 5160 

3.  5161 

3.5163 

3.  5164 

3. 5165 

3. 5167 

3.  5168 

3. 5169 

3.5171 

54 

50 

3.5172 

3. 5173 

3.  5175 

3.5176 

3.5177 

3. 5179 

3.  5180 

3.5181 

3.  5183 

3.5184 

0  55 

0 

3.  5185 

3. 5186 

3. 5188 

3.  5189 

3. 5190 

3. 5192 

3. 5193 

3.  5194 

3.  5196 

3.  5197 

55 

10 

3.  5198 

3. 5200 

3.  5201 

3. 5202 

3. 5204 

3. 5205 

3. 5206 

3. 5207 

3. 5209 

3.  5210 

55 

20 

3.  5211 

3.5213 

3.5214 

3.  5215 

3.  5217 

3. 5218 

3. 5219 

8. 5221 

8. 5222 

3.  5228 

55 

30 

3. 5224 

3.  5226 

3. 5227 

3.  5228 

3. 5230 

3.  5231 

3.  5232 

3. 5234 

3. 5235 

3.  5286 

55 

40 

3. 5237 

3. 5239 

3. 5240 

3.  5241 

3. 5243 

3. 5244 

3.  5245 

3. 5247 

3.  5248 

3.  5249 

55 

50 

3. 5250 

3. 5252 

3. 5253 

3.5254  3.5256 

3. 5257 

3.  5258 
3. 5271 

3. 5260 
3. 5272 

8. 5261 
3. 5274 

3. 5262 

0  56 

0 

3.  5263 

3.  5265 

3. 5266 

3.5267  1  3.5269 

3. 5270 

3. 5275 

56 

10 

3. 5276 

3. 5278 

3.  5279 

3. 5280 

3. 5281 

3. 5283 

3.  5284 

3. 5285 

3. 5287 

3. 5288 

56 

20 

3. 5289 

3. 5290 

3.  5292 

3. 5293 

3. 5294 

3. 5296 

3.  5297 

8. 5298 

3. 5299 

8.  5801 

56 

30 

3. 5302 

3. 5303 

3. 5305 

3. 5306 

3. 5307 

3. 5308 

3. 5310 

3.  5311 

3. 5312 

3. 5314 

56 

40 

3. 5315 

3. 5316 

3.  5317  3. 5319 

3. 5320 

3. 5321 

3. 5322 

3. 5324 

3. 5325 

3. 5326 

56 

50 

3. 5328 

3. 5329 

3. 5330  3. 5331  3. 5333 

3. 5334 

3.  5835 

3. 5336 

3. 5388 

3.  5339 

0  57 

0 

3. 5340 

3. 5342 

3.5343  1  3.5344  3.5345 

3. 5347 

3.  5348 

3. 5849 

3. 5850 

8.  5352 

57 

10 

3. 5353 

3.  5854 

3. 5355 

3. 5357 

3. 5358 

3.  5359 

3. 5361 

3. 5862 

3. 5363 

3. 5364 

57 

20 

3. 5366 

3. 5367 

3.  5368 

3. 5369 

3. 5371 

3. 5372 

3. 5373 

3. 5374 

3. 5376 

3. 5377 

57 

30 

3. 5378 

3. 5379 

3. 5381 

3. 5382 

3. 5383 

3. 5384 

3. 5386 

3. 5387 

3. 5388 

8. 5390 

57 

40 

3. 5391 

3. 5392 

3. 5393 

3. 5395 

3. 5396 

3. 5397 

3. 5398 

3. 5400 

3. 5401 

3. 5402 

57 

50 

3. 5403 

3.  5405 

3.5406 

3. 5407 

3. 5408 
3. 5421 

3.5410 
3. 5422 

3.  5411 
3.5428 

3.  5412 
8.  5425 

3. 5413 
375426 

3.  5415 

0  58 

0 

3. 5416 

3.  5417 

3.5'418  ;  3.5420 

3. 5427 

58 

10 

3. 5428 

3. 5429 

3.5431  1  3.5432 

3. 5433 

3. 5434 

3. 5436 

3.  5437 

3.  5438 

8. 5489 

58 

20 

3. 5441 

3. 5442 

3.5443  j  3.5444 

3.5446 

3. 5447 

3. 5448 

3. 5449 

3. 5451 

3. 5452 

58 

30 

3. 5453 

3. 5454 

.3.5456  i  3.5457 

3. 5458 

3. 5459 

3. 5460 

3.  5462 

3. 5463 

3. 5464 

58 

40 

3. 5465 

3. 5467 

3.5468  i  3.5469  3.5470 

3. 5472 

3. 5473 

3. 5474 

8.  5475 

3.5477 

58 

50 

3. 5478 

3. 5479 

3.5480  1  3.5481   3.5483 

3. 5484 

3. 5485 

3.  5486 

8.  5488 

3. 5489 

0  59 

0 

3. 5490 

3. 5491 

3.5492  j  3.5494  3.5495 

3.  5496 

3. 5497 

3. 5499  8. 5500 

3. 5501 

59 

10  3. 5502 

3. 5504 

3.5505  i  3.5506  3.5507 

3. 5508 

3. 5510 

3.5511 

3. 5512 

3.5518 

59 

20  3.5514 

3. 5516 

3. 5517 

3. 5518  3.  5519 

3.  5521 

3. 5522 

8. 5528 

3. 5524 

3. 5525 

59 

30 

3. 5527 

3. 5528 

3. 5529 

3. 5530  3. 5532 

3. 5533 

3. 5534 

3. 5535 

8.  5536 

3. 5538 

59 

40 

3. 5539 

3. 5540 

3.5541 

3.5542  1  3.5544 

3. 5545 

3. 5546 

3. 5547 

8. 5549 

3. 5550 

59 

50 

3.  5551 

3. 5552 

3. 5553 

3.5555  1  3.5556 

3. 5557 

3. 5558 

3. 5559 

3. 5561 

3. 5562 

APPENDIX 

Y:  TABl^E  IX. 

[Page  319 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Are. 

0" 

1" 

2" 

3" 

4" 

5" 

6" 

7" 

8"   j    9" 

0    / 

Ih  0" 

0^ 

3. 5563 

3.  5564 

3. 5565 

3. 5567 

3. 5568 

3. 5569 

3. 5570 

3. 5571 

3. 55^3 

3. 5574 

0 

10 

3. 5575 

3. 5576 

3. 5577 

3. 5579 

3.  5580  ' 

3.  5581 

3. 5582 

3. 5583 

3. 5585 

3. 5586 

0 

20 

3.  5587 

3. 5588 

3. 5589 

3. 5591 

3. 5592 

3. 5593 

3. 5594 

3. 5595 

3. 5597 

3. 5598 

0 

30 

3. 5599 

3. 5600 

3. 5601 

3. 5603 

3. 5604 

3. 5605 

3. 5606 

3. 5607 

3. 5609 

3. 5610 

0 

40 

3.  5611 

3. 5612 

3. 5613 

3.  5615 

3.5616 

3.5617 

3.  5618 

3. 5619 

3. 5621 

3. 5622 

0 

50 

3.  5623 

3.  5624 

3.  5625 

3.  5626 

3. 5628 

3. 5629 

3.  5630 

3. 5631 

3. 5632 

3.  5634 

.  1  1 

0 

3.  5635 

3.  5636 

3. 5637 

3.  5638 

3. 5640 

3.  5641 

3. 5642 

3. 5643 

3. 5644 

3. 5645 

10 

3.  5647 

3. 5648 

3. 5649 

3.  5650 

3. 5651 

3. 5653 

3. 5654 

3. 5655 

3. 5656 

3. 5657 

20 

3.  5658 

3.  5660 

3. 5661 

3.  5662 

3. 5663 

3. 5664 

3. 5666 

3. 5667 

3. 5668 

3. 5669 

30 

3. 5670 

3. 5671 

3. 5673 

3. 5674 

3. 5675 

3. 5676 

3. 5677 

3. 5678 

3. 5680 

3. 5681 

40 

3. 5682 

3. 5683 

3. 5684 

3. 5686 

3. 5687 

3. 5688 

3.  5689 

3. 5690 

3. 5691 

3. 5693 

50 

3.  5694 

3.  5695 

3. 5696 

3. 5697 

3. 5698 

3. 5700 

3. 5701 

3. 5702 

3. 5703  i  3.  5704 

1  2 

0 

3.  5705 

3.  5707 

3.  5708 

3. 5709 

3.5710 

3.5711 

3.5712 

3.  5714 

3.5715  3.5716 

2 

10 

3.5717 

3.5718 

3. 5719 

3. 5721 

3. 5722 

3. 5723 

3. 5724 

3.  5725 

3. 5726  ]  3. 5728 

2 

20 

3. 5729 

3. 5730 

3.  5731 

3. 5732 

3. 5733 

3. 5735 

3. 5736 

3. 5737 

3. 5738  !  3. 5739 

2 

30 

3. 5740 

3.  5741 

3. 5742 

3. 5744 

3. 5745 

3. 5746 

3. 5747 

3. 5748 

3. 5750  1  3. 5751 

2 

40 

3.  5752 

3. 5753 

3. 5754 

3. 5755 

3. 5756 

3. 5758 

3. 5759 

3. 5760 

3. 5761  3. 5762 

2 

50 

3.  5763 

3. 5765 

3.  5766 

3. 5767 

3. 5768 

3.  5769 

3. 5770 

3. 5771 

3.5773  3.5774 

1  3 

0 

3.  5775 

3. 5776 

3.5777 

3. 5778 

3. 5780 

3.  5781 

3. 5782 

3. 5783 

3. 5784  i  3. 5785 

3 

10 

3.  5786 

3.  5788 

3. 5789 

3. 5790 

3.  5791 

3.  5792 

3. 5793 

3. 5794 

3. 5796 

3.  5797 

3 

20 

3.  5798 

3. 5799 

3. 5800 

3.  5801 

3.  5802 

3. 5804 

3. 5805 

3.5806 

3. 5807 

3.  5808 

3 

30 

3.  5809 

3.  5810 

3. 5812 

3. 5813 

3. 5814 

3.5815 

3.  5816 

3.  5817 

3. 5818 

3.  5819 

3 

40 

3. 5821 

3.  5822 

3.  5823 

3. 5824 

3. 5825 

3. 5826 

3. 5827 

3.5829 

3. 5830 

3. 5831 

3 

50 

3.  5832 

3.  5833 

3. 5834 

3. 5835 

3. 5837 

3. 5838 

3.  5839 

3. 5840 

3. 5841 

3. 5842 

1  4 

0 

3.  5843 

3.  5844 

3. 5846 

3. 5847 

3. 5848 

3. 5849 

3. 5850 

3. 5851 

3. 5852  1  ;i  5853 

4 

10 

3.  5855 

3.  5856 

3. 5857 

3. 5858 

3. 5859 

3. 5860 

3. 5861 

3. 5862 

3. 5864  1  3. 5865 

4 

20 

3. 5866 

3. 5867 

3. 5868 

3. 5869 

3. 5870 

3.  5871 

3. 5873 

3. 5874 

3. 5875  3. 5876 

4 

30 

3. 5877 

3. 5878 

3. 5879 

3. 5880 

3. 5882 

3. 5883 

3. 5884 

3. 5885 

3.5886  3.5887 

4 

40 

3. 5888 

3.  5889 

3. 5891 

3. 5892 

3. 5893 

3. 5894 

3. 5895 

3. 5896 

3. 5897  1  3. 5898 

4 

50 

3. 5899 

3.  5901 

3. 5902 

3^.  5903 

3.5904 

3. 5905 

3. 5906 

3. 5907 

3.  5908 

3. 5910 

1  5 

0 

3.5911 

3. 5912 

3.  5913 

3. 5914 

3. 5915 

3.  5916 

3.5917 

3. 5918 

3. 5920 

3. 5921 

5 

10 

3. 5922 

3. 5923 

3. 5924 

3. 5925 

3.  5926 

3. 5927 

3. 5928 

3. 5930 

3. 5931 

3. 5932 

5 

20 

3. 5933 

3.5934 

3.  5935 

3. 5936 

3. 5937 

3. 5938 

3. 5940 

3. 5941 

3. 5942 

3. 5943 

5 

30 

3. 5944 

3. 5945 

3. 5946 

3. 5947 

3. 5948 

3. 5949 

3. 5951 

3. 6952 

3. 5953 

3. 5954 

5 

.40 

3. 5955 

3. 5956 

3. 5957 

3. 5958 

3.  5959 

3. 5960 

3. 5962 

3. 5963 

3.5964 

3. 5965 

5 

50 

3.  5966 

3.  5967 

3.  5968  3. 5969 

3.  5970 

3. 5971 

3. 5973 

3. 5974 

3. 5975 

3. 5976 

1  6 

0 

3.  5977 

3. 5978 

3. 5979 

3. 5980 

3. 5981 

3. 5982 

3. 5984 

3. 5985 

3. 5986 

3. 5987 

6 

10 

3.  5988 

3.  5989 

3.  5990 

3. 5991 

3. 5992 

3. 5993 

3.  5994 

3. 5996 

3. 5997 

3. 5998 

6 

20 

3. 5999 

3.  6000 

3.  6001 

3. 6002 

3. 6003 

3.6004 

3.  6005 

3. 6006 

3. 6008 

3.  6009 

6 

30 

3.  6010 

3. 6011 

3.  6012 

3.  6013 

3. 6014 

3. 6015 

3.  6016 

3. 6017 

3.  6018 

3.  6020 

6 

40 

3.  6021 

3.  6022 

3.  6023 

3.  6024 

3. 6025 

3. 6026 

3. 6027 

3. 6028 

3. 6029 

3. 6030 

6 

50 

3.  6031 

3. 6033 

3.  6034 

3. 6035 

3. 6036 

3. 6037 

3.  6038 

3. 6039 

3. 6040 

3. 6041 

1  7 

0 

3.6042 

3. 6043 

3. 6044 

3. 6046 

3. 6047 

3.6048 

3. 6049 

3. 6050 

3. 6051 

3. 6052 

7 

10 

3. 6053 

3.  6054 

3.  6055 

3. 6056 

3. 6057 

3. 6058 

3. 6060 

3. 6061 

3. 6062 

3. 6063 

7 

20 

3. 6064 

3.  60a5 

3.  6066 

3. 6067 

3. 6068 

3. 6069 

3. 6070 

3. 6071 

3. 6072 

3.  6073 

7 

30 

3. 6075 

3. 6076 

3.  6077 

3.  6078 

3. 6079 

3. 6080 

3. 6081 

3. 6082 

3. 6083 

3.  6084 

7 

40 

3. 6085 

3.  6086 

3.  6087 

3. 6088 

3. 6090 

3. 6091 

3. 6092 

3. 6093 

3. 6094  3. 6095 

7 

50 

3. 6096 

3.  6097 

3.  6098 

3. 6099 

3.6100 

3. 6101 

3. 6102 

3. 6103 

3. 6104  j  3. 6106 

1  8 

0 

3.  6107 

3.  6108 

3.6109  ;  3.6110 

3.6111 

3.6112 

3.6113 

3.6114 

3.6115  i  3.6116 

8 

10 

3. 6117 

3.6118 

3.6119  i  3.6120 

3.  6121 

3. 6123 

3.  6124 

3.6125 

3.6126  3.6127 

8 

20 

3.  6128 

3.6129 

3.6130  1  3.6131 

3.  6132 

3. 6133 

3.  6134 

3.  6135 

3. 6136 

3.  6137 

8 

30 

3.  6138 

3.  6139 

3.6141  i  3.6142 

3.  6143 

3. 6144 

3.  6145 

3. 6146 

3. 6147 

3. 6148 

8 

40 

3.  6149 

3.  6150 

3.6151  i  3.6152 

3.  6153 

3. 6154 

3.  6155 

3. 6156 

3.  6157 

3.  6158 

8 

50 

3.  6160 

3.  6161 

3.6162  i  3.6163 

3.  6164 

3. 6165 

3.  6166 

3. 6167 

3.  6168 

3.  6169 
3.  6179 

1  9 

0 

3.6170 

3.6171 

3.  6172 

3. 6173 

3.  6174 

3. 6175 

3. 6176 

3. 6177 

3. 6178 

9 

10 

3. 6180 

3. 6182 

3. 6183 

3. 6184 

3.  6ia5 

3. 6186 

3. 6187 

3. 6188 

3. 6189 

3.  6190 

9 

20 

3.  6191 

3.6192 

3.  6193 

3. 6194 

3. 6195 

3. 6196 

3. 6197 

3.6198 

3. 6199 

3.  6200 

9 

30 

3. 6201 

3. 6202 

3.  6203 

3.  6204 

3.6206 

3. 6207 

3. 6208 

3.  6209 

3.6210  3.6211 

9 

40 

3.  6212 

3.  6213 

3. 6214 

3. 6215 

3.  6216 

3. 6217 

3. 6218 

3.  6219 

3. 6220  3. 6221 

9 

50 

3.  6222 

3. 6223 

3.6224  1  3.6225 

3.  6226 

3. 6227 

3. 6228 

3. 6229 

3. 6230  3. 6231 

Page  320J 

APPENDIX 

V:  TABLE  IX. 

Logarithm 

;!  of  Small  Arcs  in  Space  or 

Time. 

Are. 

0" 

1" 

3. 6235 

8" 

4"      5" 

6" 

«" 

8"   1    9" 

O     ' 

1"  10" 

0* 

3.  6232 

3. 6234 

3.  6236 

3. 6237  3. 6238  i  3. 6239 

3.  6240 

3.  6241  1  3.  6242 

10 

10 

3.  «)243 

3.  6244 

3. 6245 

3. 6246 

3. 6247 

3. 6248 

3. 6249 

3.  6250 

3. 6251  3. 6252 

10 

20 

3.  (5253 

3.  6254 

3. 6255 

3.  6256 

3. 6257 

3. 6258 

3. 6259 

3. 6260 

3. 6261  1  3. 6262 

10 

30 

3.  6263 

3.6264 

3. 6265 

3. 6266 

3. 6268 

3.  6269 

3. 6270 

3. 6271 

3. 6272  !  3. 6273 

10 

40 

3. 6274 

»3. 6275 

3. 6276 

3. 6277 

3.6278 

3. 6279 

3.  6280 

3. 6281 

3. 6282  3. 6283 

10 

50 

3. 6284 

3. 6285 

3. 6286 

3. 6287 
3. 6297 

3. 6288 
3. 6298 

3. 6289 
3. 6299 

3.6290 
376300 

3.  6291 
3. 6301 

3. 6292  3. 6293 
3.6302  1  3.6303 

1   11 

0 

3.  6294 

3. 6295 

3.6296 

11 

10 

3.  6304 

3. 6305 

3.  630() 

3.  6307 

3. 6308 

3. 6309 

3. 6310 

3.6311 

3. 6312  3. 6313 

11 

20 

3.  6314 

3.  6315 

3.6316 

3. 6317 

3. 6318 

3. 6320 

3. 6321 

3.  6322 

3. 6323  3. 6324 

11 

30 

3.  6325 

3. 6326 

3. 6327 

3. 6328 

3. 6329 

3. 6330 

3. 6331 

3. 6332 

3.  6333  3.  6334 

11 

40 

3.  6335 

3. 6336 

3. 6337 

3. 6338 

3. 6339 

3. 6340 

3.  6341 

3. 6342 

3. 6343  i  3. 6344 

11 

50 

3.  6345 

3. 6346 

3. 6347 

3. 6348 

3.  6349 

3. 6350 

3. 6351 

3. 6352 

3. 6353  !  3. 6354 

1  12 

0 

3.  6355 

"3.6356 

3. 6357 

3. 6358 

3. 6359 

3. 6360 

3.  6361 

3.6362 

3. 6363  1  3. 6364 

12 

10 

3.  6365 

3. 6366 

3. 6367 

3. 6368 

3. 6369 

3. 6370 

3. 6371 

3.  6372 

3.  6373  i  3. 6374 

12 

20 

3.  6375 

3. 6376 

3. 6377 

3. 6378 

3. 6379 

3.  6380 

3. 6381 

3.  6382 

3.  6383 

3.  6384 

12 

30 

3. 6385 

3.  6386 

3. 6387 

3. 6388 

3. 6389 

3.  6390 

3. 6391 

3.  6392 

3. 6393 

3.  6394 

12 

40 

3. 6395 

3.  6396 

3. 6397 

3.  6398 

3. 6399 

3.  6400 

3. 6401 

3.  6402 

3.  6403 

3. 6404 

12 

50 

3.6405 

3. 6406 

3. 6407 

3. 6408 
3. 6418 

3. 6409 
3.6419 

3.6410 

3.6411 

3.  6412 
3. 6422 

3. 6413 
3. 6423 

3.  6414 
3.6424  " 

1  13 

0 

3. 6415 

3.  6416 

3. 6417' 

3. 6420 

3. 6421 

13 

10 

3.  6425 

3. 6426 

3. 6427 

3. 6428 

3. 6429 

3. 6430 

3.  6431 

3. 6432 

3. 6433 

3.  6434 

13 

20 

3.  6435 

3. 6436 

3. 6437 

3. 6437 

3. 6438  3.  6439 

3. 6440 

3. 6441 

3.  6442  3.  6443 

18 

30 

3.  6444 

3. 6445 

3.  644(5 

3.64-17 

3.6448 

3. 6449 

3.6450  1  3.6451 

3.  6452  i  3. 6453 

13 

40 

3.  6454 

3. 6455 

3. 6456 

3.  6457 

3. 6458 

3. 6459 

3. 6460 

3. 6461 

3.6462  3.6463 

13 

50 

3.  6464 

3.  6465 

3. 6466 

3. 6467 

3. 6468 

3.6469 

3. 6470 

3.6471 

3.  6472  3.  6473 

1  14 

.  0 

3.  6474 

3.  6475 

3. 6476 

3. 6477 

3. 6478 

3. 6479 

3. 6480 

3. 6481 

3.  6482  1  3.  6483 

14 

10 

3. 6484 

3.  6485 

3. 6486 

3. 6487 

3. 6488 

3. 6488 

3.  6489 

3.  6490 

3. 6491  I  3. 6492 

14 

20 

3.  6493 

3. ^494 

3. 6495 

3. 6496 

3. 6497 

3. 6498 

3.6499 

3.  6500 

3. 6501  !  3.  6502 

14 

30 

3. 6503 

3. 6504 

3. 6505 

3.  6506 

3. 6507 

3. 6508 

3. 6509 

3.  6510 

3.6511  1  3.6512 

14 

40 

3. 6513 

3. 6514 

3.  6515 

3. 6516 

3.  6517 

3. 6518 

3.6519 

3.  6520 

3. 6521  i  3. 6521 

14 

50 

3.  6522 

3. 6523 

3. 6524 

3. 6525 

3.  6.526 

3. 6527 

3. 6528 
3.  6538 

3. 6529 
3.  6539 

3. 6530 
"3.  6540 

3. 6531 

1  15 

0 

3. 6532 " 

3. 6533 

3. 6534 

3.  6535 

3. 6536 

3.  6537^ 

3.  6541 

15 

10 

3. 6542 

3.  6543 

3. 6544 

3. 6545 

3. 6546 

3. 6547 

3. 6548 

3. 6549 

3.6549  3.6550  1 

15 

20 

3.  6551 

3. 6552 

3. 6553 

3. 6554 

3.6555  i  3.6556 

3. 6557 

3.  6558 

3.6559  3.6560  | 

15 

30 

3. 6561 

3. 6562 

3. 6563 

3. 6564 

3.  6565 

3. 6566 

3. 6567 

3. 6568 

3. 6569 

3. 6570 

15 

40 

3. 6571 

3. 6572 

3. 6572 

3. 6573 

3.  6574 

3. 6575 

3.  6576 

3. 6577 

3. 6578 

3. 6579 

15 

50 

3. 6580 

3. 6581 
3. 6591 

3. 6582 
3. 6592 

3. 6583 

3.  6584 

3. 6585 

3. 6586 

3.  6587 

3. 6588 

3. 6589 

1  16 

0 

3. 6590 

3. 6593 

3.  6593" 

3. 6594 

3. 6595 

3.  6596 

3.6597 

3. 6598 

16 

10 

3.  6599 

3. 6600 

3.  6601 

3. 6602 

3.  6603 

3. 6604 

3. 6605 

3.  6606 

3. 6607  !  3. 6608  | 

16 

20 

3.  6609 

3. 6610 

3.6611 

3.6611 

3. 6612 

3.  6613 

3.  6614 

3.  6615 

3. 6616 

3. 6617 

16 

30 

3. 6618 

3. 6619 

3. 6620 

3. 6621 

3.  6622 

3. 6623 

3.  6624 

3. 6625 

3. 6626 

3. 6627 

16 

40 

3. 6628 

3. 6629 

3. 6629 

3. 6630 

3. 6631 

3. 6632 

3.  6633 

3. 6634 

3. 6635 

3. 6636 

16 

50 

3. 6637 

3.  6638 

3. 6639 

3.  6640 

3. 6641 

3. 6642 

3.  6643 

3.  6644 

3. 6645 

3. 6645 

1  17 

0 

3. 6646^ 

3. 6647 

3.6648 

3.  6649 

3.  6650  3. 6651 

3.  6652 

3.  6653 

3. 6654 

3. 6655 

17 

10 

3. 6656 

3. 6657 

3. 6658 

3. 6659 

3.  6660  3. 6660 

3.  6661 

3. 6662 

3. 6663 

3. 6664 

17 

20 

3.  6665 

3. 6666 

3. 6667 

3. 6668 

3.6669  j  3.6670 

3. 6671 

3.  6672 

3. 6673 

3. 6674 

17 

30 

3. 6675 

3.  6675 

3.  6676 

3. 6677 

3.6678  '  3.6679 

3.  6680 

3. 6681 

3. 6682 

3. 6683 

17 

40 

3. 6684 

3. 6685 

3. 6686 

3. 6687 

3. 6688 

3. 6689 

3. 6689 

3. 6690 

3. 6691 

3. 6692 

17 

50 

3. 6693 

3. 6694 
"3.6703 

3.  6695 
3. 6704 

3. 6696 

3. 6697 

3. 6698 
"3. 6707" 

3. 6699 

3. 6700 

3. 6701 
3.  6710 

3.  6702 
3.6711 

1  18 

0 

3.  6702 

3.  6705 

3. 6706 

3.  6708 

3. 6709 

18 

10 

3. 6712 

3. 6713 

3. 6714 

3.  6715 

3.6715 

3.6716 

3.6717 

3. 6718 

3.  6719 

3. 6720 

18 

20 

3. 6721 

3.  6722 

3. 6723 

3.  6724 

3.  6725 

3. 6726 

3.  6727 

3. 6727 

3.  6728 

3. 6729 

18 

30 

3.  6730 

3.  6731 

3. 6732 

3. 6733 

3. 6734 

3.  6735 

3. 6736 

3. 6737 

3.  6738 

3. 6738 

18 

40 

3. 6739 

3.  6740 

3. 6741 

3. 6742 

3.  6743 

3.  6744 

3. 6745 

3.  6746 

3.  6747 

3. 6748 

18 

50 

3. 6749 

3. 6750 
3.6759 

3. 6750 
3. 6760 

3.  6751 
3.  6761 

3.  6752 

3.  6753 

3.  6754 

3. 6755 

3.  6756 

3. 6757 

1  19 

0 

3. 6758 

3.  6761 

3. 6762 

3.  6763 

3.  6764" 

3.  6765 

3.6766 

19 

10 

3. 6767 

3. 6768 

3. 6769 

3.  6770 

3. 6771 

3. 6772 

3.  6772 

3. 6773 

3. 6774 

3.  6775 

19 

20 

3. 6776 

3. 6777 

3. 6778 

3.  6779 

3. 6780 

3. 6781 

3.  6782 

3. 6782 

3. 6783 

3.  6784 

19 

30 

3. 6785 

3. 6786 

3. 6787 

3.  6788 

3. 6789 

3. 6790 

3.  6791 

3. 6792 

3. 6792 

3.  6793 

19 

40 

3. 6794 

3.  6795 

3. 6796 

3.  6797 

3. 6798 

3. 6799 

3.  6800 

3. 6801 

3.  6802 

3. 6802 

19 

50 

3.  6803 

3.  6804 

3. 6805 

3.  6806 

3. 6807 

3. 6808 

3.  6809 

3. 6810 

3. 6811 

3. 6812 

APPENDIX  V:  TABLE  IX. 

[Page  321  | 

Logarithms  of  Small  Arcs  in 

Space  or 

Time. 

Arc. 

0" 

1" 

2" 

3" 

4" 

5" 

6" 

7" 

8" 

9" 

o    / 

1»  20'" 

0« 

3.  6812 

3.  6813 

3.  6814 

3.  6815 

3.  6816 

3.  6817 

3.  6818 

3.  6819 

3.  6820 

3. 6821 

20 

10 

3. 6821 

3.  6822 

3.  6823 

3. 6824 

3.  6825 

3.  6826 

3.  6827 

3. 6828 

3.  6829 

3. 6830 

20 

20 

3. 6830 

3.  6831 

3.  6832 

3. 6833 

3. 6834 

3.  6835 

3. 6836 

3. 6837 

3. 6838 

3. 6839 

20 

30 

3.  6839 

3.  6840 

3.  6841 

3. 6842 

3. 6843 

3. 6844 

3. 6845 

3.  6846 

3.  6847 

3. 6848 

20 

40 

3.  6848 

3.  6849 

3.  6850 

3.  6851 

3. 6852 

3. 6853 

3.  6854 

3. 6855 

3. 6856 

3.  6857 

20 

50 

3.  6857 

3. 6858 

3.  6859 

3.  6860 

3. 6861 

3. 6862 

3. 6863 

3. 6864 

3. 6865 

3.6865 

1  21 

0 

3. 6866 

3. 6867 

3. 6868 

3.  6869 

3. 6870 

3. 6871 

3. 6872 

3. 6873 

3. 6874 

3. 6874 

21 

10 

3.  6875 

3. 6876 

3. 6877 

3.  6878 

3. 6879 

3. 6880 

3. 6881 

3. 6882 

3. 6882 

3.  6883 

21 

20 

3.  6884 

3.  6885 

3. 6886 

3.  6887 

3. 6888 

3. 6889 

3. 6890 

3. 6890 

3. 6891 

3. 6892 

21 

30 

3. 6893 

3. 6894 

3. 6895 

3. 6896 

3.  6897 

3. 6898 

3. 6898 

3. 6899 

3. 6900 

3. 6901 

21 

40 

3.  6902 

3. 6903 

3. 6904 

3.  6905 

3.  6906 

3. 6906 

3. 6907 

3. 6908 

3.6909 

3. 6910 

21 

50 

3.6911 

3. 6912 

3. 6913 

3. 6913 

3.6914 
3. 6923 

3.  6915 

3.  6916 

3.6917 

3. 6918 
3. 6927 

3.  6919 

1  22 

0 

3. 6920 

3.  6921 

3. 6921 

3. 6922 

3. 6924 

3. 6925 

3.  6926 

3. 6928 

22 

10 

3. 6928 

3. 6929 

3. 6930 

3. 6931 

3. 6932 

3. 6933 

3.  6934 

3. 6935 

3. 6936 

3. 6936 

22 

20 

3. 6937 

3. 6938 

3. 6939 

3. 6940 

3. 6941 

3. 6942 

3.  6943 

3. 6943 

3. 6944 

3. 6945 

22 

30 

3. 6946 

3.  6947 

3. 6948 

3. 6949 

3.  6950 

3. 6950 

3. 6951 

3.  6952 

3. 6953 

3. 6954 

22 

40 

3.  6955 

3. 6956 

3. 6957 

3. 6957 

3. 6958 

3. 6959 

3. 6960 

3. 6961 

3. 6962 

3. 6963 

22 

50 

3.6964 

3.6964 

3. 6965 

3. 6966 

3. 6967 

3. 6968 

3. 6969 

3.  6970 

3. 6971 

3.  6971 

1  23 

0 

3.  6972 

3.  6973 

3. 6974 

3. 6975 

3.  6976 

3. 6977 

3. 6978 

3. 6978 

3. 6979 

3. 6980 

23 

10 

3.  6981 

3.  6982 

3. 6983 

3.  6984 

3. 6984 

3.  6985 

3. 6986 

3. 6987 

3. 6988 

3. 6989 

23 

20 

3.  6990 

3.  6991 

3. 6991 

3. 6992 

3. 6993 

3. 6994 

3. 6995 

3. 6996 

3. 6997 

3. 6998 

23 

30 

3. 6998 

3. 6999 

3.7000 

3.7001 

3.7002 

3. 7003 

3. 7004 

3.  7004 

3.7005 

3.  7006 

23 

40 

3. 7007 

3.  7008 

3.7009 

3.  7010 

3.  7010 

3.  7011 

3. 7012 

3.  7013 

3.  7014 

3.  7015 

23 

50 

3. 7016 

3.  7017 

3,  7017 
3. 7026 

3.  7018 

3.  7019 

3.  7020 

3.  7021 

3.  7022 

3.  7023 

3.  7023 

1  24 

0 

3.  7024 

3.  7025 

3. 7027 

3.  7028 

3. 7029 

3.7029 

3.  7030 

3.  7031 

3.  7032 

24 

10 

3.  7033 

3.  7034 

3. 7035 

3.  7035 

3.  7036 

3. 7037 

3. 7038 

3.  7039 

3. 7040 

3. 7041 

24 

20 

3.  7042 

3.  7042 

3.  7043 

3.  7044 

3.7045 

3. 7046 

3.  7047 

3.  7048 

3.  7048 

3.  7049 

24 

30 

3.  7050 

3. 7051 

3.  7052 

3.  7053 

3.  7054 

3. 7054 

3. 7055 

3.  7056 

3. 7057 

3.  7058 

24 

40 

3.  7059 

3.7060 

3.  7060 

3.  7061 

3. 7062 

3. 7063 

3. 7064 

3.  7065 

3. 7065 

3.  7066 

24 

50 

3.  7067 

3. 7068 

3.  7069 

3. 7070 

3. 7071 

3.  7071 

3. 7072 

3.  7073 

3. 7074 

3. 7075 

1  25 

0 

3. 7076 

3. 7077 

3.  7077 

3.  7078 

3.  7079 

3.  7080 

3. 7081 

3.  7082 

3. 7083 

3. 7083 

25 

10 

3.  7084 

3. 7085 

3. 7086 

3. 7087 

3.  7088 

3.  7088 

3. 7089 

3.  7090 

3.7091 

3.  7092 

25 

20  3. 7093 

3. 7094 

3. 7094 

3.7095 

3.  7096 

3.  7097 

3. 7098 

3.7099 

3.7099 

3.7100 

25 

30 

3.  7101 

3. 7102 

3.  7103 

3.  7104 

3.  7105 

3.  7105 

3. 7106 

3.  7107 

3.  7108 

3.  7109 

25 

.40 

3. 7110 

3.  7110 

3.7111 

3. 7112 

3. 7113 

3. 7114 

3.  7115 

3.7116 

3. 7116 

3.7117 

25 

50 

3.7118 

3.  7119 

3.  7120 

3. 7121 

3.  7121 

3. 7122 

3.  7123 

3.  7124 

3.  7125 

3. 7126 

1  26 

0 

3.  7126 

3.  7127 

3.  7128 

3.  7129 

3.  7130 

3. 7131 

3. 7132 

3.  7132 

3.  7133 

3. 7134 

26 

10 

3.  7135 

3.  7136 

3. 7137 

3.  7137 

3.  7138 

3. 7139 

3.7140 

3.  7141 

3.  7142 

3. 7142 

26 

20 

3.  7143 

3.  7144 

3. 7145 

3.  7146 

3.  7147 

3. 7147 

3.  7148 

3.  7149 

3. 7150 

3. 7151 

26 

30 

3. 7152 

3.  7153 

3. 7153 

3.  7154 

3.  7155 

3.  7156 

3.  7157 

3.  7158 

3. 7159 

3. 7159 

26 

40 

3. 7160 

3.  7161 

3. 7162 

3.  7163 

3.  7163 

3.  7164 

3.  7165 

3.  7166 

3. 7167 

3. 7168 

26 

50 

3.  7168 

3.  7169 

3.  7170 

3.7171 

3. 7172 

3. 7173 

3. 7173 

3.  7182 

3.  7174 

3. 7175 

3.  7176 

1  27 

0 

3.7177 

3.  7178 

3.  7178 

3. 7179  1  3.  7180 

3.  7181 

3.  7183 

3.  7183 

3.  7184 

27 

10 

3.7185 

3.  7186 

3.  7187 

3.7188  1  3.7188 

3.  7189 

3.  7190 

3.  7191 

3. 7192 

3.  7192 

27 

20 

3.  7193 

3.  7194 

3.  7195 

3.  7196  I  3.  7197 

3.7197 

3. 7198 

3.  7199 

3. 7200 

3.  7201 

27 

30 

3.  7202 

3.  7202 

3.  7203 

3.  7204 

3.  7205 

3.7206 

3. 7207 

3.  7207 

3. 7208 

3.  7209 

27 

40 

3.  7210 

3. 7211 

3.  7212 

3.7212 

3. 7213 

3.  7214 

3.  7215 

3.  7216 

3. 7216 

3. 7217 

27 

50 

3.  7218 

3.  7219 

3.  7220 

3. 7221 

3.  7221 

3.  7222 

3. 7223 

3.  7224 

3.  7225 

3. 7226 

1  28 

0 

3.  7226 

3. 7227 

3.  7228 

3.7229 

3.  7230 

3.  7230 

3. 7231 

3.  7232 

3.  7233 

3. 7234 

28 

10 

3.  7235 

3.  7235 

3.  7236 

3. 7237 

3. 7238 

3. 7239 

3. 7239 

3.  7240 

3.  7241 

3.  7242 

28 

20 

3.  7243 

3. 7244 

3.  7244 

3. 7245 

3. 7246 

3. 7247 

3. 7248 

3.  7248 

3.  7249 

3. 7250 

28 

30 

3.  7251 

3. 7252 

3.  7253 

3. 7253 

3.  7254 

3.  7255 

3. 7256 

3.  7257 

3. 7257 

3. 7258 

28 

40 

3.  7259 

3.  7260 

3.  7261 

3. 7262 

3.  7262 

3.  7263 

3. 7264 

3. 7265 

3. 7266 

3. 7266 

28 

50 

3.  7267 

3. 7268 

3.  7269 

3. 7270 
3. 7278 

3.  7271 
3.  7279 

3.  7271 

3. 7272 

3. 7273 

3.  7274 

3. 7275 

1  29 

0 

3.  7275 

3. 7276 

3.  7277 

3. 7279 

3. 7280 

3.  7281 

3. 7282 

3. 7283 

29 

10 

3.  7284 

3. 7284 

3.  7285 

3.  7286 

3.  7287 

3.  7288 

3.  7288 

3.  7289 

3. 7290 

3. 7291 

29 

20 

3.  7292 

3. 7292 

3.  7293 

3.  7294 

3.  7295 

3.7296 

3. 7297 

3.  7297 

3. 7298 

3.  7299 

29 

30 

3.  7300 

3.  7301 

3.  7301 

3.  7302 

3.  7303 

3. 7304 

3. 7305 

3.  7305 

3.  7306 

3. 7307 

29 

40 

3.  7308 

3. 7309 

3.  7309 

3. 7310 

3.  7311 

3. 7312 

3.  7313 

3. 7313 

3. 7314 

3.  7315 

29 

50 

3.7316 

3.  7317 

3.  7317 

3. 7318 

3.  7319 

3. 7320 

3. 7321 

3. 7322 

3. 7322 

3.  7323 

22489—03- 


-21 


Page  322]           APPENDIX  V:  TABLE 

[X. 

Logarithms  of  Small  Arcs  in 

Space  or 

Time. 

Arc. 

0"   i   X" 

2" 

8" 

4" 

5" 

6" 

7" 

8"      9"   1 

O      I          II 

1"  30"'  0" 

3. 7324 

3.  7325 

3. 7326 

3.  7326 

3. 7327 

3. 7328 

3.7329 

3.  7330 

3.  7330 

3.7331 

30  10 

3. 7332 

3.  7333 

3.  7334 

3.  7334 

3. 7335 

3. 7336 

3. 7337 

3.  7338 

3.  7338 

3. 7339 

30  20 

3. 7340 

3.  7341 

3.  7342 

3. 7342 

3. 7343 

3.7344 

3.  7345 

3.  7346 

3.7346 

3. 7347 

30  30 

3. 7348 

3.  7349 

3. 7350 

3. 7350 

3. 7351 

3. 7352 

3. 7353 

3.  7354 

3. 7354 

3.  7355 

30  40 

3.7356 

►3.  7357 

3.7358 

3,  7358 

3. 7359 

3.7360 

3. 7361 

3. 7362 

3. 7362 

3.  7363 

30  50 

3. 7364 

3.7365 

3. 7366 

3.  7366 

3.  7367 

3. 7368 

3. 7369 

3.  7370 

3. 7370 

3.  7371 

1  31  0 

3.  7372 

3. 7373 

3.  7374 

3.  7374 

3.  7375 

3. 7376 

3. 7377 

3.  7377 

3.  7378 

3.  7379 

31  10 

3.  7380 

3. 7381 

3.  7381 

3.  7382 

3.  7383 

3.  7384 

3.7385 

3.  7385 

3.  7386 

3.  7387 

31  20 

3.  7388 

3. 7389 

3.  7389 

3.  7390 

3.  7391 

3.  7392 

3.  7393 

3. 7393 

3.  7394 

3.  7395 

31  30 

3.  7396 

3. 7397 

3.  7397 

3. 7398 

3.  7399 

3.7400 

3.7400 

3. 7401 

3.  7402 

3.  7403 

31  40 

3.  7404 

3.  7404 

3.  7405 

3. 7406 

3.7407 

3.  7408 

3.  7408 

3.  7409 

3.  7410 

3.  7411 

31  50 

3. 7412 

3. 7412 

3.  7413 

3. 7414 

3.  7415 

3. 7415 

3. 7416 

3. 7417 

3.  7418 

3. 7419 

1  32  0 

3.  7419 

3.  7420 

3.  7421 

3. 7422 

3.  7423 

3.  7423 

3.  7424 

3.  7425 

3.  7426 

3.  7426 

32  10 

3. 7427 

3.  7428 

3.  7429 

3. 7430 

3.  7430 

3. 7431 

3.  7432 

3. 7433 

3.  7434 

3.  7434 

32  20 

3.7435 

3.  7436 

3.  7437 

3. 7437 

3. 7438 

3. 7439 

3.  7440 

3. 7441 

3.  7441 

3.  7442 

32  30 

3. 7443 

3.7444 

3.7444 

3. 7445 

3.  7446 

3. 7447 

3.7448 

3. 7448 

3.  7449 

3.  7450 

32  40 

3. 7451 

3. 7452 

3.7452 

3. 7453 

3. 7454 

3. 7455 

3.  7455 

3. 7456 

3.  7457 

3.7468 

32  50 

3. 7459 

3. 7459 

3.7460 

3. 7461 

3. 7462 

3. 7462 

3.  7463 

3.7464 

3.7465 

3.  7466 

1  33  0 

3.  7466 

3. 7467 

3. 7468 

3. 7469 

3.  7469 

3. 7470 

3. 7471 

3.  7472 

3.  7473 

3. 7473 

33  10 

3.  7474 

3.  7475 

3.  7476 

3. 7476 

3. 7477 

3.  7478 

3. 7479 

3.  7480 

3.  7480 

3. 7481 

33  20 

3.  7482 

3.  7483 

3.  7483 

3. 7484 

3. 7485 

3.  7486 

3. 7487 

3.  7487 

3.  7488 

3. 7489 

33  30 

3.  7490 

3.  7490 

3.  7491 

3. 7492 

3. 7493 

3.  7493 

3.  7494 

3. 7495 

3.  7496 

3. 7497 

33  40 

3.  7497 

3.  7498 

3.  7499 

3.7500 

3.7500 

3.  7501 

3.  7502 

3.  7503 

3.  7504 

3. 7504 

33  50 

3.  7505 

3. 7506 

3.  7507 

3. 7507 

3. 7508 

3.  7509 

3. 7510 

3. 7510 

3.  7511 

3. 7512 

1  34  0 

3.  7513 

3. 7514 

3. 7514 

3. 7515 

3. 7516 

3.  7517 

3. 7517 

3. 7518 

3.  7519 

3. 7520 

34  10 

3.  7520 

3. 7521 

3.  7522 

3. 7523 

3. 7524 

3.  7524 

3.  7525 

3. 7526 

3.  7527 

3. 7527 

34  20 

3.  7528 

3. 7529 

3. 7530 

3. 7530 

3. 7531 

3.  7532 

3.  7533 

3. 7534 

3.  7534 

3. 7535 

34  30 

3.  7536 

3. 7537 

3. 7537 

3. 7538 

3. 7539 

3.  7540 

3.  7540 

3. 7541 

3.  7542 

3. 7543 

34  40 

3.  7543 

3. 7544 

3. 7545 

3. 7546 

3. 7547 

3.  7547 

3. 7548 

3. 7549 

3.  7550 

3. 7550 

34  50 

3.  7551 

3. 7552 

3. 7553 

3. 7553 

3. 7554 

3.  7555 

3. 7556 

3. 7556 

3.  7557 

3. 7558 

1  35  0 

3.  7559 

3. 7560 

3.7560 

3.  7561 

3. 7562 

3.  7563 

3. 7563 

3.  7564 

3.  7565 

3. 7566 

35  10 

3.  7566 

3. 7567 

3. 7568 

3. 7569 

3. 7569 

3.  7570 

3.  7571 

3.  7572 

3.  7572 

3.  7573 

35  20 

3.  7574 

3. 7575 

3. 7575 

3. 7576 

3.  7577 

3.  7578 

3.  7579 

3.  7579 

3.  7580 

3.  7581 

35  30 

3.  7582 

3. 7582 

3. 7583 

3.  7584 

3. 7585 

3.  7585 

3.  7586 

3.  7587 

3.  7588 

3.  7588 

35  40 

3.  7589 

3. 7590 

3. 7591 

3. 7591 

3. 7592 

3.  7593 

3. 7594 

3.  7594 

3.  7595 

3.  7596 

35  50 

3.  7597 

3.  7597 

3. 7598 

3. 7599 

3. 7600 

3.  7600 

3.  7601 

3. 7602 

3.  7603 

3.  7603 

1  36  0 

3.  7604 

3. 7605 

3. 7606 

3. 7606 

3. 7607 

3.  7608 

3. 7609 

3.  7609 

3.  7610 

3.  7611 

36  10 

3.  7612 

3. 7613 

3.  7613 

3.  7614 

3.  7615 

3.  7616 

3.  7616 

3.  7617 

3.  7618 

3.  7619 

36  20 

3.  7619 

3. 7620 

3.  7621 

3.  7622 

3.  7622 

3.  7623 

3.  7624 

3. 7625 

3.  7625 

3.  7626 

36  30 

3.  7627 

3. 7628 

3.  7628 

3.  7629 

3. 7630 

3.  7631 

3.  7631 

3. 7632 

3.  7633 

3.  7634 

36  40 

3. 7634 

3. 7635 

3. 7636 

3.  7637 

3.  7637 

3.  7638 

3.  7639 

3. 7640 

3.  7640 

3.  7641 

36  50 

3. 7642 

3. 7643 

3. 7643 

3.7644 

3.  7645 

3.  7645 

3.  7646 

3. 7647 

3.  7648 

3.7648 

1  37  0 

3.  7649 

3. 7650 

3. 7651 

3.7651 

3. 7652 

3.  7653 

3.  7654 

3. 7654 

3.7655 

3. 7666 

37  10 

3.  7657 

3.7667 

3. 7658 

3.  7659 

3. 7660 

3.  7660 

3.  7661 

3. 7662 

3. 7663 

3. 7663 

37  20 

3.  7664 

3.  7665 

3. 7666 

3.  7666 

3. 7667 

3.  7668 

3.  7669 

3. 7669 

3.  7670 

3. 7671 

37  30 

3.  7672 

3. 7672 

3. 7673 

3.  7674 

3. 7675 

3.  7675 

3.  7676 

3. 7677 

3. 7677 

3. 7678 

37  40 

3.  7679 

3.  7680 

3. 7681 

3.  7681 

3. 7682 

3.  7683 

3.  7683 

3. 7684 

3. 7685 

3.  7686 

37  50 

3.  7686 

3. 7687 

3. 7688 

3.  7689 

3.  7689 

3.  7690 

3.  7691 

3. 7692 

3. 7692 

3.  7693 

1  38  0 

3.  7694 

3. 7695 

3. 7695 

3.  7696 

3.  7697 

3.  7697 

3.  7698 

3. 7699 

3. 7700 

3.  7700 

38  10 

3.  7701 

3. 7702 

3. 7703 

3.  7703 

3.  7704 

3.  7705 

3.  7706 

3.  7706 

3. 7707 

3.  7708 

38  20 

3.  7709 

3. 7709 

3. 7710 

3. 7711 

3. 7711 

3.  7712 

3. 7713 

3. 7714 

3. 7714 

3.7715 

38  30 

3.  7716 

3. 7717 

3. 7717 

3.  7718 

3. 7719 

3.  7720 

3.  7720 

3.  7721 

3. 7722 

3. 7722 

38  40 

3.  7723 

3. 7724 

3. 7725 

3.  7725 

3. 7726 

3.  7727 

3.  7728 

3.  7728 

3. 7729 

3. 7730 

38  50 

3.  7731 

3. 7731 

3. 7732 

3.  7733 

3. 7733 

3.  7734 

3.  7735 

3. 7736 

3. 7736 

3. 7737 

1  39  0 

3.  7738 

3. 7739 

3. 7739 

3.  7740 

3. 7741 

3.  7742 

3.  7742 

3. 7743 

3. 7744 

3. 7744 

39  10 

3.  7745 

3. 7746 

3. 7747 

3.  7747 

3. 7748 

3. 7749 

3.  7750 

3. 7750 

3. 7751 

3. 7752 

39  20 

3.  7752 

3. 7753 

3. 7754 

3.  7755 

3. 7755 

3. 7756 

3.  7757 

3. 7758 

3. 7758 

3.  7759 

39  30 

3.  7760 

3. 7760 

3.  7761 

3.  7762 

3. 7763 

3. 7763 

3.  7764 

3. 7765 

3. 7766 

3.  7766 

39  40 

3.  7767 

3. 7768 

3.  7768 

3.  7769 

3. 7770 

3. 7771 

3.  7771 

3. 7772 

3. 7773 

3. 7774 

39  50 

3.  7774 

3. 7775 

3. 7776 

3. 7776 

3. 7777 

3. 7778 

3.  7779 

3. 7779 

3.  7780 

3.  7781 

APPENDIX  V:  TABLE  IX. 

[Page  323 

Logarithms  of  Small  Arcs  in 

I  Space  or  Time. 

Arc.    1 

0" 

1" 

2" 

8" 

4" 

5" 

6" 

7" 

8" 

9" 

0    / 
Ih  40.n 

II 
0^ 

3. 7782 

3. 7782 

3. 7783 

3. 7784 

3.  7784 

3. 7785 

3. 7786 

3. 7787 

3. 7787 

3. 7788 

40 

10 

3.  7789 

3. 7789 

3.  7790 

3. 7791 

3. 7792 

3. 7792 

3. 7793 

3.  7794 

3. 7795 

3.  7795 

40 

20 

3.  7796 

3. 7797 

3. 7797 

3. 7798 

3. 7799 

3. 7800 

3. 7800 

3. 7801 

3. 7802 

3.  7802 

40 

30 

3.  7803 

3.  7804 

3. 7805 

3. 7805 

3.  7806 

3.  7807 

3. 7807 

3. 7808 

3.  7809 

3. 7810 

40 

40 

3.7810 

3.  7811 

3. 7812 

3. 7813 

3.  7813 

3. 7814 

3. 7815 

3.  7815 

3. 7816 

3. 7817 

40 

50 

3.  7818 

3.  7818 

3. 7819 
3. 7826 

3. 7820 

3. 7820 
3. 7828 

3. 7821 

3. 7822 

3.  7823 

3. 7823 

3.  7824 

1  41 

0 

3.  7825 

3.  7825 

3. 7827 

3.  7828 

3.  7829 

3.  7830 

3. 7830 

3.  7831 

41 

10 

3.  7832 

3.  7833 

3. 7833 

3. 7834 

3.  7835 

3. 7835 

3.  7836 

3. 7837 

3. 7838 

3. 7838 

41 

20 

3.  7839 

3.  7840 

3. 7840 

3. 7841 

3.7842 

3. 7843 

3.  7843 

3. 7844 

3. 7845 

3. 7845 

41 

30 

3.  7846 

3. 7847 

3. 7848 

3. 7848 

3.  7849 

3.  7850 

3.  7850 

3. 7851 

3. 7852 

3. 7853 

41 

40 

3.  7853 

3. 7854 

3. 7855 

3. 7855 

3. 7856 

3.  7857 

3.  7858 

3.7858 

3. 7859 

3. 7860 

41 

50 

3.  7860 

3. 7861 

3.  7862 

3. 7863 

3. 7863 

3. 7864 

3.  7865 

3. 7865 

3. 7866 

3. 7867 

1  42 

0 

3.  7868 

3. 7868 

3.  7869 

3.  7870 

3. 7870 

3. 7871 

3.  7872 

3. 7872 

3. 7873 

3. 7874 

42 

10 

3.  7875 

3. 7875 

3. 7876 

3.  7877 

3. 7877 

3. 7878 

3.  7879 

3. 7880 

3. 7880 

3. 7881 

42 

20 

3.  7882 

3. 7882 

3. 7883 

3.  7884 

3. 7885 

3. 7885 

3.  7886 

3. 7887 

3. 7887 

3.  7888 

42 

30 

3.  7889 

3. 7889 

3. 7890 

3. 7891 

3. 7892 

3. 7892 

3.  7893 

3. 7894 

3. 7894 

3.  7895 

42 

40 

3.  7896 

3.  7897 

3.  7897 

3. 7898 

3.  7899 

3. 7899 

3.  7900 

3. 7901 

3. 7901 

3.  7902 

42 

50 

3.  7903 

3.  7904 

3.  7904 

3. 7905 

3. 7906 

3. 7906 

3.  7907 

3. 7908 

3.  7908 

3.  7909 

1  43 

0 

3.  7910 

3.  7911 

3. 7911 

.  3. 7912 

3. 7913 

3.7913 

3.  7914 

3.  7915 

3. 7916 

3.  7916 

43 

10 

3. 7917 

3.  7918 

3. 7918 

3.  7919 

3.  7920 

3. 7920 

3. 7921 

3.  7922 

3. 7923 

3.  7923 

43 

20 

3.  7924 

3.  7925 

3.  7925 

3.  7926 

3. 7927 

3. 7927 

3. 7928 

3.  7929 

3.  7930 

3.  7930 

43 

30 

3.  7931 

3.  7932 

3. 7932 

3.  7933 

3.  7934 

3.  7934 

3. 7935 

3.  7936 

3.  7937 

3.  7937 

43 

40 

3.  7938 

3.  7939 

3. 7939 

3.  7940 

3. 7941 

3. 7941 

3. 7942 

3. 7943 

3.  7943 

3.  7944 

43 

50 

3.  7945 

3.  7946 

3. 7946 

3.  7947 

3.  7948 

3. 7948 

3. 7949 

3.  7950 

3.  7950 

3.  7951 

1  44 

0 

3.  7952 

3.  7953 

3. 7953 

3.  7954 

3.  7955 

3. 7955 

3. 7956 

3.  7957 

3. 7957 

3. 7958 

44 

10 

3. 7959 

3.  7959 

3. 7960 

3.  7961 

3. 7962 

3. 7962 

3. 7963 

3.  7964 

3. 7964 

3. 7965 

44 

20 

3.  7966 

3.  7966 

3. 7967 

3.  7968 

3. 7969 

3.  7969 

3. 7970 

3. 7971 

3. 7971 

3. 7972 

44 

30 

3. 7973 

3.  7973 

3.  7974 

3.  7975 

3.  7975 

3. 7976 

3. 7977 

3.  7978 

3. 7978 

3. 7979 

44 

40 

3.  7980 

3.  7980 

3.  7981 

3.  7982 

3.  7982 

3. 7983 

3. 7984 

3. 7984 

3. 7985 

3. 7986 

44 

50 

3.  7987 

3.  7987 

3.  7988 

3.  7989 

3.  7989 

3. 7990 

3. 7991 

3.  7991 

3. 7992 

3.  7993 

1  45 

0 

3.  7993 

3.  7994 

3.  7995 

3.  7995 

3.  7996 

3. 7997 

3. 7998 

3.  7998 

3.  7999 

3.8000 

45 

10 

3.  8000 

3.  8001 

3.  8002 

3.  8002 

3.  8003 

3.  8004 

3. 8004 

3.8005 

3.  8006 

3.8006 

45 

20 

3.  8007 

3.  8008 

3.  8009 

3.  8009 

3.  8010 

3.8011 

3.  8011 

3.  8012 

3. 8013 

3.  8013 

45 

30 

3.  8014 

3.  8015 

3. 8015 

3.  8016 

3.  8017 

3.  8017 

3.8018 

3.  8019 

3. 8020 

3.  8020 

45 

•40 

3. 8021 

3.  8022 

3.  8022 

3.  8023 

3. 8024 

3.  8024 

3. 8025 

3.  8026 

3. 8026 

3.  8027 

45 

50 

3. 8028 

3.  8028 

3. 8029 

3.  8030 

3.  8030 

3.  8031 

3. 8032 

3.  8033 

3.  8033 

3.  8034 

1  46 

0 

3.  8035 

3.  8035 

3. 8036 

3.  8036 

3.  8037 

3.  8038 

3. 8039 

3.  8039 

3. 8040 

3. 8041 

46 

10 

3.  8041 

3.  8042 

3.  8043 

3. 8043 

3.  8044 

3. 8045 

3.  8045 

3.  8046 

3. 8047 

3. 8048 

46 

20 

3.  8048 

3.  8049 

3. 8050 

3. 8050 

3.  8051 

3. 8052 

3.  8052 

3.  8053 

3. 8054 

3. 8054 

46 

30 

3.  8055 

3. 8056 

3.  8056 

3. 8057 

3.  8058 

3.  8058 

3. 8059 

3.  8060 

3. 8060 

3. 8061 

46 

40 

3.  8062 

3. 8062 

3. 8063 

3. 8064 

3. 8065 

3.  8065 

3. 8066 

3.8067 

3. 8067 

3. 8068 

46 

50 

3.  8069 

3. 8069 

3. 8070 

3. 8071 

3.  8071 
3.  8078 

3. 8072 

3. 8073 

3. 8073 

3. 8074 

3.  8075 

1  47 

0 

3.  8075 

3. 8076 

3. 8077 

3. 8077 

3. 8079 

3. 8079 

3.  8080 

3.  8081 

3.  8081 

47 

10 

3. 8082 

3. 8083 

3.  8083 

3. 8084 

3. 8085 

3.  8085 

3.  8086 

3. 8087 

3.  8088 

3.  8088 

47 

20 

3.  8089 

3. 8090 

3.  8090 

3. 8091 

3.  8092 

3.  8092 

3. 8093 

3. 8094 

3.  8094 

3.  8095 

47 

30 

3.  8096 

3. 8096 

3. 8097 

3.8098 

3.  8098 

3.8099 

3. 8099 

3.  8100 

3. 8101 

3.  8102 

47 

40 

3.  8102 

3. 8103 

3. 8104 

3.  8104 

3.  8105 

3.  8106 

3. 8106 

3.  8107 

3. 8108 

3. 8108 

47 

50 

3.  8109 

3.8110 

3. 8110 

3.8111 

3.  8112 

3.8112 

3.  8113 

3. 8114 

3.8114 

3.8115 

1  48 

0 

3.8116 

3.  8116 

3.8117 

3.8118 

3.8118 

3.8119 

3.  8120 

3.  8120 

3.8121 

3.  8122 

48 

10 

3.  8122 

3.  8123 

3.  8124 

3.  8124 

3. 8125 

3.  8126 

3.  8126 

3.  8127 

3.  8128 

3.  8128 

48 

20 

3.  8129 

3.8130 

3.  8130 

3.  8131 

3.  8132 

3.8132 

3. 8133 

3.  8134 

3.  8134 

3.  8135 

48 

30 

3.  8136 

3.8136 

3.  8137 

3.  8138 

3.  8138 

3.  8139 

3.  8140 

3.  8140 

3.  8141 

3.  8142 

48 

40 

3.  8142 

3.  8143 

3.8144 

3. 8144 

3. 8145 

3. 8146 

3. 8146 

3. 8147 

3.  8148 

3. 8148 

48 

50 

3.  8149 

3.  8150 

3.  8150 

3.  8151 

3.  8152 

3.  8152 

3.  8153 

3.  8154 

3. 8154 

3.  8155 

1  49 

0 

3.8156 

3.  8156 

3.  8157 

3. 8158 

3.  8158 

3. 8159 

3.  8160 

3.  8160 

3. 8161 

3.  8162 

49 

10 

3.  8162 

3.  8163 

3.  8164 

3.  8164 

3.  8165 

3. 8166 

3.  8166 

3. 8167 

3. 8168 

3.  8168 

49 

20 

3.  8169 

3.  8170 

3.  8170 

3. 8171 

3.  8172 

3. 8172 

3.8173 

3. 8174 

3.  8174 

3.  8175 

49 

30 

3.  8176 

3.8176 

3.  8177 

3.8178 

3.  8178 

3.8179 

3.  8180 

3. 8180 

3. 8181 

3.  8182 

49 

40 

3.  8182 

3.  8183 

3.  8184 

3.  8184 

3. 8185 

3.  8185 

3.  8186 

3. 8187 

3.  8188 

3.  8188 

49 

50 

3.  8189 

3.  8190 

3.  8190 

3.  8191 

3.  8191 

3.  8192 

3.  8193 

3.  8193 

3.  8194 

3.  8195 

Page  324] 

APPENDIX  V:  TABLE  IX. 

Logarithms  of  Small  Arcs  in  Space  or 

Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

6" 

6" 

7" 

8" 

9" 

O    1 

1"  50™ 

II 
0» 

3.  8195 

3. 8196 

3.  8197 

3. 8197 

3.  8198 

3.  8199 

3. 8199 

3.8200 

3. 8201 

3.  8201 

50 

10 

3.  8202 

3.  8203 

3.  8203 

3.  8204 

3. 8205 

3. 8205 

3. 8206 

3. 8207 

3. 8207 

3.  8208 

50 

20 

3.8209 

3.  8209 

3.8210 

3.8211 

3.  8211 

3. 8212 

3. 8213 

3.  8213 

3.  8214 

3. 8214 

50 

30 

3.  8215 

3. 8216 

3.  8216 

3.  8217 

3.  8218 

3.  8218 

3.  8219 

3.  8220 

3.  8220 

3. 8221 

50 

40 

3.  8222 

•3. 8222 

3.  8223 

3.  8224 

3.  8224 

3.  8225 

3. 8226 

3. 8226 

3.  8227 

3.  8228 

50 

50 

3.  8228 

3. 8229 

3.  8230 
3.  8236 

3.  8230 

3.  8231 

3.  8231 

3. 8232 

3.  8233 
3. 8239 

3.  8233 
3.  8240 

3.  8234 
3.  8241 

1  51 

0 

3.  8235 

3. 8235 

3.  8237 

3.  8237 

3. 8238 

3. 8239 

51 

10 

3. 8241 

3. 8242 

3.  8243 

3. 8243 

3. 8244 

3. 8245 

3. 8245 

3. 8246 

3. 8246 

3. 8247 

51 

20 

3.  8248 

3. 8248 

3.  8249 

3. 8250 

3.  8250 

3. 8251 

3. 8252 

3.  8252 

3. 8253 

3. 8254 

51 

30 

3. 8254 

3. 8255 

3.  8256 

3.  8256 

3. 8257 

3. 8258 

3. 8258 

3. 8259 

3. 8259 

3. 8260 

51 

40 

3.  8261 

3. 8261 

3. 8262 

3. 8263 

3. 8263 

3.8264 

3.8265 

3. 8265 

3. 8266 

3,  8267 

51 

50 

3.  8267 

3. 8268 

3.  8269 

3.  8269 

3. 8270 

3.  8270 

3. 8271 

3. 8272 

3. 8272 

3. 8273 

1  52 

0 

3.  8274 

3.  8274 

3. 8275 

3.  8276 

3. 8276 

3.  8277 

3. 8278 

3. 8278 

3.  8279 

3. 8280 

52 

10 

3. 8280 

3. 8281 

3. 8281 

3.  8282 

3. 8283 

3.  8283 

3. 8284 

3. 8285 

3.  8285 

3. 8286 

52 

20 

3. 8287 

3. 8287 

3. 8288 

3.  8289 

3. 8289 

3. 8290 

3. 8290 

3. 8291 

3.  8292 

3. 8292 

52 

30 

3.8293 

3. 8294 

3. 8294 

3. 8295 

3. 8296 

3.  8296 

3. 8297 

3. 8298 

3.  8298 

3. 8299 

52 

40 

3.  8299 

3.8300 

3. 8301 

3. 8301 

3. 8302 

3.  8303 

3.  8303 

3. 8304 

3. 8305 

3.  8305 

52 

50 

3.  8306 

3. 8307 

3.  8307 

3.  8308 

3. 8308 

3.  8309 

3. 8310 

3. 8310 

3. 8311 

3. 8312 

1  53 

0 

3. 8312 

3.  8313 

3. 8314 

3.  8314 

3.  8315 

3.  8315 

3. 8316 

3.  8317 

3. 8317 

3.  8318 

53 

10 

3.  8319 

3.  8319 

3. 8320 

3.  8321 

3.  8321 

3.  8322 

3. 8323 

3. 8323 

3. 8324 

3.  8324 

53 

20 

3.  8325 

3.  8326 

3. 8326 

3.  8327 

3.  8328 

3.  8328 

3. 8329 

3. 8330 

3.  8330 

3. 8331 

53 

30 

3.  8331 

3.  8332 

3. 8333 

3.  8333 

3.  8334 

3.  8335 

3. 8335 

3.  8336 

3. 8337 

3. 8337 

53 

40 

3.  8338 

3. 8338 

3. 8339 

3. 8340 

3. 8340 

3.  8341 

3. 8342 

3.  8342 

3. 8343 

3. 8344 

53 

1  54 

50 
0 

3.  8344 

3. 8345 

3. 8345 

3. 8346 

3. 8347 

3. 8347 

3. 8348 

3.  8349 

3. 8349 

3. 8350 

3.  8351 

3. 8351 

3. 8352 

3. 8352 

3. 8353 

3. 8354 

3. 8354 

3.  8355 

3. 8356 

3. 8356 

54 

10 

3.  8357 

3. 8358 

3. 8358 

3. 8359 

3.  8359 

3.  8360 

3. 8361 

3.  8361 

3. 8362 

3. 8363 

54 

20 

3. 8363 

3. 8364 

3. 8365 

3. 8365 

3.  8366 

3.  8366 

3.8367 

3. 8368 

3. 8368 

3. 8369 

54 

30 

3. 8370 

3. 8370 

3. 8371 

3. 8371 

3.  8372 

3. 8373 

3. 8373 

3. 8374 

3. 8375 

3.  8375 

54 

40 

3.  8376 

3. 8377 

3. 8377 

3. 8378 

3.  8378 

3.  8379 

3. 8380 

3. 8380 

3. 8381 

3.  8382 

54 

50 

3.  8382 

3. 8383 

3. 8383 

3. 8384 

3. 8385 
3. 8391 

3. 8385 
3.  8392 

3. 8386 

3. 8387 
3.  8393 

3. 8387 

3.  8388 

1  55 

0 

3.  8388 

3. 8389 

3. 8390 

3.  8390 

3. 8392 

3. 8394 

3. 8394 

55 

10 

3.  8395 

3. 8395 

3. 8396 

3.  8397 

3.  8397 

3.  8398 

3. 8399 

3. 8399 

3. 8400 

3. 8400 

55 

20 

3.  8401 

3.  8402 

3. 8402 

3.  8403 

3. 8404 

3.  8404 

3. 8405 

3. 8405 

3.  8406 

3. 8407 

55 

30 

3.  8407 

3.  8408 

3.  8409 

3.  8409 

3. 8410 

3.  8410 

3. 8411 

3. 8412 

3. 8412 

3.8413 

55 

40 

3. 8414 

3. 8414 

3. 8415 

3. 8415 

3.  8416 

3.  841/ 

3. 8417 

3.  8418 

3.  8419 

3.  8419 

55 

50 

3. 8420 

3. 8420 

3. 8421 

3.  8422 

3.  8422 

3. 842S 

3. 8424 

3.  8424 

3.  8425 

3.  8425 

1  56 

0 

3.  8426 

3.  8427 

3. 8427 

3. 8428 

3.  8429 

3. 8429 

3. 8430 

3.  8430 

3. 8431 

3.  8432 

56 

10 

3.  8432 

3.  8433 

3. 8434 

3. 8434 

3.8435 

3. 8435 

3. 8436 

3. 8437 

3. 8437 

3.  8438 

56 

20 

3.  8439 

3. 8439 

3. 8440 

3. 8440 

3. 8441 

3. 8442 

3.8442 

3. 8443 

3. 8444 

3.  8444 

56 

30 

3.  8445 

3.8445 

3. 8446 

3. 8447 

3. 8447 

3.8448 

3. 8448 

3.  8449 

3. 8450 

3. 8450 

56 

40 

3.  8451 

3. 8452 

3. 8452 

3. 8453 

3. 8453 

3. 8454 

3. 8455 

3.  8455 

3. 8456 

3. 8457 

56 

50 

3.  8457 

3. 8458 

3. 8458 

3. 8459 

3. 8460 

3. 8460 

3. 8461 

3.  8462 

3. 8462 

3. 8463 

1  57 

0 

3.  8463 

3.  8464 

3.8465 

3. 8465 

3. 8466 

3. 8466 

3. 8467 

3. 8468 

3. 8468 

3.  8469 

57 

10 

3. 8470 

3. 8470 

3. 8471 

3. 8471 

3.  8472 

3.  8473 

3.  8473 

3. 8474 

3.  8474 

3. 8475 

57 

20 

3.  8"476 

3. 8476 

3. 8477 

3. 8478 

3. 8478 

3.  8479 

3.  8479 

3. 8480 

3.  8481 

3. 8481 

57 

30 

3. 8482 

3. 8483 

3. 8483 

3. 8484 

3.  8484 

3.  8485 

3.  8486 

3. 8486 

3.  8487 

3.  8487 

57 

40 

3. 8488 

3. 8489 

3. 8489 

3.  8490 

3. 8491 

3.  8491 

3.  8492 

3.  8492 

3.  8493 

3. 8494 

57 

50 

3.  8494 

3. 8495 

3.  8495 

3.  8496 

3. 8497 
3.8503' 

3. 8497 

3.  8498 

3. 8499 

3.  8499 

3.  8500 

1  58 

0 

3.  8500 

3.  8501 

3.  8502 

3.  8502 

3.  8503 

3.  8504 

3.  8505 

3.  8505 

3. 8506 

58 

10 

3.  8506 

3.  8507 

3;  8508 

3. 8508 

3. 8509 

3.  8510 

3.  8510 

3. 8511 

3.  8511 

3. 8512 

58 

20 

3. 8513 

3. 8513 

3.  8514 

3. 8514 

3. 8515 

3. 8516 

3. 8516 

3.8517 

3.  8517 

3. 8518 

58 

30 

3. 8519 

3.  8519 

3.  8520 

3.  8521 

3. 8521 

3.  8522 

3.  8522 

3. 8523 

3.  8524 

3.  8524 

58 

40 

3.  8525 

3.  8525 

3. 8526 

3. 8527 

3. 8527 

3.  8528 

3.  8528 

3. 8529 

3.  8530 

3. 8530 

58 

50 

3. 8531 

3. 8532 

3. 8532 

3. 8533 

3. 8533 

3.  8534 

3. 8535 

3.  8535 

3.  8536 

3.8536 

1  59 

0 

3.  8537 

3.  8538 

3. 8538 

3. 8539 

3. 8539 

3.  8540 

3. 8541 

3.8541 

3.  8542 

3. 8542 

59 

10 

3. 8543 

3. 8544 

3. 8544 

3. 8545 

3. 8545 

3. 8546 

3. 8547 

3. 8547 

3.  8548 

3. 8549 

59 

20 

3. 8549 

3. 8550 

3. 8550 

3. 8551 

3. 8552 

3.  8552 

3. 8553 

3. 8553 

3.  8554 

3. 8555 

59 

30 

3. 8555 

3. 8556 

3. 8556 

3. 8557 

3. 8558 

3. 8558 

3.  8559 

3.  8559 

3. 8560 

3. 8561 

59 

40 

3.  8561 

3. 8562 

3. 8562 

3. 8563 

3. 8564 

3.  8564 

3.  8565 

3. 8565 

3. 8566 

3. 8567 

59 

50 

3.  8567 

3. 8568 

3. 8568 

3. 8569 

3. 8570 

3.8570 

3. 8571 

3.  8572 

3.  8572 

3.  8573 

APPENDIX 

V:  TABLE  IX. 

[Page  325 

Logarithms  of  Small  Arcs  in 

Space  or  Time. 

Arc. 

0" 

1" 

2" 

3" 

4" 

6" 

6" 

7" 

8" 

9" 

o   / 

2"  0™ 

0« 

3.  8573 

3.  8574 

3.  8575 

3.8575 

3. 8576 

3. 8576 

3.  8577 

3. 8578 

3.  8578 

3.  8579 

0 

10 

3. 8579 

3.  8580 

3.  8581 

3.  8581 

3.  8582 

3.  8582 

3. 8583 

3. 8584 

3.  8584 

3.  8585 

0 

20 

3.  8585 

3.  8586 

3.  8587 

3. 8587 

3.  8588 

3. 8588 

3. 8589 

3. 8590 

3. 8590 

3. 8591 

0 

80 

3.  8591 

3. 8592 

3.  8593 

3. 8593 

3. 8594 

3. 8594 

3. 8595 

3. 8596 

3. 8596 

3. 8597 

0 

40 

3.  8597 

3. 8598 

3.  8599 

3. 8599 

3.  8600 

3. 8600 

3. 8601 

3. 8602 

3. 8602 

3. 8603 

0 

50 

3.  8603 

3. 8604 

3.  8605 

3. 8605 

3. 8606 

3. 8606 

3. 8607 

3. 8608 

3. 8608 

3. 8609 

2  1 

0 

3.  8609 

3. 8610 

3.  8611 

3. 8611 

3. 8612 

3. 8612 

3.  8613 

3.  8614 

3.  8614 

3. 8615 

10 

3.  8615 

3. 8616 

3.  8617 

3. 8617 

3.  8618 

3.  8618 

3.  8619 

3.  8620 

3. 8620 

3.  8621 

20 

3. 8621 

3. 8622 

3.  8623 

3. 8623 

3. 8624 

3.  8624 

3. 8625 

3.  8625 

3.  8626 

3.  8627 

30 

3.  8627 

3. 8628 

3.  8628 

3. 8629 

3. 8630 

3. 8630 

3. 8631 

3.  8631 

3. 8632 

3.  8633 

40 

3.  8633 

3. 8634 

3.  8634 

3.  8635 

3. 8636 

3.  8636 

3. 8637 

3. 8637 

3. 8638 

3. 8639 

50 

3.  8639 

3.  8640 

3.  8640 

3.  8641 

3.8642 

3. 8642 

3. 8643 

3. 8643 

3. 8644 

3. 8645 

2  2 

0 

3.  8645 

3. 8646 

3.  8646 

3. 8647 

3.8647 

3. 8648 

3. 8649 

3. 8649 

3. 8650 

3. 8650 

2 

10 

3. 8651 

3. 8652 

3.  8652 

3. 8653 

3. 8653 

3. 8654 

3. 8655 

3.  8655 

3. 8656 

3. 8656 

2 

20 

3. 8657 

3.  8658 

3.  8658 

3. 8659 

3. 8659 

3. 8660 

3. 8661 

3.  8661 

3. 8662 

3. 8662 

2 

30 

3.  8663 

3.  8663 

3.  8664 

3.  8665 

3. 8665 

3. 8666 

3. 8666 

3. 8667 

3. 8668 

3. 8668 

2 

40 

3.  8669 

3.  8669 

3.  8670 

3. 8671 

3. 8671 

3. 8672 

3. 8672 

3. 8673 

3. 8673 

3. 8674 

2 

50 

3. 8675 

3.  8675 

3. 8676 

3.  8676 

3. 8677 

3. 8678 

3.  8678 

3. 8679 

3.  8679 

3. 8680 
3. 8686 

2  3 

0 

3.  8681 

3. 8681 

3. 8682 

3.  8682 

3. 8683 

3. 8684 

3.  8684 

3.  8685 

3. 8685 

3 

10 

3. 8686 

3. 8687 

3. 8688 

3.  8688 

3.  8689 

3. 8689 

3.  8690 

3.  8691 

3. 8691 

3. 8692 

3 

20 

3.  8692 

3. 8693 

3. 8693 

3. 8694 

3. 8695 

3. 8695 

3.  8696 

3. 8696 

3.  8697 

3. 8698 

3 

30 

3.  8698 

3. 8699 

3. 8699 

3. 8700 

3. 8701 

3. 8701 

3. 8702 

3.  8702 

3. 8703 

3. 8703 

3 

40 

3.  8704 

3. 8705 

3. 8705 

3. 8706 

3.  8706 

3. 8707 

3. 8708 

3. 8708 

3.  8709 

3.  8709 

3 

50 

3. 8710 

3. 8710 

3. 8711 

3.8712 

3. 8712 

3.8713 

3. 8713 

3. 8714 

3.  8715 

3.  8715 

2  4 

0 

3. 8716 

3. 8716 

3.8717 

3.8717 

3. 8718 

3.  8719 

3. 8719 

3. 8720 

3.  8720 

3.  8721 

4 

10 

3.  8722 

3. 8722 

3. 8723 

3. 8723 

3. 8724 

3.  8724 

3.  8725 

3.  8726 

3. 8726 

3.  8727 

4 

20 

3.  8727 

3. 8728 

3.  8729 

3. 8729 

3. 8730 

3.  8730 

3. 8731 

3. 8731 

3. 8732 

3.  8733 

4 

30 

3.  8733 

3. 8734 

3.  8734 

3. 8735 

3.  8736 

3. 8736 

3. 8737 

3. 8737 

3. 8738 

3.  8738 

4 

40 

3.  8739 

3. 8740 

3.  8740 

3. 8741 

3.  8741 

3.  8742 

3. 8742 

3. 8743 

3.  8744 

3.  8744 

4 

50 

3.  8745 

3.  8745 

3.  8746 

3.  8747 

3.  8747 

3.  8748 

3. 8748 

3. 8749 

3.  8749 

3.  8750 

2  5 

0 

3. 8751 

3.  8751 

3.  8752 

3.  8752 

3.  8753 

3. 8754 

3.  8754 

3. 8755 

3.  8755 

3.  8756 

5 

10 

3.  8756 

3. 8757 

3.  8758 

3.  8758 

3.  8759 

3. 8759 

3. 8760 

3. 8760 

3. 8761 

3.  8762 

5 

20 

3.  8762 

3.  8763 

3.  8763 

3. 8764 

3.  8764 

3. 8765 

3. 8766 

3.  8766 

3. 8767 

3. 8767 

5 

30 

3. 8768 

3. 8769 

3.  8769 

3.  8770 

3. 8770 

3. 8771 

3. 8771 

3. 8772 

3. 8773 

3.  8773 

5 

.40 

3. 8774 

3.  8774 

3.  8775 

3. 8775 

3. 8776 

3. 8777 

3. 8777 

3.  8778 

3. 8778 

3. 8779 

5 

50 

3. 8779 

3. 8780 

3.  8781 

3. 8781 

3.  8782 

3. 8782 

3. 8783 

3.  8783 

3. 8784 
3.  8790 

3.  8785 

2  6 

0 

3.  8785 

3. 8786 

3.  8786 

3. 8787 

3. 8788 

3.8788  i  3.8789 

3.  8789 

3. 8790 

6 

10 

3.  8791 

3. 8792 

3.  8792 

3. 8793 

3.  8793 

3. 8794 

3.  8794 

3. 8795 

3. 8796 

3. 8796 

6 

20 

3.  8797 

3. 8797 

3. 8798 

3. 8798 

3.  8799 

3. 8800 
3. 8805 

3.8800 

3. 8801 

3. 8801 

3. 8802 

6 

30 

3.  8802 

3.  8803 

3.  8804 

3. 8804 

3.  8805 

3. 8806 

3. 8806 

3. 8807 

3. 8808 

6 

40 

3.  8808 

3.  8809 

3. 8809 

3.  8810 

3.  8810 

3.  8811 

3.8812 

3. 8812 

3.  8813 

3. 8813 

6 

50 

3. 8814 

3. 8814 
3. 8820 

3.8815  i  3.8816 

3.  8816 
3. 8822 

3. 8817 
3.  8822 

3.  8817 

3.  8818 
3.  8824 

3.  8818 
3.  8824 

3.  8819 
3.  8825 

2  7 

0 

3.  8820 

3. 8821 

3.  8821 

3.  8823 

( 

10 

3. 8825 

3. 8826 

3.  8826 

3.  8827 

3.  8828 

3. 8828 

3.  8829 

3.  8829 

3. 8830 

3.  8830 

7 

20 

3.  8831 

3. 8832 

3. 8832 

3.  8833 

3. 8833 

3. 8834 

3. 8834 

3.  8835 

3. 8835 

3. 8836 

7 

30 

3. 8837 

3. 8837 

3. 8838  3. 8838 

3. 8839 

3. 8839 

3. 8840 

3. 8841 

3.8841 

3. 8842 

7 

40 

3.  8842 

3. 8843 

3. 8843 

3. 8844 

3.  8845 

3. 8845 

3. 8846 

3.  8846 

3. 8847 

3. 8847 

7 

50 

3.  8848 

3. 8849 

3. 8849 

3. 8850 

3.  8850 

3. 8851 

3. 8851 

3. 8852 

3. 8852 

3. 8853 

2  8 

0 

3. 8854 

3. 8854 

3. 8855 

3.  8855 

3.  8856 

3. 8856 

3. 8857 

3. 8858 

3.8858 

3. 8859 

8 

10 

3. 8859 

3. 8860 

3. 8860 

3.  8861 

3. 8862 

3.  8862 

3. 8863 

3. 8863 

3. 8864 

3. 8864 

8 

20 

3.  8865 

3. 8865 

3.  8866 

3.  8867 

3. 8867 

3. 8868 

3. 8868 

3. 8869 

3. 8869 

3. 8870 

8 

30 

3. 8871 

3. 8871 

3.  8872 

3. 8872 

3. 8873 

3. 8873 

3. 8874 

3. 8874 

3. 8875 

3. 8876 

8 

40 

3. 8876 

3. 8877 

3.  8877 

3. 8878 

3. 8878 

3.8879 

3. 8880 

3. 8880 

3. 8881 

3. 8881 

8 

50 

3.  8882 

3. 8882 

3.  8883 

3. 8883 

3. 8884 

3. 8885 

3. 8885 

3. 8886 

3. 8886 

3. 8887 

2  9 

0 

3.  8887 

3. 8888 

3.  8889 

3. 8889 

3.  8890 

3.8890 

3. 8891 

3. 8891 

3. 8892 

3. 8892 

9 

10 

3.  8893 

3. 8894 

3.  8894 

3. 8895 

3. 8895 

3. 8896 

3. 8896 

3. 8897 

3. 8897 

3. 8898 

9 

20 

3.  8899 

3. 8899 

3. 8900 

3. 8900 

3. 8901 

3. 8901 

3. 8902 

3. 8903 

3. 8903 

3. 8904 

9 

30 

3.  8904 

3.  8905 

3. 8905 

3.  8906 

3. 8906 

3. 8907 

3. 8908 

3. 8908 

3. 8909 

3. 8909 

9 

40 

3. 8910 

3.  8910 

3. 8911 

3. 8911 

3. 8912 

3.  8912 

3.  8913 

3.  8914 

3.  8914 

3. 8915 

9 

50 

3. 8915 

3. 8916 

3.  8916 

3. 8917 

3.  8918 

3.  8918 

3. 8919 

3.  8919 

3. 8920 

3. 8920 

Page  326J 

APPENDIX  V:  TABLE  IX.                  1 

Logarithms  of  Small  Arcs  in 

Space  or 

Time. 

Arc.    1 

0" 

1" 

2" 

8" 

4" 

5" 

6" 

V 

8" 

9" 

o    / 

2h  10"' 

0' 

3. 8921 

3. 8922 

3.  8922 

3. 8923 

3. 8923 

3. 8924 

3. 8924 

3. 8925 

3.  8925 

3. 8926 

10 

10 

5. 8927 

3.  8927 

3.  8928 

3.  8928 

3. 8929 

3.8929 

3. 8930 

3. 8930 

3. 8931 

3. 8932 

10 

20 

3.  8932 

3.  8933 

3.  8933 

3. 8934 

3. 8934 

3.  8935 

3.  8935 

3. 8936 

3. 8937 

3. 8937 

10 

30 

3.  8938 

3. 8938 

3. 8939 

3.  8939 

3. 8940 

3. 8940 

3. 8941 

3. 8941 

3. 8942 

3. 8943 

10 

40 

3. 8943 

3. 8944 

3. 8944 

3.  8945 

3. 8945 

3. 8946 

3. 8946 

3. 8947 

3. 8948 

3.  8948 

10 

50 

3. 8949  * 

>  3. 8949 

3. 8950 

3.  8950 

3. 8951 

3. 8951 

3. 8952 

3.  8953 

3. 8953 

3. 8954 

2  11 

0 

3. 8954 

3. 8955 

3. 8955 

3. 8956 

3. 8956 

3.  8957 

3.  8958 

3.  8958 

3. 8959 

3. 8959 

11 

10 

3. 8960 

3. 8960 

3.  8961 

3.  8961 

3. 8962 

3. 8963 

3.  8963 

3.8964 

3.8964 

3.  8965 

11 

20 

3. 8965 

3. 8966 

3. 8966 

3. 8967 

3. 8967 

3. 8968 

3. 8969 

3. 8969 

3. 8970 

3. 8970 

11 

30 

3. 8971 

3. 8971 

3. 8972 

3.  8972 

3. 8973 

3. 8974 

3. 8974 

3. 8975 

3.  8975 

3.  8976 

11 

40 

3. 8976 

3. 8977 

3.  8977 

3.  8978 

3. 8978 

3.  8979 

3. 8980 

3. 8980 

3.  8981 

3.  8981 

11 

50 

3.  8982 

3. 8982 

3. 8983 

3. 8983 
3. 8989 

3. 8984 
3. 8989 

3.8985 

3. 8985 
3. 8991 

3. 8986 
3.  8991 

3.  8986 
3."8992 

3. 8987 
3. 8992 

2  12 

0 

3. 8987 

3. 8988 

3.  8988 

3. 8990 

12 

10 

3. 8993 

3. 8993 

3.  8994 

3. 8994 

3.  8995 

3. 8995 

3. 8996 

3. 8997 

3. 8997 

3. 8998 

12 

20 

3. 8998 

3. 8999 

3.  8999 

3.9000 

3. 9000 

3. 9001 

3.9001 

3. 9002 

3. 9003 

3. 9003 

12 

30 

3. 9004 

3. 9004 

3.  9005 

3. 9005 

3.9006 

3. 9006 

3. 9007 

3. 9007 

3. 9008 

3. 9009 

12 

40 

3. 9009 

3.  9010 

3.  9010 

3. 9011 

3.9011 

3.  9012 

3. 9012 

3. 9013 

3. 9013 

3. 9014 

12 

50 

3. 9015 

3. 9015 

3. 9016 

3. 9016 

3.9017 

3. 9017 

3.  9018 

3.  9018 

3.9019 

3. 9019 

2  13 

0 

3. 9020 

3. 9021 

3. 9021 

3. 9022 

3. 9022 

3.  9023 

3. 9023 

3.  9024 

3.  9024 

3.  9025 

13 

10 

3. 9025 

3. 9026 

3. 9027 

3. 9027 

3. 9028 

3. 9028 

3. 9029 

3.  9029 

3. 9030 

3. 9030 

13 

20 

3. 9031 

3. 9031 

3. 9032 

3. 9033 

3. 9033 

3. 9034 

3. 9034 

3.  9035 

3. 9035 

3. 9036 

13 

30 

3. 9036 

3. 9037 

3. 9037 

3. 9038 

3. 9038 

3. 9039 

3. 9040 

3.  9040 

3. 9041 

3.  9041 

13 

40 

3. 9042 

3. 9042 

3.9043 

3. 9043 

3. 9044 

3.  9044 

3. 9045 

3. 9046 

3. 9046 

3. 9047 

13 

50 

3. 9047 

3. 9048 

3. 9048 

3. 9049 

3. 9049 

3. 9050 

3. 9050 

3. 9051 

3. 9051 

3. 9052 

2  14 

0 

3.  9053 

3. 9053 

3.  9054 

3. 9054 

3. 9055 

3. 9055 

3. 9056 

3. 9056 

3. 9057 

3. 9057 

14 

10 

3. 9058 

3.  9058 

3.  9059 

3. 9060 

3. 9060 

3. 9061 

3. 9061 

3. 9062 

3. 9062 

3. 9063 

14 

20 

3. 9063 

3. 9064 

3.  9064 

3. 9065 

3. 9066 

3.  9066 

3.  9067 

3. 9067 

3. 9068 

3. 9068 

14 

30 

3. 9069 

3.  9069 

3.  9070 

3. 9070 

3. 9071 

3. 9071 

3.  9072 

3. 9073 

3. 9073 

3. 9074 

14 

40 

3. 9074 

3. 9075 

3.  9075 

3. 9076 

3.  9076 

3. 9077 

3.  9077 

3.  9078 

3. 9078 

3. 9079 

14 

50 

3. 9079 

3. 9080 

3. 9081 

3. 9081 

3.  9082 
3. 9087 

3. 9082 
3. 9088 

3.  9083 
3. 9088 

3. 9083 
3. 9089 

3.  9084 
"3.  9089 

3. 9084 
3. 9090 

2  15 

0 

3. 9085 

3. 9085 

3. 9086 

3. 9086 

15 

10 

3.  9090 

3. 9091 

3.  9091 

3. 9092 

3.  9092 

3. 9093 

3. 9093 

3. 9094 

3. 9094 

3.  9095 

15 

20 

3. 9096 

3.  9096 

3. 9097 

3. 9097 

3. 9098 

3. 9098 

3. 9099 

3.  9099 

3. 9100 

3.  9100 

15 

30 

3. 9101 

3. 9101 

3. 9102 

3. 9103 

3. 9103 

3. 9104 

3.9104 

3.  9105 

3. 9105 

3.  9106 

15 

40 

3. 9106 

3.  9107 

3. 9107 

3.  9108 

3. 9108 

3.  9109 

3.  9109 

3. 9110 

3.  9111 

3.9111 

15 

50 

3.9112 

3. 9112 

3. 9113 

3.  9113 

3.9114 

3.9114 

3.9115 

3. 9115 

3.  9116 

3. 9116 

2  16 

0 

3.9117 

3.9117 

3.9118 

3.9118 

3.9119 

3.  9120 

3.9120 

3. 9121 

3.9121 

3.  9122 

16 

10 

3. 9122 

3.9123 

3.  9123 

3.  9124 

3.  9124 

3.  9125 

3.  9125 

3. 9126 

3.  9126 

3.9127 

16 

20 

3.  9128 

3. 9128 

3. 9129 

3.  9129 

3. 9130 

3. 9130 

3. 9131 

3. 9131 

3.  9132 

3. 9132 

16 

30 

3.  9133 

3. 9133 

3.  9134 

3.  9134 

3.  9135 

3. 9135 

3. 9136 

3. 9137 

3.9137 

3. 9138 

16 

40 

3.  9138 

3. 9139 

3.  9139 

3.  9140 

3. 9140 

3. 9141 

3. 9141 

3.  9142 

3.  9142 

3. 9143 

16 

50 

3. 9143 

3.  9144 

3. 9144 

3. 9145 

3.  9146 

3.9146 

3. 9147 

3. 9147 

3.  9148 

8. 9148 

2  17 

0 

3. 9149 

3. 9149 

3. 9150 

3. 9150 

3. 9151 

3.  9151 

3. 9152 

3. 9152 

3.  9153 

3.9153 

17 

10 

3. 9154 

3.9155 

3. 9155 

3.  9156 

3.  9156 

3.9157 

3. 9157 

3. 9158 

3. 9158 

3.9159 

17 

20 

3. 9159 

3. 9160 

3.  9160 

3.  9161 

3. 9161 

3.  9162 

3. 9162 

3. 9163 

3. 9163 

3. 9164 

17 

30 

3.  9165 

3. 9165 

3.  9166 

3. 9166 

3.  9167 

3.9167 

3. 9168 

3.9168 

3. 9169 

3. 9169 

17 

40 

3.  9170 

3. 9170 

3.  9171 

3.9171 

3. 9172 

3.  9172 

3. 9173 

3.9173 

3. 9174 

3. 9175 

17 

50 

3. 9175 

3. 9176 

3.  9176 

3.9177 

3.9177 

3.  9178 

3. 9178 

3. 9179 

3.  9179 

3.  9180 

2  18 

0 

3. 9180 

3.  9181 

3.  9181 

3. 9182 

3. 9182 

3.  9183 

3. 9183 

3. 9184 

3. 9184 

3. 9185 

18 

10 

3. 9186 

3.  9186 

3.  9187 

3. 9187 

3. 9188 

3. 9188 

3. 9189 

3. 9189 

3. 9190 

3. 9190 

18 

20 

3.  9191 

3. 9191 

3. 9192 

3.  9192 

3.  9193 

3.  9193 

3. 9194 

3. 9194 

3. 9195 

3.  9195 

18 

30 

3. 9196 

3.  9197 

3. 9197 

3.  9198 

3. 9198 

3. 9199 

3. 9199 

3. 9200 

3. 9200 

3. 9201 

18 

40 

3. 9201 

3. 9202 

3. 9202 

3.  9203 

3.  9203 

3. 9204 

3.9204 

3. 9205 

3. 9205 

3.9206 

18 

50 

3.  9206 

3. 9207 

3.  9207 

3. 9208 

3. 9209 
3. 9214 

3. 9209 

3.  9210 

3. 9210 
3. 9215 

3. 9211 
3.  9216 

3.  9211 

2  19 

0 

3. 9212 

3. 9212 

3. 9213 

3. 9213 

3. 9214 

3.  9215 

3. 9216 

19 

10 

3. 9217 

3.  9217 

3. 9218 

3.  9218 

3. 9219 

3.  9219 

3.  9220 

3. 9221 

3. 9221 

3. 9222 

19 

20 

3. 9222 

3. 9223 

3.  9223 

3. 9224 

3. 9224 

3. 9225 

3.  9225 

3. 9226 

3. 9226 

3. 9227 

19 

30 

3. 9227 

3. 9228 

3.  9228 

3. 9229 

3.9229 

3. 9230 

3. 9230 

3. 9231 

3. 9231 

3.  9232 

19 

40 

3. 9232 

3. 9233 

3. 9233 

3. 9234 

3. 9235 

3. 9235 

3. 9236 

3. 9236 

3. 9237 

3. 9237 

19 

50 

3. 9238 

3. 9238 

3. 9239 

3. 9239 

3. 9240 

3. 9240 

3. 9241 

3. 9241 

3. 9242 

3. 9242 

1 

APPENDIX  V:  TABLE  IX. 

[Page  327 

Logarithms  of  Small  Arcs  in  Space  or 

Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

5" 

6" 

7" 

8" 

9" 

0      / 

2*^  20™ 

0' 

3.  9243 

3. 9243 

3. 9244 

3. 9244 

3. 9245 

3. 9245 

3. 9246 

3.9246 

3. 9247 

3, 9247 

20 

10 

3.  9248 

3. 9248 

3. 9249 

3. 9250 

3. 9250 

3. 9251 

3. 9251 

3. 9252 

3. 9252 

3. 9253 

20 

20 

3.  9253 

3. 9254 

3. 9254 

3. 9255 

3. 9255 

3. 9256 

3. 9256 

3. 9257 

3. 9257 

3.  9258 

20 

30 

3.  9258 

3. 9259 

3.  9259 

3. 9260 

3. 9260 

3. 9261 

3. 9261 

3. 9262 

3. 9262 

3.  9263 

20 

40 

3.  9263 

3. 9264 

3.  9264 

3.  9265 

3. 9265 

3. 9266 

3. 9267 

3. 9267 

3. 9268 

3. 9268 

20 

50 

3.  9269 

3. 9269 

3. 9270 

3. 9270 

3. 9271 

3. 9271 

3. 9272 

3. 9272 

3.  9273 

3. 9273 

2  21 

0 

3.  9274 

3.  9274 

3. 9275 

3. 9275 

3.9276  i  3.9276 

3. 9277 

3. 9277 

3.  9278 

3. 9278 

21 

10 

3.  9279 

3.  9279 

3.  9280 

3. 9280 

3.9281  1  3.9281 

3. 9282 

3. 9282 

3. 9283 

3. 9283 

21 

20 

3.  9284 

3.  9284  . 

3. 9285 

3. 9285 

3.9286  1  3.9287 

3. 9287 

3. 9288 

3. 9288 

3. 9289 

21 

30 

3.  9289 

3. 9290 

3.  9290 

3. 9291 

3. 9291  3. 9292 

3. 9292 

3.9293  3.9293 

3.  9294 

21 

40 

3.  9294 

3.  9295 

3. 9295 

3.  9296 

3. 9296 

3. 9297 

3. 9297 

3.9298  3.9298 

3. 9299 

21 

50 

3. 9299 

3.9300 

3. 9300 

3. 9301 

3. 9301 

3. 9302 

3. 9302 

3. 9303 

3. 9303 

3. 9304 

2  22 

0 

3. 9304 

3. 9305 

3. 9305 

3. 9306 

3. 9306 

3. 9307 

3. 9307 

3. 9308 

3. 9308  1  3. 9309  | 

22 

10 

3. 9309 

3. 9310 

3. 9311 

3.9311 

3. 9312 

3. 9312 

3. 9313 

3. 9313 

3. 9314 

3. 9314 

22 

20 

3. 9315 

3. 9315 

3. 9316 

3.  9316 

3.9317 

3.9317 

3. 9318 

3. 9318 

3. 9319 

3. 9319 

22 

30 

3. 9320 

3. 9320 

3. 9321 

3.  9321 

3.9322  1  3.9322 

3. 9323 

3. 9323 

3. 9324 

3. 9324 

22 

40 

3. 9325 

3. 9325 

3. 9326 

3. 9326 

3.9327  3.9.327 

3. 9328 

3. 9328 

3. 9329 

3. 9329 

22 

50 

3. 9330 

3. 9330 

3. 9331 

3. 9331 
379336" 

3.9332  3.9332 

3. 9333 

3. 9333 

3. 9334 

3.  9334 

2  23 

0 

3. 9335 

3. 9335 

3. 9336 

3.9337  ;  3.9337 

3. 9338 

3.9338  3.9339 

3. 9339 

23 

10 

3. 9340 

3.  9340 

3. 9341 

3. 9341 

3. 9342  3.' 9342 

3. 9343 

3.  9343 

3. 9344 

3. 9344 

23 

20 

3. 9345 

3.  9345 

3. 9346 

3. 9346 

3. 9347  3.  9348 

3. 9348 

3. 9349 

3. 9349 

3. 9350 

23 

30 

3. 9350 

3.  9351 

3.  9351 

3. 9352 

3.9352  !  3.9353 

3. 9353 

3.9354 

3. 9354 

3. 9355 

23 

40 

3. 9355 

3.  9356 

3.  9356 

3. 9357 

3.9357  1  3.9358 

3. 9358 

3. 9359 

3. 9359 

3. 9360 

23 

50 

3. 9360 

3. 9361 

3.  9361 

3. 9362 

3.9362  1  3.9363 

3. 9363 

3. 9364 

3. 9364 

3.  9365 

2  24 

0 

3. 9365 

3. 9366 

3. 9366 

3. 9367 

3. 9367 

3. 9368 

3.  9368 

3.  9369 

3. 9369  i  3. 9370 

24 

10 

3. 9370 

3.  9371 

3. 9371 

3. 9372 

3. 9372 

3. 9373 

3. 9373 

3. 9374 

3.9374  3.9375 

24 

20 

3. 9375 

3. 9376 

3. 9376 

3. 9377 

3. 9377 

3. 9378 

3. 9378 

3. 9379 

3. 9379  3. 9380 

24 

30 

3. 9380 

3. 9381 

3. 9381 

3. 9382 

3. 9382 

3.  9383 

3. 9383 

3. 9384 

3. 9384  i  3. 9385 

24 

40 

3. 9385 

3. 9386 

3. 9386 

3. 9387 

3. 9387 

3. 9388 

3. 9388 

3. 9389 

3. 9389  i  3. 9390 

24 

50 

3. 9390 

3.  9391 

3. 9391 

3. 9392 

3.  9392 
3. 9397 

3. 9393 
3. 9398 

3. 9393 

3. 9394 

3. 9394 
3. 9399 

3. 9395 

2  25 

0 

3. 9395 

3. 9396 

3.  9396 

3. 9397 

3. 9398 

3. 9399 

3.9400 

25 

10 

3. 9400 

3. 9401 

3. 9401 

3. 9402 

3. 9402 

3. 9403 

3. 9403 

3. 9404 

3. 9404 

3. 9405 

25 

20 

3. 9405 

3. 9406 

3. 9406 

3. 9407 

3. 9407 

3. 9408 

3. 9408 

3. 9409 

3.  9409 

3. 9410 

25 

30 

3. 9410 

3.9411 

3.  9411 

3. 9412 

3. 9412 

3. 9413 

3. 9413 

3. 9414 

3. 9414 

3.  9415 

25 

40 

3. 9415 

3.  9416 

3. 9416 

3.  9417 

3. 9417 

3. 9418 

3. 9418 

3. 9419 

3. 9419 

3. 9420 

25 

50 

3. 9420 

3. 9421 

3.  9421 

3.  9422 

3. 9422 

3.  9423 

3. 9423 

3. 9424 

3. 9424 

3.  9425 

2  26 

0 

3. 9425 

3. 9426 

3.  9426 

3. 9427 

3. 9427 

3. 9428 

3. 9428 

3.  9429 

3. 9429 

3. 9430 

26 

10 

3. 9430 

3. 9430 

3.  9431 

3. 9431 

3. 9432 

3. 9432 

3. 9433 

3. 9433 

3. 9434 

3. 9434 

26 

20 

3. 9435 

3. 9435 

3.  9436 

3. 9436 

3. 9437 

3. 9437 

3. 9438 

3. 9438 

3. 9439 

3.  9439 

26 

30 

3. 9440 

3.9440 

3.  9441 

3. 9441 

3. 9442 

3. 9442 

3. 9443 

3. 9443 

3.  9444 

3.  9444 

26 

40 

3. 9445 

3.9445 

3.  9446 

3. 9446 

3. 9447 

3. 9447 

3. 9448 

3. 9448 

3.9449 

3. 9449 

26 

50 

3. 9450 

3. 9450 

3. 9451 

3. 9451 

3. 9452 

3. 9452 

3. 9453 

3. 9453 

3. 9454 

3. 9454 

2  27 

0 

3. 9455 

3. 9455 

3. 9456 

3. 9456 

3. 9457 

3. 9457 

3. 9458 

3. 9458 

3. 9459 

3. 9459 

27 

10 

3. 9460 

3.  9460 

3. 9461 

3. 9461 

3. 9462 

3. 9462 

3. 9463 

3. 9463 

3.9464 

3. 9464 

27 

20 

3. 9465 

3. 9465 

3. 9466 

3. 9466 

3.  9466 

3. 9467 

3.  9467 

3. 9468 

3. 9468 

3. 9469 

2-' 

30 

3. 9469 

3. 9470 

3.  9470 

3. 9471 

3. 9471 

3. 9472 

3. 9472 

3.  9473 

3. 9473 

3. 9474 

27 

40 

3. 9474 

3. 9475 

3.  9475 

3. 9476 

3. 9476 

3. 9477 

3. 9477 

3. 9478 

3. 9478 

3. 9479 

27 

50 

3. 9479 

3. 9480 

3. 9480 

3. 9481 

3. 9481 

3. 9482 

3. 9482 

3. 9483 

3. 9483 

3.  9484 

2  28 

0 

3. 9484 

3. 9485 

3.  9485 

3. 9486 

3. 9486 

3. 9487 

3. 9487 

3. 9488 

3. 9488 

3.  9489 

28 

10 

3. 9489 

3. 9490 

3.  9490 

3. 9490 

3. 9491 

3.  9491 

3. 9492 

3. 9492 

3.  9493 

3.  9493 

28 

20 

3.  9494 

3.  9494 

3. 9495 

3. 9495 

3.  9496 

3. 9496 

3. 9497 

3. 9497 

3. 9498 

3. 9498 

28 

30 

3.  9499 

3. 9499 

3. 9500 

3. 9500 

3. 9501 

3. 9501 

3. 9502 

3. 9502 

3.  9503 

3. 9503 

28 

40 

3. 9504 

3.  9504 

3. 9505 

3. 9505 

3.  9506 

3. 9506 

3. 9507 

3. 9507 

3.  9508 

3. 9508 

28 

50 

3.  9509 

3.  9509 

3.9509 

3. 9510 

3. 9510 

3.  9511 

3. 9511 

3. 9512 

3. 9512 

3.  9513 

2  29 

0 

3.  9513 

3. 9514 

3. 9514 

3. 9515 

3. 9515 

3. 9516 

3. 9516 

3. 9517 

3. 9517 

3. 9518 

29 

10 

3. 9518 

3.  9519 

3.  9519 

3. 9520 

3.  9520 

3. 9521 

3. 9521 

3.  9522 

3. 9522 

3. 9523 

29 

20 

3. 9523 

3.  9524 

3. 9524 

3. 9525 

3.  9525 

3. 9526 

3. 9526 

3. 9526 

3. 9527 

3. 9527 

29 

30 

3. 9528 

3.  9528 

3. 9529 

3. 9529 

3. 9530 

3. 9530 

3. 9531 

3. 9531 

3. 9532 

3. 9532 

29 

40 

3.  9533 

3. 9533 

3. 9534 

3. 9534 

3. 9535 

3. 9435 

3. 9536 

3. 9536 

3. 9537 

3. 9537 

29 

50 

3.  9538 

3. 9538 

3. 9539 

3. 9539 

3. 9540 

3.  9540 

3. 9540 

3. 9541 

3. 9541 

3.9542 

Page 

328] 

APPENDIX  V:  TABLE  IX. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

5" 

6" 

7"   1   8"   1    9"    1 

o    / 

2^   30" 

0' 

3.9542  1  3.9543 

3.9543 

3.9544 

3.9544 

3. 9545 

3. 9545 

3. 9546 

3.9546 

3. 9547 

30 

10 

3.9547  1  3.9548 

3. 9548 

3. 9549 

3. 9549 

3.9550 

3. 9550 

3. 9551 

3. 9551 

3. 9552 

30 

20 

3. 9552 

3. 9553 

-3.9553 

3. 9554 

3. 9554 

3. 9554 

3. 9555 

3. 9555 

3. 9556 

3. 9556 

30 

30 

3. 9557 

3. 9557 

3. 9558 

3. 9558 

3. 9559 

3. 9559 

3. 9560 

3. 9560 

3. 9561 

3. 9561 

30 

40 

3. 9562  1  ^. 9562 
3.9566  !  3.9567 

3. 9563 

3. 9563 

3. 9564 

3. 9564 

3. 9565 

3. 9565 

3. 9566 

3. 9566 

30 

50 

3. 9567 

3. 9568 
3. 9573 

3. 9568 
3. 9573 

3. 9569 
3.9574 

3. 9569 

3. 9570 

3. 9570 
3:9575' 

3. 9571 
3.  9576 

2  31 

0 

3.9571  3.9572 

3. 9572 

3. 9574 

3.  9575 

31 

10 

3.9576  3.9577 

3. 9577 

3. 9578 

3. 9578 

3. 9578 

3. 9579 

3. 9579 

3. 9580 

3. 9580 

31 

20 

3.9581  t  3.9581 

3. 9582 

3. 9582 

3. 9583 

3. 9583 

3. 9584 

3. 9584 

3. 9585 

3. 9585 

31 

30 

3.9586  3.9586 

3. 9587 

3. 9587 

3. 9588 

3. 9588 

3.  9589 

3.9589  3.9589 

3. 9590 

31 

40 

3.9590  3.9591 

3. 9591 

3. 9592 

3. 9592 

3. 9593 

3. 9593 

3. 9594  3. 9594 

3. 9595 

31 

50 

3.9595  !  3.9596 

3. 9596 

3. 9597 

3. 9597 

3. 9598 

3. 9598 

3. 9599  !  3. 9599 

3. 9599 

2  32 

0 

3.9600  1  3.9600 

3. 9601 

3. 9601 

3. 9602 

3. 9602 

3. 9603 

3. 9603 

3. 9604 

3. 9604 

32 

10 

3.  9605 

3. 9605 

3. 9606 

3. 9606 

3. 9607 

3. 9607 

3. 9608 

3.  9608 

3. 9609 

3. 9609 

32 

20 

3.  9609 

3. 9610 

3. 9610 

3. 9611 

3.9611 

3. 9612 

3. 9612 

3.  9613 

3. 9613 

3. 9614 

32 

30 

3. 9614 

3. 9615 

3. 9615 

3. 9616 

3. 9616 

3. 9617 

3. 9617 

3. 9618 

3. 9618 

3. 9618 

32 

40 

3. 9619 

3. 9619 

3.  9620 

3. 9620 

3. 9621 

3.  9621 

3. 9622 

3. 9622 

3. 9623 

3. 9623 

32 

50 

3. 9624 

3. 9624 

3.  9625 

3. 9625 

3. 9626 

3. 9626 

3. 9627 

3. 9627 

3. 9627 
3. 9632 

3. 9628 
3. 9633 

2  33 

0 

3. 9628 

3. 9629 

3. 9629 

3. 9630 

3. 9630 

3. 9631 

3. 9631 

3. 9632 

33 

10 

3. 9633 

3. 9634 

3. 9634 

3. 9634 

3. 9635 

3.  9635 

3. 9636 

3. 9636 

3. 9637 

3. 9637 

33 

20 

3. 9638 

3.  96.38 

3. 9639 

3. 9639 

3. 9640 

3.  9640 

3.9641 

3.9641 

3. 9642 

3. 9642 

33 

30 

3. 9642 

3. 9643 

3. 9643 

3. 9644 

3.9644 

3.9645 

3. 9645 

3. 9646 

3.9646 

3. 9647 

33 

40 

3. 9647 

3. 9648 

3. 9648 

3. 9649 

3. 9649 

3. 9650 

3. 9650 

3. 9651 

3. 9651 

3. 9652 

33 

50 

3. 9652 

3. 9653 

3. 9653 

3. 9653 

3. 9654 

3. 9654 

3.  9655 

3. 9655 

3. 9656 

3. 9656 

2  34 

0 

3.9657 

3. 9657 

3. 9658 

3. 9658 

3. 9658 

3. 9659 

3. 9659 

3. 9660 

3. 9660 

3. 9661 

34 

10 

3. 9661 

3. 9662 

3. 9662 

3. 9663 

3. 9663 

3. 9664 

3.  9664 

3. 9665 

3. 9665 

3. 9665 

34 

20 

3. 9666 

3. 9666 

3. 9667 

3. 9667 

3. 9668 

3. 9668 

3. 9669 

3. 9669 

3. 9670 

3. 9670 

34 

30 

3. 9671 

3. 9671 

3. 9672 

3. 9672 

3. 9672 

3. 9673 

3.9673 

3. 9674 

3. 9674 

3.  9675 

34 

40 

3. 9675 

3. 9676 

3. 9676 

3. 9677 

3. 9677 

3.9678  I  3.9678 

3. 9679 

3. 9679 

3. 9680 

34 

50 

3. 9680 

3. 9681 

3. 9681 

3. 9682 

3. 9682 

3. 9682 

3. 9683 

3.  9683 

3. 9684  3. 9684 

2  35 

0 

3.  9685 

3. 9685 

3. 9686 

3. 9686 

3. 9687 

3. 9687 

3. 9688 

3. 9688 

3. 9689  i  3. 9689 

35 

10 

3.  9689 

3. 9690 

3. 9690 

3. 9691 

3. 9691 

3. 9692 

3. 9692 

3. 9693 

3. 9693 

3. 9694 

35 

20 

3.  9694 

3. 9695 

3.  9695 

3. 9696 

3.  9696 

3. 9696 

3. 9697 

3. 9697 

3. 9698 

3. 9698 

35 

30 

3.  9699 

3. 9699 

3. 9700 

3.  9700 

3. 9701 

3. 9701 

3. 9702 

3. 9702 

3. 9703 

3.  9703 

35 

40 

3.  9703 

3. 9704 

3. 9704 

3. 9705 

3. 9705 

3. 9706 

3. 9706 

3. 9707 

3. 9707  i  3.  9708  | 

35 

50 

3.  9708 
3.9713 

3.  9709 

3. 9709 

3. 9710 

3. 9710 

3. 9710 

3.9711 

3.9711 

3. 9712 

3. 9712 

2  36 

0 

3.9713 

3. 9714 

3.  9714 

3. 9715 

3. 9715 

3. 9716 

3.  9716 

3. 9716 

3. 9717 

36 

10 

3. 9717 

3.9718 

3. 9718 

3.  9719 

3.  9719 

3.  9720 

3. 9720 

3.  9721 

3. 9721 

3.  9722 

36 

20 

3. 9722 

3. 9722 

3.  9723 

3.  9723 

3. 9724 

3.  9724 

3.  9725 

3.  9725 

3.  9726 

3. 9726 

36 

30 

3. 9727 

3. 9727 

3.  9728 

3.  9728 

3.  9729 

3. 9729 

3.  9729 

3. 9730 

3.9730  3.9731 

36 

40 

3. 9731 

3. 9732 

3. 9732 

3. 9733 

3. 9733 

3.  9734 

3.  9734 

3. 9735 

3. 9735  1  3.  9735 

36 

50 

3.  9736 

3. 9736 

3. 9737 

3. 9737 

3. 9738 

3. 9738 

3.  9739 

3.  9739 

3. 9740  :  3. 9740 

2  37 

0 

3. 9741 

3. 9741 

3. 9741 

3. 9742 

3. 9742 

3. 9743 

3. 9743 

3. 9744 

3. 9744  i  3.  9745 

37 

10 

3. 9745 

3. 9746 

3.  9746 

3. 9746 

3. 9747 

3. 9747 

3. 9748 

3.  9748 

3. 9749  i  3. 9749 

37 

20 

3. 9750 

3. 9750 

3. 9751 

3. 9751 

3. 9752 

3.  9752 

3. 9752 

3. 9753 

3. 9753 

3.  9754 

37 

30 

3. 9754 

3. 9755 

3. 9755 

3. 9756 

3.  9756 

3.  9757 

3. 9757 

3. 9758 

3.  9758 

3.  9758 

37 

40 

3.  9759 

3. 9759 

3. 9760 

3. 9760 

3. 9761 

3. 9761 

3.  9762 

3.  9762 

3. 9763 

3. 9763 

37 

50 

3. 9763 

3. 9764 

3.9764 

3. 9765 

3. 9765 

3.  9766 

3.  9766 

3. 9767 

3.  9767 

3. 9768 

2  38 

0 

3.  9768 

3. 9769 

3. 9769 

3. 9769 

3. 9770 

3.  9770 

3. 9771 

3. 9771 

3.  9772 

3. 9772 

38 

10 

3.  9773 

3. 9773 

3.  9774 

3. 9774 

3. 9774 

3.  9775 

3. 9775 

3. 9776 

3. 9776 

3. 9777 

38 

20 

3. 9777 

3. 9778 

3. 9778 

3. 9779 

3. 9779 

3.  9779 

3. 9780 

3. 9780 

3.  9781 

3. 9781 

38 

30 

3.  9782 

3. 9782 

3. 9783 

3. 9783 

3.  9784 

3. 9784 

3. 9785 

3. 9785 

3. 9785 

3. 9786 

38 

40 

3.  9786 

3. 9787 

3. 9787 

3. 9788 

3. 9788 

3.  9789 

3.  9789 

3.  9790 

3. 9790 

3.  9790 

38 

50 

3. 9791 

3. 9791 

3. 9792 

3. 9792 

3. 9793 

3. 9793 

3. 9794 

3. 9794 

3.  9795 

3. 9795 

2  39 

0 

3. 9795 

3. 9796 

3. 9796 

3.  9797 

3. 9797 

3. 9798 

3. 9798 

3. 9799 

3.  9799 

3.  9800 

39 

10 

3. 9800 

3. 9800 

3. 9801 

3.  9801 

3. 9802 

3. 9802 

3.  9803 

3. 9803 

3.  9804 

3.  9804 

39 

20 

3.  9805 

3. 9805 

3. 9805 

3.  9806 

3. 9806 

3.  9807 

3. 9807 

3. 9808 

3. 9808 

3. 9809 

39 

30 

3.  9809 

3.9810 

3. 9810 

3. 9810 

3.9811 

3. 9811 

3. 9812 

3. 9812 

3. 9813 

3. 9813 

39 

40 

3. 9814 

3.9814 

3. 9815 

3.  9815 

3. 9815 

3. 9816 

3. 9816 

3.9817 

3.9817 

3.9818 

39 

50 

3.  9818 

3.9819 

.3.  9819 

3.9819 

3. 9820 

3.  9820 

3.  9821 

3. 9821 

3. 9822 

3. 9822 

APPENDIX  V:  TABLE  IX. 

[Page  329 

Logarithms  of  Small  Arcs  in 

Space  or  Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

5" 

6" 

7"    1   8" 

9" 

o     /     // 

2h  40m   0* 

3. 9823 

3.  9823 

3. 9824 

3.  9824 

3. 9825 

3.  9825 

3. 9825 

3. 9826 

3. 9826 

3. 9827 

40 

10 

3. 9827 

3. 9828 

3. 9828 

3. 9829 

3. 9829 

3. 9829 

3. 9830 

3. 9830 

3. 9831 

3. 9831 

40 

20 

3. 9832 

3. 9832 

3. 9833 

3. 9833 

3.  9834 

3. 9834 

3. 9834 

3. 9835 

3. 9835 

3. 9836 

40 

30 

3. 9836 

3. 9837 

3. 9837 

3. 9838 

3.  9838 

3. 9839 

3. 9839 

3. 9839 

3. 9840 

3. 9840 

40 

40 

3. 9841 

3. 9841 

3. 9842 

3. 9842 

3. 9843 

3. 9843 

3. 9843 

3. 9844 

3. 9844 

3. 9845 

40 

50 

3. 9845 

3. 9846 

3. 9846 

3. 9847 

3. 9847 

3. 9848 

3. 9848 

3. 9848 

3. 9849 

3. 9849 

2  41 

0 

3. 9850 

3.9850 

3. 9851 

3. 9851 

3.  9852 

3. 9852 

3. 9852 

3. 9853 

3. 9853 

3.  9854 

41 

10 

3. 9854 

3. 9855 

3. 9855 

3. 9856 

3.  9856 

3. 9857 

3.  9857 

3. 9857 

3. 9858 

3. 9858 

41 

20 

3. 9859 

3. 9859 

3. 9860 

3. 9860 

3. 9861 

3. 9861  3.  9861 

3. 9862 

3. 9862 

3.  9863 

41 

30 

3.  9863 

3.  9864 

3. 9864 

3. 9865 

3. 9865 

3. 9865  3. 9866 

3.9866 

3. 9867 

3. 9867 

41 

40 

3.  9868 

3. 9868 

3. 9869 

3. 9869 

3. 9870 

3.9870 

3. 9870 

3. 9871 

3. 9871 

3. 9872 

41 

50 

3.  9872 

3. 9873 

3.  9873 

3. 9874  3. 9874 

3. 9874 

3. 9875 

3. 9875 

3. 9876 

3. 9876 

2  42 

0 

3.  9877 

3. 9877 

3. 9878 

3. 9878 

3.  9878 

3. 9879 

3. 9879 

3. 9880 

3. 9880 

3.  9881 

42 

10 

3.  9881 

3. 9882 

3. 9882 

3. 9882 

3. 9883 

3. 9883 

3. 9884 

3. 9884 

3. 9885 

3.  9885 

42 

20 

3. 9886 

3.  9886 

3. 9886 

3. 9887 

3. 9887 

3. 9888 

3. 9888 

3. 9889  i  3. 9889 

3. 9890 

42 

30 

3. 9890 

3. 9890 

3. 9891 

3. 9891 

3.  9892 

3.  9892 

3. 9893 

3. 9893  i  3.  9894 

3. 9894 

42 

40 

3. 9894 

3. 9895 

3. 9895 

3.9896  i  3.9896 

3. 9897 

3. 9897 

3. 9898  i  3.  9898 

3. 9898 

42 

50 

3. 9899 

3. 9899 

3.9900 

3.9900  !  3.9901 

3. 9901 

3. 9902 

3. 9902 

3. 9903 

3. 9903 

2  43 

0 

3. 9903 

3.  9904 

3. 9904 

3. 9905  3. 9905 

3.9906 

3. 9906 

3. 9906 

3. 9907  1  3. 9907 

43 

10 

3. 9908 

3.  9908 

3. 9909 

3. 9909  3. 9910 

3. 9910 

3. 9910 

3.9911 

3.9911  1  3.9912 

43 

20 

3.  9912 

3. 9913 

3. 9913 

3.9914  :  3.9914 

3.  9914 

3.  9915 

3. 9915 

3.9916!  3.9916 

43 

30 

3. 9917 

3. 9917 

3. 9918 

3.9918  I  3.9918 

3.  9919 

3.  9919 

3. 9920 

3. 9920  1  3. 9921 

43 

40 

3. 9921 

3. 9922 

3. 9922 

3. 9922 

3. 9923 

3. 9923 

3. 9924 

3. 9924 

3. 9925  !  3. 9925 

43 

50 

3. 9926 

3. 9926 

3. 9926 

3. 9927 

3. 9927 

3. 9928 

3.  9928 

3. 9929 

3. 9929 

3. 9930 

2  44 

0 

3. 9930 

3. 9930 

3. 9931 

3.  9931 

3. 9932 

3. 9932 

3. 9933 

3. 9933  1  3. 9933 

3. 9934 

44 

10 

3.  9934 

3. 9935 

3. 9935 

3.  9936 

3. 9936 

3. 9937 

3. 9937 

3. 9937  1  3. 9938  [   3. 9938 

44 

20 

3. 9939 

3.  9939 

3.  9940  1  3. 9940 

3. 9941 

3. 9941 

3. 9941 

3. 9942  3. 9942  3. 9943 

44 

30 

3. 9943 

3.  9944 

3. 9944 

3. 9944 

3.  9945 

3. 9945 

3. 9946 

3.  9946  I  3. 9947  ;  3.  9947 

44 

40 

3. 9948 

3. 9948 

3. 9948 

3. 9949 

3. 9949 

3. 9950 

3. 9950 

3. 9951 

3. 9951  i  3. 9952  | 

44 

50 

3. 9952 

3. 9952 

3. 9953 

3. 9953 

3. 9954 

3.9954  i  3.9955 

3. 9955 

3. 9955 

3. 9956 

2  45 

0 

3.  9956 

3. 9957 

3. 9957 

3. 9958 

3. 9958 

3. 9959 

3. 9959 

3. 9959 

3. 9960 

3. 9960 

45 

10 

3.  9961 

3.  9961 

3. 9962 

3. 9962 

3. 9962 

3. 9963 

3. 9963 

3. 9964 

3. 9964 

3. 9965 

45 

20 

3.  9965 

3.  9966 

3. 9966 

3. 9966 

3.  9967 

3. 9967 

3. 9968 

3. 9968 

3. 9969 

3. 9969 

45 

30 

3.  9969 

3. 9970 

3. 9970 

3. 9971 

3. 9971 

3. 9972 

3.9972 

3. 9973 

3. 9973 

3.  9973 

45. 

40 

3. 9974 

3. 9974 

3. 9975 

3. 9975 

3. 9976 

3.  9976 

3. 9976 

3. 9977 

3.9977 

3.  9978 

45 

50 

3.  9978 

3. 9979 

3. 9979 

3. 9980 

3. 9980 

3.  9980 

3. 9981 

3. 9981 

3. 9982 

3. 9982 

2  46 

0 

3. 9983 

3. 9983 

3.9983  1  3.9984 

3. 9984 

3. 9985 

3. 9985 

3. 9986 

3. 9986 

3. 9987 

46 

10 

3. 9987 

3. 9987 

3. 9988 

3. 9988 

3. 9989 

3. 9989 

3. 9990 

3. 9990 

3.  9990 

3. 9991 

46 

20 

3. 9991 

3. 9992 

3. 9992 

3. 9993 

3. 9993 

3. 9993 

3. 9994 

3. 9994 

3. 9995 

3. 9995 

46 

30 

3. 9996 

3. 9996 

3. 9997 

3. 9997 

3. 9997 

3. 9998 

3. 9998 

3.9999 

3. 9999 

4.  0000 

46 

40 

4.  0000 

4.  0000 

4. 0001 

4.0001 

4. 0002 

4.  0002 

4. 0003 

4.0003 

4. 0003 

4.0004 

46 

50 

4.  0004 

4.  0005 

4.  0005 

4.0006 

4. 0006 

4.0007 

4. 0007 

4.0007 

4. 0008 

4. 0008 

2  47 

0 

4.  0009 

4.0009 

4.  0010 

4.  0010 

4.  0010 

4.0011 

4.0011 

4. 0012 

4.0012!  4.0013  1 

47 

10 

4.  0013 

4. 0013 

4.  0014 

4.0014 

4.  0015 

4. 0015 

4.  0016 

4. 0016 

4.  0016 

4.0017 

47 

20 

4.  0017 

4.0018 

4.  0018 

4.  0019 

4.  0019 

4.  0019 

4. 0020 

4. 0020 

4. 0021 

4.0021 

47 

30 

4.  0022 

4.0022 

4.0023 

4. 0023 

4.  0023 

4.  0024 

4. 0024 

4. 0025 

4. 0025 

4. 0026 

47 

40 

4.  0026 

4.  0026 

4. 0027 

4. 0027 

4.  0028 

4.0028 

4. 0029 

4.0029 

4. 0029 

4. 0030 

47 

50 

4.  0030 

4. 0031 

4.0031 

4. 0032 

4.  0032 

4. 0032 

4. 0033 
4. 0037 

4. 0033 
4. 0038 

4. 0034 
4.0038 

4. 0034 
4. 0038 

2  48 

0 

4. 0035 

4.0035 

4. 0035 

4. 0036 

4. 0036 

4. 0037 

48 

10 

4.  0039 

4.0039 

4.0040 

4. 0040 

4. 0041 

4. 0041 

4. 0041 

4.0042 

4. 0042 

4.  0043 

48 

20 

4.  0043 

4.  0044 

4. 0044 

4. 0045 

4.  0045 

4. 0045 

4. 0046 

4. 0046 

4.0047 

4. 0047 

48 

30 

4. 0048 

4.  0048 

4. 0048 

4.  0049 

4. 0049 

4. 0050 

4. 0050 

4. 0051 

4. 0051 

4.0051 

48 

40 

4.  0052 

4.0052 

4. 0053 

4. 0053 

4. 0054 

4.0054 

4. 0054 

4. 0055 

4.0055 

4. 0056 

48 

50 

4.  0056 

4.  0057 

4. 0057 

4.0057 

4.  0058 

4. 0058 

4.0059 

4. 0059 

4.0060 

4. 0060 

2  49 

0 

4. 0060 

4.  0061 

4.  0061 

4. 0062 

4. 0062 

4. 0063 

4. 0063 

4. 0063 

4.0064 

4.  0064 

49 

10 

4. 0065 

4. 0065 

4. 0066 

4.0066 

4.  0066 

4.  0067 

4. 0067 

4.  0068 

4. 0068 

4. 0069 

49 

20 

4.  0069 

4. 0069 

4. 0070 

4.  0070 

4. 0071 

4.  0071 

4. 0072 

4. 0072 

4. 0072 

4.0073 

49 

30 

4. 0073 

4.0074 

4.0074 

4.  0074 

4. 0075 

4. 0075 

4. 0076 

4. 0076 

4. 0077 

4. 0077 

49 

40 

4.0077 

4.  0078 

4.  0078 

4.0079 

4. 0079 

4. 0080 

4. 0080 

4. 0080 

4. 0081 

4. 0081 

49 

50 

4. 0082 

4.0082 

4.  0083 

4. 0083 

4.  0083 

4.  0084 

4. 0084 

4. 0085 

4. 0085 

4.0086 

Page  330]           APPENDIX  V:  TABLE  IX. 

Logarithms  of  Small  Arcs  in  Space  or  Time. 

Arc. 

0" 

1" 

2" 

8" 

4" 

6" 

6" 

7" 

8" 

9" 

O     '      II 

2"  50™  0' 
50  10 
50  20 
50  30 
50  40 
50  50 

4.0086 
4. 0090 
4.0095 
4. 0099 
4.  0103 
4.  0107 

4.0086 
4. 0091 
4.0095 
4.  0099 
4. 0103 
'4. 0108 

4.0087 
4.0091 
4.0095 
4. 0100 
4.  0104 
4.  0108 

4.0087 
4.0092 
4.0096 
4. 0100 
4. 0104 
4.0109 

4.0088 
4.0092 
4.0096 
4.  0100 
4.  0105 
4.  0109 

4.0088 
4.  0092 
4.0097 
4.  0101 
4.  0105 
4.  0109 

4.0089 
4. 0093 
4. 0097 
4. 0101 
4. 0106 
4.0110 

4.0089 
4.0093 
4.0097 
4.  0102 
4.  0106 
4.0110 

4.0089 
4. 0094 
4. 0098 
4. 0102 
4. 0106 
4.0111 

4.0090 
4. 0094 
4.0098 
4.  0103 
4.  0107 
4.0111 

2  51   0 
51  10 
51  20 
51  30 
51  40 
51  50 

4.  0111 
4.0116 
4.  0120 
4.  0124 
4.  0128 
4.  0133 

4.0112 
4.0116 
4.  0120 
4.  0125 
4.  0129 
4.  0133 

4.0112 
4.0117 
4.  0121 
4.  0125 
4.  0129 
4. 0133 

4.  0113 
4.0117 
4. 0121 
4. 0125 
4. 0130 
4. 0134 

4.0113 
4.0117 
4. 0122 
4.0126 
4.  0130 
4.  0134 

4. 0114 
4.0118 
4.0122 
4.  0126 
4.  0130 
4.  0135 

4.0114 
4.0118 
4.  0122 
4.  0127 
4.  0131 
4.  0135 

4.  0114 
4.0119 
4.  0123 
4.  0127 
4.  0131 
4.  0136 

4.0115 
4.  0119 
4.  0123 
4. 0128 
4.  0132 
4. 0136 

4.0115 
4.  0120 
4.  0124 
4.  0128 
4.  0132 
4. 0136 

2  52   0 
52  10 
52  20 
52  30 
52  40 
52  50 

4.  0137 
4. 0141 
4.  0145 
4.  0149 
4. 0154 
4.  0158 

4. 0137 
4. 0141 
4. 0146 
4. 0150 
4. 0154 
4. 0158 

4. 0138 
4. 0142 
4. 0146 
4. 0150 
4.  0154 
4. 0159 

4.  0138 
4.  0142 
4.  0146 
4.  0151 
4. 0155 
4. 0159 

4.  0138 
4. 0143 
4.  0147 
4. 0151 
4.  0155 
4. 0159 

4.  0139 
4.  0143 
4. 0147 
4. 0152 
4. 0156 
4.  0160 

4.  0139 
4.0144 
4.  0148 
4.  0152 
4.  0156 
4.  0160 

4. 0140 
4.0144 
4.  0148 
4.  0153 
4. 0157 
4. 0161 

4.  0140 
4.  0144 
4.  0149 
4. 0153 
4. 0157 
4. 0161 

4. 0141 
4. 0145 
4. 0149 
4. 0153 
4. 0157 
4.  0162 

2  53   0 
53  10 
53  20 
53  30 
53  40 
53  50 

4.  0162 
4.  0166 
4.0170 
4. 0175 
4. 0179 
4. 0183 

4. 0162 
4. 0167 
4. 0171 
4. 0175 
4. 0179 
4.  0183 

4. 0163 
4. 0167 
4. 0171 
4. 0175 
4. 0180 
4.  0184 

4. 0163 
4.  0167 
4. 0172 
4. 0176 
4. 0180 
4.  0184 

4. 0164 
4.  0168 
4. 0172 
4. 0176 
4. 0180 
4. 0185 

4.  0164 
4.  0168 
4.  0172 
4.0177 
4.0181 
4.  0185 

4.  0164 
4. 0169 
4. 0173 
4. 0177 
4.0181 
4. 0185 

4.  0165 
4.  0169 
4.  0173 
4.0177 
4.  0182 
4. 0186 

4. 0165 
4. 0169 
4. 0174 
4.  0178 
4.  0182 
4. 0186 

4.  0166 
4. 0170 
4. 0174 
4. 0178 
4. 0182 
4. 0187 

2  54   0 
54  10 
54  20 
54  30 
54  40 
54  50 

4.  0187 
4. 0191 
4. 0195 
4. 0199 
4.0204 
4. 0208 

4.  0187 
4. 0192 
4.  0196 
4.  0200 
4.  0204 
4.  0208 

4.  0188 
4. 0192 
4.  0196 
4.  0200 
4.  0204 
4.  0209 

4.0188 
4.  0192 
4.  0197 
4.  0201 
4.  0205 
4.  0209 

4.  0189 
4. 0193 
4.  0197 
4.  0201 
4.  0205 
4. 0209 

4. 0189 
4. 0193 
4.  0197 
4.  0202 
4. 0206 
4. 0210 

4. 0190 
4.  0194 
4:0198 
4. 0202 
4. 0206 
4. 0210 

4.  0190 
4. 0194 
4.  0198 
4.  0202 
4.  0207 
4.0211 

4. 0190 
4.  0194 
4.  0199 
4. 0203 
4.  0207 
4. 0211 

4. 0191 
4. 0195 
4. 0199 
4.  0203 
4.  0207 
4. 0211 

2  55   0 
55  10 
55  20 
55  30 
55  40 
55  50 

4. 0212 
4.  0216 
4. 0220 
4. 0224 
4. 0228 
4. 0233 

4. 0212 
4.  0216 
4.  0221 
4.  0225 
4. 0229 
4. 0233 

4. 0213 
4. 0217 
4. 0221 
4.  0225 
4. 0229 
4. 0233 

4. 0213 
4. 0217 
4.  0221 
4. 0225 
4. 0230 
4. 0234 

4. 0214 
4. 0218 
4. 0222 
4.  0226 
4. 0230 
4. 0234 

4.  0214 
4.  0218 
4. 0222 
4. 0226 
4. 0230 
4. 0235 

4. 0214 
4. 0219 
4. 0223 
4. 0227 
4. 0231 
4.  0235 
4.  0239 
4.  0243 
4. 0247 
4. 0251 
4. 0256 
4.  0260 

4.  0215 
4.0219 
4. 0223 
4. 0227 
4. 0231 
4. 0235 
4. 0240 
4. 0244 
4. 0248 
4. 0252 
4. 0256 
4. 0260 

4.  0215 
4.  0219 
4. 0223 
4. 0228 
4. 0232 
4. 0236 
4. 0240 
4.  0244 
4.  0248 
4.  0252 
4. 0256 
4. 0260 

4. 0216 
4.  0220 
4.  0224 
4. 0228 
4. 0232 
4.  0236 

2  56   0 
56  10 
56  20 
56  30 
56  40 
56  50 

4. 0237 
4. 0241 
4.0245 
4. 0249 
4. 0253 
4. 0257 

4. 0237 
4. 0241 
4.  0245 
4.  0249 
4. 0253 
4.  0258 

4. 0237 
4. 0242 
4. 0246 
4. 0250 
4.0254 
4. 0258 

4. 0238 
4. 0242 
4. 0246 
4. 0250 
4. 0254 
4. 0258 

4. 0238 
4. 0242 
4. 0246 
4. 0251 
4. 0255 
4. 0259 

4. 0239 
4. 0243 
4. 0247 
4.  0251 
4. 0255 
4. 0259 

4. 0240 
4.  0244 
4. 0249 
4. 0253 
4. 0257 
4. 0261 
4.  0265 
4.  0269 
4. 0273 
4. 0277 
4. 0281 
4. 0285 
4.  0289 
4.  0293 
4.  0297 
4.  0302 
4.  0306 
4. 0310 

2  57   0 
67  10 
57  20 
57  30 
57  40 
57  50 

4.  0261 
4. 0265 
4. 0269 
4. 0273 
4. 0278 
4. 0282 

4. 0262 
4.  0266 
4. 0270 
4. 0274 
4. 0278 
4.  0282 

4.  0262 
4. 0266 
4. 0270 
4. 0274 
4. 0278 
4. 0282 

4. 0262 
4. 0267 
4. 0271 
4. 0275 
4. 0279 
4. 0283 

4. 0263 
4. 0267 
4.  0271 
4. 0275 
4. 0279 
4.  0283 

4. 0263 
4. 0267 
4.  0271 
4. 0276 
4. 0280 
4. 0284 

4. 0264 
4. 0268 
4. 0272 
4. 0276 
4. 0280 
4. 0284 

4. 0264 
4. 0268 
4. 0272 
4.  0276 
4.  0280 
4.  0284 

4. 0265 
4.  0269 
4.  0273 
4.  0277 
4. 0281 
4.  0285 

2  58   0 
58  10 
58  20 
58  30 
58  40 
58  50 

4. 0286 
4. 0290 
4. 0294 
4. 0298 
4. 0302 
4. 0306 

4. 0286 
4.0290 
4.  0294 
4.  0298 
4.  0302 
4.  0306 

4. 0287 
4. 0291 
4. 0295 
4. 0299 
4. 0303 
4. 0307 

4.  0287 
4. 0291 
4.  0295 
4. 0299 
4. 0303 
4. 0307 

4. 0287 
4.  0291 
4. 0295 
4. 0300 
4. 0304 
4. 0308 

4.  0288 
4. 0292 
4. 0296 
4.  0300 
4.  0304 
4.  0308 

4. 0288 
4.  0292 
4.  0296 
4.0300 
4. 0304 
4. 0308 

4. 0289 
4. 0293 
4.  0297 
4.  0301 
4. 0305 
4. 0309 

4.  0289 
4.  0293 
4. 0297 
4. 0301 
4. 0305 
4. 0309 

2  59   0 
59  10 
59  20 
59  30 
59  40 
59  50 

4. 0310 
4.  0314 
4.  0318 
4. 0322 
4. 0326 
4. 0330 

4.  0310 
4. 0314 
4. 0319 
4. 0323 
4. 0327 
4. 0331 

4.0311 
4.  0315 
4. 0319 
4. 0323 
4. 0327 
4. 0331 

4. 0311 
4. 0315 
4. 0319 
4. 0323 
4. 0327 
4. 0331 

4. 0312 
4.  0316 
4.  0320 
4. 0324 
4. 0328 
4. 0332 

4. 0312 
4. 0316 
4. 0320 
4. 0324 
4. 0328 
4. 0332 

4. 0312 
4. 0317 
4. 0321 
4.  0325 
4. 0329 
4. 0333 

4. 0313 
4. 0317 
4. 0321 
4.  0325 
4.  0329 
4.  0333 

4.  0313 
4.  0317 
4. 0321 
4. 0325 
4. 0329 
4. 0333 

4. 0314 
4.  0318 
4.  0322 
4.  0326 
4.  0330 
4. 0334 

APPENDIX  V:  TABLE  X.                             [Page  331 

Table  showing  the  correction  required,  on  account  of  Second  Differences  of  the  Moon's  Motion,  in 
Finding  the  Greenwich  Time  corresponding  to  a  Corrected  Lunar  Distance. 

Approximate 
interval. 

Difference  of  the  proportional  logarithms  in  the  Ephemeris.                                        1 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

82 

34 

36 

h.  m. 
0     0 
0  10 
0  20 

h.  m. 
3    0 
2  50 
2  40 

8. 
0 

0 
0 

s. 
0 
0 

8. 

0 
0 

1 
1 

1 

2 
2 
2 
2 
2 

8. 

0 

1 
1 

2 
2 
2 
2 
2 
3 
3 

8. 
0 
1 
1 

2 
2 
3 
3 
3 
3 
3 

8. 

0 

1 

2 
2 
3 
3 
3 
4 
4 
4 

8. 

0 

1 

2 
2 
3 
4 
4 
4 
4 
4 

8. 

0 

1 

2 
■    3 
3 
4 
4 
5 
5 
5 

8. 

0 

1 

2 
3 
4 
5 
5 
5 
6 
6 

8. 

0 

1 

2 
3 
4 
5 
6 
6 
6 
6 

8. 

0 

1 

3 

4 
5 
5 
6 
6 
7 
7 

8. 

0 
2 
3 

4 
5 
6 

7 
7 
7 
8 

8. 

0 
2 
3 

8. 

0 
2 
3 

8. 

0 
2 

4 

8. 

0 
2 
4 

8. 

0 
2 
4 

8. 

0 
2 

4 

0  30 
0  40 
0  50 

2  30 
2  20 
2  10 

0 
0 

1 

5 
6 
6 
7 
8 
8 
8 

5 
6 

7 

5 
6 

7 

6 

7 
8 

6 

7 
8 

6 
8 
9 

1     0 
1  10 
1  20 
1  30 

h.  TO. 
0     0 
0  10 
0  20 

2  0 
1  50 
1  40 

1  30 

h.  m. 

3  0 

2  50 
2  40 

1 
1 
1 
1 

8 
8 
9 
9 

8 
9 
9 
9 

9 

9 

10 

10 

9 
10 
10 
11 

10 
11 
11 
11 

Difference  of  the  proportional  logarithms  in  the  Ephemeris. 

38 

». 
0 
2 
5 

40 

8. 

0 
3 

5 
7 
9 
10 
11 
12 
12 
12 

42 

8. 

0 
3 
5 

7 
9 
10 
12 
12 
13 
13 

44 

8. 

0 
3 
5 
8 

10 
11 
12 
13 
14 
14 

46 

8. 

0 

3 

6 

8 

10 

12 

13 

14 

14 

14 

48 

8. 

0 

3 

6 

8 

10 

12 

13 

14 

15 

15 

50 

8. 

0 
3 
6 
9 
11 
13 

62 

54 

56 

58 

60 

62 

64 

66        68 

70 

8. 

0 
3 
6 

8. 
0 

4 

7 

8. 
0 

4 

7 

8. 
0 

4 

7 

8. 

0 

4 

7 

8. 

0 
4 

8 

8. 

0 
4 
8 

8.               8. 

0         0 

4  i      4 
8         8 

8. 

0 
5 
9 

0  30 
0  40 
0  50 

2  30 
2  20 
2  10 

7 
8 
9 
10 
11 
12 
12 

9 
11 
13 

9 
12 
14 

10       10 
12       13 
14       15 

10 
13 
15 

11 
13 
16 

11 
14 
16 

12  ]     12 
14  1     15 
16  1     17 

12 
15 
17 

1     0 
1  10 
1  20 
1  30 

h.   TO. 

0    0 
0  10 
0  20 
0  30 
0  40 
0  50 

2  0 

1  50 
1  40 

1  30 

h.  m. 

3  0 
•2  50 

2  40 
2  30 
2  20 
2  10 

14 
15 
15 
16 

14 
15 
16 
16 

15 
16 
17 
17 

16 
17 
17 
18 

16 

17 
18 
18 

17 
18 
19 
19 

17 
18 
19 
19 

18 
19 
20 
20 

18  19 

19  ,    20 

20  \    21 

21  ;    21 

19 
21 
21 
22 

Difference  of  the  proportional  logarithms  in  the  Ephemeris. 

72 

74 

76 

78 

80 

82 

84 

86 

88 

90         92 

94 

06 

98 

100 

102 

104 

8. 

0 
5 
9 
13 
16 
18 
20 
21 
22 
23 

8. 

0 
5 
9 
13 
16 
19 
21 
22 
23 
23 

8. 

0 
5 
9 
13 
16 
19 
21 
22 
23 
24 

8. 

0 
5 
10 
14 
17 
20 
22 
23 
24 
24 

8. 

0 
5 
10 
14 
17 
20 
22 
24 
25 
25 

8. 

0 
5 

10 
14 
18 
21 
23 
24 
25 
25 

8. 

0 
6 
10 
14 
18 
21 
23 
25 
26 
26 

8. 

0 

6 

11 

8. 

0 

6 

11 

8. 

0 

6 

11 

8. 

0 

6 

11 

8. 

0 

6 

12 

8. 

0 

6 

12 

8. 

0 

6 

12 

8. 

0 

7 
12 

8. 

0 

i 

13 

8. 

0 

7 
13 

15 
19 
22 

15 
19 
22 

16 
19 
22 

16 
20 
23 

16 
20 
23 

17 
21 
24 

17 
21 
24 

17 
22 
25 

18 
22 
26 

18 
22 
26 

1    0 
1  10 
1  20 
1  30 

h.  m. 
0    0 
0  10 
0  20 

2  0 
1  50 
1  40 

1  30 

/(.  m. 

3  0 

2  50 
2  40 

24 
25 
26 

27 

24 
26 
27 

27 

25 
27 

28 
28 

25 

27 
28 
29 

26 
28 
29 
29 

27 
28 
29 
30 

27 
29 
30 
31 

38 
30 
31 
31 

28 
30 
31 
32 

29 
31 
32 
32 

Difference  of  the  proportional  logarithms  in  the  Ephemeris.                                    .   1 

106 

108 

110 

112 

114 

116 

118 

120 

122 

124 

126 

128 

180 

132 

134 

136 

138 

s. 
0 
7 

13 

8. 

0 

7 

13 

8. 

0 
7 
14 
19 
24 
27 
30 
32 
34 
34 

8. 

0 
7 
14 
19 
24 
28 
31 
33 
34 
35 

8. 

0 
7 
14 
20 
25 
29 
31 
34 
35 
35 

8. 

0 
8 
14 
20 
25 
29 

8. 

0 

8 

15 

8. 

0 

8 

15 

8. 

0 

8 

15 

8. 

0 

8 

15 

8. 

0 

8 

15 

8. 

0 

8 

16 

8. 

0 

8 

16 

8. 

0 

9 

16 

8. 

0 

9 

16 

8. 

0 
9 

17 

8. 

0 

9 

17 

0  30 
0  40 
0  50 

2  30 
2  20 
2  10 

18 
23 
26 

19 
23 
27 
30 
32 
33 
34 

20 
25 
29 

21 
26 
30 

21 
26 
30 

21 
27 
31 

22 

27 

22 
28 
32 

22 

28 
32 

23 

28 
33 

23 
29 
33 
37 
40 
41 
42 

24 
29 
34 
38 
40 
42 
42 

24 
30 
34 
38 
41 
42 
43 

1     0 
1  10 
1  20 
1  30 

2     0 
1  50 
1  40 
1  30 

29 
31 
33 
33 

32 
34 
35 
36 

33 
35 
36 
36 

33 
35 
37 
37 

34 
36 

38 
38 

34 
37 

38 
39 

J5 
J7 
J9 
J9 

35 
38 
39 
40 

36 
38 
40 
40 

37 
39 
41 
41 

The  correction  is  to  be  added  to  the  approximate  Greenwich  time  when  the  proportional  logarithms  in  the  Ephemeris 
are  decreasing,  and  subtracted  when  they  are  increasing. 


Page  332] 

APPENDIX  V:  TABLE  XI. 

1 

For  finding  the  value  of  N  for  Correcting  Lunar  Distances  for  the  Compres 

sion 

of  the  Earth. 

Table  XI  A,  giving  1st  part  of  N. 

Table  XI  B,  giving  2d  part  of  N.                         1 

Moon's  declination. 

Other  body' 

3  declination. 

App. 
dist. 

App. 
dist. 

1 

0° 

3° 

6° 

9° 

12° 

15° 

18° 

21° 

24° 

27° 

80° 

0° 

8° 

6° 

9° 

12° 

16° 

18° 

21° 

24° 

27° 

80° 

II 

0 

„ 

„ 

„ 

„ 

„ 

„ 

„ 

It 

„ 

0 

/' 

rt 

It 

// 

// 

„ 

It 

II 

20 

-0 

3 

6 

10 

13 

16 

19 

22 

25 

28 

31 

20 

+0 

3 

7 

10 

14 

17 

20 

24 

27 

30 

33 

22 

0 

3 

6 

9 

12, 

.  14 

17 

20 

23 

25 

28 

22 

0 

3 

6 

9 

13 

16 

19 

22 

25 

27 

30 

24 

0 

3 

5 

8 

11 

13 

16 

18 

21 

23 

25 

24 

0 

3 

6 

9 

12 

14 

17 

20 

23 

25 

28 

26 

0 

2 

5 

7 

10 

12 

14 

17 

19 

21 

23 

26 

0 

3 

5 

8 

11 

13 

16 

18 

21 

23 

26 

28 

0 

2 

4 

7 

9 

11 

13 

15 

17 

19 

21 

28 

0 

3 

5 

8 

10 

12 

15 

17 

20 

22 

24 

30 

-0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

30 

+0 

2 

5 

7 

9 

12 

14 

16 

18 

21 

23 

32 

0 

2 

4 

6 

8 

9 

11 

13 

15 

16 

18 

32 

0 

2 

4 

7 

9 

11 

13 

15 

17 

19 

21 

34 

0 

2 

4 

5 

7 

9 

10 

12 

14 

15 

17 

34 

0 

2 

4 

6 

8 

11 

13 

15 

16 

18 

20 

36 

0 

2 

3 

5 

7 

8 

10 

11 

13 

14 

16 

36 

0 

2 

4 

6 

8 

10 

12 

14 

16 

17 

19 

38 

0 

2 

3 

5 

6 

8 

9 

8 

10 
10 

12 
11 

13 

12 

14 

38 

0 

2 
2 

4 
4 

6 
6 

8 

7 

10 
9 

11 
11 

13 
13 

15 
14 

17 
16 

18 
18 

40 

-0 

3 

4 

6 

7 

13 

40 

+0 

42 

0 

3 

4 

5 

7 

8 

9 

10 

11 

13 

42 

0 

2 

4 

5 

7 

9 

10 

12 

14 

15 

17 

44 

0 

2 

4 

5 

6 

7 

8 

10 

11 

12 

44 

0 

2 

3 

5 

7 

8 

10 

12 

13 

15 

16 

46 

0 

\ 

2 

3 

5 

6 

7 

8 

9 

10 

11 

46 

0 

2 

3 

5 

6 

8 

10 

11 

13 

14 

16 

48 

0 

2 

3 

4 

5 

6 

7 

8 

9 

10 

48 

0 

2 

3 

5 

6 

8 

9 

11 

12 

14 

15 

50 

-0 

2 

3 

4 

5 

6 

7 

8 

9 

10 

50 

+0 

2 

3 

5 

6 

8 

9 

11 

12 

13 

15 

52 

0 

3 

4 

5 

5 

6 

7 

8 

9 

52 

0 

2 

3 

4 

6 

7 

9 

10 

12 

13 

14 

54 

0 

3 

3 

4 

5 

6 

7 

7 

8 

54 

0 

3 

4 

6 

7 

9 

10 

11 

13 

14 

56 

0 

2 

3 

4 

5 

5 

6 

7 

8 

56 

0 

3 

4 

6 

7 

8 

10 

11 

12 

14 

58 

0 

J 

y 

2 
2 

3 
3 

4 
3 

4 
4 

5 
5 

6 
5 

6 
6 

7 
7 

58 

0 

Y 

3 
3 

4 
4 

6 
5 

7 
7 

8 
8 

10 
9 

11 
11 

12 
12 

13 
13 

60 

-0 

60 

+0 

m 

0 

2 

3 

3 

4 

4 

5 

5 

6 

62 

0 

3 

4 

5 

7 

8 

9 

10 

12 

13 

64 

0 

2 

2 

3 

3 

4 

4 

5 

6 

64 

0 

3 

4 

5 

7 

8 

9 

10 

11 

13 

66 

0 

2 

2 

3 

3 

4 

4 

5 

5 

66 

0 

3 

4 

5 

6 

8 

9 

10 

11 

12 

68 

0 

0 
0 

Y 

-Y 

2 
2 

2 
2 

3 
3 

3 
3 

4 
3 

4 
4 

5 
4 

68 
70 

0 

+0 

Y 

3 
3 

4 
4 

5 
5 

6 
6 

8 

7 

9 
9 

10 
10 

11 
11 

12 

12 

70 

-0 

72 

0 

0 

2 

2 

2 

3 

3 

3 

4 

72 

0 

2 

4 

5 

6 

7 

9 

10 

11 

12 

74 

0 

0 

2 

2 

2 

3 

3 

3 

74 

0 

2 

4 

5 

6 

7 

8 

10 

11 

12 

76 

0 

0 

2 

2 

2 

3 

3 

76 

0 

2 

4 

5 

6 

7 

8 

9 

11 

12 

78 

0 

0 
0 

0 
0 

"Y 

"Y 

1 

1 

2 

1 

2 
2 

2 
2 

2 

78 

0 

Y 

2 
2 

4 
4 

5 
5 

6 
6 

7 
7 

8 
8 

9 
9 

11 
10 

12 
11 

80 

-0 

2 

80 

+0 

82 

0 

0 

0 

0 

1 

1 

1 

1 

2 

82 

0 

2 

4 

5 

6 

7 

8 

9 

10 

11 

84 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

84 

0 

2 

4 

5 

6 

7 

8 

9 

10 

11 

86 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

86 

0 

2 

4 

5 

6 

7 

8 

9 

10 

11 

88 

0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

88 

0 

Y 

2 
2 

4 

4 

5 
5 

6 
6 

7 
7 

8 
8 

9 
9 

10 
10 

11 
11 

90 

-0 

90 

+0 

92 

+0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

92 

0 

2 

4 

5 

6 

7 

8 

9 

10 

11 

94 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

94 

0 

2 

4 

5 

6 

7 

8 

9 

10 

11 

96 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

96 

0 

2 

4 

5 

6 

7 

8 

9 

10 

11 

98 

0 

0 
0 

0 
0 

_o 

"Y 

1 
1 

1 
1 

1 

2 

1 

2 

2 

2r 

98 

0 

Y 

2 
2 

4 
4 

5 
5 

6 
6 

7 
7 

8 
8 

9 
9 

10 
10 

11 
11 

100 

+0 

100 

+0 

102 

0 

0 

0 

1 

2 

2 

2 

2 

102 

0 

2 

4 

5 

6 

7 

8 

9 

11 

12 

104 

0 

0 

2 

2 

2 

3 

3 

104 

0 

2 

4 

5 

6 

7 

8 

9 

11 

12 

106 

0 

0 

2 

2 

2 

3 

3 

3 

106 

0 

2 

4 

5 

6 

7 

8 

10 

11 

12 

108 
110 

0 

+0 

0 
0 

Y 

-^ 

2 
2 

2 
2 

2 

3 

3 

3 

4 

108 

0 

2 
3 

4 
4 

5 
5 

6 
6 

7 
7 

9 
9 

10 
10 

11 
11 

12 

12 

3 

3 

3 

4 

4 

110 

+0 

112 

0 

0 

2 

2 

3 

3 

4 

4 

5 

112 

0 

3 

4 

5 

6 

8 

9 

10 

11 

12 

114 

0 

2 

2 

3 

3 

4 

4 

5 

5 

114 

0 

3 

4 

5 

6 

8 

9 

10 

11 

12 

116 

0 

2 

2 

3 

3 

4 

4 

5 

6 

116 

0 

3 

4 

5 

7 

8 

9 

10 

11 

13 

118 

0 

Y 

1 

2 
2 

3 
3 

3 
3 

4 
4 

4 
5 

5 
5 

5 
6 

6 

7 

118 

0 

Y 

3 
3 

4 
4 

5 
5 

7 
7 

8 
8 

9 
9 

10 
11 

12 
12 

13 
13 

120 

+0 

120 

+0 

122 

0 

2 

3 

4 

4 

5 

6 

6 

7 

122 

0 

3 

4 

6 

7 

8 

10 

11 

12 

13 

124 

0 

2 

2 

3 

4 

5 

5 

6 

7 

8 

124 

0 

3 

4 

6 

7 

8 

10 

11 

12 

14 

126 

0 

2 

3 

3 

4 

5 

6 

7 

7 

8 

126 

0 

3 

4 

6 

7 

9 

10 

11 

13 

14 

128 

0 

2 

3 

4 

5 

5 

6 

7 

8 

9 

128 

0 

2 

3 

4 

6 

7 

9 

10 

12 

13 

14 

130 

+0 

\ 

2 

3 

4 

5 

6 

7 

8 

9 

10 

130 

+0 

2 

3 

5 

6 

8 

9 

11 

12 

13 

15 

The  signs  in  the  0°  column  apply  to  all  the  numbers  in  the  same  line,  and  are  to  be  used  when  the  declination  is  North. 
When  the  declination  is  South  change  the  sign  +  to  —  and  —  to  +. 


INDEX  TO  PART  I. 


Subject. 


Abbreviations 

Account.     (»S'ee  Dead  reckoning. ) 

Adjustments,  horizon  mirror 

index  mirror 

plane  table 

sextant 

permanent 

theodolite  or  transit 

Afternoon  sights 

Agulhas  current 

Airy's  method  for  great  circle  sailing.. 

Alidade,  plane  table 

Almanac,  Nautical.     {See  Nautical  Al- 
manac. ) 

Altitude  and  azimuth 

time  azimuth 

azimuth 

circle,  definition  . . .' 

circum-meridian 

forms  for  . . . 

definition 

ex-meridian 

forma  for 

meridian,  constant 

form  for  . . 

forms  for 

latitude  by 

observation  of 

reduction  to 

forms. 

observed,  how  corrected 

of  Polaris  for  latitude 

single,  for  chronometer  error. 

latitude 

longitude  ashore .. 
at  sea... 

true,  definition 

Altitudes,  equal,  forchro.  error 

form 

longitude  ashore . . 
at  sea... 

Amplitude,  definition 

determination  of 

Anchorage,  position  to  be  plotted 

Angle,  danger.     {See  Danger  angle.) 
hour.     {See  Hour  angle.) 

to  repeat 

Angles,  between  three  known  objects . 
horizon,  for  finding  distance.. 

round  of 

sextant  and  theodolite  in  hy- 
drography  

vertical  terrestrial,  to  measure. 

26J°-45°  on  bow 

Anticyclonic  regions,  features  of 

Apparent  day,  definition 

variation  in  length 

noon,  definition 

time,  conversion  to  mean 

definition 


Art. 


246 
245 
417 
244 
248 
414 
399 
550 
194 
416 


235 
366 
363 
217 
334 


220 
334 


333 


329 
330 
334 


294 
340 
316 
339 
346 
349 
294 
321 


347 
352 
224 
357 
166 


415 
151 
139 
415 

458 
139 
146 
481 
273 
273 
273 
292 
273 


Page. 


67 
133 

67 

68 
132 
125 
161 

58 
133 


65 

112 

111 

63 

97 

174 

64 

97 

174 

96 

174 

173 

94 

94 

97 

174 

82 

101 

88 

99 

104 

105 

82 

90 

176 

104 

107 

64 

109 

49 


132 

45 

43 

132 

140 
43 
44 

148 
74 
74 
74 
80 
74 


Subject. 


Art. 


Page. 


Apparent  time,  inequality  of 

relation  to  mean 

Arctic  current 

Aries,  first  point  of,  definition 

Arming  of  lead 

Artificial  horizon,  description 

method  of  use 

should  be  tested 

Ascension,  right.     {See  Right  ascen- 
sion. ) 

Astronomical  base 

bearing 

time 

transit  instruments 

work  of  survey 

Atlantic  ocean  currents 

storms 

Attraction,  local 

Australia  current 

Axis  of  rotation,  definition 

Azimuth,  altitude 

and  altitude 

circle 

definition 

from  Sumner  line 

how  determined 

named 

of  body  determines  use 

terrestrial  object 

time  and  altitude 

determination 

diagram 

for  compass  errors 

in  great  circle  sailing . . 

tables 

Barometer,  aneroid 

comparisons 

definition 

effect  of,  on  tides 

mercurial 


sea 

standard 

temperature  correction 

to  determine  height 

vernier  

Base,  astronomical 

line,  description 

Beam  compass,  description 

Bearing  and  angle,  position  by 

distance,  position  by 

danger 

method  of  observing  and  plot- 
ting  

of  terrestrial  object 

Bearings,  bow  and  beam 

cross 

sun,  for  compass  error 

two,  of  object,  with  run  be- 
tween  

Beaufort's  scale  for  wind 


273 
288 
536 
226 
19 
256 
257 
258 


446 

369 

277 

431 

450 

529 

494 

75 

546 

6 

363 

235 

33 

223 

380 

355 

354 

407 

369 

366 

359 

361 

88 

191 

361 

55 

56 

47 

501 

48 

50 

50 

54 

57 

51 

446 

438 

434 

142 

138 

157 

134 
369 
145 
134 


143 
67 


333 


334 


INDEX    TO    PART    1. 


Subject. 


Bench  mark,  definition 

Binnacles,  description 

Bottom,  quality  of,  on  chart 

Boxing  the  compass 

Brazil  current 

Buoys  

C  —  W,  definition • 

Cape  Horn  current 

Celestial  coordinates 

equator,  definition 

horizon,  definition 

latitude  and  longitude 

definition 

longitude  and  latitude 

definition 

meridian,  definition 

sphere  or  concave,  definition . 

Celo-Navigation,  definition 

Chart  {See  also  Projection). 

as  record  of  piloting 

employment  in  piloting 

general  features 

great  circle 

for  composite  sailing. 

isobaric 

measures  of  depth  on 

Mercator,  to  construct 

quality  of  bottom  on 

standard  meridians  on 

Chilean  current 

Chronometer,  advantage  of  more  than 

one 

C  —  W,  definition 

care  on  shipboard 

comparison 

record 

correction.     {See  Chro- 
nometer error. ) 

description 

error,  by  equal  alts 

form, 
single  altitude . 

time  sight 

signals . . . 

transits 

definition 

differs  from  corr  . 

from  rate 

hack,  use  of 

max.   and    min.    ther- 
mometer   

minus  watch,  definition. 

second  difference 

sight.    ( »S'ee  Time  sight. ) 

temperature  curve 

transportation  of 

winding 

Circle,  declination,  definition 

hour,  definition 

of  altitude,  definition 

equal  altitude 

illumination 

vertical,  definition 

Circum-meridian  altitude 

forms 

Civil  time 

Clouds,  description  and  symbols 

Coefficients,  constant 

quadrantal ^ . . . 

semicircular 

value  and  relation 

Collimation,  line  of,  definition 


Art. 


516 

34 

45 

27 

538 

162 

268 

547 

234 

215 

213 

238 

229 

238 

229 

216 

210 

4 

166 

165 

36 

189 

197 

465 

46 

40 

45 

44 

547 

265 
268 
260 
263 
264 


259 
321 


316 
316 
314 
315 
261 
312 
311 
268 

262 
268 
265 

266 
260 
262 
216 
216 
217 
373 
373 
217 
334 


Page. 


277 
70 
112 
107 
103 
114 
414 


156 
17 
20 
16 

160 
47 
72 

161 
66 
63 
63 
65 
64 
65 
64 
63 
63 
11 

49 
48 
18 
57 
59 

143 
21 
19 
20 
20 

161 

72 
72 
71 
71 
72 


71 

90 

176 

88 
88 
87 
88 
71 
87 
87 
72 

71 
72 
72 

72 
71 
71 
63 
63 
63 

114 

114 
63 
97 

174 
74 
27 
38 
37 
36 
38 

132 


Subject. 


Page. 


Comparing  watch,  use  of 

Comparison,  barometer 

chronometer,  method  ... 

record 

Compass,  beam,  description 

boxing 

compensation.     {See  Devia- 
tion. ) 

declination 

definition 

deviation.     (.S'fe  Deviation.) 

divisions  on  card 

dry 

error.    (*See  Error,  compass.) 

local  attraction 

Lord  Kelvin 

Navy  service,  7  J-inch 

variation 

wet 

Compasses  (drawing) 

Compensation,  compass.     {See  Devia- 
tion. ) 

Composite  sailing,  computation 

definition 

graphic  approxima- 
tion   

shortest  course  for. . 

terrestrial  globe 

Concave,  celestial,  definition 

Constant  deviation.     {See  Deviation.) 

for  meridian  altitude 

form 

Conversion  of  time,  apparent  to  mean. 

definition 

mean  to  apparent . 

sidereal  . 

sidereal  to  mean . . 

Coordinates,  celestial 

definition 

Correction,  chro.    (>See Chronometer.) 

index,  sextant 

of  observed  altitude 

Course,  definition 

to  lay 

Culmination,  definition 

Current,  Agulhas 

allowance  for 

Arctic 

Australia 

Brazil 

Cape  Horn 

Chilean 

determined  at  noon 

effect  in  piloting 

equatorial,  Atlantic 

Indian  

Pacific 

Guinea 

Gulf  Stream 

Humboldt 

Japan  Stream 

Kamchatka 

Kuro  Si  wo 

Labrador 

ocean,  Atlantic 

cause  of 

definition 

determination  of 

drift,  definition 

of  Atlantic 

Indian 

Pacific 


268 
56 
263 
264 
434 
27 


74 
25 

26 
30 

75 
32 
31 
74 
30 


198 
184 

199 
196 
200 
210 

333 


292 
286 
292 
290 
291 
234 
230 

250 
294 
6 
132 
271 
550 
206 
536 
546 
538 
547 
547 
398 
164 
529 
549 
541 
535 
532 
547 
542 
543 
542 
536 
529 
522 
521 
525 
523 
533 
548 
541 


72 
23 
71 
72 
136 
16 


29 
15 

16 
17 

29 
17 
17 
29 
17 
13 


59 
66 

59 
59 
59 
63 

96 

174 
80 
79 
80 
80 
80 
65 
64 

69 
82 
12 
42 
74 
161 
61 
160 
161 
160 
161 
161 
126 
48 
169 
161 
160 
160 
159 
161 
160 
161 
160 
160 
169 
168 
158 
158 
158 
160 
160 
161 


INDEX    TO    PART   I. 


335 


Subject. 


Current,  ocean,  stream,  definition 

submarine ! 

Oya  Si  wo 

Peruvian 

Rennell's 

Rossel 

Southern  connecting 

tidal,  definitions 

description  of 

observation  of 

to  find 

Curve,  temperature,  chronometer 

Cyclones  and  cyclonic  circulations . 

Cyclonic  regions,  features  of 

storms,  description 

maneuvering  in 

summary  of  rules 

tropical 

character 

Danger  angle,  horizontal 

vertical 

bearing 

Data,  useful,  miscellaneous 

Day's  work,  routine 

Dead  reckoning,  always  kept 

definition 

form  for 

method  of  working  . . 

value  of 

Decimal  fractions 

Declination  and  hour  angle 

right  ascension 

circle,  definition 

definition 

of  compass 

Declinatoire,  plane  table 

Definitions,  nautical  astronomy 

navigation 

Departure,  definition 

on  beginning  voyage 

to  take 

Depth,  measures  of,  on  charts 

recorder,  sounding  machine 

Deviation,  causes  of 

classes  of 

compensation  of 

constant,  coefficient 

definition 

definition 

heeling  error,  compensation 

definition 

I^apier  diagram  for 

quadrantal,  coefficients 

definition 

recompensation 

semicircular,  coefficients 

definition 

table 

theory  of 

to  apply 

find 

Diagram,  time  azimuth 

Difference,  second.     {See  Second  dif- 
ference. ) 

Dip  of  horizon,  definition 

how  applied 

none    with    artificial 

horizon 

variation  in 

"when  land  intervenes. 

Distance  and  bearing 

by  horizon  angle 


Art. 


523 

524 
544 
547 
537 
546 
539 
495 
505 
511 
207 
266 
480 
481 
482 
491 
492 
483 
486 
155 
156 
157 


393 

392 
202 


236 

237 

216 

218 

74 

416 

209 

1 

6 

392 

204 

46 

23 

98 

99 

119 

112 

111 

76 

126 

116 

93 

107 

106 

129 

103 

100 

91 

95 

77 

83 

361 


300 
303 

294 
301 
302 
138 
139 


Page. 


158 

158 

161 

161 

160 

161 

160 

153 

154 

156 

62 

72 

147 

148 

148 

150 

150 

148 

149 

46 

46 

46 

189 

124 

124 

60 

171 

60 

60 

178 

65 

65 

63 

64 

29 

133 

63 

11 

11 

124 

60 

21 

15 

35 

35 

38 

38 

38 

29 

40 

38 

32 

37 

37 

41 

36 

35 

32 

34 

29 

31 

110 


83 
84 

82 
83 
84 
43 
43 


Subject. 

Art. 

Page. 

Distance,  definition 

6 

139 
219 

90 
503 
503 

7 
435. 
470 
144 
523 
533 

6 
248 
225 
214 

321 

12 

lunar.    {See  Lunar  distance. ) 
of  objects  of  known  height. . 
polar,  definition 

43 
64 

zenith.  (»S'i?^  Zenith  distance. ) 

Distant  object  for  compass  error 

Diurnal  inequality  of  tide 

31 
154 

type  of  tide 

154 

Dividers,  description 

13 

proportional,  description 

Doldrums 

136 

144 

Doubling  angle  on  bow 

44 

Drift  current,  definition 

158 

currents,  Atlantic 

160 

Earth,  definitions  relating  to 

11 

Eccentricitv,  sextant 

68 

Ecliptic,  definition 

64 

Elevated  pole 

63 

Ephemens.     (>See  Nautical  Almanac.) 

Equal  altitudes  for  chro.  error 

form 

90 
176 

longitude  ashore  . . 

at  sea  . . . 

Equation  of  time,  definition 

347 
352 
275 
288 
215 
6 

6 
215 
226 

73 

77 
82 

249 

410 

497 
334 

104 

107 

74 

in  conversion  of  time . 
Equator,  celestial,  definition 

79 
63 

earth's 

11 

Equatorial  currents.     {See  Current. ) 
Equiangular  spiral 

12 

Equinoctial,  definition 

63 

Equinox,  definition 

64 

vernal.     {See  First  point  of 
Aries. ) 
Error,  chro.     (»S'ee  Chronometer. ) 

compass,  causes 

29 

to  applv 

29 

find 

31 

heeling.     ((See  Deviation.) 

index,  sextant,  description 

probable,     of     position,     how 

shown 

sextant.     ( See  Sextant. ) 

Establishment,  tidal,  definitions 

Ex-meridian  altitudes 

68 
130 

153 

97 

forms 

174 

Extraordinary  refraction  near  horizon. 

Extra-tropical  cyclonic  storms 

First  point  of  Aries,  definition 

hour  angle  is  si- 

i                                          dereal  time 

Flinders  bar,  definition 

301 
493 
226 

276 
105 
127 
163 

83 

152 

64 

74 
37 

to  place 

40 

Fogs  and  fog  signals 

48 

Forms  for  sights,  etc 

171 

notes  on 

177 

use  recommended . 
Fractions,  decimal 

411 

130 
178 

Gauges,  tide,  description 

518 
412 

157 

}  Geodesy,  definition 

131 

i  Geometry 

180 

!                    formulae  derived  from 

181 

'  Geo-Navigation,  definition 

4 

28 

259 

200 
193 
248 
189 
197 
6 
186 

11 

Gimbals,  compass 

16 

chronometer 

71 

i  Glasses,  shade.     (»9('e  Shade  glasses.) 
Globe,  terrestrial,  for  comp.  sailing. . . 
gt.  circle  sailing. 

Graduation,  sextant,  error - 

Great  circle  charts 

59 
58 
68 
57 

for  comp.  sailing. . . 
course 

59 
12 

sailing,  advantages 

56 

336 


INDEX    TO    PART   I. 


Subject. 


Great  circle  sailing,  Airy's  method  ... 

computation 

definition 

graphic  approx 

methods 

terrestrial  globe., 
time    azimuth 

rifethods 

Greenwich  adopted  as  prime  meridian. 

time,  to  find 

Guinea  current 

Gulf  Stream,  description 

extraordinary  dip  in 

Hack  chronometer,  use  of 

Heading,  magnetic,  determination  of.. 
Heeling  error.     {See  Deviation.) 
Height,  determination  by  barometer. . 

Heliograph,  use  in  surveymg 

Heliotrope,  use  in  surveying 

Horizon  angle,  distance  by 

artificial,  description 

method  of  use 

no  dip  with 

should  be  tested  . . . 

celestial,  definition 

dip  of,  definition 

how  applied 

none    with    artificial 

horizon 

variation  in 

when  land  intervenes . 

mirror,  adjustment 

description 

prismatic 

visible  or  sea,  definition 

Horse  latitudes 

Hour  angle  and  declination 

time,  conversion 

definition 

how  measured 

circle,  definition 

Humboldt  current 

Hydrographic  survey,  method  of 

surveying,  definition 

Hydrography  in  survey,  description  . . 

to  plot 

Identification  of  unknown  bodies 

Index  correction,  sextant,  to  find 

error,  sextant,  description 

mirror,  adjustment 

description 

prismatic 

Induction,  magnetic 

Instruments,  astronomical  transit 

nautical  astronomy 

navigation 

surveying  

Interpolation,  Nautical  Almanac  . 

Intersection,  Sumner.     {See  Sumner. ) 

Intervals,  lunitidal,  definitions 

list  of 

mean  and  sidereal  time 

Iron,  hard  and  soft 

Isobars,  chart  showing 

Japan  stream 

Kamchatka  current 

Knot,  length  of 

Kuro  Si  wo  current 

Labrador  current 

Lagging  of  tide „ 

Land  and  sea  breezes 


Art. 
194 

Page. 

58 

190 

57 

183 

56 

192 

58 

188 

57 

193 

58 

191 

58 

342 

103 

280 

75 

535 

160 

532 

159 

301 

83 

268 

72 

122 

39 

57 

23 

430 

135 

430 

135 

139 

43 

256 

70 

257 

70 

294 

82 

258 

71 

213 

63 

300 

83 

303 

84 

294 

82  i 

301 

83  1 

302 

84 

246 

67 

240 

66 

248 

68 

213 

63 

471 

145 

236 

65 

293 

81 

222 

64 

278 

75 

216 

63 

547 

161 

436 

137 

412 

131 

457 

140 

458 

140 

402 

126 

250 

69 

249 

68 

245 

67 

240 

66 

248 

68  '• 

96 

34 

431 

135 

239 

66 

7 

13 

413 

131 

283 

76 

497 

153 

190 
79 

289 

96 

34 

465 

143 

542 

160 

543 

160 

6 

12 

542 

160 

536 

160 

502 

154 

474 

145 

Subject. 


Latitude,  by  meridian  altitude 

forms  .. 

Polaris 

reduction  to  meridian 

reduction    to    meridian, 

forms 

single  altitude 

forms 

9/  cp'^  method 

forms 

celestial,  definition 

definition 

difference  of,  definition 

horse 

Lead,  arming 

description 

line,  marking  of 

Level  of  bench  mark 

surveying,  use  of 

description 

Lights,  employment  in  piloting 

Line,  base,  description  of 

of  collimation,  definition 

position.     ( iSt'^  Sumner  line. ) 

sight,  definition 

Sumner.     {See  Sumner  line.) 

Local  attraction 

time,  to  find 

Log  book 

chip : 

ground 

patent 

electric  registers 

revolutions  as  substitute . . 

Logarithms,  explanation 

Longitude,  by  equal  altitudes  ashore . . 

at  sea... 

single  altitude  ashore  . . 

at  sea  . . . 

time  sights,  forms 

transit  observations 

celestial,  definition 

definition 

difference  of 

of  secondary  meridians 

tertiary  meridians 

Loxodromic  Curve 

Lubber's  line 

Lunar  distance,  explanation  of 

tables 

observations,  value  of 

Lunitidal  intervals,  definitions 

list  of 

Magnetic  observations  in  survey 

Magnetism,  acquired  in  building  vessel. 

features  of  earth's 

subpermanent 

transient 

Main  triangulation 

Maneuvering,  cyclonic  storms 

summary  of  rules 

Marine  surveying 

Mean  day,  definition 

directive  force 

noon,  definition 

sun,  definition 

time,  conversion  to  apparent 

sidereal 

definition 

intervals,  relation  to  side- 
real   


Art. 


329 


340 
334 


339 

339" 

"229" 


471 

19 

18 

18 

517 

429 

428 

161 

438 

414 

414 

75 
281 
64 
10 
12 
13 
15 
17 


347 
352 
346 
349 

'344' 

229 

6 

6 

343 

345 

6 

28 


406 
497 


461 

97 

95 

98 

98 

448 

491 

492 

412 

274 

115 

274 

274 

292 

290 

274 

289 


INDEX   TO    PART   I. 


337 


Subject. 


Mean  time,  relation  to  apparent 

sidereal 

Mercator  projection,  description 

to  construct 

sailing 

Meridian  altitude,  constant 

forms  for 

latitude  by 

observation  of 

reduction  to 

celestial,  definition 

of  earth,  definition 

passage,  definition 

prime,  Greenwich  adopted . . 

secondary,  definition 

determination  of  . 

standard,  on  charts 

tertiary,  definition 

determination  of 

Meridional  parts 

Middle  latitude  sailing 

correction 

Mile,  nautical  or  sea,  length  of 

Mirror,  horizon.    (See  Horizon  mirror. ) 
index.     (*See  Index  mirror.) 

sextant,  resilvering 

Monsoon  winds 

Moon,  correction  of  observed  altitude . 

form  for  latitude  sights 

meridian  altitude 

time  sight 

planets,  and  stars,  use  of 

value  of  observations  of 

Morning  sights 

Nadir,  definition 

Napier  diagram 

Nautical  Almanac,  description 

for  1879,  extracts  . . 
gives  horizontal 

parallax 

interpolation 

reduction    of    ele- 
ments   

second  differences  . 

Astronomy,  definitions 

instruments 

mile,  length  of 

Navigation,  definitions 

instruments  and  accessories 

Neap  tides 

Noon  sights 

Notes  on  forms  for  sights,  etc 

Occupying  a  station 

Ocean  current.     {See  Current,  ocean.) 

Octant,  description 

Optical  principle  of  sextant 

Orient,  to,  a  i)lane  table 

Oya  Siwo  current 

Parallax,  definition 

horizontal,  in   Nautical  Al- 
manac   

how  applied 

of  planet  or  star 

Parallel  of  latitude,  definition 

rulers,  description 

sailing,  description 

Passage,  meriaian,  definition 

Pelorus,  description 

Peruvian  current 

Piloting,  definition 

requisites '.. 


Art. 


288 
287 
38 
40 
179 
333 


329 
330 
334 
216 
6 
271 
342 
342 
343 

44 
342 
345 

39 

175 

178 

6 


254 
473 
294 


401 
406 
394 
212 
93 
282 


305 
283 

283 

285 

209 

239 

6 

1 

7 

499 

396 


415 

255 
242 

418 
544 
304 

305 
306 
294 


173 
271 
35 
547 
130 
131 


Page. 


79 

79 

18 

19 

55 

96 

173 

94 

94 

97 

63 

11 

74 

103 

103 

103 

20 

103 

103 

18 

53 

54 

12 


69 

145 

82 

176 

174 

173 

126 

128 

124 

63 

32 

76 

163 

84 
76 

76 

78 

63 

66 

12 

11 

13 

153 

125 

177 

132 

70 

67 

1.33 

161 

84 

84 
85 
82 
11 
13 
52 
74 
18 
161 
42 
42 


Subject. 


Art. 


Plane  of  reference,  tidal 514 

sailing 169 

417 

416 
420 
418 
294 


table,  adjustments 

description 

to  improvise 

use  of 

Planet,  correction  of  observed  altitude 

form  for  latitude  sights 

meridian  altitude  . . . 

time  sight 

identification  of  unknown 402 

401 
219 
340 
214 
340 
6 
431 
151 
146 
142 
138 
145 
134 
144 
143 
133 
166 
407 
458 


Planets,  stars,  and  moon,  use  of 

Polar  distance,  definition 

Polaris,  latitude  by 

Pole,  elevated 

star,  latitude  by 

Poles  of  earth 

Portable  transit 

Position  by  angles  between  3  objects 
26i°-45°onbow-.. 

bearing  and  angle 

distance 

bow  and  beam  bearings  . . 

cross  bearings 

doubling  angle  on  bow . . . 

two  bearings  and  run 

methods  of  fixing 

of  anchorage  to  be  plotted. . . 
body  determines  its  use... 

soundings  in  survey 

probable  error  of  by  Sumner 

lines,  how  shown 

Pressure,  effect  in  wind 

progressive  areas  of 

seasonal  variations  in 

variation  of  atmospheric 

Prime  meridian,  Greenwich  adopted  .. 

vertical,  .definition 

Priming  of  tide 

Projection,  gnomonic 

Mercator 

polyconic 

systems  in  use 

Proportional  dividers,  description 

Prosection  method,  plane  table 

Protractor,  ordinary 

three  armed,  description  . . 

substitute 

use  of 

Quadrantal  deviation.  {See  Deviation.) 

Quintant,  description 

Range  of  tide  at  various  places 

definitions 

Ranges  for  finding  compass  error 

in  piloting 

Rate,  chronometer.  (jSee  Chronometer 

rate. ) 
Reciprocal  bearings  for  compass  error. 
Reckoning,  dead.     {See  Dead  reckon- 
ing- ) 

Record  of  astronomical  work 

chronometer  comparisons . . 

piloting 

tidal 

Red  sea,  extraordinary  dip  in 

Reduction  to  meridian 

forms  for 

Reference,  planes  of,  tidal 

Refraction,  correction  for 

definition 

effect  on  dip 


410 

465 

479 

466 

476 

342 

217 

502 

43 

38 

42 

37 

435 

418 

9 

432 

433 

151 

255 


498 

89 

158 


411 
264 
166 
512 
301 
334 


Page. 


514 
298 
296 
300 


156 

50 

133 

132 

134 

133 

82 

175 

173 

172 

126 

126 

64 

101 

63 

101 

11 

135 

45 

44 

43 

43 

44 

42 

44 

43 

42 

49 

128 

140 

130 

142 

147 

144 

147 

103 

64 

154 

20 

18 

20 

18 

136 

134 

13 

136 

136 

45 

70 

190 

153 

31 

47 


31 


130 
72 
49 

156 
83 
97 

174 

156 
82 
82 
83 


22489—03- 


338 


INDEX   TO    PART   I. 


Subjet't. 


Refraction,  extraordinary,near  horizon 

how  applied 

Relative  humidity 

Rennell's  current 

Repeat,  to,  an  angle 

Resection  method,  plane  table 

Residual  deviation ---^ 

Rhumb  line,  definition 

not  shortest  course 

Right  ascension  and  declination 

definition 

Roaring  forties 

Rossel  ctirrent 

Round  of  angles 

Run,  calculation  of 

determined  at  noon 

Running  survey,  description 

Sailing,  composite.     (See  Composite. ) 
great  circle.    {See  Great  circle. ) 

Mercator 

middle  latitude 

correction 

parallel 

plane 

spherical 

traverse  

Sailings,  definition 

kinds  of 

Sargasso  sea 

Sea  and  land  breezes 

mile,  length  of 

symbols  for  state  of 

water  temperature 

Second  difference,  chronometer 

Nautical  Almanac. 

Secondary  meridian,  definition 

determination  of. 

triangulation 

Seconds,  employment  in  naut.  sights.. 

Semicircles,  storm 

Semicirculardeviation.  (*SeeDeviation. ) 

Semidiameter,  definition 

how  applied 

measured 

of  planet  or  star 

Semidiurnal  type  of  tide 

Sextant  adjustments 

permanent 

angles  for  plotting  soundings  . 

choice  of 

definition 

description 

eccentricity 

graduation  errors 

index  correction,  to  find 

error,  description 

method  of  use 

optical  principle 

prismatic  mirrors 

shade  glasses 

resilvering  mirrors 

surveying 

vernier  

Shade  glasses,  for  artificial  horizon 

sextant,  description 

prismatic 

Sidereal  day,  definition 

noon,  definition 

time,  conversion  to  mean 

definition 

intervals,    relation    to 
mean 


Art.  1  Page. 


301 

83 

299 

83 

62 

25 

537 

160 

415 

132 

418 

134 

124 

40 

6 

12 

185 

56 

237 

65 

228 

64 

472 

145 

546 

161 

415 

132 

208 

,62 

398 

125 

462 

140 

179 

55 

175 

53 

178 

54 

173 

52 

169 

50 

168 

50 

172 

52 

167 

50 

168 

50 

534 

160 

474 

145 

6 

12 

72 

28 

63 

25 

265 

72 

285 

78 

342 

103 

343 

103 

449 

139 

409 

129 

490 

150 

307 

85 

308 

85 

251 

69 

294 

82 

503 

154 

244 

67 

248 

68 

458 

140 

253 

69 

239 

66 

240 

66 

248 

68 

248 

68 

250 

69 

249 

68 

252 

69 

242 

67 

248 

68 

248 

68 

254 

69 

427 

135 

241 

66 

256 

70 

240 

66 

248 

68 

276 

74 

276 

74 

291 

80 

276 

74 

289 


Subject. 


Sidereal  time,  relation  to  mean 

Sight,  chronometer.  ( See  Time  sight. ) 
equal  alts.  {See  Equal  altitudes. ) 
latitude.     (♦See  Latitude. ) 

line  of,  definition 

longitude.     {See  Longitude.) 
time.     ( Sec  Time  sight. ). 

Sights,  afternoon 

employment  of  various 

morning 

noon 

Signals,  surveying,  description 

time,  for  chronometer  error 

Silvering  sextant  mirrors 

Solar  time.     {See  Apparent  time. ) 

Solstice,  definition 

Sound,  velocity  of 

Sounding  machine,  barometric  corr 

depth  recorder 

description 

tubes 

Soundings,  surveying,  how  plotted 

use  in  piloting 

Southern  connecting  current 

Sphere,  celestial,  definition 

Spherical  sailing 

Spring  tides 

Stadia.     {See  Telemeter. ) 

Star,  correction  of  observed  altitude 

equal  altitudes  for  chro.  error 

form  for  latitude  sights 

meridian  altitude 

time  sight 

identification 

observations  in  surveying 

Starboard  angle,  definition 

Stars,  planets,  and  moon,  use  of 

Station  pointer.    {See  Protractor,  three 
armed. ) 

Storm  center,  motion  of 

rate  of  progress 

to  avoid 

fix  bearing 

distance 

semicircles 

tables 

Storms,  along  transatlantic  routes 

cyclonic.   (»%cCyclonicstorms. ) 

Stream  current,  definition 

Submarine  ocean  currents 

Sumner  line,  always  recommended 

applications  of 

choice  of  bodies 

description 

'  determination 


287 


414 


399 
408 
394 
396 
447 
314 
254 


227 

314 

24 

i     23 

!     20 

I     21 

458 

159 

539 

210 

168 

499 

294 
326 


79 


uses 

lines,  intersection,computation 
graphically . 
when  run  in- 
tervenes.. 
Sun,  correction  of  observed  altitude . . . 

equal  altitudes  for  chro.  error 

long,  ashore . . 

form  for  equal  altitudes 

latitude  sights 

meridian  altitude 

time  sight 

mean,  definition 

observations  in  surveying 

Survey,  astronomical  work  of 

hydrographic,  method  of 

running,  description 


402 
454 
102 
401 


484 
485 
489 
487 
488 
490 
492 
494 

523 
524 
394 
400 
400 
372 
379 
377 
384 
382 

390 
294 
322 
347 


274 
454 
450 
436 
462 


INDEX    TO    PART    I. 


339 


Subject. 


Survey,  to  plot  soundinga  in 

Surveying,  hydrograpliic,  definition 

instruments 

marine,  definition 

topographic,  definition 

transit,  description 

Symbols  for  clouds 

sea , 

weather  

Ta))le,  plane,    (See  Plane  table.) 

tide 

time  azimuth 

Telemeter,  descrii)tion 

substitute  for  . . , 

use  of 

Telescope,  direct  and  reversed 

sextant,  adjustment 

description 

zenith 

Temperature  curve,  chronometer 

Terrestrial  object,  true  bearing  of 

Tertiary  meridian,  definition 

determination  of  . . 

Theodolite,  adjustments 

angles  for  plotting  sound  - 

ings 

description 

method  of  use 

Thermometer,  classes  of 

description 

dry  and  wet  bulb 

max.  and  min.,  chro 

Three-armed    protractor.      {See  Pro- 
tractor. ) 

point  problem,  conditions 

explanation 

Tidal  current.     {See  Current,  tidal.) 

day,  definition 

establishment,  definitions 

observations  in  survey 

instructions  for 

record  

Tide,  bench  mark,  definition 

cause  of 

definitions  relating  to 

diurnal  inequality 

type-,- 

effect  of,  in  piloting 

wind  and  barometer  on 

gauges,  description 

observation  of 

planes  of  reference  of 

priming  and  lagging  of 

range  of,  at  various  places 

definitions 

semidiurnal  type 

spring  and  neap 

tables 

time  of  high  and  low 

form  for 

tropic 

types  of 

Time  and  altitude  azimuth 

hour  angle,  conversion  of 

apparent.     {See  Apparent  time.) 

astronomical 

at  different  meridians 

azimuth.     (/Sf'e  Azimuth,  time.) 

civil 

conversion  of.  (/See  Conversion.) 
equation  of.  {See   Equation  of 
time. ) 


458 

412 

413 

412 

412 

413 

70 

72 

69 

506 
361 
421 
426 
424 
415 
247 
240 
431 
266 
369 
342 
345 
414 

458 
413 
415 

58 

58 

61 

262 


153 
152 

502 
497 
460 
508 
512 
516 
496 
495 
503 
503 
164 
501 
518 
509 
514 
502 


498 
503 
499 
506 
506 


503 
503 
366 
293 

277 
279 

277 


Page. 


140 

131 

131 

131 

131 

131 

27 

28 

27 

155 

110 

134 

135 

135 

132 

68 

66 

135 

72 

112 

103 

103 

132 

140 
131 
1.32 
24 
24 
24 
71 


46 
45 

154 
153 
140 
156 
156 
156 
153 
153 
154 
154 

48 
154 
157 
156 
156 
154 
190 
153 
154 
153 
155 
155 
176 
154 
154 
112 

81 

74 

75 

74 


Subject. 


Time,  Greenwich,  to  find 

local,  to  find 

mean.     {See  Mean  time. ) 

of  high  and  low  water 

form  for . . 

transit,  how  found 

sidereal.     (/SVe  Sidereal  time.) 

signals  for  chrenometer  error 

sight  for  chronometer  error 

longitude  ashore 

at  sea 

forms  for 

solar.     {See  Apparent  time.) 

Topographic  surveying,  definition 

Topography  in  hydrographic  survey  . . 

Tracing  paper  to  plot  soundings 

3  -point  problem  . 

Trade  wind 

Transit,  astronomical 

definition 

observations  for  chronometer 

error 

longitude 

portable 

surveying.     (*S'ce  Theodolite.) 

time  of,  how  found 

Traverse  sailing 

tables,  use  of 

Triangulation,  main 

secondary  

Trigonometric  functions 

logarithms 

Tropic  tide 

Tropical  cyclonic  storms 

character 

Tubes,  sounding  machine 

Unknown  bodies,  identification  of 

Useful  data,  miscellaneous 

Variation  of  compass,  definition 

to  apply 

find 

Variations,  atmospheric 

non-periodic . . 

periodic 

Vernier,  barometer 

sextant 

theodolite 

Vertical  angles,  terrestrial,  to  measure . 

circle,  definition 

prime 

Visible  horizon,  definition 

Watch,  comparing,  use  of 

Weather  symbols 

Wind,  Beaufort's  scale 

causes  of 

definition 

doldrums 

effect  of,  on  tides 

land  and  sea  breezes 

monsoon 

normal  i)ressure 

prevailing 

westerly 

'  *  Roaring  forties  " 

storms.    {See  Cyclonic  storms. ) 

Trade 

true  direction  and  force 

Zenith,  definition 

distance,  definition 

how  named 

telescope 


Page. 


280 

281 

506 


331 

314 
316 
346 
349 


412 
456 
160 
433 
469 
431 
271 

315 
344 
431 

331 

172 
170 
448 
449 


603 
483 
486 
21 
402 


74 
77 
82 
476 
478 
477 
51 
241 
413 
139 
217 
217 
213 
268 
69 
67 
464 
463 
470 
501 
474 
473 
465 
467 
472 
472 

469 
68 
212 
221 
329 
431 


P^BT    II. 


TABLES 


341 


CONTENTS    OF    I>A.IIT    II. 


Page. 

Explanation  of  the  Tables 345 

Table    1.      Traverse  Table,  Quarter  Points 352 

2.  Traverse  Table,  Degrees 368 

3.  Meridional  Parts 458 

4.  Length  of  Degrees  of  Latitude  and  Longitude 466 

5A.  Distance  of  an  Object  by  Two  Bearings,  Quarter  Points 468 

5B.  Distance  of  an  Object  by  Two  Bearings,  Degrees 471 

6.  Distance  of  Visibility  of  Objects  of  different  Heights 477 

7.  Conversion  of  Arc  and  Time 478 

8.  Conversion  of  Sidereal  into  Mean  Solar  Time 479 

9.  Conversion  of  Mean  Solar  into  Sidereal  Time 482 

10.  Local  mean  time  of  Sun's  visible  Rising  and  Setting 485 

11.  Reduction  of  Moon's  Meridian  Passage  for  Longitude 509 

12.  Reduction  of  Quantities  from  Nautical  Almanac 510 

13.  Change  of  Sun's  Right  Ascension 520 

14.  Dip  of  Sea  Horizon 522 

15.  Dip  at  Distances  short  of  Horizon 522 

16.  Parallax  of  Sun 522 

17.  Parallax  of  Planet 523 

18.  Augmentation  of  Moon's  Semidiameter 524 

19.  Augmentation  of  Moon's  Horizontal  Parallax 524 

20A.  Mean  Refraction 525 

20B.  Mean  Refraction  and  Parallax  of  Sun 526 

21.  Correction  of  Refraction  for  Barometer 527 

22.  Correction  of  Refraction  for  Thermometer 528 

23.  Mean  Refraction  and  Mean  Parallax  of  Moon 530 

24.  Mean  Refraction  and  Parallax  of  Moon 530 

25.  Variation  of  Altitude  due  to  change  of  Declination 539 

26.  Variation  of  Altitude  in  one  minute  from  Meridian 541 

27.  Variation  of  Altitude  in  given  time  from  Meridian 551 

28A.  First  Correction  of  Polaris •. 554 

28B.  Second  Correction  of  Polaris 555 

28C.  Third  Correction  of  Polaris 555 

28D.  Fourth  Correction  of  Polaris 560 

29.  Nautical  and  Statute  Miles 562 

30.  Conversion  of  Metric  and  English  Linear  Measure. .., 563 

31.  Fahrenheit,  Centigrade,  and  Reaumur  Temperatures 564 

32.  True  Force  and  Direction  of  Wind 565 

33.  Distance  by  Vertical  Angle 566 

34.  Distance  by  Horizon  Angle 568 

35.  Speed  Table  for  Measured  Mile , 569 

36.  Local  Mean  and  Standard  Meridian  Times 570 

37.  Logarithms  for  Equation  of  Equal  Altitudes 571 

38.  Error  in  Longitude  produced  by  Error  in  Latitude 575 

39.  Amplitudes 576 

40.  Correction  for  Amplitude  observed  in  Apparent  Horizon 581 

41.  Natural  Sines  and  Cosines 582 

42.  Logarithms  of  Numbers 591 

43.  Logarithms  of  Trigonometric  Functions,  Quarter  Points 607 

.44.     Logarithms  of  Trigonometric  Functions,  Degrees 608 

343 


EXPLANATION  OF  THE  TABLES. 


TABLES  1,  2:  TRAVERSE  TABLES. 

Tables  1  and  2  were  originally  calculated  by  the  natural  sines  taken  from  the  fourth  edition  of 
Sherwin's  Logarithms,  which  were  previously  examined,  by  differences;  when  the  proof  sheets  of  the 
first  edition  were  examined  the  numbers  were  again  calculated  by  the  natural  sines  in  the  second  edition 
of  Hutton's  Logarithms;  and  if  any  difference  was  found,  the  numbers  were  calculated  a  third  time  by 
Taylor's  Logarithms. 

The  first  table  contains  the  difference  of  latitude  and  departure  corresponding  to  distances  not 
exceeding  300  miles,  and  for  courses  to  every  quarter  point  of  the  compass.  Table  2  is  of  the  same 
nature,  but  for  courses  consisting  of  whole  degrees;  it  was  originally  of  the  same  extent  as  Table  1,  but 
has  been  extended  to  include  distances  up  to  600  miles.  The  manner  of  using  these  tables  is  particularly 
explained  imder  the  different  problems  of  Plane,  Middle  Latitude,  and  Mercator  Sailing  in  Chapter  V. 

The  tables  may  be  employed  in  the  solution  of  any  right  triangle. 

TABLE  3:    MERIDIONAL  PARTS. 

This  table  contains  the  meridional  parts,  or  increased  latitudes,  for  every  degree  and  minute  to  80°, 
calculated  by  the  following  formula: 


in  which 


~ivr  ^^^  ^^  \  '*'^°   '^  2  y  ~  "  (^^  *^^"  I-"  +  4  ^*  sin'  T-i  +  5  <^  sin*  L  +     .     .     .     .     ), 

10800'' 
the  Equatorial  radius  a  =  — ~ — =  3437^74677  (log  3.5362739); 

M,  the  modulus  of  common  logarithms  =  0.4342945; 

^=  2.3025^51  ( log  0.3622157) ; 

C,  the  comprenKion  or  meridional  eccentricity  of  the  earth 

according  to  Clarke  ( 1880)  =  293  465  =  0.003407562  (log  7.5324437) ; 
^  =v/ 27 -V^  =  0.0824846  (log  8.9163666) ; 
from  which 

^     =7915^  7044558  ( log  3. 8984895) ; 

ae^   =      23^38871  (log  1.3690072); 
^ae*  =        0^05.3042  (log  8. 7246192 ) ; 
!«<?«=        0^000216523  (log  6.33550.38). 

The  results  are  tabulated  to  one  decimal  i)lace,  which  is  sufficient  for  the  ordinary  problems  of 
navigation. 

The  practical  application  of  this  table  is  illustrated  in  Chapters  II  and  V,  in  articles  treating  of  the 
Mercator  Chart  and  Mercator  Sailing. 

TABLE  4:    LENGTH  OF  DEGREES  OF  LATITTTDE  AND  LONGITXTDE. 

This  table  gives  the  length  of  a  degree  in  both  latitude  and  longitude  at  each  parallel  of  latitude  on 
the  earth's  surface,  in  nautical  and  statute  miles  and  in  meter.-!,  based  upon  Clarke's  value  (1866)  of  the 

earth's  compression,  200  i-"      1"  the  case  of  latitude,  the  length  relates  to  an  arc  of  which  the  given 
degree  is  the  center. 

TABLES  5 A,   5B:    DISTANCE  BY  TWO  BEARINGS. 

These  tables  have  been  calculated  to  facilitate  the  operation  of  finding  the  distance  from  an  object  by 
two  bearings  from  a  given  distance  run  and  course.  In  Table  5A  the  arguments  are  given  in  points, 
in  Table  5B  in  degrees;  the  first  column  contains  the  multiplier  of  the  distance  run  to  give  the  distance 
of  observed  object  at  second  bearing;  the  second,  at  time  of  passing  abeam. 

The  method  is  explained  in  article  143,  Chapter  IV. 

345 


346 


EXPLANATION    OF    THE    TABLES. 


TABLE  6:    DISTANCE  OF  VISIBILITY  OF  OBJECTS. 

This  table  contains  the  distances,  in  nautical  and  statute  miles,  at  which  any  object  is  visible  at  sea. 
It  is  calculated  by  the  formulae: 

rf  =  1. 15  \/x^  and  d'  =  1.32  x/x, 
in  which  rf  is  the  distance  in  nautical  miles,  d^  the  distance  in  statute  miles,  and  x  the  height  of  the  eye 
or  the  object  in  feet. 

To  find  the  distance  of  visibility  of  an  object,  the  distance  given  by  the  table  corresponding  to  its 
height  should  be  added  to  that  corresponding  to  the  height  of  the  observer's  eye. 

Example:  Required  the  distance  of  visibility  of  an  object  420  feet  high,  the  observer  being  at  an 
elevation  of  15  feet. 

Dist.  corresponding  to  420  feet,  23.5  naut.  miles. 
Dist.  corresponding  to    15  feet,    4.4  naut.  miles. 


Dist.  of  visibility. 


27.9  naut.  miles. 


TABLE  7:    CONVERSION  OF  ABC  AND  TIME. 

In  the  first  column  of  each  pair  in  this  table  arfe  contained  angular  measures  expressed  in  arc 
(degrees,  minutes,  or  seconds),  and  in  the  second  column  the  corresponding  angles  expressed  in  time 
(hours,  minutes,  or  seconds).  As  will  be  seen  from  the  headings  of  columns,  the  time  corresponding 
to  degrees  (°)  is  given  in  hours  and  minutes;  to  minutes  of  arc  {/),  in  minutes  and  seconds  of  time; 
and  to  seconds  of  arc  ('''),  in  seconds  and  sixtieths  of  a  second  of  time. 

The  table  will  be  especially  convenient  in  dealing  with  longitude  and  hour  angle.  The  method  of 
its  employment  is  best  illustrated  by  examples. 


Example  I. 
Required  the  time  corresponding  to  50°  31''  21'^. 

50°  00'  00'''  =  3"  20"'  00^ 
31    00    =         2    04 

21  =         m 


50    31    21    =3    22     05.4 


Example  II. 

Required  the  arc  corresponding  to  6^  33™  26\5. 


gh  32m  00^    =  98° 
1     24      = 

03  0    


00 
37.5 


33    26.5  =  ' 


21    37.5 


TABLES  8  AND  9:    SIDEREAL  AND  MEAN  SOLAR  TIMES. 

These  tables  give,  respectively,  the  reductions  necessary  to  convert  intervals  of  sidereal  time  into 
those  of  mean  solar  time,  and  intervals  of  mean  solar  into  those  of  sidereal  time.  The  reduction  for  any 
interval  is  found  by  entering  with  the  number  of  hours  at  the  top  and  the  number  of  minutes  at  the  side, 
adding  the  reduction  for  seconds  as  given  in  the  margin. 

The  relations  between  mean  solar  and  sidereal  time  intervals,  and  the  methods  of  conversion  of 
these  times,  are  given  in  articles  289-291,  Chapter  IX. 


TABLE  10:    SUN'S   RISING   AND    SETTING. 

This  table  gives  the  local  mean  time  of  the  sun's  visible  rising  and  setting — that  is,  of  the  appearance 
and  disappearance  of  the  sun's  upper  limb  in  the  unobstructed  horizon  of  a  person  whose  eye  is  15  feet 
above  the  level  of  the  earth's  surface,  the  atmospheric  conditions  being  normal. 

The  local  apparent  times  of  rising  and  setting  were  determined  from  the  formula  for  a  time  sight, 
the  altitude  employed  being  —  0°  56'  08",  made  up  of  the  following  terms:  Refraction,  —  36''  29''';  semi- 
diameter,  -  16' 00";  dip,  —  3' 48";  and  parallax,  +  9". 

To  ascertain  the  time  of  rising  or  setting  for  any  given  date  and  place,  enter  the  table  with  the 
latitude  and  declination,  interpolating  if  the  degrees  are  not  even.  In  the  line  R  will  be  found  the  time 
of  rising;  in  the  line  S,  the  time  of  setting.  Be  careful  to  choose  the  page  in  which  the  latitude  is  of 
the  correct  name,  and  in  which  the  "approximate  date"  corresponds,  nearly  or  exactly,  with  the 
given  date. 

This  table  is  computed  with  the  intention  that,  if  accuracy  is  desired,  it  will  be  entered  with  the 
declination  as  an  argument — not  the  date — as  it  is  impossible  to  construct  any  table  based  upon  dates 
whose  application  shall  be  general  to  all  years.  But  as  a  given  degree  of  declination  will,  in  the 
majority  of  years,  fall  upon  the  date  given  in  the  table  as  the  "approximate  date,"  and  as,  when  it 
does  not  do  so,  it  can  never  be  more  than  one  day  removed  therefrom,  it  will  answer,  where  a  slight 
inaccuracy  may  be  admitted,  to  enter  the  table  with  the  date  as  an  argument,  thus  avoiding  the  neces- 
sity of  ascertaining  the  declination. 

Example:  Find  the  local  mean  time  of  sunset  at  Rio  de  Janeiro,  Brazil  (lat.  22°  54'  S.,  long. 
43°  10'  W.),  on  January  1,  1903  (dec.  23°  04'  S.). 


Exact  method. 

Lat.  22°) 

Dec.  23°  i  

Corr.  for  +  54'  lat +02 

Corr.  for -f  04' dec 00 


Approximate  method. 


6"  48° 


Lat.  22°..  ) 

January  2  i 

Corr.  for  +  54'  lat. 
Corr.  for  1  dav 


L.  M.  T.  sunset 6  50 


L.  M.  T.  sunset.. 


6"   48'" 

+  02 
-01 

6    49 


EXPLANATION    OB^    THE    TABLES.  •  347 

TABIiE  11:  REDUCTION  FOR  IffiOON'S  TRANSIT. 

This  table  was  calculated  by  proportioning  the  daily  variation  of  the  time  of  the  moon's  passing  the 
meridian. 

The  numbers  taken  from  the  table  are  to  be  added  to  the  Greenwich  time  of  moon's  transit  in  west 
longitude,  but  subtracted  in  east  longitude. 

TABLE  12:  REDUCTIONS  FOR  NAUTICAL  ALMANAC. 

This  is  a  table  of  proportional  parts  for  finding  the  variation  of  the  sun's  right  ascension  or  declination, 
or  of  the  equation  of  time,  in  any  number  of  minutes  of  time,  the  horary  motion  being  given  at  the  top  of 
the  page  in  seconds,  and  the  number  of  minutes  of  time  in  the  side  column ;  also  for  finding  the  variation 
of  the  moon's  declination  or  right  ascension  in  any  number  of  seconds  of  time,  the  motion  in  one  minute 
being  given  at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

TABLE  13:  CHANGE  OF  SUN'S  RIGHT  ASCENSION. 

This  is  a  table  that  may  \)e  employed  for  finding  the  change  of  the  sun's  right  ascension  for  any 
given  number  of  hours,  the  hourly  change,  as  taken  from  the  Nautical  Almanac,  being  given  in  the 
marginal  columns. 

TABLE  14:  DIP  OF  SEA  HORIZON. 

This  table  contains  the  dip  of  the  sea  horizon,  calculated  by  the  formula: 

D  =  58'^8\/F, 

in  which  F  =  height  of  the  eye  above  the  level  of  the  sea  in  feet. 
It  is  explained  in  article  300,  Chapter  X. 

TABLE  16:  DIP  SHORT  OF  HORIZON. 

This  table  ijontains  the  dip  for  various  distances  and  heights,  calculated  ]jy  the  formula: 

D  =  ?  rf  +  0.56514  X  i 
'  a 

in  which  D  represents  the  dip  in  miles  or  minutes,  d,  the  distance  of  the  land  in  sea  miles,  and  Ji,  the 
height  of  the  eye  of  the  observer  in  feet. 

TABLE   16:  PARALLAX  OF  SUN. 
This  table  contains  the  sun's  parallax  in  altitude  calculated  by  the  formula: 

par.  =  sin  2  X  8'''.75, 

in  which  z  =  apparent  zenith  distance,  the  sun's  horizontal  parallax  being  8'''''.75. 
It  is  explained  in  article  304,  Chapter  X. 

TABLE  17:  PARALLAX  OF  PLANET. 

Parallax  in  altitude  of  a  planet  is  found  by  entering  at  the  top  with  the  planet's  horizontal  parallax, 
and  at  the  side  with  the  altitude. 

TABLE  18:  AUGMENTATION  OF  MOON'S  SEMIDIAMETER. 

V 

This  table  gives  the  augmentation  of  the  moon's  semidiameter  calculated  by  the  formula: 

X  =  c  s''  sin  /i  +  ^  c*  s*  sin^  h  -{-  ^  c'^  .v', 

where  /i  =  moon's  apparent  altitude; 

8  =  moon's  horizontal  semidiameter; 
X  =  augmentation  of  semidiameter  for  altitude  h;  and 
log  c  =  5.25021. 

TABLE  19:  AUGMENTATION  OF  MOON'S  HORIZONTAL  PARALLAX. 

This  table  contains  the  augmentation  of  the  moon's  horizontal  parallax,  or  the  correction  to  reduce 
the  moon's  equatorial  horizontal  parallax  to  that  point  of  the  earth's  axis  which  lies  in  the  vertical  oi 
the  observer  in  any  given  latitude;  it  is  computed  by  the  formulae: 

A7t  =  7t{b-1),  ^^^il-e'sw?!.)' 

where     *  =  equatorial  horizontal  parallax; 
L=  latitude; 

e  =  eccentricity  of  the  meridian;  log  ^  =  7.81602;  and 
A  Tf  =  augmentation  of  the  horizontal  parallax  for  the  latitude  L. 


348  .  EXPLANATION    OF    THE    TABLES. 

TABLE  20A:  MEAN  REFRACTION. 

This  table  gives  the  refraction,  reduced  from  Bessel's  tables,  for  a  mean  atmospheric  condition  in 
which  the  barometer  is  30.00  inches,  and  thermometer  50°  Fahr. 

TABLE  20B:    MEAN  REFRACTION  AND  PARALLAX  OF  SUN. 

This  table  contains  the  correction  to  be  applied  to  the  sun's  apparent  altitude  for  mean  refraction 
and  parallax,  being  a  combination  of  the  quantities  for  the  altittides  given  in  Tables  16  and  20A. 

TABLES  21,  2t:    CORRECTIONS  OF  REFRACTION  FOR  BAROMETER  AND 

THERMOMETER. 

These  are  deduced  from  Bessel's  tables.     The  method  of  their  employment  will  be  evident. 

TABLE  23:    MEAN  REFRACTION  AND  MEAN  PARALLAX  OF  MOON. 

This  table  contains  the  correction  of  the  moon's  altitude  for  refraction  and  parallax  corresponding 
to  the  mean  refraction  (Table  20A),  and  a  horizontal  parallax  of  the  mean  value  of  hi'  30''^. 

TABLE  24:    MEAN  REFRACTION  AND  PARALLAX  OF  MOON. 

This  table  contains  the  correction  to  be  applied  to  the  moon's  apparent  altitude  for  each  minute  of 
horizontal  parallax,  and  for  every  10''  of  altitude  from  5°,  with  height  of  barometer  30.00  inches,  and 
thermometer  50°  Fahr. 

For  seconds  of  parallax,  enter  the  table  abreast  the  approximate  correction  and  find  the  seconds  of 
horizontal  parallax,  the  tens  of  seconds  at  the  side  and  the  units  at  the  top.  Under  the  latter  and 
opposite  the  former  will  be  the  seconds  to  add  to  the  correction. 

For  minutes  of  altitude,  take  the  seconds  from  the  extreme  right  of  the  page,  and  apply  them  as 
there  directed. 

TABLE  25:    CHANGE  OF  ALTITUDE  DUE  TO  CHANGE  OF  DECLINATION. 

♦ 

This  table  gives  the  variation  of  the  altitude  of  any  heavenly  body  arising  from  a  change  of  100^''  in 
the  declination.  It  is  useful  for  finding  the  equation  of  equal  altitudes  by  the  approximate  method 
explained  in  article  324,  Chapter  XI,  and  for  other  purposes. 

If  the  change  move  the  body  toward  the  elevate<i  pole,  apply  the  correction  to  the  altitude  with  the 
signs  in  the  table;  otherwise  change  the  signs. 

TABLE  26:    CHANGE  OF  ALTITUDE  IN  ONE  MINUTE  FROM  MERIDIAN. 

This  table  gives  the  variation  of  the  altitude  of  any  heavenly  body,  for  one  minute  of  time  from 
meridian  passage,  for  latitudes  up  to  60°,  declinations  to  63°,  and  altitudes  between  6°  and  86°.  It  is 
based  upon  the  method  set  forth  in  aii;icle  334,  Chapter  XII,  and  the  values  may  be  computed  by  the 
formula: 

1^^9635  cos  L  cos  r? 
"~         sin  (L-rf) 

where  a  =  variation  of  altitude  in  one  minute  from  meridian, 
L  =  latitude,  and 

d  =  declination — positive  for  same  name  and  negative  for  opposite  name  to  latitude  at  upper 
transit,  and  negative  for  same  name  at  lower  transit. 

The  limits  of  the  table  take  in  all  values  of  latitude,  declination,  and  altitude  which  are  likely  to 
be  required.  In  its  employment,  care  must  be  taken  to  enter  the  table  at  a  place  where  the  declination 
is  appropriately  named  (of  the  same  or  opposite  name  to  the  latitude) ;  it  should  also  be  noted  that  at 
the  bottom  of  the  last  three  pages  values  are  given  for  the  variation  of  a  body  at  lower  transit,  which  can 
only  be  observed  when  the  declination  and  latitude  are  of  the  same  name,  and  in  which  case  the  reduc- 
tion to  the  meridian  is  subtractive;  ihe  limitations  in  this  case  are  stated  at  the  Joot  of  the  page,  and 
apply  to  all  values  below  the  heavy  rules. 

TABLE  27:    CHANGE  OF  ALTITUDE  IN  GIVEN  TIME  FROM  MERIDIAN. 

This  table  gives  the  pro<lact  of  the  variation  in  altitude  in  one  minute  of  a  heavenly  body  near  the 
meridian,  by  the  square  of  the  number  of  minutes.  Values  are  given  for  every  half  minute  between 
0'"  30' and  26'"  0%  and  for  all  variations  likely  to  be  employed  in  the  method  of  "reduction  to  the 
meridian." 

The  formula  for  computing  is: 

Red.  =  a  X  f, 
where  a  =  variation  in  one  minute  (Table  26) ,  and 

t  =  number  of  minutes  (in  units  and  tenths)  from  time  of  meridian  passage. 

The  table  is  entered  in  the  column  of  the  nearest  interval  of  time  from  meridian,  and  the  value 
taken  out  corrresponding  to  the  value  of  a  found  from  Table  26.  The  units  and  tenths  are  picked  out 
separately  and  combined,  each  being  corrected  by  interpolation  for  intermediate  intervals  of  time. 

The  result  is  the  amount  to  be  applied  to  the  observed  altitude  to  reduce  it  to  the  meridian  altitude, 
which  is  always  to  be  added  for  upper  transits  and  subtracted  for  lower. 


EXPLANATION    OF    THE    TABLE8.  ^  349 

TABLE  28,  A,  B,  C,  D:  LATITUDE  BY  POLARIS.  ' 

The  formula  on  which  these  tables  are  based  is : 

h  =  h  —  p  (!08  t-'r^jJ^  sin  V^  sin^  t  tan  h 

—  Ip^  sin'^  V^  cos  t  sin^  t  +  ^p*  sin^*  V^  sin*  t  tan*  h; 

in  which  L  =  the  latitude  of  the  place; 

h  —  the  true  altitude; 
p  =  the  polar  distance;  and 
t  —  the  hour  angle  of  the  star. 

Table  A  contains  for  the  declination  88°  48',  or/»„  =  l°  12' =  4320''',  the^rs^  correction, 

A  =  —p„  cos  t  —  ^p^g  sin^  1"  cos  t  sin^  t; 

Argument,  the  hour  angle  of  the  star,  or  24''  —  the  hour  angle. 
Table  B  contains  the  second  correction, 

B  =  i  p^o  sin  1"  sin^  tta.nh+  lp\  sin*  1"  sin*  t  tan*  h; 

Arguments,  the  true  altitude  of  the  star  and  the  hour  angle,  or  24'' — the  hour  angle.     This 
correction  is  always  additive. 
Table  C  contains  the  third  correction, 

C  =  \  (p*  —p^o)  sin  1"  sin"''  t  tan  h; 

Arguments,  B  and  the  declinaium  of  the  star  from  88°  47'  20"  to  88°  49'  20". 
Table  D  contains  the  fourth  correction, 

—  {p  —Pa)  cos  l  —  i  {p^  —  P^o)  sii^*  1''''  COS  <8in^/; 

Arguments,  J  and  the  declination  of  the  star  from  88°  47'  20"  to  88°  49'  20". 
The  method  of  employing  this  table  is  illustrated  in  article  341,  Chapter  XII. 

TABLES  29,  30,  31:  CONVERSION  TABLES. 

These  are  self-explanatory. 

TABLE  32:  TRUE  FORCE  AND  DIRECTION  OF  WIND. 

This  table  enables  an  observer  on  board  of  a  moving  vessel  to  determine  the  true  force  and  direction 
of  the  wind  from  its  apparent  force  and  direction.  Enter  the  table  with  the  apparent  direction  of  the 
wind  (number  of  points  on  the  lx)w)  and  force  (Beaufort  scale)  as  arguments,  and  pick  out  the  direc- 
tion relatively  to  the  ship's  head  and  the  force  corresponding  to  the  known  speed  of  the  ship. 

Example:  A  vessel  steaming  SE.  at  a  speed  of  15  knots  appears  to  have  a  wind  blowing  from  three 
points  on  the  starboard  bow  with  a  force  of  6,  Beaufort  scale.     What  is  the  true  direction  and  force? 

In  the  column  headed  3  (meaning  three  points  on  bow,  apparent  direction)  and. in  the  line  6 
(apparent  force,  Beaufort  scale),  we  find  abreast  15  (knots,  speed  of  vessel)  that  the  true  direction  is  5 
points  on  starboard  bow,  i.  e.,  S.  by  W.,  and  true  force  4. 

TABLE  33:    VERTICAL  ANGLES. 

This  table  gives  the  distance  of  an  object  of  known  height  by  the  vertical  angle  that  it  subtends  at 
the  position  of  the  observer.     It  was  computed  by  the  formula: 

/* 
tan  a  =  . ,  ■ 

where  a  =  the  vertical  angle;  , 

h  =  the  height  of  the  observed  object  in  feet;  and 
d  =  the  distance  of  the  object,  also  converted  into  feet. 

The  employment  of  this  method  of  finding  distance  is  explained  in  article  139,  chapter  IV. 

TABLE  34:  HORIZON  ANGLES. 

This  shows  the  distance  in  yards  corresponding  to  any  observed  angle  between  an  object  and  the 
sea  horizon  beyond,  the  observer  being  at  a  known  height. 
The  method  of  une  is  explained  in  article  139,  chapter  IV. 

TABLE  35:    SPEED  TABLE. 

This  table  shows  the  rate  of  speed,  in  nautical  miles  per  hour,  of  a  vessel  which  traverses  a  measured 
mile  in  any  given  number  of  minutes  and  seconds.  It  is  entered  with  the  number  of  minutes  at  the  top 
and  the  number  of  seconds  at  the  side;  under  one  and  abreast  the  other  is  the  number  of  knots  of  speed. 


350  '  EXPLANATION    OF   THE    TABLES. 

TABLE  36:    LOCAL  AND  STANDARD  TIMES. 

This  table  contains  the  reduction  to  be  applied  to  the  local  time  to  obtain  the  corresponding  time 
at  any  other  meridian  whose  time  is  adopted  as  a  standard.  The  results  are  given  to  the  nearest  minute 
of  time  only,  being  intended  for  the  reduction  of  such  approximate  quantities  as  the  time  of  high  water 
or  time  of  sunset.     More  exact  reductions,  when  required,  may  be  made  by  Table  7. 

TABLE  37:    LOGARITHMS  FOR  EQUAL  ALTITUDE  SIGHTS. 

Logarithms  of  A  Mid  B,  for  computing  the  Equation  of  Equal  Altitudes,  are  calculated  by  the 
formulae: 


■    '      1800  sin  i  E'  -^"ISOO  tan  §  E ' 

where  E  in  the  numerator  is  the  elapsed  time  in  minutes,  and  E  in  the  denominator  the  elapsed  time 
expressed  in  arc. 


If  we  put 


we  have 


L  =  latitude  of  the  place  of  observation,  +  north,  —  south, 
d  =  declination  of  the  sun,  -f  north,  —  south, 

71  =  hourly  change  of  declination,  -j-  north,  —  south, 

C  =  correction  to  reduce  the  middle  chronometer  time  to  chronometer  time  of  apparent 

noon,  algebraically  additive, 
C''  =  the  same  for  midnight, 

C  ——An  tan  L  +  B  n  tan  d; 
C  =      An  tan  L  +  B  n  tan  d. 


This  is  Chauvenet's  table  to  aid  the  solution  of  the  problem  of  Equal  Altitudes,  and  is  explained  in 
article  322  and  following  articles.  Chapter  XI. 

TABLE  38:   EFFECT  UPON  LONGITUDE  OF  ERROR  IN  LATITUDE. 

Table  38  shows,  approximately,  the  error  in  longitude  in  miles  and  tenths  of  a  mile,  occasioned  by 
an  error  of  one  mile  in  the  latitude. 

Thus,  when  the  sun's  altitude  is  30°,  the  latitude  30°,  and  the  polar  distance  100°,  the  error  is 
eight-tenths  of  a  mile. 

The  effect  of  an  increase  of  latitude  is  as  follows: 

In  West  longitude,  /  East  \  of  meridian,  the  /  decreased  \  except  where  marked  f  increased  1 
the  body  being   \  West  J      longitude  is     \  increased  / '       by  *,  when  it  is      \  decreased  /" 

In  East  longitude,/  East  1  of  meridian,  the/  increased!  except  where  marked / decreased  1 
the  body  being    \  West  j      longitude  is     \  decreased  /'       by  *,  when  it  is      \  increased  /* 

A  decrease  of  latitude  has  the  contrary  effect. 

The  direction  of  error  may  readily  be  seen  by  drawing  the  Sumner  line  in  a  direction  at  right  angles 
to  the  approximate  bearing  of  the  body. 

TABLE  39:   AMPLITUDES. 

This  table  contains  amplitudes  of  heavenly  bodies,  at  rising  and  setting,  for  various  latitudes  and 
declinations,  computed  by  the  formula: 

sin  amp.  =  sec  Lat.  X  sin  dec. 

It  is  entered  with  the  declination  at  the  top  and  the  latitude  at  the  side. 
Its  use  is  explained  in  article  358,  Chapter  XIV. 

TABLE  40:    CORRECTION  FOR  AMPLITUDES. 

This  table  gives  a  correction  to  be  applied  to  the  observed  amplitude  to  counteract  the  vertical 
displacement  due  t(j  refraction,  parallax,  and  dip,  when  the  body  is  observed  with  its  center  in  the 
visible  horizon. 

The  correction  is  to  be  applied  for  the  sun,  a  planet,  or  a  star,  as  follows: 

^'  SSfg  r„  a  ^i;  }  "PP'J'  the  correction  to  the  right. 
""^wSI  ta  I  !il:  }  -PP'y  'he  eerrection  to  the  left. 
For  the  moon,  apply  half  the  correction  in  the  contrary  manner. 


EXPLANATION    OF    THE    TABLES.  351 

TABLE  41:    NATURAL  SINES  AND  COSINES. 

This  table  contains  the  natural  sine  and  cosine  for  every  minute  of  the  quadrant,  and  is  to  be 
entered  at  the  top  or  bottom  with  the  degrees,  and  at  the  side  marked  M.,  with  the  minutes;  the 
corresponding  numbers  will  be  the  natural  sine  and  cosine,  respectively,  observing  that  if  the  degrees 
are  found  at  the  top,  the  name  sine,  cosine,  and  M.  must  also  be  found  at  the  top,  and  the  contrary  if 
the  degrees  are  found  at  the  bottom.  It  should  be  understood  that  all  numbers  given  in  the  table 
should  be  divided  by  100,000 — that  is,  ]iointed  off  to  contain  five  decimal  places.  Thus,  .43366  is  the 
natural  sine  of  25°  42^,  or  the  cosine  of  64°  18^. 

In  the  outer  columns  of  the  margin  are  given  tables  of  proportional  parts,  for  the  purpose  of  finding, 
approximately,  by  inspection,  the  proportional  part  corresponding  to  any  number  of  seconds  in  the 
proposed  angle,  the  seconds  being  found  in  the  marginal  column  marked  M.,  and  the  correction  in 
the  adjoining  column.  Thus,  if  we  suppose  that  it  were  required  to  find  the  natural  sine  corresponding 
to  25°  42^  19'^  the  difference  of  the  sines  of  25°  42^  and  25°  43^  is  26,  being  the  same  as  at  the  top  of  the 
left-hand  column  of  the  table;  and  in  this  column,  and  opposite  19  in  the  column  M.,  is  the  correc- 
tion 8.  Adding  this  to  the  above  number  .43366,  because  the  numbers  are  increamng,  we  get  .4c374  for 
the  sine  of  25°  42^  19'^.  In  like  manner,  we  find  the  cosine  of  the  same  angle  to  be  .90108  — 4  =  .90104, 
using  the  right-hand  columns,  and  subtracting  Ijecause  the  numbers  are  decreasing;  observing,  however, 
that  the  number  14  at  the  top  of  this  column  varies  1  from  the  difference  between  the  cosines  of  25°  42'' 
and  25°  43',  which  is  only  13;  so  that  the  talole  may  give  in  some  cases  a  unit  too  much  between  the 
angles  25°  42'  and  25°  43';  but  this  is,  in  general,  of  but  little  importance,  and  when  accuracy  is  required, 
the  usual  method  of  proportional  parts  is  to  be  resorted  to,  using  the  actual  tabular  difference. 

TABLE  42:    LOGARITHMS  OF  NUMBERS. 

This  table,  containing  the  common  logarithms  of  numbers,  was  compared  with  Sherwin's,  Mutton's, 
and  Taylor's  logarithms;  its  use  is  explained  in  an  article  on  Logarithms  in  Appendix  III. 

TABLE  43:    LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS,   QUARTER  POINTS. 

This  table  contains  the  logarithms  of  the  sines,  tangents,  etc.,  corresponding  to  points  and  quarter 
points  of  the  compass.     This  Avas  compared  with  Sherwin's,  Hutton's,  and  Taylor's  logarithms. 

TABLE  44:    LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS,  DEGREES. 

This  table  contains  the  common  logarithms  of  the  sines,  tangents,  secants,  etc.  It  was  compared 
with  Sherwin's,  Hutton's,  and  Taylor's  tables.  Two  additional  columns  are  given  in  this  table,  which 
are  very  convenient  in  finding  the  time  from  an  altitude  of  the  sun;  also,  three  columns  of  proportional 
parts  for  seconds  of  space,  and  a  small  table  at  the  bottom  of  each  page  for  finding  the  proportional  parts 
for  seconds  of  time.  The  degrees  are  marked  to  180°,  which  saves  the  trouble  of  subtracting  the  given 
angle  from  180°  when  it  exceeds  90°. 

The  use  of  this  table  is  fully  explained  in  Appendix  III  in  an  article  on  Logarithms. 


Page  352 

TABLE 

1. 

1 

Difference  of  Latitude  and 

Departure  for  J  Point.                                               | 

N.  JE. 

N.  i  W. 

S. 

tE. 

s.  i  w.                    1 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.0 

61 

60.9 

3.0 

121 

120.9 

5.9 

181 

180.8 

8.9 

241     240. 7 

,11.8 

2 

2.0 

0.1 

62 

61.9 

3.0 

22 

121.9 

6.0 

82 

181.8 

8.9 

42     241. 7 

Ml.  9 

3 

3.0 

0.1 

63 

62.9 

3.1 

23 

122.9 

6.0 

83 

182.8 

9.0 

43     242. 7 

11.9 

4 

4.0 

0.2 

64 

63.9 

3.1 

24 

123.9 

6.1 

84 

183.8 

9.0 

44     243.7 

12.0 

5 

5.0 

0.2 

^5 

64.9 

3.2 

25 

124.8 

6.1 

85 

184.8 

9.1 

45  1  244.7 

12.0 

6 

6.0 

0.3 

^ 

65.9 

3.2 

26 

125.8 

6.2 

86 

185.8 

9.1 

46  ;  245.7 

12.1 

7 

7.0 

0.3 

67 

66.9 

3.3 

27 

126.8 

6.2 

87 

186.8 

9.2 

47     246. 7 

12.1 

8 

8.0 

0.4 

68 

67.9 

3.3 

28 

127.8 

6.3 

88 

187.8 

9.2 

48  1  247.7 

12.2 

9 

9.0 

0.4 

69 

68.9 

3.4 

29 

128.8 

6.3 

89 

188.8 

9.3 

49     248.7 

12.2 

10 

10.0 

0.5 

70 

69.9 

3.4 
3.5 

30 

129.8 

6.4 

90 

189.8 

9.3 
9.4 

50  1  249.7 
251  1  250.7 

12.3 

11 

11.0 

0.5 

71 

70.9 

131 

130.8 

6.4 

191 

190.8 

12.3 

12 

12.0 

0.6 

72 

71.9 

3.5 

32 

131.8 

6.5 

92 

191.8 

9.4 

52  !  251.  7 

12.4 

13 

13.0 

0.6 

73 

72.9 

3.6 

33 

132.8 

6.5 

93 

192.8 

9.5 

53  i  252.7 

12.4 

14 

14.0 

0.7 

74 

73.9 

3.6 

34 

133.8 

6.6 

94 

193.8 

9.5 

54  1  253.7 

12.5 

15 

15.0 

0.7 

75 

74.9 

3.7 

35 

134.8 

6.6 

95 

194.8 

9.6 

55     254.7 

12.5 

16 

16: 0 

0.8 

76 

75.9 

3.7 

36 

135.8 

6.7 

96 

195.8 

9.6 

56     255. 7 

12.6 

17 

17.0 

0.8 

77 

76.9 

3.8 

37 

136.8 

6.7 

97 

196.8 

9.7 

57 

256.7 

12.6 

18 

18.0 

0.9 

78 

77.9 

3.8 

38 

137.8 

6.8 

98 

197.8 

9.7 

58 

257.7 

12.7 

19 

19.0 

0.9 

79 

78.9 

3.9 

39 

138.8 

6.8 

99 

198.8 

9.8 

59  i  258.7 

12.7 

20 

20.0 

1.0 

80 

79.9 

3.9 

40 

139.8 

6.9 

200 
201 

199.8 

9.8 

60  1  259.7 

12.8 

21 

21.0 

1.0 

81 

80.9 

4.0 

141 

140.8 

6.9 

200.8 

9.9 

261  I  260.7 

12.8 

22 

22.0 

1.1 

82 

81.9 

4.0 

42 

141.8 

7.0 

02 

201.8 

9.9 

62  I  261.  7 

12.9 

23 

23.0 

1.1 

83 

82.9 

4.1 

43 

142.8 

7.0 

03 

202.8 

10.0 

63     262.7 

12.9 

24 

24.0 

1.2 

84 

83.9 

4.1 

44 

143.8 

7.1 

04 

203.  8 

10.0 

64     263.7 

13.0 

25 

25.0 

1.2 

85 

84.9 

4.2 

45 

144.8 

7.1 

05 

204.8 

10.1 

65  i  264.  7 

13.0 

26 

26.0 

1.3 

86 

85.9 

4.2 

46 

145.8 

7.2 

06 

205.  8 

10.1 

66     265.7 

13.1 

27 

27.0 

1.3 

87 

86.9 

4.3 

47 

146.8 

7.2 

07 

206.8 

10.2 

67     266.7 

13.1 

28 

28.0 

1.4 

88 

87.9 

4.3 

48 

147.8 

7.3 

08 

207.7 

10.2 

68 

267.7 

13.2 

29 

29.0 

1.4 

89 

88.9 

4.4 

49 

148.8 

7.3 

09 

208.7 

10.3 

69 

268.7 

13.2 

30 

30.0 

1.5 

90 

89.9 

4.4 

50 

149.8 

7.4 

10 

209.7 
210.  7 

10.3 
10.4 

70 

269.7 

13.2 
13.3 

31 

31.0 

1.5 

91 

90.9 

4.5 

151 

150.8 

7.4 

211 

271 

270.7 

32 

32.0 

1.6 

92 

91.9 

4.5 

52 

151.8 

7.5 

12 

211.7 

10.4 

72 

271.7 

13.3 

33 

33.0 

1.6 

93 

92.9 

4.6 

53 

152.8 

7.5 

13 

212.7 

10.5 

73 

272.7 

13.4 

34 

34.0 

1.7 

94 

93.9 

4.6 

54 

153.8 

7.6 

14 

213.7 

10.5 

74 

273.7 

13.4 

35 

35.0 

1.7 

95 

94.9 

4.7 

55 

154.8 

7.6 

15 

214.7 

10.5 

75  1  274.  7 

13.5 

36 

36.0 

1.8 

96 

95.9 

4.7 

56 

155.8 

7.7 

16 

215.7 

10.6 

76     275.7 

13.5 

37 

37.0 

1.8 

97 

96.9 

4.8 

57 

156.8 

7.7 

17 

216.7 

10.6 

77     276.7 

13.6 

38 

38.0 

1.9 

98 

97.9 

4.8 

58 

157.8 

7.8 

18 

217.7 

10.7 

78  ;  277.7 

13.6 

39 

39.0 

1.9 

99 

98.9 

4.9 

59 

158.8 

7.8 

19 

218.7 

10.7 

79  1  278.7 

13.7 

40 
41 

40.0 
41.0 

2.0 

100 

99.9 

4.9 

60 
161 

159.8 

7.9 
7.9 

20 

219.7 

10.8 
10.8 

80  t  279.  7 

13.7 

2.0 

101 

100.9 

5.0 

160.8 

221 

220.7 

281 

280.7 

13.8 

42 

41.9 

2.1 

02 

101.9 

5.0 

62 

161.8 

7.9 

22 

221.7 

10.9 

82 

281.7 

13.8 

43 

42.9 

2.1 

03 

102.9 

5.1 

63 

162.8 

8.0 

23 

222.7 

10.9 

83 

282.7 

13.9 

44 

43.9 

2.2 

04 

103.9 

5.1 

64 

163.8 

8.0 

24 

223.7 

11.0 

84 

283.7 

13.9 

45 

44.9 

2.2 

05 

104.9 

5.2 

65 

164.8 

8.1 

25 

224.7 

11.0 

85 

284.7 

14.0 

46 

45.9 

2.3 

06 

105.9 

5.2 

66 

165.8 

8.1 

26 

225.7 

11.1 

86 

285.7 

14.0 

47 

46.9 

2.3 

07 

106.9 

5.3 

67 

166.8 

8.2 

27 

226.7 

11.1 

87 

286.7 

14.1 

48 

47.9 

2.4 

08 

107.9 

5.3 

68 

167.8 

8.2 

28 

227.7 

11.2 

88 

287.7 

14.1 

49 

48.9 

2.4 

09 

108.9 

5.3 

69 

168.8 

8.3 

29 

228.7 

11.2 

89 

288.7 

14.2 

50 
51 

49.9 
50.9 

2.5 

10 

109.9 

5.4 

70 

169.8 

8.3 

30 

229.7 

11.3 

90 
"291 

289.7 

14.2 
14.3 

2.5 

111 

110.9 

5.4 

171 

170.8 

8.4 

231 

230.  7 

11.3 

290.6 

52 

51.9 

2.6 

12 

111.9 

5.5 

72 

171.8 

8.4 

32 

231.7 

11.4 

92 

291.6 

14.3 

53 

52.9 

2.6 

13 

112.9 

5.5 

73 

172.8 

8.5 

33 

232.7 

11.4 

93 

292.6 

14.4 

54 

53.9 

2.6 

14 

113.9 

5.6 

74  1  173.8 

8.5 

34 

233.7 

11.5 

94 

293.6 

14.4 

55 

54.9 

2.7 

15 

114.9 

5.6 

75     174.8 

8.6 

35 

234.7 

11.5 

95  i  294.6 

14.5 

56 

55.9 

2.7 

16 

115.9 

5.7 

76  \  175.8 

8.6 

36 

235.7 

11.6 

96  1  295.6 

14.5 

57 

56.9 

2.8 

17 

116.9 

5.7 

77 

176.8 

8.7 

37 

236.  7 

11.6 

97  '  296.6 

14.6 

58 

57.9 

2.8 

18 

117.9 

5.8 

78 

177.8 

8.7 

38 

237.7 

11.7 

98  ;  297.6 

14.6 

59 

58.9 

2.9 

19 

118.9 

5.8 

79 

178.8 

8.8 

39 

238.7 

11.7 

99  ;  298.6 

14.7 

60 

59.9 

2.9 

20 

119.9 

5.9 

80 

179.8 

8.8 

40 

239.7 

11.8 

300     299.6 

1 

14.7 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

I^t. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  i     Dep. 

Lat. 

E. 

^N. 

E.  JS 

W.  iN. 

A 

V.  i  S. 

[For  7J  Points.       1 

TABLE 

1. 

[Page  353 

Difference  of  Latitude  and 

Depari 

ure  for  \  Point. 

N.  h  E. 

N.  J  W. 

S.  J  E.                         S.  . 

\\Y. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.        Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.7 

6.0 

121 

120.4 

11.9 

181 

180.1 

17.7 

241 

239.8 

23.6 

?, 

2.0 

0.2 

62 

61.7 

6.1 

22 

121.4 

12.0 

82 

181.1 

17.8 

42 

240.8 

23.7 

3 

3.0 

0.3 

63 

62.7 

6.2 

23 

122.4 

12.1 

83 

182.1 

17.9 

43     241. 8 

23.8 

4 

4.0 

0.4 

64 

63.7 

6.3 

24  \  123.4 

12.2 

84 

183. 1 

18.0 

44  !  242.8 

23.9 

5 

5.0 

0.5 

65 

64.7 

6.4 

25 

124.4 

12.3 

85 

184.1 

18.1 

45 

243.8 

24.0 

6 

6.0 

0.6 

66 

65.7 

6.5 

26 

125.4 

12.4 

86 

185.1 

18.2 

46 

244.8 

24.1 

7 

7.0 

0.7 

67 

66.7 

6.6 

27 

126.4 

12.4 

87 

186.1 

18.3 

47 

245.8 

24.2 

8 

8.0 

0.8 

68 

67.7 

6.7 

28 

127.4 

12.5 

88 

187.1 

18.4 

48 

246.8 

24.3 

9 

9.0 

0.9 

69 

68.7 

6.8 

29 

128.4 

12.6 

89 

188.1 

18.5 

49 

247.8 

24.4 

10 

10.0 

1.0 
1.1 

70 

69.7 

6.9 

30 

129.4 

12.7 

12.8 

90 
191 

189.1 
190.1 

18.6 

50 

248.8 

24.5 

11 

10.9 

71 

70.7 

7.0 

131 

130.4 

18.7 

251 

249.8 

24.6 

12 

11.9 

1.2 

72 

71.7 

7.1 

32 

131.4 

12.9 

92 

191.1  '•  18.8 

52 

250.8 

24.7 

13 

12.9 

1.3 

73 

72.6 

7.2 

33 

132.4 

13.0 

93 

192.1 

18.9 

53 

251.  8 

24.8 

14 

13.9 

1.4 

74 

73.6 

7.3 

34 

133.4 

13.1 

94 

193.1 

19.0 

54 

252.8 

24.9 

15 

14.9 

1.5 

75 

74.6 

7.4 

35 

134.3 

13.2 

95 

194.1 

19.1 

55 

253.8 

25.0 

16 

15.9 

1.6 

76 

75.6 

7.4 

36 

135.3 

13.3 

96 

195.1 

19.2 

56 

254.8 

25.1 

17 

16.9 

1.7 

77 

76.6 

7.5 

37 

136.3 

13.4 

97 

196.1 

19.3 

57 

255.8 

25.2 

18 

17.9 

1.8 

78 

77.6 

7.6 

38 

137.3 

13.5 

98 

197.0 

19.4 

58 

256.8 

25.3 

19 

18.9 

1.9 

79 

78.6 

7.7 

39 

138.  3 

13.6 

99 

198.0 

19.5 

59 

257.8 

25.4 

20 

19.9 

2.0 

80 

79.6 

7.8 
7.9 

40 

139.3 

13.7 

200 

199.0 

19.6 

60 

258.7 

25.5 

21 

20.9 

2.1 

81 

80.6 

141 

140.3 

13.8 

201 

200.0 

19.7 

261 

259.7 

25.6 

22 

21.9 

2.2 

82 

81.6 

8.0 

42 

141.3 

13.9 

02 

201.0 

19.8 

62 

260.7 

25.7 

23 

22.9 

2.3 

83 

82.6 

8.1 

43 

142.3 

14.0 

03 

202.0 

19.9 

63 

261.7 

25.8 

24 

23.9 

2.4 

84 

83.6 

8.2 

44 

143.3 

14.1 

04 

203.  0 

20.0 

64 

262.7 

25.9 

25 

24.9 

2.5 

85 

84.6 

8.3 

45 

144.3 

14.2 

05 

204.0 

20.1 

65 

263.7 

26.0 

26 

25.9 

2.5 

86 

85.6 

8.4 

46. 

145.  3 

14.3 

06 

205. 0 

20.2 

66 

264.7 

26.1 

27 

26.9 

2.6 

87 

86.6 

8.5 

47 

146.3 

14.4 

07 

206.0 

20.3 

67 

265.7 

26.2 

28 

27.9 

2.7 

88 

87.6 

8.6 

48 

147.3 

14.5 

08 

207.0 

20.4 

68 

266.7 

26.3 

29 

28.9 

2.8 

89 

88.6 

8.7 

49 

148.  3 

14.6 

09 

208.0 

20.5 

69 

267.7 

26.4 

30 
31 

29.9 
30.9 

2.9 

90 

89.6 
90.6 

8.8 
8.9 

50 
151 

149.3 

14.7 

10 

209.0 
210.0 

20.6 
20.7 

70 
271 

268.7 
269.7 

26.5 

3.0 

91 

150.3 

14.8 

211 

26.6 

32 

31.8 

3.1 

92 

91.6 

9.0 

52 

151. 3 

14.9 

12 

211.0 

20.8 

72 

270.7 

26.7 

33 

32.8 

3.2 

93 

92.6 

9.1 

53 

152.3 

15.0 

13 

212.0 

20.9 

73 

271.7 

26.8 

34 

33.8 

3.3 

94 

93.5 

9.2 

54 

153.3 

15.1 

14 

213.0 

21.0 

74 

272.7 

26.9 

35 

34.8 

3.4 

95 

94.5 

9.3 

55 

154.3 

15.2 

15 

214.0 

21.1 

75 

273.7 

27.0 

36 

•35.8 

3.5 

96 

95.5 

9.4 

56 

155.2 

15.3 

16 

215.0 

21.2 

76 

274.7 

27.1 

37 

36.8 

3.6 

97 

96.5 

9.5 

57 

156.2 

15.4 

17 

216.0 

21.3 

77 

275.  7 

27.2 

38 

37.8 

3.7 

98 

97.5 

9.6 

58 

157.2 

15.5 

18 

217.0 

21.4 

78 

276.7 

27.2 

39 

38.8 

3.8 

99 

98.5 

9.7 

59 

158.2 

15.6 

19 

217.9 

21.5 

79 

277.7 

27.3 

40 

39.8 

3.9 

100 

99.5 

9.8 

60 

159.2 

15.7 

20 

218.9 

21.6 

80 

278.7 

27.4 

41 

40.8 

4.0 

101 

100.5 

9.9 

161 

160.2 

15.8 

221 

219.9 

21.7 

281 

279.6 

27.5 

42 

41.8 

4.1 

02 

101.5 

10.0 

62 

161.2 

15.9 

22 

220.9 

21.8 

82 

280.6 

27.6 

43 

42.8 

4.2 

03 

102.5 

10.1 

63 

162.2 

16.0 

23 

221.9 

21.9 

83 

281.6 

27.7 

44 

43.8 

4.3 

04 

103.5 

10.2 

64 

163.2 

16.1 

24 

222.9 

22.0 

84 

282.6 

27.8 

45 

44.8 

4.4 

05 

104.5 

10.3 

65 

164.2 

16.2 

25 

223.9 

22.1 

85 

283.6 

27.9 

46 

45.8 

4.5 

06 

105.5 

10.4 

66 

165.2 

16.3 

26 

224.9 

22.2 

86 

284.6 

28.0 

47 

46.8 

4.6 

07 

106.5 

10.5 

67 

166.2 

16.4 

27 

225.9 

22.2 

87 

285.6 

28.1 

48 

47.8 

4.7 

08 

107.5 

10.6 

68 

167.2 

16.5 

28 

226.9 

22.3 

88 

286.6 

28.2 

49 

48.8 

4.8 

09 

108.5 

10.7 

69 

168.2 

16.6 

29 

227.9 

22.4 

89 

287.6 

28.3 

50 

49.8 

4.9 
5.0 

10 

109.5 

10.8 

70 

169.2 

16.7 

30 

228.9 

22.5 
22.6 

90 

288.6 

28.4 

51 

50.8 

111 

110.5 

10.9 

171 

170.2 

16.8 

231 

229.9 

291      289. 6 

28.5 

52 

51.7 

5.1 

12 

111.5 

11.0 

72 

171.2 

16.9 

32 

230.9 

22.7 

92 

290.6 

28.6 

53 

52.7 

5.2 

13 

112.5 

11.1 

73 

172.2 

17.0 

33 

231.9 

22.8 

93 

291.6 

28.7 

54 

53.7 

5.3 

14 

113.5 

11.2 

74 

173.2 

17.1 

34 

232.9 

22.9 

94 

292.6 

28.8 

55 

54.7 

5.4 

15 

114.4 

11.3 

75 

174.2 

17.2 

35 

233.9 

23.0 

95 

293.6 

28.9 

56 

55.7 

5.5 

16 

115.4 

11.4 

76 

175.2 

17.3 

36 

234.9 

23.1 

96 

294.6 

29.0 

57 

56.7 

5.6 

17 

116.4 

11.5 

77 

176.1 

17.3 

37 

235.9 

23.2 

97 

295.6 

29.1 

58 

57.7 

5.7 

18 

117.4 

11.6 

78 

177.1 

17.4 

38 

236.9 

23.3 

98 

296.6 

29.2 

59 

58.7 

5.8 

19 

118.4 

11.7 

79 

178.1 

17.5 

39 

237.8 

23.4 

99 

297.6 

29.3 

60 

59.7 

5.9 

20 

119.4 

11.8 

80 

179.1 

17.6 

40 

238.8 

23.5 

300 

298.6 

29.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  JN. 

E.  J  S. 

W.  J  N 

W  *  S. 

[For  7i  Points.       1 

22489—03- 


-23 


Page  354 

TABLE  1. 

Difference  of  Latitude  and  Depart 

Lire  for  J  Point. 

N.  IE. 

N.  1  W 

S.  JE. 

S.  1  AV 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.3 

9.0 

121 

119.7 

17.8 

181 

179.0 

26.6 

241 

238.4 

35.4 

2 

2.0 

0.3 

62 

61.3 

,    9.1 

22 

120.7 

17.9 

82 

180.0 

26.7 

42 

239.4 

35.5 

3 

3.0 

0.4 

63 

62.3 

9.2 

23 

121.7 

18.0 

83 

181.0 

26.9 

43 

240.4 

35.7 

4 

4.0 

0.6 

64 

63.3 

9.4 

24 

122.7 

18.2 

84 

182.0 

27.0 

44 

241.4 

35.8 

5 

4.9 

0.7 

ei 

64.3 

9.5 

25 

123.6 

18.3 

85 

183.0 

27.1 

45 

242.3 

35.9 

6 

5.9 

0.9 

65.3 

9.7 

26 

124.6 

18.5 

86 

184.0 

27.3 

46 

243.3 

36.1 

7 

6.9 

1.0 

67 

66.3 

9.8 

27 

125.6 

18.6 

87 

185.0 

27.4 

47 

244.3 

36.2 

8 

7.9 

1.2 

68 

67.3 

10.0 

28 

126.6 

18.8 

88 

186.0 

27.6 

48 

245.3 

36.4 

9 

8.9 

1.3 

69 

68.3 

10.1 

29 

127.6 

18.9 

89 

187.0 

27.7 

49 

246.  3 

36.5 

10 

9.9 

1.5 

70 

69.2 

10.3 

30 

128.6 

19.1 

90 

187.9 

27.9 

.50 

247.3 

36.7 

11 

10.9 

1.6 

71 

70.2 

10.4 

131 

129.6 

19.2 

191 

188.9 

28.0 

251 

248.3 

36.8 

12 

11.9 

1.8 

72 

71.2 

10.6 

32 

130.6 

19.4 

92 

189.9 

28.2 

52 

249.  3 

37.0 

13 

12.9 

1.9 

73 

72.2  t  10.7 

33 

131.6 

19.5 

93 

190.9 

28.3 

53 

250.3 

37.1 

14 

13.8 

2.1 

74 

73.2 

10.9 

34 

132.5 

19.7 

94 

191.9 

28.5 

54 

251.3 

37.3 

15 

14.8 

2.2 

75 

74.2 

11.0 

35 

133.5 

19.8 

95 

192.9 

28.6 

55 

252.2 

37.4 

16 

15.8 

2.3 

76 

75.2 

11.2 

36 

134.5 

20.0 

96 

193.9 

28.8 

56 

253.2 

37.6 

17 

16.8 

2.5 

77 

76.2 

11.3 

37 

135.5 

20.1 

97 

194.9 

28.9 

57 

254.2 

37.7 

18 

17.8 

2.6 

78 

77.2 

11.4 

38 

136.5 

20.2 

98 

195.9 

29.1 

58 

255.2 

37.9 

19 

18.8 

2.8 

79 

78.1 

11.6 

39 

137.5 

20.4 

99 

196.8 

29.2 

59 

256.2 

38.0 

20 

19.8 

2.9 

80 

79.1 

11.7 

40 

138.5 

20.5 

200 

197.8 

29.3 

60 

257.2 

38.1 
38.3 

21 

20.8 

3.1 

81 

80.1 

11.9 

'141 

139.5 

20.7 

201 

198.8 

29.5 

261 

258.2 

22 

21.8 

3.2 

82 

81.1 

12.0 

42 

140.5 

20.8 

02 

199.8 

29.6 

62 

259.2 

38.4 

23 

22.8 

3.4 

83 

82.1 

12.2 

43 

141.5 

21.0 

03 

200.8 

29.8 

63 

260.2 

38.6 

24 

23.7 

3.5 

84 

83.1 

12.3 

44 

142.4 

21.1 

04 

201.8 

29.9 

64 

261.1 

38.7 

25 

24.7 

3.7 

85 

84.1 

12.5 

45 

143.4 

21.3 

05 

202.8 

30.1 

65 

262.1 

38.9 

26 

25.7 

3.8 

86 

85.1 

12.6 

46 

144.4 

21.4 

06 

203.  8 

30.2 

66 

263.1 

39.0 

27 

26.7 

4.0 

87 

86.1 

12.8 

47 

145.4 

21.6 

07 

204.8 

30.4 

67 

264.1 

39.2 

28 

27.7 

4.1 

88 

87.0 

12.9 

48 

146.4 

21.7 

08 

205.7 

30.5 

68 

265.1 

39.3 

29 

28.7 

4.3 

89 

88.0 

13.1 

49 

147.4 

21.9 

09 

206.7 

30.7 

69 

266.1 

39.5 

30 

29.7 

4.4 

90 

89.0 

13.2 
13.4 

50 
151 

148.4 

22.0 

10 

207.7 

30.8 

70 

267.1 

39.6 

31 

30.7 

4.5 

91 

90.0 

149.4 

22.2 

211 

208.7 

31.0 

271 

268. 1 

39.8 

32 

31.7 

4.7 

92 

91.0 

13.5 

52 

150.4 

22.3 

12 

209.7 

31.1 

72- 

269.1 

39.9 

33 

32.6 

4.8 

93 

92.0 

13.6 

53 

151.3 

22.4 

13 

210.7 

31.3 

73 

270.0 

40.1 

34 

33.6 

5.0 

94 

93.0 

13.8 

54 

152.3 

22.6 

14 

211.7 

31.4 

74 

271.0 

40.2 

35 

34.6 

5.1 

95 

94.0 

13.9 

55 

153.3 

22.7 

15 

212.7 

31.5 

75 

272.0 

40.4 

36 

35.6 

5.3 

96 

95.0 

14.1 

56 

154.3 

22.9 

16 

213.7 

31.7 

76 

273.0 

40.5 

37 

36.6 

5.4 

97 

96.0 

14.2 

57 

155.3 

23.0 

17 

214.7 

31.8 

77 

274.0 

40.6 

38 

37.6 

5.6 

98 

96.9 

14.4 

58 

156.3 

23.2 

18 

215.6 

32.0 

78 

275.0 

40.8 

39 

38.6 

5.7 

99 

97.9 

14.5 

59 

157.3 

23.3 

19 

216.6 

32.1 

79 

276.0 

40.9 

40 

39.6 

5.9 

100 

98.9 

14.7 

60 

158.3 
159.3 

23.5 

20 

217.6 
218.6 

32.3 

80 

277.0 
278.0 

41.1 

41 

40.6 

6.0 

101 

99.9 

14.8 

161 

23.6 

221 

32.4 

281 

41.2 

42 

41.5 

6.2 

02 

100.9 

15.0 

62 

160.2 

23.8 

22 

219.6 

32.6 

82 

278.9 

41.4 

43 

42.5 

6.3 

03 

101.9 

15.1 

63 

161.2 

23.9 

23 

220.6 

32.7 

83 

279.9 

41.5 

44 

43.5 

6.5 

04 

102.9 

15.3 

64 

162.2 

24.1 

24 

221.6 

32.9 

84 

280.9 

41.7 

45 

44.5 

6.6 

05 

103.9 

15.4 

65 

163.2 

24.2 

25 

222.6 

33.0 

85 

281.9 

41.8 

46 

45.5 

6.7 

06 

104.9 

15.6 

66 

164.2 

24.4 

26 

223.6 

33.2 

86 

282.9 

42.0 

47 

46.5 

6.9 

07 

105.8 

15.? 

67 

165.2 

24.5 

27 

224.5 

33.3 

87 

283.9 

42.1 

48 

47.5 

7.0 

08 

106.8 

15.8 

68 

166.2 

24.7 

28 

225.5 

33.5 

88 

284.9 

42.3 

49 

48.5 

7.2 

09 

107.8 

16.0 

69 

167.2 

24.8 

29 

226.5 

33.6 

89 

285.9 

42.4 

50 

49.5 

7.3 

10 

108.8 

16.1 

70 

168.2 

24.9 

30 

227.5 

33.7 
33.9 

90 

286.9 

42.6 
42.7 

51 

50.4 

7.5 

111 

109.8 

16.3 

171 

169.1 

25.1 

231 

228.5 

291 

287.9 

52 

51.4 

7.6 

12 

110.8 

16.4 

72 

170.1 

25.2 

32 

229.5 

34.0 

92 

288.8 

42.8 

53 

52.4 

7.8 

13 

111.8 

16.6 

73 

171.1 

25.4 

33 

230.5 

34.2 

93 

289.8 

43.0 

54 

53.4 

7.9 

U 

112.8 

16.7 

74 

172.1 

25.5 

34 

231.  5 

34.3 

94 

290.8 

43.1 

55 

54.4 

8.1 

15 

113.8 

16.9 

75 

173.1 

25.7 

35 

232.5 

34.5 

95 

291.8 

43.3 

56 

55.4 

8.2 

16 

114.7 

17.0 

76 

174.1 

25.8 

36 

233.4 

34.6 

96 

292.8 

43.4 

57 

56.4 

8.4 

17 

115.7 

17.2 

77 

175.1 

26.0 

37 

234.4 

34.8 

97 

293.8 

43.6 

58 

57.4 

8.5 

18 

116.7 

17.3 

78 

176.1 

26.1 

38 

235.  4 

34.9 

98 

294.8 

43.7 

59 

58.4 

8.7 

19 

117.7 

17.5 

79 

177.1 

26.3 

39 

236.  4 

35.1 

99 

295.8 

43.9 

60 

59.4 

8.8 

20 

118.7 

17.6 

80 

178.1 

26.4 

40 

237.4 

35.2 

300 

296.8 

44.0 

Dlst, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E.  IN 

K  1  S. 

W,  |N 

W.  f  S 

U 

For  7i  P 

oints. 

TABLE  1. 

[Page  355    | 

Difference  of  Latitude  and  Departure  for  1  Point. 

N.  by  E 

N.  by 

w. 

S.  by  E.                                S.  by  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.8 

11.9 

121 

118.7 

23.6 

181 

177.5 

35.3 

241 

236.4 

47.0 

2 

2.0 

0.4 

62 

60.8 

12.1 

22 

119.7 

23.8 

82 

178.5 

35.5 

42 

237.4 

47.2 

3 

2.9 

0.6 

63 

61.8 

12.3 

23 

120.6 

24.0 

83 

179.5 

35.7 

43 

238.3 

47.4 

4 

3.9 

0.8 

64 

62.8 

12.5 

24 

121.6 

24.2 

84 

180.5 

35.9 

44 

239.3 

47.6 

5 

4.9 

1.0 

65 

63.8 

12.7 

25 

122.6 

24.4 

85 

181.4 

36.1 

45 

240.3 

47.8 

6 

5.9 

1.2 

66 

64.7 

12.9 

26 

123.6 

24.6 

86 

182,4 

36.3 

46 

241.3 

48.0 

7 

6.9 

1.4 

67 

65.7 

13.1 

27 

124.6 

24.8 

87 

183.4 

36.5 

47 

242.3 

48.2 

8 

7.8 

1.6 

68 

66.7 

13.3 

28 

125.5 

25.0 

88 

184.4 

36.7 

48 

243.2 

48.4 

9 

8.8 

1.8 

69 

67.7 

13.5 

29 

126.5 

25.2 

89 

185.4 

36.9 

49 

244.2 

48.6 

10 

9.8 

2.0 

70 

68.7 

13.7 

30 

127.5 

25.4 

90 

186.3 

37.1 

50 

245.2 

48.8 

11 

10.8 

2.1 

71 

69.6 

13.9 

131 

128.5 

25.6 

191 

187.3 

37.3 

251 

246.2 

49.0 

12 

11.8 

2.3 

72 

70.6 

14.0 

32 

129.5 

25.8 

92  !  188.  3 

37.5 

52 

247.2 

49.2 

13 

12.8 

2.5 

73 

71.6 

14.2 

33 

130.4 

25.9 

93  '  189.3 

37.7 

53 

248.1 

49.4 

14 

13.7 

2.7 

74 

72.6 

14.4 

34 

131.4 

26.1 

94      190.3 

37.8 

54 

249.1 

49.6 

15 

14.7 

2.9 

75 

73.6 

14.6 

35 

132.4 

26.3 

95      191.3 

38.0 

55 

250.1 

49.7 

16 

15.7 

3.1 

76 

74.5 

14.8 

36 

133.4 

26.5 

96 

192.2 

38.2 

56 

251.1 

49.9 

17 

16.7 

3.3 

77 

75.5 

15.0 

37 

134.4 

26.7 

97 

193.2 

38.4 

57 

252.1 

50.1 

18 

17.7 

3.5 

78 

76.5 

15.2 

38 

135.3 

26.9 

98 

194.2 

38.6 

58 

253.0 

50.3 

19 

18.6 

3.7 

79 

77.5 

15.4 

39 

136.3 

27.1 

99 

195.2 

38.8 

59 

254.0 

50.5 

20 

19.6 

3.9 

80 

78.5 

15.6 

40 

137.3 

27.3 

200 

196.2 

39.0 

60 

255.0 

50.7 

21 

20.6 

4.1 

81 

79.4 

15.8 

141 

138.3 

^7.5 

201 

197.1 

39.2 

261 

256.0 

50.9 

22 

21.6 

4.3 

82 

80.4 

16.0 

42 

139.3 

27.7 

02  1  198. 1 

39.4 

62 

257.0 

51.1 

23 

22.6 

4.5 

83 

81.4 

16.2 

43 

140.3 

27.9 

03  !  199.1 

39.6 

63 

257.9 

51.3 

24 

23.5 

4.7 

84 

82.4 

16.4 

44 

141.2 

28.1 

04  t  200. 1 

39.8 

64 

258.9 

51.5 

25 

24.5 

4.9 

85 

83.4 

16.6 

45 

142.2 

28.3 

05  !  201. 1 

40.0 

65 

259.9 

51.7 

26 

25.5 

5.1 

86 

84.3 

16.8 

46 

143.2 

28.5 

06     202.0 

40.2 

66 

260.9 

51.9 

27 

26.5 

5.3 

87 

85.3 

17.0 

47 

144.2 

28.7 

07 

203.0 

40.4 

67 

261.9 

52.1 

28 

27.5 

5.5 

88 

86.3 

17.2 

48 

145.2 

28.9 

08 

204.0 

40.6 

68 

262.9 

52.3 

29 

28.4 

5.7 

89 

87.3 

17.4 

49 

146.1 

29.1 

09 

205.0 

40.8 

69 

263.8 

52.5 

30 

29.4 

5.9 

90 

88.3 

17.6 

50 

147.1 

29.3 

10 
211 

206.0 
206.9 

41.0 
41.2 

70 

264.8 

52.7 

31 

30.4 

6.0 

91 

89.3 

17.8 

151 

148.1 

29.5 

271 

265.8 

52.9 

32 

31.4 

6.2 

92 

90.2 

17.9 

52 

149.1 

29.7 

12 

207.9 

41.4 

72 

266.8 

53.1 

33 

32.4 

6.4 

93 

91.2 

18.1 

53 

150.1 

29.8 

13 

208.9 

41.6 

73 

267.8 

53.3 

34 

33.3 

6.6 

94 

92.2 

18.3 

54 

151.0 

30.0 

14 

209.9 

41.7 

74 

268.7 

53.5 

35 

34.3 

6.8 

95 

93.2 

18.5 

55 

152.  0 

30.2 

15 

210.9 

41.9 

75 

269.7 

53.6 

36 

S5.3 

7.0 

96 

94.2 

18.7 

56 

153.0 

30.4 

16 

211.8 

42.1 

76 

270.7 

53.8 

37 

36.3 

7.2 

97 

95.1 

18.9 

57 

154.0 

30.6 

17     212.8 

42.3 

77 

271.7 

54.0 

38 

37.3 

7.4 

98 

96.1 

19.1 

58 

155.  0 

30.8 

18 

213.8 

42.5 

78 

272.7 

54.2 

39 

38.3 

7.6 

99 

97.1 

19.3 

59 

155.9 

31.0 

19 

214.8 

42.7 

79 

273.6 

54.4 

40 

39.2 

7.8 

100 

98.1 

19.5 

60 

156.9 

31.2 
31.4 

20 
221 

215.8 
216.8 

42.9 

80 

274.6 
275.6 

54.6 

41 

40.2 

8.0 

101 

99.1 

19.7 

161 

157. 9 

43.1 

281 

54.8 

42 

41.2 

8.2 

02 

100.0 

19.9 

62 

158.9 

31.6 

22 

217.7 

43.3 

82 

276.6 

55.0 

43 

42.2 

8.4 

03 

101.0 

20.1 

63 

159.  9 

31.8 

23 

218.7 

43.5 

83 

277.6 

55.2 

44 

43.2 

8.6 

04 

102.0 

20.3 

64 

160.8 

32.0 

24 

219.7 

43.7 

84 

278.5 

55.4 

45 

44.1 

8.8 

05 

103.0 

20.5 

65 

161.8 

32.2 

25 

220.7 

43.9 

85 

279.5 

55.6 

46 

45.1 

9.0 

06 

104.0 

20.7 

66 

162.8 

32.4 

26 

221.7 

44.1 

86 

280.5 

55.8 

47 

46.1 

9.2 

07 

104.9 

20.9 

67 

163.8 

32.6 

27 

222.6 

44.3 

87 

281.5 

56.0 

48 

47.1 

9.4 

08 

105.9 

21.1 

68 

164.8 

32.8 

28 

223.6 

44.5 

88 

282.5 

56.2 

49 

48.1 

9.6 

09 

106.9 

21.3 

69 

165.8 

33.0 

29 

224.6 

44.7 

89 

283.4 

56.4 

50 

49.0 

9.8 

10 

107.9 

21.5 

70 

166.7 

33.2 

30 

225.6 

44.9 

90 

284.4 

56.6 

51 

50.0 

9.9 

111 

108.9 

21.7 

171 

167.7 

33.4 

231 

226.6 

45.1 

291 

285.4 

56.8 

52 

51.0 

10.1 

12 

109.8 

21.9 

72 

168.7 

33.6 

32 

227.5 

45.3 

92 

286.4 

57.0 

53 

52.0 

10.3 

13 

110.8 

22.0 

73 

169.7 

33.8 

33 

228. 5     45.  5  | 

93 

287.4 

57.2 

54 

53.0 

10.5 

14 

111.8 

22.2 

74 

170.7 

33.9 

34 

229.5 

45.7 

94 

288.4 

57.4 

55 

53.9 

10.7 

15 

112.8 

22.4 

75 

171.6 

34.1 

35 

230.5 

45.8 

95 

289.3 

57.6 

56 

54.9 

10.9 

16 

113.8 

22.6 

76 

172.6 

34.3 

36 

231.5 

46.0 

96 

290.3 

57.7 

57 

55.9 

11.1 

17 

114.8 

22.8 

77 

173.  6 

34.5 

37 

232.4 

46.2 

97 

291.3 

57.9 

58 

56.9 

11.3 

18 

115.7 

23.0 

78 

174.6 

34.7 

38 

233.4 

46.4 

98 

292.3 

58.1 

59 

57.9 

11.5 

19 

116.7 

23.2 

79 

175.6 

34.9 

39 

234.4 

46.6 

99 

293.3 

58.3 

60 

58.8 

11.7 

20 

117.7 

23.4 

80 

176.5 

35.1 

40 

235.4 

46.8 

300 

294.2 

58.5 

Dist. 

pep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1     Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E. 

byX. 

E.  I 

)y  S. 

W.  by 

N.                 W.  by  S.                    [ 

For  7  p( 

lints. 

Page  356] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  IJ  Points. 

N. 

by  E.  J  E. 

N.  by  \\ 

\  i  w. 

S.  b> 

'  E.  i  E. 

s. 

by  w.  i  \y. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.2 

14.8 

121 

117.4 

29.4 

181 

175.6 

44.0 

241 

233.8 

58.6 

2 

1.9 

0.5 

62 

60.1 

15.1 

22 

118.  3 

29.6 

82 

176.5 

44.2 

42 

234.7 

58.8 

3 

2.9 

0.7 

63 

61.1 

15.3 

23 

119.3 

29.9 

83 

177.5 

44.5 

43 

235.7 

59.0 

4 

3.9 

1.0 

64 

62.1 

15.6 

24 

120.3 

30.1 

84 

178.5 

44.7 

44 

236.7 

59.  3 

5 

4.9 

1.2 

^ 

63.1 

15.8 

25 

121.3 

30.4 

85 

179.5 

45.0 

45 

237.7 

59.  5 

6 

5.8 

1.5 

66 

64.0 

16.0 

26 

122.2 

30.6 

86 

180.4 

45.2 

46 

238.6 

59.8 

7 

6.8 

1.7 

67 

65.0 

16.3 

27 

123.2 

30.9 

87 

181.4 

45.4 

47 

239.6 

60.0 

8 

7.8 

1.9 

68 

66.0 

16.5 

28 

124.2 

31.1 

88 

182.4 

45.7 

48 

240.6 

60.3 

9 

8.7 

2.2 

69 

66.9 

16.8 

29 

125.1 

31.3 

89 

183.3 

45.9 

49 

241.5 

60.5 

10 

9.7 

2.4 

70 

67.9 

17.0 
17.3 

30 

126.1 

31.6 

90 
191 

184.  3 
185.3 

46.2 
46.4 

50 

242.5 

60.7 

11 

10.7 

2.7 

71 

68.9 

131 

127.1 

31.8 

251  ,  243.5 

61.0 

12 

11.6 

2.9 

72 

69.8 

17.5 

32 

128.0 

32.1 

92 

186.2 

46.7 

52     244.4 

61.2 

13 

12.6 

3.2 

73 

70.8 

17.7 

33 

129.0 

32.  3 

93 

187.2 

46.9 

53  i  245.4 

61.5 

14 

13.6 

3.4 

74 

71.8 

18.0 

34 

130.  0 

32.6 

94 

188.2 

47.1 

54     246.4 

61.7 

15 

14.6 

3.6 

75 

72.8 

18.2 

35 

131.0 

32.8 

95 

189.2 

47.4 

55     247.4 

62.  0 

16 

15.5 

3.9 

76 

73.7 

18.5 

36 

131.  9 

33.  0 

96 

190.1 

47.6 

56     248.3 

62.2 

17 

16.5 

4.1 

77 

74.7 

18.7 

37 

132.9 

33.3 

97 

191.1 

47.9 

57     249. 3 

62.4 

18 

17.5 

4.4 

78 

75.7 

19.0 

38 

133.9 

33.  5 

98 

192.1 

48.1 

58     250. 3 

62.7 

19 

18.4 

4.6 

79 

76.6 

19.2 

39 

134.8 

33.8 

99 

193.0 

48.4 

59     251.2 

62.9 

20 

19.4 

4.9 

80 

77.6 
78.6 

19.4 

40 

135.8 

34.0 

200 

194.0 

48.6 

60     252.2 
261      253.2 

63.2 

21 

20.4 

5.1 

81 

19.7 

141 

136.8 

34.3 

201 

195.  0 

48.8 

63.4 

22 

21.3 

5.3 

82 

79.5 

19.9 

42 

137.7 

34.5 

02 

195.9 

49.1 

62     254.1 

63.7 

23 

22.3 

5.6 

83 

80.5 

20.2 

43 

138.7 

34.7 

03 

196.9 

49.3 

63  ;  255.1 

63.9 

24 

23.3 

5.8 

84 

81.5 

20.4 

44 

139.7 

35.0 

04 

197.9 

49.6 

64  ,  256. 1 

64.1 

25 

24.3 

6.1 

85 

82.5 

20.7 

45 

140.7 

35.2 

05 

198.9 

49.8 

65  i  257. 1 

64.4 

26 

25.2 

6.3 

86 

83.4 

20.9 

46 

141.6 

35.5 

06 

199.8 

50.1 

66     258. 0 

64.6 

27 

26.2 

6.6 

87 

84.4 

21.1 

47 

142.6 

35.7 

07 

200.8 

50.  3 

67  :  259.0 

64.9 

28 

27.2 

6.8 

88 

85.4 

21.4 

48 

143.6 

36.0 

08 

201.8 

50.5 

68     260.0 

65.1 

29 

28.1 

7.0 

89 

86.3 

21.6 

49 

144.5 

36.2 

09 

202.7 

50.8 

69  '  260.9 

65.4 

30 

29.1 

7.3 

90 

87.3 

21.9 

50 

145.5 

36.4 

10 

203.  7 

51.0 
51.  3 

70  1  261.9 
271  '  262.9 

65.6 

31 

30.1 

7.5 

91 

88.3 

22.1 

151 

146.5 

36.7 

211 

204.7 

65.8 

32 

31.0 

7.8 

92 

89.2 

22.4 

52 

147.4 

36.9 

12 

205.  6 

51.5 

72 

263.  8 

66.1 

33 

32.0 

8.0 

93 

90.2 

22.6 

53 

148.4 

37.2 

13 

206.6 

51.8 

73 

264.8 

66.3 

34 

33.0 

8.3 

94 

91.2 

22.8 

54 

149.4 

37.4 

14 

207.6 

52.0 

74 

265.  8 

66.6 

35 

34.0 

8.5 

95 

92.2 

23.1 

55 

150.4 

37.7 

15 

208.6 

52.2 

75  i  266.8 

66.8 

36 

34.9 

8.7 

96 

93.1 

23.3 

56 

151.3 

37.9 

16 

209.5 

52.5 

76  i  267.  7 

67.1 

37 

35.9 

9.0 

97 

94.1 

23.6 

57 

152.3 

38.1 

17 

210.5 

52.7 

77  :  268.7 

67.3 

38 

36.9 

9.2 

98 

95.1 

23.8 

58 

153.  3 

38.4 

18 

211.5 

53.0 

78  i  269.7 

67.5 

39 

37.8 

9.5 

99 

96.0 

24.1 

59 

154.2 

38.6 

19 

212.4 

53.2 

79     270.6 

67.8 

40 

38.8 

9.7 

100 

97.0 

24.3 

60 
161 

155.2 
156.2 

38.9 
39.] 

20 

213.4 

53.5 

53.  7' 

80  i  271.6 
281  i  272.6 

68.0 
68.3 

41 

39.8 

10.0 

101 

98.0 

24.5 

221 

214.4 

42 

40.7 

10.2 

02 

98.9 

24.8 

62 

157.1 

39.4 

22 

215.3 

53.9 

82     273.5 

68.5 

43 

41.7 

10.4 

03 

99.9 

25.0 

63 

158.1 

39.6 

23 

216.3 

54.2 

83     274. 5 

68.8 

44 

42.7 

10.7 

04 

100.9 

25.3 

64 

159. 1 

39.8 

24 

217.3 

54.4 

84     275. 5 

69.0 

45 

43.7 

10.9 

05 

101.9 

25.5 

65 

160.1 

40.1 

25 

218.  3 

54.7 

85  j  277.5 

69.2 

46 

44.6 

11.2 

06 

102.8 

25.8 

66 

161.0 

40.  3 

26 

219.2 

54.9 

86     277.4 

69.5 

47 

45.6 

11.4 

07 

103.8 

26.0 

67 

162.0 

40.6 

27 

220.2 

55.  2 

87  i  278.4 

69.7 

48 

46.6 

11.7 

08 

104.8 

26.2 

68 

163. 0 

40.8 

28 

221.2 

55.4 

88 

279.4 

70.0 

49 

47.5 

11.9 

09 

105.7 

26.5 

69 

163.9 

41.1 

29 

222. 1 

55.6 

89 

280.3 

70.2 

50 

48.5 

12.1 
12.4 

10 
111 

106.7 
107.  7" 

26.7 

70 

164.9 

41.3 
41.5 

30 
231 

223.1 
224.1 

55.  9 
56.1 

90 

281.3 

70.5 

51 

49.5 

27.0 

171 

165.9 

291 

282.3 

70.7 

52 

50.4 

12.6 

12 

108.6 

27.2 

72 

166.8 

41.8 

32 

225.0 

56.4 

92 

283.2 

71.0 

53 

51.4 

12.9 

13 

109.6 

27.5 

73 

167.8 

42.0 

33 

226.0 

56.6 

93 

284.2 

71.2 

54 

52.4 

13.1 

14 

110.6 

27.7 

74 

168.8 

42.3 

34 

227.0 

56.9 

94 

285.  2 

71.4 

55 

53.4 

13.4 

15 

111.6 

27.9 

75 

169.8 

42.5 

35 

228.0 

57.1 

95 

286.2 

71.7 

56 

54.3 

13.6 

16 

112.5 

28.2 

76 

170.7 

42.8 

36 

228.  9 

57.3 

96 

287.1 

71.9 

57 

55.3 

13.8 

17 

113.5 

28.4 

77 

171.7 

43.0 

37 

229.9 

57.6 

97 

288.1 

72.2 

58 

56.3 

14.1 

18 

11-4.5 

28.7 

78 

172.7 

43.  3 

38 

230.9 

57.8 

98 

289.1 

72.4 

59 

57.2 

14.3 

19 

115.4 

28.9 

79 

173.6 

43.5 

39 

231.8 

58.1 

99 

290.9 

72.7 

60 

58.2 

14.6 

20 

116.4 

29.2 

80 

174.6 

43.7 

40 

232.8 

58.3 

300 

291.0 

72.9 

Diat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

E] 

J?E.  f  E 

Ef 

?E.  1  E. 

WNW.  1  V 

V. 

WSW.  1 

VV. 

[For  6|  P 

aints. 

TABLE 

1. 

[Page  357 

Difference  of  Latitud 

e  and  Departure  for  1  i  Points. 

N 

.  byE. 

^E. 

N.  by  W.  ^  W. 

S.  by  E.  i  E.                S. 

by  W.  i  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.4 

17.7 

121 

115.8 

35.1 

181 

173.2 

52.5 

241 

230.6 

70.0 

2 

1.9 

0.6 

62 

59.3 

18.0 

22 

116.7 

35.4 

82 

174.2 

52.8 

42 

231.6 

70.2 

3 

2.9 

0.9 

63 

60.3 

18.3 

23 

117.7 

35.7 

83 

175.1 

53.1 

43 

232.5 

70.5 

4 

3.8 

1.2 

64 

61.2 

18.6 

24 

118.7 

36.0 

84 

176.1 

53.4 

44 

233.5 

70.8 

5 

4.8 

1.5 

65 

62.2 

18.9 

25 

119.6 

36.3 

85 

177.0 

53.7 

45 

234.5 

71.1 

6 

5.7 

1.7 

66 

63.2 

19.2 

26 

120.6 

36.6 

86 

178.0 

54.0 

46 

235.4 

71.4 

7 

6.7 

2.0 

67 

64.1 

19.4 

27 

121.5 

36.9 

87 

178.9 

54.3 

47 

236.4 

71.7 

8 

7.7 

2.3 

68 

65.1 

19.7 

28 

122.5 

37.2 

88 

179.9 

54.6 

48 

237.3 

72.0 

9 

8.6 

2.6 

69 

66.0  i  20.0 

29 

123.4 

37.4 

89 

180.9 

54.9 

49 

238.3  \  72.3 

10 

9.6 

2.9 

70 

67. 0     20.  3 

30 

124.4 

37.7 

90 

181.8 

55.2 

50 

239.2  i  72.6 

11 

10.5 

3.2 

71 

67.9 

20.6 

131 

125.4 

38.0 

191 

182.8 

55.4 

251 

240.2 

72.9 

12 

11.5 

3.5 

72 

68.9 

20.9 

32 

126.3 

38.3 

92 

183.7 

55.7 

52 

241.1 

73.2 

13 

12.4 

3.8 

73 

69.9 

21.2 

33 

127.3 

38.6 

93 

184.7  i  56.0 

53 

242.1 

73.4 

14 

13.4 

4.1 

74 

70.8 

21.5 

34 

128.2 

38.9 

94 

185.6  j  56.3 

54 

243.1 

73.7 

15 

14.4 

4.4 

75 

71.8 

21.8 

35 

129.2 

39.2 

95 

186.6  I  56.6 

55 

244.0 

74.0 

16 

15.3 

4.6 

76 

72.7 

22.1 

36 

130.1 

39.5 

96 

187.6  1  56.9 

56 

245.0 

74.3 

17 

16.3 

4.9 

77 

73.7 

22.4 

37 

131.1 

39.8 

97 

188.  5     57.  2 

57 

245.  9      74.  6 

18 

17.2 

5.2 

78 

74.6 

22.6 

38 

132.1 

40.1 

98 

189.  5     57.  5 

58 

246.9  ,  74.9 

19 

18.2 

5.5 

79 

75.6 

22.9 

39 

133.0 

40.3 

99 

190.4  1  57.8 

59 

247.8  1  75.2 

20 

19.1 

5.8 

80 

76.6 

23.2 

40 

134.0 

40.6 

200 

191.4  1  58.1 

60 

248.8  1  75.5 

21 

20.1 

6.1 

81 

77.5 

23.5 

141 

134.9 

40.9 

201 

192.  3     58.  3 

261 

249.8  !  75.8 

22 

21.1 

6.4 

82 

78.5 

23.8 

42 

135.9 

41.2 

02 

193.3 

58.6 

62 

250.7  !  76.1 

23 

22.0 

6.7 

83 

79.4 

24.1 

43 

136.8 

41.5 

03 

194.3 

58.9 

63 

251.7  i  76.3 

24 

23.0 

7.0 

84 

80.4 

24.4 

44 

137.8 

41.8 

04 

195.  2 

59.2 

64 

252.6  i  76.6 

25 

23.9 

7.3 

85 

81.3 

24.7 

45 

138.8 

42.1 

05 

196.2 

59.5 

65 

253.6  i  76.9 

26 

24.9 

7.5 

86 

82.3 

25.0 

46 

139.7 

42.4 

06 

197.1 

59.8 

66 

254.5     77.2 

27 

25.8 

7.8 

87 

83.3 

25.3 

47 

140.7 

42.7 

07 

198.1 

60.1 

67 

255.  5     77. 5 

28 

26.8 

8.1 

88 

84.2 

25.5 

48 

141.6 

43.0 

08 

199.0 

60.4 

68 

256.5     77.8 

29 

27.8 

8.4 

89 

85.2 

25.8 

49 

142.6 

43.3 

09 

200.0 

60.7 

69 

257.4  ;  78.1 

30 

28.7 

8.7 

90 

86.1 

26.1 

50 

143.5 

43.5 

10 

201.0 
201.9 

61.0 

70 
271 

258.4  1  78.4 

31 

29.7 

9.0 

91 

87.1 

26.4 

151 

144.5 

43.8 

211 

61.3 

259.  3  i  78.  7 

32 

30.6 

9.3 

92 

88.0 

26.7 

52 

145.5 

44.1 

12 

202.9 

61.5 

72 

260.3  !  79.0 

33 

31.6 

9.6 

93 

89.0 

27.0 

53 

146.4 

44.4 

13 

203.8 

61.8 

73 

261.  2     79.  2 

34 

32.5 

9.9 

94 

90.0 

27.3 

54 

147.4 

44.7 

14 

204.8 

62.1 

74 

262.  2     79.  5 

35 

.  33.  5 

10.2 

95 

90.9 

27.6 

55 

148.3 

45.0 

15 

205.7 

62.4 

75 

263.2     79.8 

36 

34.4 

10.5 

96 

91.9 

27.9 

56 

149.3 

45.3 

16 

206.7 

62.7 

76 

264.1  1  80.1 

37 

35.4 

10.7 

97 

92.8 

28.2 

57 

150.2 

45.6 

17 

207.7 

63.0 

77 

265.1     80.4 

38 

36.4 

11.0 

98 

93.8 

28.4 

58 

151.2 

45.9 

18 

208.6 

63.3 

78 

266. 0  1  80.  7 

39 

37.3 

11.3 

99 

94.7 

28.7 

59 

152.2 

46.2 

19  ;  209.6 

63.6 

79 

267.0 

81.0 

40 

38.3 

11.6 
11.9 

100 
101 

95.7 
96.7 

29.0 

60 

153.1 

46.4 

20     210.5 

63.9 

80 

267.9 
268.9 

81.3 

41 

39.2 

29.3 

161 

154.1 

46.7 

221  i  211.5 

64.2 

281 

81.6 

42 

40.2 

12.2 

02 

97.6 

29.6 

62 

155.0 

47.0 

22     212.4 

64.4 

82 

269.9 

81.9 

43 

41.1 

12.5 

03 

98.6 

29.9 

63 

156.0 

47.3 

23  1  213.4 

64.7 

83 

270.8 

82.2 

44 

42.1 

12.8 

04 

99.5 

30.2 

64 

156.9 

47.6 

24  !  214.4 

65.0 

84 

271.8 

82.4 

45 

43.1 

13.1 

05 

100.5 

30.5 

65 

157.9 

47.9 

25  1  215.3 

65.3 

85 

272.7 

82.7 

46 

44.0 

13.4 

06 

101.4 

30.8 

66 

158.9 

48.2 

26     216.3 

65.6 

86 

273.7 

83.0 

47 

45.0 

13.6 

07 

102.4 

31.1 

67 

159.8 

48.5 

27  1  217.2 

65.9 

87 

274.6 

83.3 

48 

45.9 

13.9 

08 

103.  3 

31.4 

68 

160.8 

48.8 

28     218.2 

66.2 

88 

275.6 

83.6 

49 

46.9 

14.2 

09 

104.3 

31.6 

69 

161.7 

49.1 

29     219.1 

66.5 

89 

276.6 

83.9 

50 

47.8 

14.5 

10 

105.3 

31.9 

70 

162.7 

49.3 

30  i  220. 1 

66.8 

90 

277.5 

278.5 

84.2 
84.5 

51 

48.8 

14.8 

111 

106.2 

32.2 

171 

163.6 

49.6 

231     221. 1 

67.1 

291 

52 

49.8 

15.1 

12 

107.2 

32.5 

72 

164.6 

49.9 

32     222. 0 

67.3 

92 

279.4 

84.8 

53 

50.7 

15.4 

13 

108.1  !  32.^ 

73 

165.6 

50.2 

33  !  223.0 

67.6 

93 

280.4 

85.1 

54 

51.7 

15.7 

14 

109.1  i  33.1 

74 

166.5 

50.5 

34  I  223.9 

67.9 

94 

281.3 

85.3 

55 

52.6 

16.0 

15 

110.0     33.4 

75 

167.5 

50.8 

35  i  224.9 

68.2 

95 

282.3 

85.6 

56 

53.6 

16.3 

16 

111.0     33.7 

76 

168.4 

51.1 

36 

225.8 

68.5 

96 

283.3 

85.9 

57 

54.5 

16.5 

17 

'  112.0     34.0 

77 

169.4 

51.4 

37 

226.8 

68.8 

97 

284.2 

86.2 

58 

55.5 

16.8 

18 

!  112.9     34.3 

78 

170.3 

51.7 

38 

227.8 

69.1 

98 

285.2 

86.5 

59 

56.5 

17.1 

19 

113.9  i  34.5 

79 

171.3 

52.0 

39 

228.7 

69.4 

99 

286.1 

86.8 

60 

57.4 

17.4 

20 

114.8     34.8 

80 

172.2 

52.3 

40 

229.7 

69.7 

300 

287.1 

87.1 

Dlst. 

Dep. 

Lat. 

Dist. 

1    Dep.         Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

EJ 

TE.  h  E. 

ES 

E.  i  E. 

WN 

\V.  *  W 

WSW.  i  W. 

[For  6J  Point?. 

Page  358J 

TABLE 

-   1. 

Difference  of  Latitude  and  Departure  for  1|  Points. 

N.  by 

E.  1  E. 

N.  by  W.  1  AV. 

S.  by  E.  %  E. 

S.  by  W.  J  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.3 

61 

57.4 

20.6 

121 

113.9 

40.8 

181 

170.4 

61.0 

241 

226.9 

81.2 

2 

1.9 

0.7 

62 

58.4 

20.9 

22 

114.9 

41.1 

82 

171.4 

61.3 

42 

227.9 

81.5 

3 

2.8 

1.0 

63 

59.3 

21.2 

23 

115.8 

41.4 

83 

172.3 

61.7 

43 

228.8 

81.9 

4 

3.8 

1.3 

64 

60.3 

21.6 

24 

116.8 

41.8 

84 

173.2 

62.0 

44 

229.7 

82.2 

5 

4.7 

1.7 

6% 

61.2 

21.9 

25 

117.7 

42.1 

85 

174.2 

62.3 

45 

230.7 

82.5 

6 

5.6 

2.0 

66 

62.1 

22.2 

26 

118.6 

42.4 

86 

175.1 

62.7 

46 

231.6 

82.9 

1 

6.6 

2.4 

67 

63.1 

22.6 

27 

119.6 

42.8 

87 

176.1 

63.0 

47 

232.6 

83.2 

8 

7.5 

2.7 

68 

64.0 

22.9 

28 

120.5 

43.1 

88 

177.0 

63.3 

48 

233.5 

83.5 

9 

8.5 

3.0 

69 

65.0 

23.2 

29 

121.5 

43.5 

89 

178.0 

63.7 

49 

234.4 

83.9 

10 
11 

9.4 
10.4 

3.4 
3.7 

70 

65.9 

23.6 

30 

122.4 
123.3 

43.8 
44.1 

90 

178.9 

64.0 

50 

235.4 
236.3 

84.2 

71 

66.8 

23.9 

131 

191 

179.8 

64.3 

251 

84.6 

12 

11.3 

4.0 

72 

67.8 

24.3 

32 

124.3 

44.5 

92 

180.8 

64.7 

52 

237.3 

84.9 

13 

12.2 

4.4 

73 

68.7 

24.6 

33 

125.2 

44.8 

93 

181.  7 

65.0 

53 

238.2 

85.2 

14 

13.2 

4.7 

74 

69.7 

24.9 

34 

126.2 

45.1 

94 

182.7 

65.4 

54 

239.2 

85.6 

15 

14.1 

5.1 

75 

70.6 

25.3 

35 

127.1 

45.5 

95 

183.6 

65.7 

55 

240.1 

85.9 

16 

15.1 

5.4 

76 

71.6 

25.6 

36 

128.0 

45.8 

96 

184.  5 

66.0 

56 

241.0 

86.2 

17 

16.0 

5.7 

77 

72.5 

25.9 

37 

129.0 

46.2 

97 

185.5 

66.4 

57 

242.0 

86.6 

18 

16.9 

6.1 

78 

73.4 

26.3 

38 

129.9 

46.5 

98 

186.4 

66.7 

58 

242.9 

86.9 

19 

17.9 

6.4 

79 

74.4 

26.6 

39 

130.9 

46.8 

99 

187.4 

67.0 

59 

243.9 

87.3 

20 

18.8 

6.7 
7.1 

80 

75.3 

27.0 

40 
141 

131.8 
132.8 

47.2 
47.5 

200 

2or 

188.3 
189.3 

67.4 
67.7 

60 
261 

244.8 
245.  7 

87.6 

21 

19.8 

81 

76.3 

27.3 

87.9 

22 

20.7 

7.4 

82 

77.2 

27.6 

42 

133.7 

47.8 

02 

190.2 

68.1 

62 

246.7 

88.3 

23 

21.7 

7.7 

83 

78.1 

28.0 

43 

134.6 

48.2 

03 

191.1 

68.4 

63 

247.6 

88.6 

24 

22.6 

8.1 

84 

79.1 

28.3 

44 

135.6 

48.5 

04 

192.1 

68.7 

64 

248.6 

88.9 

25 

23.5 

8.4 

85 

80.0 

28.6 

45 

136.5 

48.8 

05 

193.0 

69.1 

65 

249.5 

89.3 

26 

24.5 

8.8 

86 

81.0 

29.0 

46 

137.5 

49.2 

06 

194.0 

69.4 

66 

250.5 

89.6 

27 

25.4 

9.1 

87 

81.9 

29.3 

47 

138.4 

49.5 

07 

194.-9 

69.7 

67 

251.4 

89.9 

28 

26.4 

9.4 

88 

82.9 

29.6 

48 

139.  3 

49.9 

08 

195.8 

70.1 

68 

252.  3 

90.3 

29 

27.3 

9.8 

89 

83.8 

30.0 

49 

140.3 

50.2 

09 

196.8 

70.4 

69 

253.3 

90.6 

30 

28.2 

10.1 

90 

84.7 
85.7 

30.3 

50 

141.2 
142.2 

50.5 

10 

197.7 
198.7 

70.7 

70 
271 

254.2 
255.2 

91.0 
91.3 

31 

29.2 

10.4 

91 

30.7 

151 

50.9 

211 

71.1 

32 

30.1 

10.8 

92 

86.6 

31.0 

52 

143. 1 

51.2 

12 

199.6 

71.4 

72 

256.1 

91.6 

33 

31.1 

11.1 

93 

87.6 

31.3 

53 

144.1 

51.5 

13 

200.5 

71.8 

73 

257.0 

92.0 

34 

32.0 

11.5 

94 

88.5 

31.7 

54 

145.0 

51.9 

14 

201.5 

72.1 

74 

258.0 

92.3 

35 

33.0 

11.8 

95 

89.4 

32.0 

55 

145.9 

52.2 

15 

202.4 

72.4 

75 

258.9 

92.6 

36 

33.9 

12.1 

96 

90.4 

32.3 

56 

146.9 

52.6 

16 

203.4 

72.8 

76 

259.9 

93.0 

37 

34.8 

12.5 

97 

91.3 

32.7 

57 

147.8 

52.9 

17 

204.3 

73.1 

77 

260.8 

93.3 

38 

35.8 

12.8 

98 

92.3 

33.0 

58 

148.8 

53.2 

18 

205.3 

73.4 

78 

261.7 

93.7 

39 

36.7 

13.1 

99  ;     93.2 

33.4 

59 

149.7 

53.6 

19 

206.2 

73.8 

79 

262.7 

94.0 

40 

37.7 

13.5 

100  1     94.2 

33.7 

60 

150.6 

53.9 
54.2 

20 

207.1 

74.1 

80 

263.6 

94.3 

41 

38.6 

13.8 

101       95.1 

34.0 

161 

151.6 

221 

208.1 

74.5 

281 

264.6 

94.7 

42 

39.5 

14.1 

02       96.0 

34.4 

62 

152.5 

54.6 

22  I  209.0 

74.8 

82 

265.5 

95.0 

43 

40.5 

14.5 

03  •     97.0 

34.7 

63 

153.5 

54.9 

23  i  210.0 

75.1 

83 

266.5 

95.3 

44 

41.4 

14.8 

04 

97.9 

35.0 

64 

154.4 

55.2 

24     210.9 

75.5 

84 

267.4 

95.7 

45 

42.4 

15.2 

05 

98.9 

35.4 

65 

155.4 

55.6 

25  '  211.8 

75.8 

85 

268.3 

96.0 

46 

43.3 

15.5 

06 

99.8 

35.7 

66 

156.3 

55.9 

26 

212.8 

76.1 

86 

269.3 

96.4 

47 

44.3 

15.8 

07 

100.7 

36.0 

67 

157.2 

56.3 

27 

213.7 

76.5 

87 

270.2 

96.7 

48 

45.2 

16.2 

08  i  101. 7 

36.4 

68 

158.  2 

56.6 

28 

214.7 

76.8 

88 

271.2 

97.0 

49 

46.1 

16.5 

09 

102.6 

36.7 

69 

159.1 

56.9 

29  i  215.6 

77.1 

89 

272.1 

97.4 

50 
51 

47.1 
48.0 

16.8 
17.  2" 

10 

103.6 
104.  5 

37.1 

70 
171" 

160.1 
161.0 

57.3 
57.6 

30 

216.6 

77.5 

77.8 

90 
291 

273.0 
274.0 

97.7 
98.0 

111 

37.4 

231 

217.5 

52 

49.0 

17.5 

12 

105.5 

37.7 

72 

161.9 

57.9 

32 

218.4 

78.2 

92 

274.9 

98.4 

53 

49.9 

17.9 

13 

106.4 

38.1 

73 

162.9 

58.3 

33 

219.4 

78.5 

93 

275.9 

98.7 

54 

50.8 

18.2 

14 

107.3 

38.4 

74 

163.8 

58.6 

34 

220.  3 

78.8 

94 

276.8 

99.0 

55 

51.8 

18.5 

15 

108.3 

.38.7 

75 

164.8 

59.0 

35 

221.3 

79.2 

95 

277.8 

99.4 

56 

52.7 

18.9 

16 

109.2 

39.1 

76 

165.7 

59.3 

36 

222.2 

79.5 

96 

278.7 

99.7 

57 

53.7 

19.2 

17 

110.2 

39.4 

77 

166.7 

59.6 

37 

223.1 

79.8 

97 

279.6 

100. 1 

58 

54.6 

19.5 

18 

111.1 

39.8 

78 

167.6 

60.0 

38 

224.1 

80.2 

98 

280.6 

100.4 

59 

55.6 

19.9 

19 

112.0 

40.1 

79 

168.5 

60.3 

39 

225.0 

80.5 

99 

281.5 

100.7 

60 

56.5 

20.2 

20 

113.0 

40.4 

80 

169.5 

60.6 

40 

226.0 

80.9 

300 

282.5 

101.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

ENE.  \ 

E. 

ESE.  \  } 

"^ 

A^ 

'NW.  \ 

w.           wsw.  \ 

W. 

[F 

or  61  To 

ints. 

TABLE  1. 

[Page 

359 

Di£ferenc3  of  Latitude  and  Departure  for 

2  Points. 

NNE. 

NNW. 

SSE. 

ssw. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

56.4 

23.3 

121 

111.8 

46.3 

181 

167.2 

69.3 

241 

222.7 

92.2 

2 

1.8 

0.8 

62 

57.3 

23.7 

22 

112.7 

46.7 

82 

168.1 

69.6 

42 

223.6 

92.6 

3 

2.8 

1.1 

63 

58.2 

24.1 

23 

113.6 

47.1 

83 

169.1 

70.0 

43 

224.5 

93.0 

4 

3.7 

1.5 

64 

59.1 

24.5 

24 

114.6 

47.5 

84 

170.0 

70.4 

44 

225.4 

93.4 

5 

4.6 

1.9 

65 

60.1 

24.9 

25 

115.5 

47.8 

85 

170.9 

70.8 

45 

226.4 

93.8 

6 

5.5 

2.3 

66 

61.0 

25.3 

26 

116.4 

48.2 

86 

171.8 

71.2 

46 

227.3 

94.1 

7 

6.5 

2.7 

67 

61.9 

25.6 

27 

117.3 

48.6 

87 

172.8 

71.6 

47 

228.2 

94.5 

8 

7.4 

3.1 

68 

62.8 

26.0 

28 

118.3 

49.0 

88 

173.7 

71.9 

48 

229.1 

94.9 

9 

8.3 

3.4 

69 

63.7 

26.4 

29 

119.2 

49.4 

89 

174.6 

72.3 

49 

230.0 

95.3 

10 

9.2 
10.2 

3.8 
4.2 

70 

64.7 

26.8 
27.2 

30 

120.1 

49.7 
50.1 

90 

175.5 

72.7 

50 

231.0 
231.9 

95.7 

11 

71 

65.6 

131 

121.0 

191 

176.5 

73.1 

251 

96.1 

12 

11.1 

4.6 

72 

66.5 

27.6 

32 

122.0 

50.5 

92 

177.4 

73.5 

52 

232.8 

96.4 

13 

12.0 

5.0 

73 

67.4 

27.9 

33 

122.9 

50.9 

93 

178.3 

73.9 

53 

233.7 

96.8 

14 

12.9 

5.4 

74 

68.4 

28.3 

34 

123.8 

51.3 

94 

179.2 

74.2 

54 

234.7 

97.2 

15 

13.9 

5.7 

75 

69.3 

28.7 

35 

124.7 

51.7 

95 

180.2 

74.6 

55 

235.6 

97.6 

16 

14.8 

6.1 

76 

70.2 

29.1 

36 

125.6 

52.0 

96 

181.1 

75.0 

56 

236.5 

98.0 

17 

15.7 

6.5 

77 

71.1 

29.5 

37 

126.6 

52.4 

97 

182.0 

75.4 

57 

237.4 

98.3 

18 

16.6 

6.9 

78 

72.1 

29.8 

38 

127.5 

52.8 

98 

182.9 

75.8 

58 

238.4 

98.7 

19 

17.6 

7.3 

79 

73.0 

30.2 

39 

128.4 

53.2 

99 

183.9 

76.2 

59 

239.3 

99.1 

20 

18.5 
19.4 

7.  7 
8.0 

80 

73.9 

30.6 

40 

129.3 

53.6 

200 

184.8 
185.7 

76.5 

60 

240.2 

99.5 

21 

81 

74.8 

31.0 

141 

130.3 

54.0 

201 

76.9 

261 

241.1 

99.9 

22 

20.3 

8.4 

82 

75.8 

31.4 

42 

131.2 

54.3 

02 

186.6 

77.3 

62 

242.1 

100.3 

23 

21.2 

8.8 

83 

76.7 

31.8 

43 

132.1 

54.7 

03 

187.5 

77.7 

63 

243.0 

100.6 

24 

22.2 

9.2 

84 

77.6 

32.1 

44 

133.0 

55.1 

04 

188.5 

78.1 

64 

243.9 

101.0 

25 

23.1 

9.6 

85 

78.5 

32.5 

45 

134.0 

55.5 

05 

189.4 

78.5 

65 

244.8 

101.4 

26 

24.0 

9.9 

86 

79.5 

32.9 

46 

134.9 

55.9 

06 

190.3 

78.8 

66 

245.8 

101.8 

27 

24.9 

10.3 

87 

80.4 

33.3 

47 

135.8 

56.3 

07 

191.2 

79.2 

67 

246.7 

102.2 

28 

25.9 

10.7 

88 

81.3 

33.7 

48 

136.7 

56.6 

08 

192.2 

79.6 

68 

247.6 

102.6 

29 

26.8 

11.1 

89 

82.2 

34.1 

49 

137.7 

57.0 

09 

193.1 

80.0 

69 

248.5 

102.9 

30 
31 

27.7 

11.5 

90 
91 

83.1 
84.1 

34.4 

50 

138.6 
139.5 

57.4 

10 

194.0 

80.4 

70 

249.4 

103.3 

28.6 

11.9 

34.8 

151 

57.8 

211 

194.9 

80.7 

271 

250.4 

103.7 

32 

29.6 

12.2 

92 

85.0 

35.2 

52 

140.4 

58.2 

12 

195.9 

81.1 

72 

251.3 

104.1 

33 

30.5 

12.6 

93 

85.9 

35.6 

53 

141.4 

58.6 

13 

196.8 

81.5 

73 

252.2 

104.5 

34 

31.  4 

13.0 

94 

86.8 

36.0 

54 

142.3 

58.9 

14 

197.7 

81.9 

74 

253.1 

104.9 

35 

32.3 

13.4 

95 

87.8 

36.4 

55 

143.2 

59.3 

15 

198.6 

82.3 

75 

254.1 

105.2 

36 

33.3 

13.8 

96 

88.7 

36.7 

56 

144.1 

59.7 

16 

199.6 

82.7 

76 

255.  0 

105.6 

37 

34.2 

14.2 

97 

89.6 

37.1 

57 

145.0 

60.1 

17 

200.5 

83.0 

77 

255.9 

106.0 

38 

35.1 

14.5 

98 

90.5 

37.5 

58 

146.0 

60.5 

18 

201.4 

83.4 

78 

256.8 

106.4 

39 

36.0 

14.9 

99 

91.5 

37.9 

59 

146.9 

60.8 

19 

202.3 

83.8 

79 

257.8 

106.8 

40 

37.0 

15.3 

100 

92.4 

38.3 

60 

147.8 
148.7 

61.2 

20 

203.3 

84.2 

80 

258.7 
259.6 

107.2 

41 

37.9 

15.7 

101 

93.3 

38.7 

161 

61.6 

221 

204.2 

84.6 

281 

107.5 

42 

38.8 

16.1 

02 

94.2 

39.0 

62 

149.7 

62.0 

22 

205.1 

85.0 

82 

260.  5 

107.9 

43 

39.7 

16.5 

03 

95.2 

39.4 

63 

150.6 

62.4 

23 

206.0 

85.3 

83 

261.5 

108.3 

44 

40.7 

16.8 

04 

96.1 

39.8 

64 

151.5 

62.8 

24 

206.9 

85.7 

84 

262.4 

108.7 

45 

41.6 

17.2 

05 

97.0 

40.2 

65 

152.4 

63.1 

25 

207.9 

86.1 

85 

263.3 

109.1 

46 

42.5 

17.6 

06 

97.9 

40.6 

66 

153.4 

63.5 

26 

208.8 

86.5 

86 

264.2 

109.4 

47 

43.4 

18.0 

07 

98.9 

40.9 

67 

154.3 

63.9 

27 

209.7 

86.9 

87 

265.  2 

109.8 

48 

44.3 

18.4 

08 

99.8 

41.3 

68 

155.2 

64.3 

28 

210.6 

87.3 

88 

266.1 

110.2 

49 

45.3 

18.8 

09 

100.7 

41.7 

69 

156.1 

64.7 

29 

211.6 

87.6 

89 

267.0 

110.6 

50 

46.2 

19.1 

10 

101.6 

42.1 

70 

157.1 

65.1 

30 

212.5 

88.0 

90 

267.9 

111.0 

51 

47.1 

19.5 

111 

102.6 

42.5 

171 

158.0 

65.4 

231 

213.4 

88.4 

291 

268.8 

111.4 

52 

48.0 

19.9 

12 

103.5 

42.9 

72 

158.9 

65.8 

32 

214.3 

88.8 

92 

269.8 

111.7 

53 

49.0 

20.3 

13 

104.4 

43.2 

73 

159.  8 

66.2 

33 

215.3 

89.2 

93 

270.7 

112.1 

54 

49.9 

20.7 

14 

105. 3 

43.6 

74 

160.8 

66.6 

34 

216.2 

89.5 

94 

271.6 

112.5 

55 

50.8 

21.0 

15 

106.2 

44.0 

75 

161.7 

67.0 

35 

217.1 

89.9 

95 

272.5 

112.9 

56 

51.7 

21.4 

16 

107.2 

44.4 

76 

162.6 

67.4 

36 

218.0 

90.3 

96 

273.5 

113.3 

57 

52.7 

21.8 

17 

108.1 

44.8 

77 

163.5 

67.7 

37 

219.0 

90.7 

97 

274.4 

113.7 

58 

53.6 

22.2 

18 

109.0 

45.2 

78 

164.5 

68.1 

38 

219.9 

91.1 

98 

275.3 

114.0 

59 

54.5 

22.6 

19 

109.9 

45.5 

79 

165.4 

68.5 

39 

220.8 

91.5 

99 

276.2 

114.4 

60 

55.4 

23.0 

20 

110.9 

45.9 

80 

166.3 

68.9 

40 

221.7 

91.8 

300 

277.2 

114.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

ENE. 

ESE. 

WNW 

wsw 

[F 

or  6  Poi 

nts. 

Page  360 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  2J  Points. 

NNE 

iE. 

NNW 

.  i  W.                SSE. 

iE. 

ssw. 

iW. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep.. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

55.1 

26.1 

121 

109.4 

51.7 

181 

163.6 

77.4 

241 

217.9 

103.0 

2 

1.8 

0.9 

62 

56.0 

26.5 

22 

110.3 

52.2 

82 

164.5 

77.8 

42 

218.8 

103.5 

3 

2.7 

1.3 

63 

57.0 

26.9 

23 

111.2 

52.6 

83 

165.4 

78.2 

43 

219.7 

103.9 

4 

3.6 

1.7 

64 

57.9 

27.4 

24 

112.1 

53.0 

84 

166.3 

78.7 

44 

220.6 

104.3 

5 

4.5 

2.1 

65 

58.8 

27.8 

25 

113.0 

53.4 

85 

167.2 

79.1 

45 

221.5 

104.8 

6 

5.4 

2.6 

6» 

59.7 

28.2 

26 

113.9 

53.9 

86 

168.1 

79.5 

46 

222.  4 

105.2 

7 

6.3 

3.0 

67 

60.6 

28.6 

27 

114.8 

54.3 

87 

169.0 

80.0 

47 

223.3 

105.6 

8 

7.2 

3.4 

68 

61.5 

29.1 

28 

115.7 

54.7 

88 

169.9 

80.4 

48 

224.2 

106.0 

9 

8.1 

3.8 

69 

62.4 

29.5 

29 

116.6 

55.2 

89 

170.9 

80.8 

49 

225.1 

106.5 

10 

9.0 

4.3 

70 

63.3 

29.9 
30.4 

30 

117.5 
118.4 

55.6 
56.0 

90 

171.8 

172.7 

81.2 

81.7 

50 
251 

226.0 
226.9 

106.9 

11 

9.9 

4.7 

71 

64.2 

131 

191 

107.3 

12 

10.8 

5.1 

72 

65.1 

30.8 

32 

119.3 

56.4 

92 

173.6 

82.1 

52 

227.8 

107.7 

13 

11.8 

5.6 

73 

66.0 

31.2 

33 

120.2 

56.9 

93 

174.5 

82.5 

53 

228.7 

108.2 

14 

12.7 

6.0 

74 

66.9 

31.6 

34 

121.1 

57.3 

94 

175.4 

82.9 

54 

229.6 

108.6 

15 

13.6 

6.4 

75 

67.8 

32.1 

35 

122.0 

57.7 

95 

176.3 

83.4 

55 

230.5 

109.0 

16 

14.5 

6.8 

76 

68.7 

32.5 

36 

122.9 

58.1 

96 

177.2 

83.8 

56 

231.4 

109.5 

17 

15.4 

7.3 

77 

69.6 

32.9 

37 

123.8 

58.6 

97 

178.1 

84.2 

57 

232.  3 

109.9 

18 

16.3 

7.7 

78 

70.5 

33.3 

38 

124.8 

59.0 

98 

179.0 

84.7 

58 

233.2 

110.3 

19 

17.2 

8.1 

79 

71.4 

33.8 

39     125.7 

59.4 

99 

179.9 

85.1 

59 

234.1 

110.7 

20 

18.1 

8.6 

80 

72.  3     34.  2 

40     126.6 

59.9 
60.3 

200 

180.8 

85.5 

60 

235.0 
235.9 

111.2 

21 

19.0 

9.0 

81 

73.2 

34.6 

141     127.5 

201 

181.7 

85.9 

261 

111.6 

22 

19.9 

9.4 

82 

74.1 

35.1 

42     128.4 

60.7 

02     182. 6 

86.4 

62 

236.8 

112.0 

23 

20.8 

9.8 

83 

75.0 

35.5 

43  i  129.3 

61.1 

03 

183.5 

86.8 

63 

237.7 

112.4 

24 

21.7 

10.3 

84 

75.9 

35.9 

44     130.2 

61.6 

04 

184.4 

87.2 

64 

238.7 

112.9 

25 

22.6 

10.7 

85 

76.8 

36.3 

45     131.1 

62.0 

05 

185.3 

87.6 

65 

239.6 

113.3 

26 

23.5 

11.1 

86 

77.7 

36.8 

46     132. 0 

62.4 

06 

186.2 

88.1 

66 

240.5 

113.7 

27 

24.4 

11.5 

87 

78.6 

37.2 

47     132. 9 

62.9 

07 

187a 

88.5 

67 

241.4 

114.2 

28 

25.3 

12.0 

88 

79.6 

37.6 

48     133. 8 

63.3 

08 

188.0 

88.9 

68 

242.3 

114.6 

29 

26.2 

12.4 

89 

80.5 

38.1 

49     134. 7 

63.7 

09 

188.9 

89.4 

69 

243.2 

115.0 

30 
31 

27.1 
28.0 

12.8 

90 

81.4 

38.5 
38.9 

50     135.6 
151     136. 5 

64.1 

10 

189.8 

89.8 

70 

244.1 
245.0 

115.4 

13.3 

91 

82.3 

64.6 

211 

190.7 

90.2 

271 

115.9 

32 

28.9 

13.7 

92 

83.2 

39.3 

52     137.4  i  65.0 

12 

191.6 

90.6 

72 

245.9 

116.3 

33 

29.8 

14.1 

93 

84.1 

39.8 

53  i  138.3  1  65.4 

13 

192.5 

91.1 

73 

246.8 

116.7 

34 

30.7 

14.5 

94 

85.0 

40.2 

54  i  139.2  1  65.8 

14 

193.5 

91.5 

74 

247.7 

117.2 

35 

31.6 

15.0 

95 

85.9 

40.6 

55     140.1     66.3 

15 

194.4 

91.9 

to 

248.6 

117.6 

36 

32.5 

15.4 

96 

86.8 

41.0 

56  i  141.  0  i  66.  7 

16 

195.3 

92.4 

76 

249.5 

118.0 

37 

33.4 

15.8 

97 

87.7 

41.5 

57  i  141.9 

67.1 

17 

196.2 

92.8 

/ 1 

250.4 

118.4 

38 

34.4 

16.2 

98 

88.6 

41.9 

58 

142.8 

67.6 

18 

197.1 

93.2 

78 

251.3 

118.9 

39 

35.3 

16.7 

99 

89.5 

42.3 

59 

143.7 

68.0 

19 

198.0 

93.6 

79 

252.2 

119.3 

40 

36.2 

17.1 

100 

90.4 

42.8 

60 

144.6 

68.4 

20 

198.9 

94.1 

80 

253.1 

119.7 

41 

37.1 

17.5 

'lOl 

91.3 

43.2 

161 

145.5 

68.8 

221 

199.8 

94.5 

281 

254.0 

120.1 

42 

38.0 

18.0 

02 

92.2 

43.6 

62 

146.4 

69.3 

22 

200.7 

94.9 

82 

254.9 

120.6 

43 

38.9 

18.4 

03 

93.1 

44.0 

63 

147.4 

69.7 

23 

201.6 

95.3 

83 

255.  8 

121.0 

44 

39.8 

18.8 

04 

94.0 

44.5 

64 

148.3 

70.1 

24 

202.5 

95.8 

84 

256.7 

121.4 

45 

40.7 

19.2 

05 

94.9 

44.9 

65 

149.2 

70.5 

25 

203.4 

96.2 

85 

257.6 

121.9 

46 

41.6 

19.7 

06 

95.8 

45.3 

66 

150.1 

71.0 

26 

204.3 

96.6 

86 

258.5 

122.3 

47 

42.5 

20.1 

07 

96.7 

45.7 

67 

151.0 

71.4 

27 

205.2 

97.1 

87 

259.4 

122.7 

48 

43.4 

20.5 

08 

97.6 

46.2 

68 

151.9 

71.8 

28 

206.1 

97.5 

88 

260.3 

123.1 

49 

44.3 

21.0 

09 

98.5 

46.6 

69 

152.8 

72.3 

29 

207.0 

97.9 

89 

261.3 

123.6 

50 

45.2 

21.4 

10 

99.4 
100.3 

47.0 

70 

153.7 

72.7 

30 

207.9 

98.3 

90 

262.2 

124.0 

51 

46.1 

21.8 

111 

47.5 

171 

154.6 

73.1 

231 

208.8 

98.8 

291 

263.1 

124.4 

52 

47.0 

22.2 

12 

101.2 

47.9 

72 

155.5 

73.5 

32 

209.7 

99.2 

92 

264.0 

124.8 

53 

47.9 

22.7 

13 

102.2 

48.3 

73 

156.4 

74.0 

33 

210.6 

99.6 

93 

264.9 

125.3 

54 

48.8 

23.1 

14 

103.1 

48.7 

74 

157.3 

74.4 

34 

211.5 

100.0 

94 

265.8 

125.7 

55 

49.7 

23.5 

15 

104.0 

49.2 

75 

158.2 

74.8 

35 

212.4 

100.5 

95 

266.7 

126.1 

56 

50.6 

23.9 

16 

104.9 

49.6 

76 

159. 1 

75.2 

36 

213.3 

100.9 

96 

267.6 

126.6 

57 

51.5 

24.4 

17 

105.8 

50.0 

77 

160.0 

75.7 

37 

214.2 

101.3 

97 

268.5 

127.0 

58 

52.4 

24.8 

18 

106.7 

50.5 

78 

160.9 

76.1 

38 

215.1 

101.8 

98 

269.4 

127.4 

59 

53.3 

25.2 

19 

107.6 

50.9 

79 

161.8 

76.5 

39 

216.1 

102.2 

99 

270.3 

127.8 

60 

54.2 

25.7 

20 

108.5 

51.3 

80 

162.7 

77.0 

40 

217.0 

102.6 

300 

271.2 

128.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NI 

:.  by  E. 

IE. 

SI 

:.  by  E.  i  E. 

NW.  by  W.  1  W. 

SW.  by  W. 

|W. 

[J 

For  5|  P 

oints. 

TABLE  1. 

[Page 

361 

Difference  of  Latitude  and  Departure  for  2J  Points. 

NNE 

^E. 

NNW 

.  i  W.                 SSE 

iE. 

SSW. 

JW. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

53.8 

28.8 

121 

106.7 

57.0 

181 

159.  6 

85.3 

241 

212.5 

113.6 

2 

1.8 

0.9 

62 

54.7 

29.2 

22 

107.6 

57.5 

82 

160.  5 

85.8 

42 

213.4 

114.1 

3 

2.6 

1.4 

63 

55.6 

29.7 

23 

108.5 

58.0 

83 

161.4 

86.3 

43 

214.3 

114.5 

4 

3.5 

1.9 

64 

56.4 

30.2 

24 

109.4 

58.5 

84 

162.3 

86.7 

44 

215.2 

115.0 

5 

4.4 

2.4 

65 

57.3 

30.6 

25 

110.2 

58.9 

85 

163.2 

87.2 

45 

216.1 

115.  5 

6 

5.3 

2.8 

66 

58.2 

31.1 

26 

111.1 

59.4 

86 

164.0 

87.7 

46 

217.0 

116.0 

7 

6.2 

3.3 

67 

59.1 

31.6 

27 

112.0 

59.9 

87 

164.9 

88.2 

47 

217.8 

116.4 

8 

7.1 

3.8 

68 

60.0 

32.1 

28 

112.9 

60.3 

88 

165.8 

88.6 

48 

218.7 

116.9 

9 

7.9 

4.2 

69 

60.9 

32.5 

29     113.8 

60.8 

89 

166.7 

89.1 

49 

219.6 

117.4 

10 

8.8 

4.7 

70 

61.7 
62. 6" 

33.0 

30     114. 6 

61.3 

90 

167.6 

89.6 

50 

220.5 

117.8 

11 

9.7 

5.2 

71 

33.5 

131     115.5 

61.8 

191 

168.4 

90.0 

251- 

221.4 

118.3 

12 

10.6 

5.7 

72 

63.5 

33.9 

32     116.4 

62.2 

92 

169.3 

90.5 

52 

222.2 

118.8 

13 

11.5 

6.1 

73 

64.4 

34.4 

33  !  117.3 

62.7 

93 

170.2 

91.0 

53 

223.1 

119.3 

14 

12.3 

6.6 

74 

65.3 

34.9 

34  {  118.2 

63.2 

94 

171.1 

91.5 

54 

224.0 

119.7 

15 

13.2 

7.1 

75 

66.1 

35.4 

35  !  119.1 

63.6 

95 

172.0 

91.9 

55 

224.9 

120.2 

16 

14.1 

7.5 

76 

67.0 

35.8 

36 

119.9 

64.1 

96 

172.9 

92.4 

56 

225.8 

120.7 

17 

15.0 

8.0 

77 

67.9 

36.3 

37 

120.8 

64.6 

97 

173.7 

92.9 

57 

226.7 

121.1 

18 

15.9 

8.5 

78 

68.8 

36.8 

38 

121.7 

65.1 

98 

174.6 

93.3 

58 

227.5 

121.  6 

19 

16.8 

9.0 

79 

69.7 

37.2 

39 

122.6 

65.5 

99 

175.5 

93.8 

59 

228.4 

122.1 

20 

17.6 

9.4 

80 

70.6 

37.7 

40 

123.5 

66.0 

200 
201 

176.4 
177.3 

94.3 

60 

229.  3 

122.6 

21 

18.5 

9.9 

81 

71.4 

38.2 

141 

124.4 

66.5 

94.8 

261 

330.2 

123.0 

22 

19.4 

10.4 

82 

72.3 

38.7 

42 

125.2 

66.9 

02 

178.1 

95.2 

62 

231.1 

123.  5 

23 

20.3 

10.8 

83 

73.2 

39.1 

43 

126.1 

67.4 

03 

179.0 

95.7 

63 

231.9 

124.0 

24 

21.2 

11.3 

84 

74.1 

39.6 

44 

127.0 

67.9 

04 

179.9 

96.2 

64 

232.8 

124.4 

25 

22.0 

11.8 

85 

75.0 

40.1 

45 

127.9 

68.4 

05 

180.8 

96.6 

65 

233.7 

124.9 

26 

22.9 

12.3 

86 

75.8 

40.5 

46 

128.8 

68.8 

06 

181.7 

97.1 

66 

234.6 

125. 4 

27 

23.8 

12.7 

87 

76.7 

41.0 

47 

129.6 

69.3 

07 

182.6 

97.6 

67 

235.5 

125.9 

28 

24.7 

13.2 

88 

77.6 

41.5 

48 

130.5 

69.8 

08 

183.4 

98.1 

68 

236.4 

126.3 

29 

25.6 

13.7 

89 

78.5 

42.0 

49 

131.4 

70.2 

09 

184.3 

98.5 

69 

237.  2 

126.8 

30 
31 

26.5 
27.3 

14.1 

90 
91 

79.4 

42.4 

50 

132.3 
133.2 

70.7 

10 

185.2 

99.0 

70 

238.1 

127.3 

14.6 

80.3 

42.9 

151 

71.2 

211 

186.1 

99.5 

271 

239.0 

127.7 

32 

28.2 

15.1 

92 

81.1 

43.4 

52 

134.1 

71.7 

12 

187.0 

99.9 

72 

239.9 

128.2 

33 

29.1 

15.6 

93 

82.0 

43.8 

53 

134.9 

72.1 

13 

187.8 

100.4 

73 

240.8 

128.7 

34 

30.0 

16.0 

94 

82.9  1  44.3 

54 

135.8 

72.6 

14 

188.7 

100.9 

74 

241.6 

129.2 

35 

.  30.9 

16.5 

95 

83.8  !  44.8 

55 

136.7 

73.1 

15 

189.6 

101.4 

75 

242.5 

129.6 

36 

31.7 

17.0 

96 

84.7 

45.3 

56 

137.6 

73.5 

16 

190.5 

101.8 

76 

243.4 

130.1 

37 

32.6 

17.4 

97 

85.5 

45.7 

57 

138.5 

74.0 

17 

191.4 

102.3 

77 

244.3 

130.6 

38 

33.5 

17.9 

98 

86.4 

46.2 

58 

139.3 

74.5 

18 

192.3 

102.8 

78 

245.2 

131.0 

39 

34.4 

18.4 

99 

87.3 

46.7 

59 

140.2 

75.0 

19 

193.1 

103.2 

79 

246.1 

131.5 

40 

35.3 

18.9 

100 
101 

88.2 

47.1 

60 

141.1 
142.0 

75.4 
75.9 

20 

194.0 

103.7 

80 

246.9 

247.8 

132.0 

41 

36.2 

19.3 

89.1 

47.6 

161 

221 

194.9 

104.2 

281 

132.5 

42 

37.0 

19.8 

02 

90.0 

48.1 

62 

142.9 

76.4 

22 

195.8 

104.7 

82 

248.7 

132.9 

43 

37.9 

20.3 

03 

90.8 

48.6 

63 

143.  8 

76.8 

23 

196.7 

105.1 

83 

249.6 

133.4 

44 

38.8 

20.7 

04 

91.7     49.0 

64 

144.6 

77.3 

24 

197.6 

105.6 

84 

250.5 

133.9 

45 

39.7 

21.2 

05 

92.6 

49.5 

65 

145.  5 

77.8 

25 

198.4 

106.1 

85 

251.3 

134.3 

46 

40.6 

21.7 

06 

93.5 

50.0 

66 

146.4 

78.3 

26 

199.3 

106.5 

86 

252.2 

134.8 

47 

41.5 

22.2 

07 

94.4 

50.4 

67 

147.3 

78.7 

27 

200.2 

107.0 

87 

253.1 

135.  3 

48 

42.3 

22.6 

08 

95.2 

50.9 

68 

148.2 

79.2 

28 

201.1 

107.5 

88 

254.0 

135.8 

49 

43.2 

23.1 

09 

96.1 

51.4 

69 

149.0 

79.7 

29 

202.0 

107.9 

89 

254.9 

136.2 

50 

44.1 

23.6 

10 

97.0 

51.9 

70 

149.9 

80.1 

30     202. 8 

108.4 

90 

255.8 

136.7 

51 

45.0 

24.0 

111 

97.9 

52.3 

171 

150.8 

80.6 

231 

203.7 

108.9 

291 

256.6 

137.2 

52 

45.9 

24.5 

12 

98.8 

52.8 

72 

151.7 

81.1 

32 

204.6 

109.4 

92 

257.5 

137.6 

53 

46.7 

25.0 

13 

99.7 

53.3 

73 

152.6 

81.6 

33 

205.  5 

109.8 

93 

258.4 

138.1 

54 

47.6 

25.5 

14 

100.5 

53.7 

74 

153.5 

82.0 

34 

206.4 

110.3 

94 

259.3 

138.6 

55 

48.5 

25.9 

15 

101.4 

54.2 

75 

154.3 

82.5 

35 

207.3 

110.8 

95 

260.2 

139.1 

56 

49.4 

26.4 

16 

102.3 

54.7 

76 

155.2 

83.0 

36 

208.1 

111.2 

96 

261.0 

139.5 

57 

50.3 

26.9 

17 

103.2 

55.2 

77 

156.1 

83.4 

37 

209.0 

111.7 

97 

261.9 

140.0 

58 

51.2 

27.3 

18 

104.1 

55.6 

78 

157.0 

83.9 

38 

209.9 

112.2 

98 

262.8 

140.  5 

59 

52.0 

27.8 

19 

104.9 

56.1 

79 

157.9 

84.4 

39 

210.8 

112.7 

99 

263.7 

140.9 

60 

52.9 

28.3 

20 

105.8 

56.6 

80 

158.7 

84.9 

40 

211.7 

113.1 

300 

264.6 

141.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE 

..  by  E. 

^E. 

SE 

.  by  E.  J  E. 

NW.  by  W.  J  W. 

SW.  by  W. 

*  w. 

[I 

^or  5^  P 

oints. 

Page  362; 

TABLE 

1. 

Difference  of  Latitude  and  Departure  for  2|  Points. 

NNE.  1  E. 

NNW. 

JW. 

SSE.  1  E 

SSW.  1  W. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist.  :     Lat. 

Dep. 

1 

0.9 

0.5 

61 

52.3 

31.4 

121 

103.8 

62.2 

181 

155.  2      93. 1 

241  '  206.7 

123.9 

2 

1.7 

1.0 

62 

53.2 

31.9 

22 

104.6 

62.7 

82 

156. 1      93.  6 

42     207.6 

124.4 

3 

2.6 

1.5 

63 

54.0 

32.4 

23 

105.5 

63.2 

83 

157.0 

94.1 

43     208.4 

124.9 

4 

3.4 

2.1 

64 

54.9 

32.9 

24 

106.4 

63.7 

84 

157.8 

94.6 

44 

209.3 

125. 4 

5 

4.3 

2.6 

Of 

55.8 

33.4 

25 

107.2 

64.3 

85 

158.7 

95.1 

45 

210.1 

126.0 

6 

5.1 

3.1 

66 

56.6 

33.9 

26 

108.1 

64.8 

86 

159.5 

95.6 

46 

211.0 

126.5 

7 

6.0 

3.6 

67 

57.5 

34.4 

27 

108.9 

65.3 

87 

160.4 

96.1 

47 

211.9 

127.0 

8 

6.9 

4.1 

68 

58.3 

35.0 

28 

109.8 

65.8 

'88 

161.3 

96.7 

48 

212.7 

127.5 

9 

7.7 

4.6 

69 

59.2 

35.5 

29 

110.6 

66.3 

89 

162.1 

97.2 

49 

213.6 

128.0 

10 

8.6 

5.1 
5.7 

70 
71 

60.0 

36.0 

30 

111.5 

66.8 

90 

163.0 
163.8 

97.7 

50 

214.4 

128.5 

11 

9.4 

60.9 

36.5 

131 

112.4 

67.3 

191 

98.2 

251 

215.3 

129.0 

12 

10.3 

6.2 

72 

61.8 

37.0 

32 

113.2 

67.9 

92 

164.7 

98.7 

52 

216.1 

129.6 

13 

11.2 

6.7 

73 

62.6 

37.5 

33 

114.1 

68.4 

93 

165.5 

99.2 

53 

217.0 

130. 1 

14 

12.0 

7.2 

74 

63.5 

38.0 

34 

114.9 

68.9 

94 

166.4 

99.7 

54 

217.9 

130.6 

15 

12.9 

7.7 

75 

64.3 

38.6 

35 

115.8 

69.4 

95 

167.3 

100.  3 

55 

218.7 

131.1 

16 

13.7 

8.2 

76 

65.2 

39.1 

36 

116.7 

69,9 

96 

168.1 

100.8 

56 

219.6 

131.6 

17 

14.6 

8.7 

77 

66.0 

39.6 

37 

117.5 

70.4 

97 

169.0 

101.3 

57  ;  220.4 

132.1 

18 

15.4 

9.3 

78 

66.9 

40.1 

38 

118.4 

70.9 

98 

169.8 

101.8 

58  ,  221.3 

132.6 

19 

16.3 

9.8 

79 

67.8 

40.6 

39 

119.2 

71.5 

99 

170.7 

102.3 

59 

222.2 

133.2 

20 

17.2 

10.3 

80 
81 

68.6 
69.5 

41.1 

40 

120.1 
120.  9 

72.0 

200 

171.  5 

102.8 

60 

223.0 

133.7 
134.2 

21 

18.0 

10.8 

41.6 

141 

72.5 

201 

172.4 

103.3 

261 

223.9 

22 

18.9 

11.3 

82 

70.3 

42.2 

42 

121.8 

73.0 

02 

173.  3 

103.8 

62 

224.7 

134.7 

23 

19.7 

11.  g 

83 

71.2 

42.7 

43 

122.7 

73.5 

03 

174.1 

104.4 

63 

225.6 

135.2 

24 

20.6 

12.3 

84 

72.0 

43.2 

44 

123.5 

74.0 

04 

175.0 

104.9 

64 

226.4 

135.7 

25 

21.4 

12.9 

85 

72.9 

43.7 

45 

124.4 

74.5 

05 

175.8 

105.4 

65 

227.3 

136.2 

26 

22.3 

13.4 

86 

73.8 

44.2 

46 

125.2 

75.1 

06 

176.7 

105.9 

66 

228.2 

136.8 

27 

23.2 

13.9 

87 

74.6 

44.7 

47 

126.1 

75.6 

07 

177.5 

106.4 

67 

229.0 

137.3 

28 

24.0 

14.4 

88 

75.5 

45.2 

48 

126.9 

76.1 

08 

178.4 

106.9 

68 

229.9 

137.8 

29 

24.9 

14.9 

89 

76.3 

45.8 

49 

127.8 

76.6 

09 

179.3 

107.4 

69 

230.7 

138.3 

30 

25.7 

15.4 

90 

77.2 

46.3 

50 

128.7 

77.1 

10 

180.1 

108.0 
108.  5 

70 

231.6 

138.8 
139.3 

31 

26.6 

15.9 

91 

78.1 

46.8 

151 

129.5 

77.6 

211 

181.0 

271 

232.4 

32 

27.4 

16.5 

92 

78.9 

47.3 

52 

130.4 

78.1 

12 

181.8 

109.0 

72 

233.3 

139.8 

33 

28.3 

17.0 

93 

79.8 

47.8 

53 

131.  2 

78.7 

13 

182.7 

109.5 

73 

234.2 

140.4 

34 

29.2 

17.5 

94 

80.6 

48.3 

54 

132.1 

79.2 

14 

183.6 

110.0 

74 

235.0 

140.9 

35 

30.0 

18.0 

95 

81.5 

48.8 

55 

132.9 

79.7 

15 

184.4 

110.5 

75 

235.9 

141.4 

36 

30.9 

18.5 

96 

82.3 

49.4 

56 

133.8 

80.2 

16 

185.3 

111.0 

76 

236.7 

141.9 

37 

31.7 

19.0 

97 

83.2 

49.9 

57  !  134.7 

80.7 

17 

186.1 

111.6 

77 

237.6 

142.4 

38 

32.6 

19.5 

98 

84.1 

50.4 

58 

135. 5 

81.2 

18 

187.0 

112.1 

78 

238.4 

142.9 

39 

33.5 

20.1 

99 

84.9 

50.9 

59 

136.4 

81.7 

19 

187.8 

112.6 

79 

239.3 

143.4 

40 

34.3 

20.6 

100 

85.8 

51.4 

60 

137.2 

82.3 

82.8 

20 
221 

188.7 

113.1 

80 

240.2 

143.9 

41 

35.2 

21.1 

101 

86.6 

51.9 

161 

138.1 

189.6 

113.6 

281 

241.0 

144.5 

42 

36.0 

21.6 

02 

87.5 

52.4 

62 

139.0 

83.3 

22 

190.4 

114.1 

82 

241.9 

145.0 

43 

36.9 

22.1 

03 

88.3 

53.0 

63 

139.8 

83.8 

23 

191.3 

114.6 

83 

242.7 

145.5 

44 

37.7 

22.6 

04 

89.2 

53.5 

64 

140.7 

84.3 

24 

192.1 

115.2 

84 

243.6 

146.0 

45 

38.6 

23.1 

05 

90.1 

54.0 

65 

141.5 

84.8 

25 

193.0 

115.7 

85 

244.5 

146.5 

46 

39.5 

23.6 

06 

90.9 

54.5 

66 

142.4 

85.3 

26 

193.8 

116.2 

86 

245.3 

147.0 

47 

40.3 

24.2 

07 

91.8 

55.0 

67 

143.2 

85.9 

27 

194.7 

116.7 

87 

246.2 

147.5 

48 

41.2 

24.7 

08 

92.6 

55.5 

68 

144.1 

86.4 

28 

195. 6 

117.2 

88 

247.0 

148.1 

49 

42.0 

25.2 

09 

93.5 

56.0 

69 

145.0 

86.9 

29 

196.4 

117.7 

89 

247.9 

148.6 

50 

42.9 
43.7 

25.7 

10 
111 

94.4 
95.2 

56.6 

70 

145.8 
146.  7" 

87.4 

30 

197.3 
198.1 

118.2 
118.8 

90 
291 

248.7 

149.1 
149.6 

51 

26.2 

57.1 

171 

87.9 

231 

249.6 

52 

44.6 

26.7 

12 

96.1 

57.6 

72 

147.5 

88.4 

32 

199.0 

119.3 

92 

250.  5 

150.1 

53 

45.5 

27.2 

13 

96.9 

58.1 

73 

148.4 

88.9 

33 

199.9 

119.8 

93 

251.3 

150.6 

54 

46.3 

27.8 

14 

97.8 

58.6 

74 

149.2 

89.5 

34 

200.7 

120.3 

94 

252.2 

151.1 

55 

47.2 

28.3 

15 

98.6 

59.1 

75 

150.1 

90.0 

35 

201.6 

120.8 

95 

253.0 

151.7 

56 

48.0 

28.8 

16 

99.5 

59.  6 

76 

151.0 

90.5 

36 

202.4 

121.3 

96 

253.9 

152.  2 

57 

48.9 

29.3 

17 

100.4 

60.2 

77 

151.8 

91.0 

37 

203.  3 

121.8 

97 

254.7 

152.7 

58 

49.7 

29.8 

18 

101.2 

60.7 

78 

152.7 

91.5 

38 

204.1 

122.4 

98 

255.6 

153.2 

59 

50.6 

30.3 

19 

102.1 

61.2 

79 

153.5 

92.0 

39 

205.0 

122.9 

99 

256.5 

153.7 

60 

51.5 

30.8 

20 

102.9 

61.7 

80 

154.4 

92.5 

40 

205.9 

123.4 

300 

257.3 

154.2 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

N. 

E.  by  E 

iE. 

SI 

<:.  by  E.  1  E. 

NW.  by  \^' 

JW. 

SW 

.  by  W.  \  W. 

[For  5i  Poi 

nt«. 

TABLE  1. 

[Page  363 

Difference  of  Latitude  and  Departure  for  3  Points. 

NE.  by 

N. 

NW.  by  N. 

SE.  by  S. 

SW.  by  S. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

50.7 

33.9 

.121 

100.6 

67.2 

181 

150.5 

100.6 

241 

200.4 

133.9 

2 

1.7 

1.1 

62 

51.6 

34.4 

22 

101.4 

67.8 

82 

151.  3 

101.1 

42 

201.2 

134.4 

3 

2.5 

1.7 

63 

52.4 

35.0 

23 

102.3 

68.3 

83 

152.  2 

101.7 

43 

202.0 

135.0 

4 

3.3 

2.2 

64 

53.2 

35.6 

24 

103. 1 

68.9 

84 

153.0 

102.2 

44 

202.9 

135.  6 

5 

4.2 

2.8 

65 

54.0 

36.1 

25 

103.9 

69.4 

85 

153.8 

102.8 

45 

203.  7 

136.1 

6 

5.0 

3.3 

66 

54.9 

36.7 

26 

104.8 

70.0 

86 

154.  7 

103.3 

46 

204.  5 

136.7 

7 

5.8 

3.9 

67 

55.7 

37.2 

27 

105.  6 

70.6 

87 

155.  5 

103.  9 

47 

205. 4 

137.2 

.  8 

6.7 

4.4 

68 

56.5 

37.8 

28 

106.4 

71.1 

88 

156.3 

104.4 

48 

206.2 

137.8 

9 

7.5 

5.0 

69 

57.4 

38.3 

29 

107.3 

71.7 

89 

157. 1 

105.0 

49 

207.0 

138.3 

10 

8.3 

5.6 

70 

58.2 

38.9 

30 

108.1 

72.2 

90 

158.0 

105.6 

50 

207.9 

138.9 

11 

9.1 

6.1 

71 

59.0 

39.4 

131 

108.9 

72.8 

191 

158.8 

106.1 

251 

"208.  7 

139.4 

12 

10.0 

6.7 

72 

59.9 

40.0 

32 

109.8 

73.3 

92 

159.6 

106.  7 

52 

209.5 

140.0 

13 

10.8 

7.2 

73 

60.7 

40.6 

33 

110.6 

73.9 

93 

160. 5 

107.2 

53 

210.4 

140.6 

14 

11.6 

7.8 

74 

61.5 

41.1 

34 

111.4 

74.4 

94 

161.  3 

107.8 

54 

211.2 

141.1 

15 

12.5 

8.3 

75 

62.4 

41.7 

35 

112.2 

75.0 

95      162. 1 

108.3 

55 

212.0 

141.7 

16 

13.3 

8.9 

76 

63.2 

42.2 

36 

113.1 

75.6 

96 

163.0 

108.9 

56 

212.9 

142.2 

17 

14.1 

9.4 

77 

64.0 

42^8 

37 

113.9 

76.1 

97 

163.8 

109.4 

57 

213.7 

142.8 

18 

15.0 

10.0 

78 

64.9 

43.3 

38 

114.7 

76.7 

98 

164.6 

110.0 

58 

214.5 

143.3 

19 

15.8 

10.6 

79 

65.7 

43.9 

39 

115.6 

77.2 

99 

165.  5 

110.6 

59 

215. 4 

143.9 

20 

16.6 

11.1 

80 

66.5 
67.3 

44.4 
45.  0 

40 

116.4 

77.8 

200 
201 

166.  3 
167.1 

111.1 

60 

216.2 
217.0 

144.4 

21 

17.5 

11.7 

81 

141 

117.2 

78.3 

111.7 

261 

145.0 

22 

18.3 

12.2 

82 

68.2 

45.6 

42 

118.1 

78.9 

02 

168.0 

112.2 

62 

217.8 

145.6 

23 

19.1 

12.8 

83 

69.0 

46.1 

43 

118.9 

79.4 

03 

168.8 

112.8 

63 

218.7 

146.1 

24 

20.0 

13.3 

84 

69.8 

46.7 

44 

119.7 

80.0 

04 

169.6 

113.3 

64 

219.5 

146.7 

25 

20.8 

13.9 

85 

70.7 

47.2 

45 

120.6 

80.6 

05 

170.5 

113.9 

65 

220.3 

147.2 

26 

21.6 

14.4 

86 

71.5 

47.8 

46 

121.4 

81.1 

06 

171.3 

114.4 

66 

221.2 

147.8 

27 

22.4 

15.0 

87 

72.3 

48.3 

47 

122.2 

81.7 

07 

172.1 

115.  0 

67 

222.0 

148.3 

28 

23.3 

15.6 

88 

73.2 

48.9 

48 

123. 1 

82.2 

08 

172.  9  !  115. 6 

68 

222.8 

148.9 

29 

24.1 

16.1 

89 

74.0 

49.4 

49 

123.9 

82.8 

09 

173.8 

116.1 

69 

223.  7 

149.4 

30 

24.9 

16.7 

90 
91 

74.8 
75.7 

50.0 

50 

124.7 
125.6 

83.3 
83.9 

10 

174.6 

116.7 

70 

224.5 
225.  3 

150.0 
150.6 

31 

25.8 

17.2 

50.6 

151 

211 

175.4 

117.2 

271 

32 

26.6 

17.8 

92 

76.5 

51.1 

52 

126.  4 

84.4 

12 

176.3 

117.8 

72 

226.2 

151.1 

33 

27.4 

18.3 

93 

77.3 

51.7 

53 

127.2 

85.0 

13 

177.1 

118.3 

73 

227.0 

151.7 

34 

28.3 

18.9 

94 

78.2 

52.2 

54 

128.  0  • 

85.6 

14 

177.9 

118.9 

74 

227.8 

152.2 

35 

"29.1 

19.4 

95 

79.0 

52".  8 

55 

128.9 

86.1 

15 

178.8 

119.4 

75 

228.7 

152.  8 

36 

29.9 

20.0 

96 

79.8 

53.3 

56 

129.7 

86.7 

16 

179.  6 

120.0 

76 

229.  5 

153.3 

37 

30.8 

20.6 

97 

80.7 

53.9 

57 

130.  5 

87.2 

17 

180.4 

120.6 

77 

230.3 

153.9 

38 

31.6 

21.1 

98 

81.5 

54.4 

58 

131.4 

87.8 

18 

181.3 

121.1 

78 

231.1 

154.4 

39 

32.4 

21.7 

99 

82.3 

55.0 

59 

132.2 

88.3 

19 

182.1 

121.7 

79 

232.0 

155.0 

40 
41 

33.3 
34.1 

22.2 

100 

83.1 

55.  6 

60 

133.0 
133.9 

88.9 

20 

182.9 

122.2 

80 

232.8 
23.3.6 

155.6 

22.8 

101 

84.0 

56.1 

161 

89.4 

221 

183.  8  1  122.  8 

281 

156.1 

42 

34.9 

23.3 

02 

84.8 

56.7 

62 

134.7 

90.0 

22 

184.6 

123.3 

82 

234.  5 

156.7 

43 

35.8 

23.9 

03 

85.6 

57.2 

63 

135.  5 

90.6 

23 

185.4 

123.9 

83 

235.3 

157.2 

44 

36.6 

24.4 

04 

86.5 

57.8 

64 

136.  4 

91.1 

24 

186.2. 

124.4 

84 

236.1 

157. 8 

45 

37.4 

25.0 

05 

87.3 

58.3 

65 

137.2 

91.7 

25 

187.1 

125.0 

85 

237.  0 

158.3 

46 

38.2 

25.6 

06 

88.1 

58.9 

66 

138.0 

92.2 

26 

187.  9 

125.6 

86 

237.  8 

158.  9 

47 

39.1 

26.1 

07 

89.0 

59.4 

67 

138.9 

92.8 

27 

188.7     126. 1| 

87 

238.  6 

159.4 

48 

39.9 

26.7 

08 

89.8 

60.0 

68 

139.7 

93.3 

28 

189.6 

126.7 

88 

239.  5 

160.0 

49 

40.7 

27.2 

09 

90.6 

60.6 

69 

140.5 

93.9 

29 

190.4 

127.2 

89 

240.3 

160.6 

50 

41.6 
42.4 

27.8 

10 

91.5 

61.1 

70 

141.3 

94.4 

30 

191.2 
192.1 

127.8 

90 
291 

241.1 

161.1 

51 

28.3 

111 

92.3 

61.7 

171 

142.2 

95.0 

231 

128.3 

242.0 

161.7 

52 

43.2 

28.9 

12 

93.1 

62.2 

72 

143.0 

95.6 

32 

192.9 

128.9 

92 

242.8 

162.2 

53 

44.1 

29.4 

13 

94.0 

62.8 

73 

143.8 

96.1 

33 

193.7 

129.4 

93 

243.6 

162.8 

54 

44.9 

30.0 

14 

94.8 

63.3 

74 

144.7 

96.7 

34 

194.6 

130.0 

94 

244.  5 

163.3 

55 

45.7 

30.6 

15 

95.6 

63.9 

75 

145.  5 

97.2 

35 

195.  4 

130. 6 

95 

245.3 

163.9 

56 

46.6 

31.1 

16 

96.5 

64.4 

76 

146.3 

97.8 

36 

196.2 

131.1 

96 

246.1 

164.4 

57 

47.4 

31.7 

17 

97.3 

65.0 

77 

147.2 

98.3 

37 

197.1 

131.7 

97 

246.9 

165.  0 

58 

48.2 

32.2 

18 

98.1 

65.6 

78 

148.0 

98.9 

38 

197.9 

132.2 

98 

247.8 

165.  6 

59 

49.1 

32.8 

19 

98.9 

66.1 

79 

148.8 

99.4 

39 

198.7 

132.8 

99 

248.6 

166.1 

60 

1 

49.9 

33.3 

20 

99.8 

66.7 

80 

149.7 

100.0 

40 

199.6 

1.33.  3 

300 

249.4 

166.7 

Dist.  j 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE.  by  E. 

(; 

E.  by  I 

:.           N^ 

V.  by  W.                SW.  by  W. 

[For  5  Points.        1 

Page  364 

1 

TABLE 

1. 

Difference  of  Latitude  and  Departure  for  S^  Points. 

NE.  i  N. 

NW. 

IN. 

SE.  1  S. 

SW. 

IS. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.          Dep. 

1 

0.8 

0.6 

61 

49.0 

36.3 

121 

97.2 

72.1 

181 

145.4 

107.8 

241 

193.6 

143.  6 

2 

1.6 

1.2 

62 

49.8 

36.9 

22 

98.0 

72.7 

82 

146.2 

108.4 

42 

194.4 

144.2 

3 

2.4 

1.8 

63 

50.6 

37.5 

23 

98.8 

73.3 

83 

147.0 

109.0 

43 

195.2 

144.8 

.  4 

3.2 

2.4 

64 

51.4 

38.1 

24 

99.6 

73.9 

84 

147.8 

109.6 

44 

196.0 

145.  4 

5 

4.0 

3.0 

«65 

52.2 

38.7 

25 

100.4 

74.5 

85 

148.6 

110.2 

45 

196.8 

145.  9 

6 

4.8 

3.6 

m 

53.0 

39.3 

26 

101.2 

75.1 

86 

149.4 

110.8 

46 

197.  6      146.  5 

7 

5.6 

4.2 

67 

53.8 

39.9 

27 

102.0 

75.7 

87 

150.2 

111.4 

47 

198.4  1  147.1 

8 

6.4 

4.8 

68 

54.6 

40.5 

28 

102.8 

76.2 

88 

151.0 

112.0 

48 

199.2  i  147.7 

9 

7.2 

5.4 

69 

55.4 

41.1 

29 

103.6 

76.8 

89 

151.8 

112.6 

49 

200.0 

148.3 

10 

8.0 

6.0 

70 

56.2 

41.7 

30 

104.4 
105.2 

77.4 

90 

152.6 

113.2 

50 

200.8 
201.6 

148.9 
149.5 

11 

8.8 

6.6 

71 

57.0 

42.3 

131 

78.0 

191 

153. 4 

113.  8 

251 

12 

9.6 

7.1 

72 

57.8 

42.9 

32 

106.0 

78.6 

92 

154.2 

114.4 

52 

202.4 

150.1 

13 

10.4 

7.7 

73 

58.6 

43.5 

33 

106.8 

79.2 

93 

155.0 

115.0 

53 

203.2 

150.7 

14 

11.2 

8.3 

74 

59.4 

44.1 

34 

107.6 

79.8 

94 

155.8 

115.6 

54 

204.0 

151.  3 

15 

12.0 

8.9 

75 

60.2 

44.7 

35 

108.4 

80.4 

95 

156.6 

116.  2 

55 

204.8 

151.9 

16 

12.9 

9.5 

76 

61.0 

45.3 

36 

109.2 

81.0 

96 

157.4 

116.8 

56 

205.6 

152.5 

17 

13.7 

10.1 

77 

61.8 

45.9 

37 

110.0 

81.6 

97 

158.2 

117.4 

57 

206.4 

153.1 

18 

14.5 

10.7 

78 

62.7 

46.5 

38 

110.8 

82.2 

98 

159.0 

117.9 

58 

207.2 

153.  7 

19 

15.3 

11.3 

79 

63.5 

47.1 

39 

111.6 

82.8 

99 

159.8 

118.5 

59 

208.0 

154.3 

20 

16.1 

11.9 

80 

64.3 

47.7 

40 

112.4 

83.4 

200 

160.6 

119.1 

60 

208.8 

154.9 

21 

16.9 

12.5 

81 

65.1 

48.3 

141 

113.3 

84.0 

201 

161.4 

119.7 

261 

209.6 

155.5 

22 

17.7 

13.1 

82 

65.9 

48.8 

42 

114.1 

84.6 

02 

162.2 

120.3 

62 

210.4 

156.1 

23 

18.5 

13.7 

83 

66.7 

49.4 

43 

114.9 

85.2 

03 

163.1 

120.9 

63 

211.2 

156.7 

24 

19.3 

14.3 

84 

67.5 

50.0 

44 

115.7 

85.8 

04 

163.9 

121.5 

64 

212.0 

157.3 

25 

20.1 

14.9 

85 

68.3 

50.6 

45 

116.5 

86.4 

05 

164.7 

122.1 

65 

212.8 

157.9 

26 

20.9 

15.5 

86 

69.1 

51.2 

46 

117.3 

87.0 

06 

165.5 

122.7 

66 

213.7 

158.5 

27 

21.7 

16.1 

87 

69.9 

51.8 

47 

118.1 

87.6 

07 

166.3 

123.  3 

67 

214.5 

159.1 

28 

22.5 

16.7 

88 

70.7 

52.4 

48 

118.9 

88.2 

08 

167.1 

123.  9 

68 

215.3 

159.6 

29 

23.3 

17.3 

89 

71.5 

53.0 

49 

119.7 

88.8 

09 

167.9 

124.  5 

69 

216.1 

160.2 

30 

24.1 

17.9 

90 

72.3 

53.6 

50 

120.5 

89.4 

10 

168.7 
169.5 

125. 1 

70 

216.9 

160.8 

31 

24.9 

18.5 

91 

73.1 

54.2 

151 

121.3 

90.0 

211 

125.7 

271 

217.7 

161.4 

32 

25.7 

19.1 

92 

73.9 

54.8 

52 

122.1 

90.5 

12 

170.3 

126.3 

72 

218.5 

162.0 

33 

26.5 

19.7 

93 

74.7 

55.4 

53 

122.9 

91.1 

13 

171.1 

126.9 

73 

219.3 

162.6 

34 

27.3 

20.3 

94 

75.  5 

56.0 

54 

123.7 

91.7 

14 

171.9 

127.5 

74 

220.1 

163.2 

35 

28.1 

20.8 

95 

76.3 

56.6 

55 

124.5 

92.3 

15 

172.7 

128.1 

75 

220.9 

163.  8 

36 

28.9 

21.4 

96 

77.1 

57.2 

56 

125.3 

92.9 

16 

173.5 

128.7 

76 

221.7 

164.4 

37 

29.7 

22.0 

97 

77.9 

57.8 

57 

126.1 

93.5 

17 

174.3 

129.3 

77 

222.5 

165.0 

38 

30.5 

22.6 

98 

78.7 

58.4 

58 

126.9 

94.1 

18 

175.1 

129.9 

78 

223.3 

165.6 

39 

31.3 

23.2 

99 

79.5 

59.0 

59 

127.7 

94.7 

19 

175.9 

130.5 

79 

224.1 

166.2 

40 
41 

32.1 
32.9 

23.8 

100 

80.3 
81.1 

59.6 
60.2 

60 

128.5 

95.3 

20 

176.7 

131.1 

80 
281 

224.9 

166.8 

24.4 

101 

161 

129.3 

95.9 

221 

177.5 

131.6 

225.7 

167.4 

42 

33.7 

25.0 

02 

81.9 

60.8 

62 

130.1 

96.5 

22 

178.3 

132.2 

82 

226.5 

168.0 

43 

34.5 

25.6 

03 

82.7 

61.4 

63 

130.9 

97.1 

23 

179.1 

132.8 

83 

227.3 

168.6 

44 

35.3 

26.2 

04 

83.5 

62.0 

64 

131.7 

97.7 

24 

179.9 

133.4 

84 

228.1 

169.2 

45 

36.1 

26.8 

05 

84.3 

62.5 

65 

132.5 

98.3 

25 

180.7 

134.0 

85 

228.9 

169.8 

46 

36.9 

27.4 

06 

85.1 

63.1 

66 

133.  3 

98.9 

26 

181.5 

134.6 

86 

229.7 

170.4 

47 

37.8 

28.0 

07 

85.9 

63.7 

67 

134.1 

99.5 

27 

182.3 

135.2 

87 

230.5 

171.0 

48 

38.6 

28.6 

08 

86.7 

64.3 

68 

134.9 

100.1 

28 

183.1 

135.8 

88 

231.3 

171.6 

49 

39.4 

29.2 

09 

87.5 

64.9 

69 

135.7 

100.7 

29 

183.9 

136.4 

89 

232.1 

172.2 

50 

40.2 

29.8 

10 
111 

88.4 
89.2 

65.5 

70 

136.5 

101.  3 

30 

184.7 
185.  5 

137.0 

90 

232.9 
233.  7 

172.8 

51 

41.0 

30.4 

66.1 

171 

137.3 

101.  9 

231 

137.6 

291 

173.3 

52 

41.8 

31.0 

12 

90.0 

66.7 

72 

138.  2 

102.5 

32 

186.3 

138.2 

92 

234.5 

173.9 

53 

42.6 

31.6 

13 

90.8 

67.3 

73 

139.0 

103. 1 

33 

187.1 

138.8 

93 

235.  3 

174.5 

54 

43.4 

32.2 

14 

91.6 

67.9 

74 

139.8 

103.7 

34 

188.0 

139.4 

94 

236.1 

175.1 

55 

44.2 

32.8 

15 

92.4 

68.5 

75 

140.6 

104.2 

35 

188.8 

140.0 

95 

236.9 

175.7 

56 

45.0 

33.4 

16 

93.2 

69.1 

76 

141.4 

104.8 

36 

189.6 

140.6 

96 

237.7 

176.3 

57 

45.8 

34.0 

17 

94.0 

69.7 

77 

142.2 

105.4 

37 

190.4 

141.  2 

97 

238.6 

176.9 

58 

46.6 

34.6 

18 

94.8 

70.3 

78 

143.0 

106.0 

38 

191.2 

141.8 

98 

239.4 

177.5 

59 

47.4 

35.1 

19 

95.6 

70.9 

79 

143.8 

106.6 

39 

192.0 

142.4 

99 

240.2 

178.1 

60 

48.2 

35.7 

20 

96.4 

71.5 

80 

144.6 

107.2 

40 

192.  8 

143.0 

300 

241.0 

178.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     j     Lat. 

NE.  1 

E. 

SE.  1  E 

X^ 

V.  f  w. 

sw.  i  w. 

[F 

or  4J  Points. 

OF  THE 

UNIVERSITY 


X^cyi/  °L. 

:l\i-     ..y 

/ 

TABLE  1. 

[Page  365 

Difference  of  Latitude  and  Departure  for  3i  Points. 

NE.  i  N. 

NW 

.  JN. 

SE 

.  ^S. 

SW.  i  s 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

47.2 

38.7 

121 

93.5 

76.8 

181 

139.9 

114.8 

241 

186.3 

152.9 

2 

1.5 

1.3 

62 

47.9 

39.3 

22 

94.3 

77.4 

82 

140.7 

115.5 

42 

187.1 

153.  5 

3 

2.3 

1.9 

63 

48.7 

40.0 

23 

95.1 

78.0 

83 

141.5 

116.1 

43 

187.8 

154.2 

4 

3.1 

2.5 

64 

49.5 

40.6 

24 

95.9 

78.7 

84 

142.2 

116.7 

44 

188.6 

154.8 

5 

3.9 

3.2 

65 

50.2 

41.2 

25 

96.6 

79.3 

85 

143.  0 

117.4 

45 

189.4 

155.4 

6 

4.6 

3.8 

66 

51.0 

41.9 

26 

97.4 

79.9 

86 

143.8 

118.0 

46 

190.2 

156.1 

7 

5.4 

4.4 

67 

51.8 

42.5 

27 

98.2 

80.6 

87 

144.6 

118.6 

47 

190.9 

156.7 

8 

6.2 

5.1 

68 

52.6 

43.1 

28 

98.9 

81.2 

88 

145.  3 

119.3 

48 

191.7 

157.3 

9 

7.0 

5.7 

69 

53.3 

43.8 

29 

99.7 

81.8 

89 

146.1 

119.9 

49 

192.5 

158.0 

10 
11 

7.7 
8.5 

6.3 

70 
71 

54.1 

44.4 

30 

100.5 

82.5 

90 

146.9 
147.6 

120.  5 

121.  2 

50 

193.3 

158.6 

7.0 

54.9 

45.0 

131 

101.3 

83.1 

191 

251 

194.0 

159.2 

12 

9.3 

7.6 

72 

55.7 

45.7 

32 

102.0 

83.7 

92 

148.4 

121.8 

52 

194.8 

159.9 

13 

10.0 

8.2 

73 

56.4 

46.3 

33 

102.8 

84.4 

93 

149.2 

122.4 

53 

195.  6 

160.5 

14 

10.8 

8.9 

74 

57.2 

46.9 

34 

103.6 

85.0 

94 

150.  0 

123.1 

54 

196.3 

161.1 

15 

11.6 

9.5 

75 

58.0 

47.6 

35 

104.4 

85.6 

95 

150.7 

123.  7 

55 

197.1 

161.8 

16 

12.4 

10.2- 

76 

58.7 

48.2 

36 

105.1 

86.3 

96 

151.5 

124.  3 

56 

197.9 

162.4 

17 

13.1 

10.8 

77 

59.5 

48.8 

37 

105.9 

86.9 

97 

152.3 

125.0 

57 

198.7 

163.0 

18 

13.9 

11.4 

78 

60.3 

49.5 

38 

106.7 

87.5 

98 

153.1 

125.6 

58 

199.4 

163.7 

19 

14.7 

12.1 

79 

61.1 

50.1 

39 

107.4 

88.2 

99 

153.  8 

126.2 

59 

200.2 

164.3 

20 

15.5 

12.7 

80 

61.8 

50.8 

40 

108.2 

88.8 

200 
201 

154.6 
155.4 

126.9 

60 

201.0 
201.8 

164.9 

21 

16.2 

13.3 

81 

62.6 

51.4 

141 

109.0 

89.4 

127.5 

261 

165.6 

22 

17.0 

14.0 

82 

63.4 

52.0 

42 

109.8 

90.1 

02 

156.1 

128.1 

62 

202.5 

166.2 

23 

17.8 

14.6 

83 

64.2 

52.7 

43 

110. 5 

90.7 

03 

156.9 

128.8 

63 

203.3 

166.8 

24 

18.6 

15.2 

84 

64.9 

53.3 

44 

111.3 

91.4 

04 

157.7 

129.4 

64 

204.1 

167.5 

25 

19.3 

15.9 

85 

65.7 

53.9 

45 

112.1 

92.0 

05 

158.5 

130.1 

65 

204.8 

168.1 

26 

20.1 

16.5 

86 

66.5 

54.6 

46 

112.9 

92.6 

06 

159.2 

130.7 

66 

205.6 

168.7 

27 

20.9 

17.1 

87 

67.3 

55.2 

47 

113.6 

93.3 

07 

160.0 

131.3 

67 

206.4 

169.4 

28 

21.6 

17.8 

88 

68.0 

55.8 

48 

114.4 

93.9 

08 

160.8 

132.0 

68 

207.2 

170.0 

29 

22.4 

18.4 

89 

68.8 

56.5 

49 

115.  2 

94.5 

09 

161.6 

132.6 

69 

207.9 

170.7 

30 
31 

23.2 
24.0 

19.0 

90 

69.6 
70.3 

57.1 

57."7 

50 
151 

116.0 

95.2 

10 
211 

162.3 
163.1 

133.2 
133.9 

70 

208.7 

171.3 

19.7 

91 

116.7 

95.8 

271 

209.5 

171.9 

32 

24.7 

20.3 

92 

71.1 

58.4 

52 

117.5 

96.4 

12 

163.9 

134.5 

72 

210.3 

172.6 

33 

25.5 

20.9 

93 

71.9 

59.0 

53 

118.3 

97.1 

13 

164.7 

135.1 

73 

211.0 

173.2 

34 

26.3 

21.6 

94 

72.7 

59.6 

54 

119.0 

97.7 

14 

165.4 

135.8 

74 

211.8 

173.8 

35 

.27. 1 

22.2 

95 

73.4 

60.3 

55 

119.8 

98.3 

15 

166.2 

136.4 

75 

212.6 

174.5 

36 

27.8 

22.8 

96 

74.2 

60.9 

56 

120.6 

99.0 

16 

167.0 

137.0 

76 

213.4 

175. 1 

37 

28.6 

23.5 

97 

75.0 

61.5 

57 

121.4 

99.6 

17 

167.7 

137.7 

77 

214.1 

175.7 

38 

29.4 

24.1 

98 

75.8 

62.2 

58 

122.1 

100.2 

18 

168.5 

138.3 

78 

214.9 

176.4 

39 

30.1 

24.7 

99 

76.5 

62.8 

59 

122.9 

100.9 

19 

169.3 

138.9 

79 

215.  7 

177.0 

40 

30.9 

25.4 

100 
101 

77.3 
78.1 

6.3.4 

60 

123.7 

101.5 
102. 1" 

20 
221 

170.1 
170.8 

139.6 
140.  2 

80 

216.4 

177.6 

41 

31.7 

26.0 

64.1 

161 

124.5 

281 

217.2 

178.3 

42 

32.5 

26.6 

02 

78.8 

64.7 

62 

125.  2 

102.8 

22 

171.6 

140.8 

82 

218.0 

178.9 

43 

33.2 

27.3 

03 

79.6 

65.3 

63 

126.0 

103.4 

23 

172.4 

141.  5 

83 

218.8 

179.5 

44 

34.0 

27.9 

04 

80.4 

66.0 

64 

126.8 

104.0 

24 

173.2 

142.1 

84 

219.5 

180.2 

45 

34.8 

28.5 

05 

81.2 

66.6 

65 

127.5 

104.7 

25 

173.9 

142.7 

85 

220.3 

180.8 

46 

35.6 

29.2 

06 

81.9 

67.2 

66 

128.3 

105.  3 

26 

174.7 

143.4 

86 

221.1 

181.4 

47 

36.3 

29.8 

07 

82.7 

67.9 

67 

'  129. 1 

105. 9 

27 

175.5 

144.0 

87 

221.9 

182.1 

48 

37.1 

30.5 

08 

83.5 

68.5 

68 

129.9 

106.6 

28 

176.2 

144.6 

88 

222.6 

182.7 

49 

37.9 

31.1 

09 

84.3 

69.1 

69 

130.6 

107.2 

29 

177.0 

145.  3 

89 

223.4 

183.3 

50 

38.7 

31.7 

10 

85.0 

69.8 

70 

131.4 

107.8 

30 

177.8 

145.9 

90 

224.2 

184. 0 

51 

39.4 

32.4 

111 

85.8 

70.4 

171 

132.2 

108.5 

231 

178.6 

146.5 

291 

224.9 

184.6 

52 

40.2 

33.0 

12 

86.6 

71.1 

72 

133.0 

109.1 

32 

179.3 

147.2 

92 

225.7 

185.2 

53 

41.0 

33.6 

13 

87.4 

71.7 

73 

133.7 

109.8 

33 

180.1 

147.8 

93 

226.5 

185.9 

54 

41.7 

34.3 

14 

88.1 

72.3 

74 

134.5 

110.4 

34 

180.9 

148.4 

94 

227.3 

186.5 

55 

42.5 

34.9 

15 

88.9 

73.0 

75 

135.3 

111.0 

35 

181.7 

149.1 

95 

228.0 

187.1 

56 

43.3 

35.5 

16 

89.7 

73.6 

76 

136.  0 

111.7 

36 

182.4 

149.7 

96 

228.8 

187.8 

57 

44.1 

36.2 

17 

90.4 

74.2 

77 

136.8 

112.3 

37 

183.2 

150.4 

97 

229.6 

188.4 

58 

44.8 

36.8 

18 

91.2 

74.9 

78 

137.6 

112.9 

38 

184.0 

151.0 

98 

230.4 

189.0 

59 

45.6 

37.4 

19 

92.0 

75.5 

79 

138.4 

113.6 

39 

184.7 

151.6 

99 

231.1 

189.7 

60 
Dist. 

46.4 

38.1 

20 

92.8 

76.1 

80 

139.1 

114.2 

40 

185.5 

152.3 

300 

231.9 

190.3 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE.  i  ] 

E. 

SE.  JE 

N 

\V.  J  ^\ 

sw.  i  -^ 

V. 

[F 

or  4J  Points.      1 

Page  366] 

TABLE  1. 

Difference  of  Latitude  and  Departure  for  3|  Points. 

NE.  i  N. 

NW. 

}N. 

3E.  J 

s. 

SW.  J  8. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
241 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

46.2 

41.0 

121 

89.7 

81.3 

181 

134.1 

121.6 

178.6 

161.8 

2 

1.5 

1.3 

62 

45.9 

41.6 

22 

90.4 

81.9 

82 

134.9 

122.2 

42 

179.3 

162.5 

3 

2.2 

2.0 

63 

46.7 

42.3 

23 

91.1 

82.6 

83 

135.6 

122.9 

43 

180.1 

163.2 

4 

3.0 

2.7 

64 

47.4 

43.0 

24 

91.9 

83.3 

84 

136.  3 

123.6 

44 

180.8 

163.9 

5 

3.7 

3.4 

^ 

48.2 

43.7 

25 

92.6 

83.9 

85 

137.1 

124.2 

45 

181.5 

164.5 

6 

4.4 

4.0 

48.9 

44.3 

26 

93.4 

84.6 

86 

137.8 

124.9 

46 

182.3 

165.2 

7 

5.2 

4.7 

67 

49.6 

45.0 

27 

94.1 

85.3 

87 

138.6 

125.  6 

47 

183.0 

165.9 

8 

5.9 

5.4 

68 

50.4 

45.7 

28 

94.8 

86.0 

88 

139.3 

126.3 

48 

183.8 

166.5 

9 

6.7 

6.0 

69 

51.1 

46.3 

29 

95.6 

86.6 

89 

140.0 

126.9 

49 

184.5 

167.2 

10 

7.4 

6.7 

70 

51.9 
52.6 

47.0 
47.7 

30 

96.3 
97.1 

87.3 
88.0 

90 
191 

140.8 
141.5 

127.6 
128.  3 

50 

185.2 

167.9 

11 

8.2 

7.4 

71 

131 

251 

186.0 

168.6 

12 

8.9 

8.1 

72 

53.3 

48.4 

32 

97.8 

88.6 

92 

142.8 

128.9 

52 

186.7 

169.2 

13 

9.6 

8.7 

73 

54.1 

49.0 

33 

98.5 

89.3 

93 

143.0 

129.6 

53 

187.5 

169.9 

14 

10.4 

9.4 

74 

54.8 

49.7 

34 

99.3 

90.0 

94 

143.7 

130.3 

54 

188.2 

170.6 

15 

11.1 

10.1 

75 

55.6 

50.4 

35 

100.0 

90.7 

95 

144.5 

131.0 

55 

188.9 

171.2 

16 

11.9 

10.7 

76 

56.3 

51.0 

36 

100.8 

91.3 

96 

145.2 

131.6 

56 

189.7 

171.9 

17 

12.6 

11.4 

77 

57.1 

51.7 

37 

101.5 

92.0 

97 

146.0 

132.3 

57 

190.4 

172.6 

18 

13.3 

12.1 

78 

57.8 

52.4 

38 

102.3 

92.7 

98 

146.7 

133.0 

58 

191.2 

173.3 

19 

14.1 

12.8 

79 

58.5 

53.1 

39 

103.0 

93.3 

99 

147.4 

133.6 

59 

191.9 

173.9 

20 
21 

14.8 

13.4 

80 
81 

59.3 
60.0 

53.7 

40 

103.7 
104.5 

94.0 

200 

148.2 

134.3 

60 

192.6 

174.6 

15.6 

14.1 

54.4 

141 

94.7 

201 

148.9 

135.0 

261 

193.4 

175.3 

22 

16.3 

14.8 

82 

60.8 

55. 1 

42 

105.2 

95.4 

02 

149.7 

135.7 

62 

194.1 

175.9 

23 

17.0 

15.4 

83 

61.5 

55.7 

43 

106.0 

96.0 

03 

150.4 

136.3 

63 

194.9 

176.6 

24 

17.8 

16.1 

84 

62.2 

56.4 

44 

106.7 

96.7 

04 

151.  2 

137.0 

64 

195.6 

177.3 

25 

18.5 

16.8 

85 

63.0 

57.1 

45 

107.4 

97.4 

05 

151.9 

137.  7 

65 

196.4 

178.0 

26 

19.3 

17.5 

86 

63.7 

57.8 

46 

108.2 

98.0 

06 

152.6 

138.3 

66 

197.1 

178.6 

27 

20.0 

18.1 

87 

64.5 

58.4 

47 

108.9 

98.7 

07 

153.  4 

139.0 

67 

197.8 

179.3 

28 

20.7 

18.8 

88 

65.2 

59.1 

48 

109.7 

99.4 

08 

154.1 

139.7 

68 

198.6 

180.0 

29 

21.5 

19.5 

89 

65.9 

59.8 

49 

110.4 

100.1 

09 

154.9 

140.4 

69 

199.3 

180.6 

30 

22.2 

20.1 

90 

66.7 

60.4 

50 

111.1 
111.9 

100.7 

10 

155.6 
156.3 

141. 0 

70 

200.1 
200.8 

181.3 

31 

23.0 

20.8 

91 

67.4 

61.1 

151 

101.4 

211 

141.7 

271 

182.0 

32 

23.7 

21.5 

92 

68.2 

61.8 

52 

112.6 

102.1 

12 

157.1 

142.4 

72 

201.5 

182.7 

33 

24.5 

22.2 

93 

68.9 

62.5 

53 

113.4 

102.7 

13 

157.8 

143.0 

73 

202.3 

183.3 

34 

25.2 

22.8 

94 

69.6 

63. 1 

54 

114.1 

103.4 

14 

158.6 

143.7 

74 

203. 0 

184.0 

35 

25.9 

23.5 

95 

70.4 

63.8 

55 

114.8 

104.1 

15 

159.3 

144.4 

75 

203.8 

184.7 

36 

26.7 

24.2 

96 

71.1 

64.5 

56 

115.6 

104.8 

16 

160.0 

145.1 

76 

204.  5 

185.4 

37 

27.4 

24.8 

97 

71.9 

65.1 

57 

116.3 

105.4 

17 

160.8 

145.7 

77 

205.2 

186.0 

38 

28.2 

25.5 

98 

72.6 

65.8 

58 

117.1 

106.1 

18 

161.5 

146.4 

78 

206.0 

186.7 

39 

28.9 

26.2 

99 

73.4 

66.5 

59 

117.8 

106.8 

19 

162.3 

147.1 

79 

206.7 

187.4 

40 
41 

29.6 
30.4 

26.9 

100 
101 

74.1 

67.2 

60 

118.6 

107.4 
108.1 

20 
221 

163.0 
163.8 

147.7 

80 

207.5 

188.0 

27.5 

74.8 

67.8 

161 

119.3 

148.4 

281 

208.2 

188.7 

42 

31.1 

28.2 

02 

75.6 

68.5 

62 

120.0 

108.8 

22 

164.5 

149.1 

82 

208.9 

189.4 

43 

31.9 

28.9 

03 

76.3 

69.2 

63 

120.8 

109.5 

23 

165.2 

149.8 

83 

209.7 

190.1 

44 

32.6 

29.5 

04 

77.1 

69.8 

64 

121.5 

110.1 

24 

166.0 

150.4 

84 

210.4 

190.7 

45 

33.  3 

30.2 

05 

77.8 

70.5 

65 

122.3 

110.8 

25 

166.7 

151.1 

85 

211.2 

191.4 

46 

34.1 

30.9 

06 

78.5 

71.2 

66 

123.  0 

111.5 

26 

167.5 

151.8 

86 

211.9 

192.1 

47 

34.8 

31.6 

07 

79.3 

71.9 

67 

123.7 

112.2 

27 

168.2 

152.4 

87 

212.7 

192.7 

48 

35.6 

32.2 

08 

80.0 

72.5 

68 

124.5 

112.8 

28 

168.9 

153.1 

88 

213.4 

193.4 

49 

36.3 

32.9 

09 

80.8 

73.2 

69 

125.2 

113.5 

29 

169.7 

153.8 

89 

214.1 

194.1 

50 

37.0 

33.6 
34.2 

10 
111 

81.5 

82.2 

73.9 

70 

126.0 
126.7 

114.2 

30 
231 

170.4 
171.2 

154.5 

90 

214.9 

194.8 

51 

37.8 

74.5 

171 

114.8 

155.1 

291 

215.6 

195.  4 

52 

38.5 

34.9 

12 

83.0 

75.2 

72 

127.4 

115.5 

32 

171.9 

155.  8 

92 

216.4 

196.1 

53 

39.3 

35.6 

13 

83.7 

75.9 

73 

128.2 

116.2 

33 

172.6 

156.5 

93 

217.1 

196.8 

54 

40.0 

36.3 

14 

84.5 

76.6 

74 

128.9 

116.9 

34 

173.4 

157.1 

94 

217.8 

197.4 

55 

40.8 

36.9 

15 

85.2 

77.2 

75 

129.7 

117.5 

35 

174. 1 

157.8 

95 

218.6 

198.1 

56 

41.5 

37.6 

16 

86.0 

77.9 

76 

130.4 

118.2 

36 

174.9 

158.5 

96 

219.3 

198.8 

57 

42.2 

38.3 

17 

86.7 

78.6 

77 

131. 1 

118.9 

37 

175.6 

159.2 

97 

220.1 

199.5 

58 

43.0 

39.0 

18 

87.4 

79.2 

78 

131.9 

119.5 

38 

176.  3 

159.8 

98 

220.8 

200.1 

59 

43.7 

39.6 

19 

88.2 

79.9 

79 

132.6 

120.2 

39 

177.1 

160.5 

99 

221.5 

200.8 

60 

44.5 

40.3 

20 

88.9 

80.6 

80 

133.4 

120.9 

40 

177.8 

161.2 

300 

222.3 

201.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

NE.  i  E. 

<; 

E.  JE. 

N) 

V.  i  W. 

S^ 

w.  \  w. 

[For  4J  Points.      1 

TABLE  1. 

[Page  367 

Difference  of  Latitude  and 

Depart 

ure  for  4  Points. 

NE 

NW. 

SE. 

sw. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

43.1 

43.1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

1.4 

1.4 

62 

43.8 

43.8 

22 

86.3 

86.3 

82 

128.7 

128.7 

42 

171.1 

171.1 

3 

2.1 

2.1 

63 

44.5 

44.5 

23 

87.0 

87.0 

83 

129.4 

129.4 

43 

171.8 

171.8 

4 

2.8 

2.8 

64 

45.3 

45.3 

24 

87.7 

87.7 

84 

130.1 

130.1 

44 

172.5 

172.5 

5 

3.5 

3.5 

65 

46.0 

46.0 

25 

88.4 

88.4 

85 

130.8 

130.8 

45 

173.2 

173.2 

6 

4.2 

4.2 

66 

46.7 

46.7 

26 

89.1 

89.1 

86 

131.5 

131.5 

46 

173.9 

173.9 

7 

4.9 

4.9 

67 

47.4 

47.4 

27 

89.8 

89.8 

87 

132.2 

132.2 

47 

174.7 

174.7 

8 

5.7 

5.7 

68 

48.1 

48.1 

28 

90.5 

90.5 

88 

132.9 

132.9 

48 

175.4 

175.4 

9 

6.4 

6.4 

69 

48.8 

48.8 

29 

91.2 

91.2 

89 

133.6 

133.6 

49 

176.1 

176.1 

10 

7.1 

7.1 

70 

49.5 

49.5 

30 

91.9 

91.9 

90 

134.4 

134.4 

50 

176.8 

176.8 

11 

7.8 

7.8 

71 

50.2 

50.2 

131 

92.6 

92.6 

191 

135.1 

135.1 

251 

177.5 

177.5 

12 

8.5 

8.5 

72 

50.9 

50.9 

32 

93.3 

93.3 

92 

135.8 

135.8 

52 

178.2 

178.2 

13 

9.2 

9.2 

73 

51.6 

51.6 

33 

94.0 

94.0 

93 

136.5 

136.5 

53 

178.9 

178.9 

14 

9.9 

9.9 

74 

52.3 

52.3 

34 

94.8 

94.8 

94 

137.2 

137.2 

54 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

35 

95.5 

95.5 

95 

137.9 

137.9 

55 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

36 

96.2 

96.2 

96 

138.6 

138.6 

56 

181.0 

181.0 

17 

12.0 

12.0 

77 

54.4 

54.4 

37 

96.9 

96.9 

97 

139.  3 

139.3 

57 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

38 

97.6 

97.6 

98 

140.0 

140.0 

58 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.9 

55.9 

39 

98.3 

98.3 

99 

140.7 

140.7 

59 

183.1 

183.1 

20 

14.1 

14.1 

80 

56.6 

56.6 

40 

99.0 

99.0 

200 
201 

141.4 
142.1 

141.4 

60 

183.8 

183.8 
184.6 

21 

14.8 

14.8 

81 

57.3 

57.3 

141 

99.7 

99.7 

142.1 

261 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

43 

101.1 

101.] 

03 

143.5 

143.5 

63 

186.0 

186.0 

24 

17.0 

17.0 

84 

59.4 

59.4 

44 

101.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.1 

60.1 

45 

102.5 

102.5 

05 

145.0 

145.0 

65 

187.4 

187.4 

26 

18.4 

18.4 

86 

60.8 

60.8 

46 

103.2 

103.2 

06 

145.7 

145.7 

66 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

47 

103.9 

103.9 

07 

146.4 

146.4 

67 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

48 

104.7 

104.7 

08 

147.1 

147.1 

68 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

49 

105.4 

105.4 

09 

147.8 

147.8 

69 

190.2 

190.2 

30 
31 

21.2 

21.2 

90 

63.6 

63.6 

50 
151 

106.1 

106.1 

10 
211 

148.5 
149.2 

148.5 
149.2 

70 

190.9 
191.6 

190.9 

21.9 

21.9 

91 

64.3 

64.3 

106.8 

106.8 

271 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

52 

107.5 

107.5 

12 

149.9 

149.9 

72 

192.  3 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

53 

108.2 

108.2 

13 

150.6 

150.6 

73 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5- 

66.5 

54 

108.9 

108.9 

14 

151.3 

151.3 

74 

193.7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

55 

109.6 

109.6 

15 

152.0 

152.0 

75 

194.5 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

56 

110.3 

110.3 

16 

152.7 

152.7 

76 

195.2 

195.2 

37 

26.2 

26.2 

97 

68.6 

68.6 

57 

111.0 

111.0 

17 

153.  4 

153.4 

77 

195.9 

195.9 

38 

.  26.9 

26.9 

98 

69.3 

69.3 

58 

111.7 

111.7 

18 

154.1 

154.1 

78 

196.6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

59 

112.4 

112.4 

19 

154.9 

154.9 

79 

197.3 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

60 
161 

113.1 

113.1 

20 

155.  6 

155.6 
156.3' 

80 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

113.8 

113.8 

221 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

02 

72.1 

72.1 

62 

114.6 

114.6 

22 

157.0 

157.0 

82 

199.4 

199.4 

43 

30.4 

30.4 

03 

72.8 

72.8 

63 

115.3 

115.3 

23 

157.7 

157.7 

83 

200.1 

200.1 

44 

31.1 

31.1 

04 

73.5 

73.5 

64 

116.0 

116.0 

24 

158.4 

158.4 

84 

200.8 

200.8 

45 

31.8 

31.8 

05 

74.2 

74.2 

65 

116.7 

116.7 

25 

159.1 

159.1 

85 

201.5 

201.5 

46 

32.5 

32.5 

06 

75.0 

75.0 

66 

il7.4 

117.4 

26 

159.  8 

159.8 

86 

202.2 

202.2 

47 

33.2 

33.2 

07 

75.7 

75.7 

67 

118.1 

118.1 

27 

160.5 

160.5 

87 

202.9 

202.9 

48 

33.9 

33.9 

08 

76.4 

76.4 

68 

118.8 

118.8 

28 

161.2 

161.2 

88 

203.6 

203.6 

49 

34.6 

34.6 

09 

77.1 

77.1 

69 

119.5 

119.5 

29 

161.9 

161.9 

89 

204.4 

204.4 

50 

35.4 

35.4 

10 

77.8 

77.8 

70 

120.2 
126.9 

120.2 
120.9 

30 

162.6 
163.3 

162.6 

90 

205.1 

205.1 

51 

36.1 

36.1 

111 

78.5 

78.5 

171 

231 

163.3 

291 

205.8 

205.8 

52 

36.8 

36.8 

12 

79.2 

79.2 

72 

121.6 

121.6 

32 

164.0 

164.0 

92 

206.5 

206.5 

53 

37.5 

37.5 

13 

79.9 

79.9 

73 

122.3 

122.3 

33 

164.8 

164.8 

93 

207.2 

207.2 

54 

38.2 

38.2 

14 

80.6 

80.6 

74 

123.0 

123.0 

34 

165.  5 

165.5 

94 

207.9 

207.9 

55 

38.9 

38.9 

15 

81.3 

81.3 

75 

123.7 

123.7 

35 

166.2 

166.2 

95 

208.6 

208.6 

56 

39.6 

39.6 

16 

82.0 

82.0 

76 

124.  5 

124.5 

36 

166.9 

166.9 

96 

209.3 

209.3 

57 

40.3 

40.3 

17 

82.7 

82.7 

77 

125.2 

125.2 

37 

167.6 

167.6 

97 

210.0 

210.0 

58 

41.0 

41.0 

18 

83.4 

83.4 

78 

125.9 

125.9 

38 

168.  3 

168.3 

98 

210.7 

210.7 

59 

41.7 

41.7 

19 

84.1 

84.1 

79 

126.6 

126.6 

39 

169.0 

169.0 

99 

211.4 

211.4 

60 

42.4 

42.4 

20 

84.9 

84.9 

80 

127.3 

127.3 

40 

169.7 

169.7 

300 

212.1 

212.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

■    NE. 

NW. 

?E. 

SW 

[1 

^'or  4  Po 

ints. 

Page  368 

TABLE 

i   2. 

Difference  of  Latitude  and  Departure  for  1°  (179",  181' 

',  359°] 

. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.0 

61 

61.0 

1.1 

121 

121.0 

2.1 

181      181.0 

3.2 

241 

241.0 

4.2 

2 

2.0 

0.0 

62 

62.0 

1.1 

22 

122.0 

2.1 

82 

182.0 

3.2 

42 

242.  0 

4.2 

3 

3.0 

0.1 

63 

63.0 

1.1 

23 

123.0 

2.1 

83 

183.0 

3.2 

43 

243.0 

4.2 

4 

4.0 

0.1 

64 

64.0 

1.1 

24 

124.0 

2.2 

84 

184.0 

3.2 

44 

244.0 

4.3 

5 

5.0 

0.1 

65 

65.0 

1.1 

25 

125.0 

2.2 

85 

185.0 

3.2 

45 

245.0 

4.3 

6 

6.0 

0.1 

^6 
•67 

66.0 

1.2 

26 

126.0 

2.2 

86 

186.0 

3.2 

46 

246.0 

4.3 

7 

7.0 

0.1 

67.0 

1.2 

27 

127.0 

2.2 

87 

187.0 

3.3 

47 

247.0 

4.3 

8 

8.0 

0.1 

68 

68.0 

1.2 

28 

128.0 

2.2 

88 

188.0 

3.3 

48 

248.0 

4.3 

9 

9.0 

0.2 

69 

69.0 

1.2 

29 

129.0 

2.3 

89      189.0 

3.3 

49 

249.0 

4.3 

10 

10.0 

0.2 

70 

70.0 

^1.2 

30 

130.0 

2.3 
2.3 

90 
191 

190.0 
191.0 

3.3 
3.3 

50 
251 

250.0 

4.4 

11 

11.0 

0.2 

71 

71.0 

1.2 

131 

131.  0 

251.0 

4.4 

12 

12.0 

0.2 

72 

72.0 

1.3 

32 

132.0 

"2.3 

92 

192.0 

3.4 

52 

252.0 

4.4 

13 

13.0 

0.2 

73 

73.0 

1.3 

33 

133.0 

2.3 

93 

193.0 

3.4 

53 

253.0 

4.4 

'  14 

14.0 

0.2 

74 

74.0 

1.3 

34 

134.0 

2.3 

94 

194.0 

3.4 

54 

254.0 

4.4 

15 

15.0 

0.3 

75 

75.0 

1.3 

35 

135.0 

2.4 

95 

195.0 

3.4 

55 

255.0 

4.5 

16 

16.0 

0.3 

76, 

76.0 

1.3 

36 

136.0 

2.4 

96 

196.0 

8.4 

56 

256.0 

4.5 

17 

17.0 

0.3 

77 

77.0 

1.3 

37 

137.0 

2.4 

97 

197.0 

3.4 

57 

257.0 

4.5 

18 

18.0 

0.3 

78 

78.0 

1.4 

38 

138.0 

2.4 

98 

198.0 

3.5 

58 

258.0 

4.5 

19 

19.0 

0.3 

79 

79.0 

1.4 

39 

139.0 

2.4 

99 

199.0 

3.5 

59 

259.0 

4.5 

20 

20.0 
21.0 

0.3 

80 

80.0 
81.0 

1.4 

40 

140.0 
141.0 

2.4 

200 
201 

200.0 

3.5 

60 
261 

260.0 
261.0 

4.5 
4.6 

21 

0.4 

81 

1.4 

141 

2.5 

201.0 

3.5 

22 

22.0 

0.4 

82 

82.0 

1.4 

42 

142.0 

2.5 

02 

202.0 

3.5 

62 

262.0 

4.6 

23 

23.0 

0.4 

83 

83.0 

1.4 

43 

143.0 

2.5 

03 

203.0 

3.5 

63 

263.0 

4.6 

24 

24.0 

0.4 

84 

84.0 

1.5 

44 

144.0 

2.5 

04 

204.0 

3.6 

64 

264.0 

4.6 

25 

25.0 

0.4 

85 

85.0 

1.5 

45 

145.0 

2.5 

05 

205.0 

3.6 

65 

265.0 

4.6 

26 

26.0 

0.5 

86 

86.0 

1.5 

46 

146.0 

2.5 

06 

206.0 

3.6 

66 

266.0 

4.6 

27 

27.0 

0.5 

87 

87.0 

1.5 

47 

147.0 

2.6 

07 

207.0 

3.6 

67 

267.0 

4.7 

28 

28.0 

0.5 

88 

88.0 

1.5 

48 

148.0 

2.6 

08 

208.0 

3.6 

68 

268.0 

4.7 

29 

29.0 

0.5 

89 

89.0 

1.6 

49 

149.0 

2.6 

09 

209.0 

3.6 

69 

269.0 

4.7 

30 
31 

30..0 

0.5 

90 
91 

90.0 

1.6 

50 

150.0 

2.6 

10 

210.0 

3.7 

70 

270.0 

4.7 
4.7 

31.0 

0.5 

91.0 

1.6 

151 

151.0 

2.6 

211 

211.0 

3.7 

271 

271.0 

32 

32.0 

0.6 

92 

92.0 

1.6 

52 

152.0 

2.7 

12 

212.0 

3.7 

72 

272.0 

4.7 

33 

33.0 

0.6 

93 

93.0 

1.6 

53 

153.0 

2.7 

13 

213.0 

3.7 

73 

273.0 

4.8 

34 

34.0 

0.6 

94 

94.0 

1.6 

54 

154.0 

2.7 

14 

214.0 

3.7 

74 

274.0 

4.8 

35 

35.0 

0.6 

95 

95.0 

1.7 

55 

155. 0 

2.7 

15 

215.0 

3.8 

75 

275.0 

4.8 

36 

36.0 

0.6 

96 

96.0 

1.7 

56 

156.0 

2.7 

16 

216.0 

3.8 

76 

276.0 

4.8 

37 

37.0 

0.6 

97 

97.0 

1.7 

57 

157.0 

2.7 

17 

217.0 

3.8 

/ 1 

277.0 

4.8 

38 

38.0 

0.7 

98 

98.0 

1.7 

58 

158.0 

2.8 

18 

218.0 

3.8 

78 

278.0 

4.9 

39 

39.0 

0.7 

99 

99.0 

1.7 

59 

159.0 

2.8 

19 

219.0 

3.8 

79 

279.0 

4.9 

40 

40.0 

0.7 
0.7 

100 

100.0 

1.7 
1.8 

60 

160.0 
161.0 

2.8 
2.8 

20 
221 

220.0 

3.8 

80 

280.0 

4.9 

41 

41.0 

101 

101.0 

161 

221.0 

3.9 

281 

281.0 

4.9 

42 

42.0 

0.7 

02 

102.0 

1.8 

62 

162.0 

2.8 

22 

222.0 

3.9 

82 

282.0 

4.9 

43 

43.0 

0.8 

03 

103.0 

1.8 

63 

163.0 

2.8 

23 

223.0 

3.9 

83 

283.0 

4.9 

44 

44.0 

0.8 

04 

104.0 

1.8 

64 

164.0 

2.9 

24 

224.0 

3.9 

84* 

284.0 

5.0 

45 

45.0 

0.8 

05 

105.0 

1.8 

65 

165.0 

2.9 

25 

225.0 

3.9 

85 

285.0 

5.0 

46 

46.0 

0.8 

06 

106.0 

1.8 

66 

166.0 

2.9 

26 

226.  0 

3.9 

86 

286.0 

5.0 

47 

47.0 

0.8 

07 

107.0 

1.9 

67 

167.0 

2.9 

27 

227.0 

4.0 

87 

287.0 

5.0 

48 

48.0 

0.8 

08 

108.0 

1.9 

68 

168.0 

2.9 

28 

228.0 

4.0 

88 

288.0 

5.0 

49 

49.0 

0.9 

09 

109.0 

1.9 

69 

169.0 

2.9 

29 

229.0 

4.0 

89 

289.0 

5.0 

50 

50.0 

0.9 

10 

110.0 

1.9 

70 

170.0 

3.0 

30 

230.0 
231. 0 

4.0 

90 

290.0 

5.1 

51 

51.0 

0.9 

111 

111.0 

1.9 

171 

171.0 

3.0 

231 

4.0 

291 

291.0 

5.1 

52 

52.0 

0.9 

12 

112.0 

2.0 

72 

172.0 

3.0 

32 

232.0 

4.0 

92 

292.0 

5.1 

53 

53.0 

0.9 

13 

113.  0 

2.0 

73 

173.0 

3.0 

33 

233.0 

4.1 

93 

293.0 

5.1 

54 

54.0 

0.9 

14 

114.0 

2.0 

74 

174.0 

3.0 

34 

234.0 

4.1 

94 

294.0 

5.1 

55 

55.0 

1.0 

15 

115.  0 

2.0 

75 

175.0 

3.1 

35 

235.0 

4.1 

95 

295.0 

5.1 

56 

56.0 

1.0 

16 

116.0 

2.0 

76 

176.0 

3.1 

36 

236.0 

4.1 

96 

296.0 

5.2 

57 

57.0 

1.0 

17 

117.0 

2.0 

77 

177.0 

3.1 

37 

237.0 

4.1 

97 

297.0 

5.2 

58 

58.0 

1.0 

18 

118.0 

2.1 

78 

178.0 

3.1 

38 

238. 0 

4.2 

98 

298.0 

5.2 

59 

59.0 

1.0 

19 

119.0 

2.1 

79 

179.0 

3.1 

39 

239.0 

4.2 

99 

299.0 

5.2 

60 

60.0 

1     1-0 

20 

120.0 

2.1 

80 

180.0 

3.1 

40 

240. 0. 

4.2 

300 

300.0 

5.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

89°  0 

n°,  269 

^  271° 

. 

TABLE  2. 

[Page  369 

Difference  of  Latitude  and  Departure  for  1°  (179°,  181 

=,  359°). 

Dist. 

Lat. 

Dep. 

Dist.        Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

301.0 

5.3 

361  '  360.9 

6.3 

421 

420.9 

7.3 

481 

480.9 

8.4 

541 

540.9 

•  9.  5 

02 

302.0 

5.3 

62     361.9 

6.3 

22 

421.9 

7.4 

82 

481.9 

8.4 

42 

541.9 

9.5 

03 

303.  0 

5.3 

63  1  362.9 

6.3 

23 

422.9 

7.4 

83 

482.9 

8.5 

43 

542.9 

9.5 

04 

304.0 

5.3 

64     363.9 

6.4 

24 

423.9 

7.4 

84 

483.9 

8.5 

44 

543.9 

9.5 

05 

305.0 

5.3 

65  1  364.9 

6.4 

25 

424.9 

7.4 

85 

484.9 

8.5 

45 

544.9 

9.5 

06 

306.0 

5.3 

66 

365.9 

6.4 

26 

425.9 

7.4 

86 

485.9 

8.5 

46 

545.9 

9.5 

07 

307.0 

5.4 

67 

366.9 

6.4 

27 

426.9 

7.4 

87 

486.9 

8.5 

47 

546.  9 

9.6 

08 

308.0 

5.4 

68 

367.9 

6.4 

28 

427.9 

7.5 

88 

487.9 

8.6 

48 

547.  9 

9.6 

09 

309.0 

5.4 

69 

368.  9 

6.4 

29 

428.9 

7.  5 

89 

488.9 

8.6 

49 

548.9 

9.6 

10 
311 

310.0 
311.6 

5.4 

70 

369.9 
370.'9^ 

6.5 
6.5 

30 
431 

429.9 
430.9 

7.5 
7.5 

90 
491 

489.9 
490.9 

8.6 

876 

50 

549.  9 

9.6 

5.4 

371 

551 

550.9 

9.6 

12 

312.0 

5.4 

72 

371.9 

6.5 

32 

-431.  9 

7.5 

92 

491.9 

8.6 

52 

551.9 

9.6 

13 

313.0 

5.5 

73 

372.9 

6.5 

33 

432.9 

7.  5 

93 

492.9 

8.7 

53 

552.9 

9.7 

14 

314.0 

5.5 

74 

373.9 

6.5 

34 

433.9 

7.6 

94 

493.9 

8.7 

54 

553.9 

9.7 

15 

315.0 

5.5 

75 

374.9 

6.5 

35 

434.9 

7.6 

95 

494.9 

8.7 

55 

554.9 

9.7 

16 

316.0 

5.5 

76- 

375.9 

6.6 

36 

435.9 

7.6 

96 

495.9 

8.7 

56 

555.  9 

9.7 

17 

317.0 

5.5 

77 

376.9 

6.6 

37 

436.9 

7.6 

97 

496.9 

8.7 

57 

556.9 

9.7 

18 

318.0 

5.5 

78 

377.9 

6.6 

38 

437.9 

7.6 

98 

497.9 

8.7 

58 

557.  9 

9.7 

19 

319.0 

5.6 

79 

378.9 

6.6 

39 

438.9 

7.  7 

99 

498.9 

8.8 

59 

558.9 

9.8 

20 
321 

320.0 

5.6 

80 
381 

379.9 
380.9 

6.6 
6.7 

40 

439.9 

7.  7 

500 

499.9 
500.9 

8.8 

60 

559.9 
"560.9 

9.8 

321.0 

5.6 

441 

440.9 

7.  7 

501 

8.8 

561 

9.8 

22 

322.0 

5.6 

82 

381.9 

6.7 

42 

441.9 

7.  7 

02 

501.9 

8.8 

62' 

561.9 

9.8 

23 

323.0 

5.6 

83 

382.9 

6.7 

43 

442.9 

7.  7 

03 

502.  9 

8.8 

63 

562.9 

9.8 

24 

324.0 

5.6 

84 

383.9 

6.7 

44 

443.9 

7.  7 

04 

503.9 

8.8 

64 

563.9 

9.8 

25 

325.0 

5.7 

85 

384.9 

6.7 

45 

444.9 

7.8 

05 

504.9 

8.8 

65 

564.  9 

9.9 

26 

326.0 

5.7 

86 

385.  9 

6.7 

46 

445.9 

7.8 

06 

505.9 

8.9 

66 

565.9 

9.9 

27 

327.0 

5.7 

87 

386.9 

6.8 

47 

446.9 

7.8 

07 

506.9 

8.9 

67 

566.9 

9.9 

28 

328.0 

5.7 

88 

387.9 

6.8 

48 

447.9 

7.8 

08 

507.9 

8.9 

68 

567.9 

9.9 

29 

329.0 

5.7 

89 

388.9 

6.8 

49 

448.9 

7.8 

09 

508.9 

8.9 

69 

568.9 

9.9 

30 

330.0 

5.8 

90 

389.  9 

390.  9 

6.8 

50 

449.  9 

7.8 

10 

509.9 

8.9 

70 
571 

569.  9 

9.9 
10.6 

331 

331.0 

5.8 

391 

6.8 

451 

450.9 

7.9 

511 

510.9 

9.0 

570.  9 

32 

332. 0 

5.8 

92 

391.  9 

6.8 

52 

451.9 

7.9 

12 

511.9 

9.0 

72 

571.9 

10.0 

33 

333.0 

5.8 

93 

392.  9 

6.9 

53 

452.9 

7.9 

13 

512.9 

9.0 

73 

572.  9 

10.0 

34 

333.9 

5.8 

94 

393.9 

6.9 

54 

453.9 

7.9 

14 

513.9 

9.0 

74 

573.9 

10.0 

35 

334.  9 

5.8 

95 

394.9 

6.9 

55 

454.  9 

7.9 

15 

514.9 

9.0 

75 

574.9 

10.0 

36 

335.9 

5.9 

96 

395.9 

6.9 

56 

455.  9 

8.0 

16 

515.9 

9.0 

76 

575.9 

10.0 

37 

336.9 

5.9 

97 

396.9 

6.9 

57 

456.  9 

8.0 

17 

516.9 

9.1 

77 

576.  9 

10.1 

38 

337.9 

5.9 

98 

397.9 

6.9 

58 

457.9 

8.0 

18 

517.9 

9.1 

78 

577. 9 

10.1 

39 

338.9 

5.9 

99 

398.9 

7.0 

59 

458.9 

8.0 

19 

518.9 

9.1 

79 

578.9 

10.1 

40 
341 

339. 9 
340.9 

5.9 
6.0 

400 
401 

399.9 
400.9 

7.0 

60 

459.9 

8.0 

20 

519.9 
520.9 

9.1 

80 

579.9 

10.1 

7.0 

461 

460.9 

8.0 

521 

9.1 

581 

580.9 

10.1 

42 

341.9 

6.0 

02 

401.9 

7.0 

62 

461.9 

8.1 

22 

521.9 

9.1 

82 

581.9 

10.1 

43 

342.9 

6.0 

03 

402.9 

7.0 

63 

462.  9 

8.1 

23 

522. 9 

9.2 

83 

582.9 

10.2 

44 

343.9 

6.0 

04 

403.  9 

7. 1' 

64 

463.  9 

8.1 

24 

523.  9 

9.2' 

84 

583.9 

10.2 

45 

344.9 

6.0 

05 

404.9 

7. 1 

65 

464.9 

8.1 

25 

524.  9 

9.2 

85 

584.9 

10.2 

46 

345.9 

6.0 

06 

405.9 

■7. 1 

66 

465.9 

8.1 

26 

525.  9 

9.2 

86 

585.9 

10.2 

47 

346.9 

6.1 

07 

406.9 

7. 1 

67 

466.9 

8.1 

27 

526.9 

9.2 

87 

586.9 

10.2 

48 

347.9 

6.1 

08 

407.9 

7. 1 

68 

467.9 

8.2 

28 

527.9 

9.2 

88 

587.9 

10.2 

49 

348.9 

6.1 

09 

408.9 

7. 1 

69 

468.9 

8.2 

29 

528.  9 

9.3 

89 

588. 9 

10.3 

50 
351 

349.9 

6.1 

10 

409.9 

7.2 

70 
471 

469.9 
470.9 

8.2 
8.2 

30 
531 

529.9 

9.3 

90 

589.9 
590.9 

10.3 

350.9 

6.1 

411 

410.9 

7.2 

530.9 

9.3 

591 

10.3 

52 

351.9 

6.1 

12 

411.9 

7.2 

72 

471.9 

8.2 

32 

531.  9 

9.3 

92 

591.  9 

10.3 

53 

352.9 

6.2 

13 

412.9  1     7.2 

73 

472.9 

8.2 

33 

532.9 

9.3 

93 

592.  9 

10.3 

54 

353.9 

6.2 

14 

413.9       7.2 

74 

473.9 

8.3 

34 

533.9 

9.3 

94 

593.9 

10.3 

55 

354. 9 

6.2 

15 

414.9 

7.2 

75 

474.9 

8.3 

35 

534.9 

9.4 

95 

594. 9 

10.4 

56 

355.9 

6.2 

16 

415.  9 

7.3 

76 

475.9 

8.3 

36 

535.  9 

9.4 

96 

595.9 

10.4 

57 

356. 9 

6.2 

17 

416.9 

7.3 

77 

476.  9 

8.3 

37 

536.9 

9.4 

97 

596. 9 

10.4 

58 

357.9 

6.2 

18 

417.9 

7.3 

78 

477.9 

8.3 

38 

537.9 

9.4 

98 

597. 9 

10.4 

59 

358.9 

6.3 

19 

418.9 

7.3 

79 

478.9 

8.4 

39 

538.9 

9.4 

99 

598.9 

10.4 

60 

359.9 

6.3 

20 

419.9 

7.3 

80 

479.9 

8.4 

40 

539.9 

9.4 

600 

599.9 

10.5 

Bist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

39°  (91°,  269° 

,  271°) 

22489—03- 


-24 


Page  370] 

TABLE  2. 

Difference  of  Latitude  and  Depart 

ure  for  2°  (178°,  182 

°,  358°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.0 

61 

61.0 

2.1 

121 

120.9 

4.2 

181 

180.9 

6.3 

241 

240.9 

8.4 

2 

2.0 

0.1 

62 

62.0 

2.2 

22 

121.9 

4.3 

82 

181.9 

6.4 

42 

241.9 

8.4 

3 

3.0 

0.1 

63 

63.0 

2.2 

23 

122.9 

4.3 

83 

182.9 

6.4 

43 

242.9 

8.5 

4 

4.0 

0.1 

64 

64.0 

2.2 

24 

123.9 

4.3 

84 

183.9 

6.4 

44 

243.9 

8.5 

5 

5.0 

0.2 

65 

65.0 

2.3 

25 

124.9 

4.4 

85 

184.9 

6.5 

45 

244.9 

8.6 

6 

6.0 

0.2 

66 

66.0 

2.3 

26 

125.9 

4.4 

86 

185.9 

6.5 

46 

245.9 

8.6 

7 

7.0 

0.2 

«7 

67.0 

2.3 

27 

126.9 

4.4 

87 

186.9 

6.5 

47 

246.8 

8.6 

8 

8.0 

0.3 

68 

68.0 

2.4 

28 

127.9 

4.5 

88 

187.9 

6.6 

48 

247.8 

8.7 

9 

9.0 

0.3 

69 

69.0 

2.4 

29 

128.9 

4.5 

89 

188.9 

6.6 

49 

248.8 

8.7 

10 

10.0 

0.3 

70 

70.0 

2.4 

30 

129.9 

4.5 

90 

189.9 

6.6 

50 

249.8 

8.7 

11 

11.0 

0.4 

71 

71.0 

2.5 

131 

130.9 

4.6 

191 

190.9 

6.7 

251 

250.8 

8.8 

12 

12.0 

0.4 

72 

72.0 

2.5 

32 

131.9 

4.6 

92 

191.9 

6.7 

52 

251.8 

8.8 

13 

13.0 

0.5 

73 

73.0 

2.5 

33 

132.9 

4.6 

93 

192.9 

6.7 

53 

252.8 

8.8 

14 

14.0 

0.5 

74 

74.0 

2.6 

34 

133.9 

4.7 

94 

193.9 

6.8 

54 

253.8 

8.9 

15 

15.0 

0.5 

75 

75.0 

2.6 

35 

134.9 

4.7 

95 

194.9 

6.8 

55 

254.8 

8.9 

16 

16.0 

0.6 

76 

76.0 

2.7 

36 

135.9 

4.7 

96 

195.9 

6.8 

56 

255.8 

8.9 

17 

17.0 

0.6 

77 

77.0 

2.7 

37 

136.9 

4.8 

97 

196.9 

6.9 

57 

256.8 

9.0 

18 

18.0 

0.6 

78 

78.0 

2.7 

38 

137.9 

4.8 

98 

197.9 

6.9 

58 

257.8 

9.0 

19 

19.0 

0.7 

79 

79.0 

2.8 

39 

138.9 

4.9 

99 

198.9 

6.9 

59 

258.8 

9.0 

20 

20.0 

0.7 

80 

80.0 

2.8 

40 

139.9 

4.9 

200 

199.9 

7.0 

60 

259.8 

9.1 

21 

21.0 

0.7 

81 

81.0 

2.8 

141 

140.9 

4.9 

201 

200.9 

7.0 

261 

260.8 

9.1 

22 

22.0 

0.8 

82 

82.0 

2.9 

42 

141.9 

5.0 

02 

201.9 

7.0 

62 

261.8 

9.1 

23 

23.0 

0.8 

83 

82.9 

2.9 

43 

142.9 

5.0 

03 

202.9 

7.1 

63 

262.8 

9.2 

24 

24.0 

0.8 

84 

83.9 

2.9 

44 

143.9 

5.0 

04 

203.9 

7.1 

64 

263.8 

9.2 

25 

25.0 

0.9 

85 

84.9 

3.0 

45 

144.9 

5.1 

05 

204.9 

7.2 

65 

264.8 

9.2 

26 

26.0 

0.9 

86 

85.9 

3.0 

46 

145. 9 

5.1 

06 

205.9 

7.2 

66 

265.8 

9.3 

27 

27.0 

0.9 

87 

86.9 

3.0 

47 

146.9 

5.1 

07 

206.9 

7.2 

67 

266.8 

9.3 

28 

28.0 

1.0 

88 

87.9 

3.1 

48 

147.9 

5.2 

08 

207.9 

7.3 

68 

267.8 

9.4 

29 

29.0 

1.0 

89 

88.9 

3.1 

49 

148.9 

5.2 

09 

208.9 

7.3 

69 

268.8 

9.4 

30 
31 

30.0 
31.0 

1.0 

90 

89.9 
90.9 

3.1 

50 

149.9 

5.2 

10 
211 

209.9 

7.3 

70 

269.8 

9.4 

1.1 

91 

3.2 

151 

150.9 

5.3 

210.9 

7.4 

271 

270.8 

9.5 

32 

32.0 

1.1 

92 

91.9 

3.2 

52 

151.9 

5.3 

12 

211.9 

7.4 

72 

271.  8 

9.5 

33 

33.0 

1.2 

93 

92.9 

3.2 

53 

152.9 

5.3 

13 

212.9 

7.4 

73 

272.8 

9.5 

34 

34.0 

1.2 

94 

93.9 

3.3 

54 

153.9 

5.4 

14 

213.9 

7.5 

74 

273.8 

9.6 

35 

35.0 

1.2 

95 

94.9 

3.3 

55 

154.9 

5.4 

15 

214.9 

7.5 

75 

274.8 

9.6 

36 

36.0 

1.3 

96 

95.9 

3.4 

56 

155.9 

5.4 

16 

215.9 

7.5 

76 

275.8 

9.6 

37 

37.0 

1.3 

97 

96.9 

3.4 

57 

156.9 

5.5 

17 

216.9 

7.6 

77 

276.8 

9.7 

38 

38.0 

1.3 

98 

97.9 

3.4 

58 

157.9 

5.5 

18 

217.9 

7.6 

78 

277.8 

9.7 

39 

39.0 

1.4 

99 

98.9 

3.5 

59 

158.9 

5.5 

19 

218.9 

7.6 

79 

278.8 

9.7 

40 

40.0 

1.4 

100 

99.9 

3.5 

60 

159.9 

5.6 

20 

219.9 

7.7 

80 

279.8 
280.8 

9.8 

9.8 

41 

41.0 

1.4 

101 

100.9 

3.5 

161 

160.9 

5.6 

221 

220.9 

7.7 

281 

42 

42.0 

1.5 

02 

101.9 

3.6 

62 

161.9 

5.7 

22 

221.9 

7.7 

82 

281.8 

9.8 

43 

43.0 

1.5 

03 

102.9 

3.6 

63 

162.9 

5.7 

23 

222.9 

7.8 

83 

282.8 

9.9 

44 

44.0 

1.5 

04 

103.9 

3.6 

64 

163. 9 

5.7 

24 

223.9 

7.8 

84 

283.8 

9.9 

45 

45.0 

1.6 

05 

104.9 

3.7 

65 

164.9 

5.8 

25 

224.9 

7.9 

85 

284.8 

9.9 

46 

46.0 

1.6 

06 

105.9 

3.7 

66 

165.9 

5.8 

26 

225.9 

7.9 

86 

285.8 

10.0 

47 

47.0 

1.6 

07 

106.9 

3.7 

67 

166.9 

5.8 

27 

226.9 

7.9 

87 

286.8 

10.0 

48 

48.0 

1.7 

08 

107.9 

3.8 

68 

167.9 

5.9 

28 

227.9 

8.0 

88 

287.8 

10.1 

49 

49.0 

1.7 

09 

108.9 

3.8 

69 

168.9 

5.9 

29 

228.9 

8.0 

89 

288.8 

10.1 

50 

50.0 

1.7 

10 

109.9 

3.8 

70 

169.9 

5.9 

30 

229.9 

8.0 

90 

289.8 

10.1 
10.  2 

51 

51.0 

1.8 

111 

110.9 

3.9 

171 

170.9 

6.0 

231 

230.9 

8.1 

291 

290.8 

52 

•  52.0 

1.8 

12 

111.9 

3.9 

72 

171.9 

6.0 

32 

231.9 

8.1 

92  i  291.8 

10.2 

53 

53.0 

1.8 

13 

112.9 

3.9 

73 

172.9 

6.0 

33 

232.9 

8.1 

93 

292.8 

10.2 

54 

54.0 

1.9 

14 

113.9 

4.0 

74 

173.9 

6.1 

34 

233.9 

8.2 

94 

293.8 

10.3 

55 

55.0 

1.9 

15 

114.9 

4.0 

75 

174.9 

6.1 

35 

234.9 

8.2 

95 

294.8 

10.3 

56 

56.0 

2.0 

16 

115.9 

4.0 

76 

175.9 

6.1 

36 

235.9 

8.2 

96 

295.8 

10.3 

57 

57.0 

2.0 

17 

116.9 

4.1 

77 

176.9 

6.2 

37 

236.9 

8.3 

97 

296.8 

10.4 

58 

58.0 

2.0 

18 

117.9 

4.1 

78 

177.9 

6.2 

38 

237.9 

8.3 

98 

297.8 

10.4 

59 

59.0 

2.1 

.  19 

118.9 

4.2 

79 

178.9 

6.2 

39 

238.  9 

8.3 

99 

298.8 

10.4 

60 

60.0 

2.1 

20 

119.9 

4.2 

80 

179.9 

6.3 

40 

239.9 

8.4 

300 

299.8 

10.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Jj&t. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

88°  (9 

2°,  268° 

,  272°) 

TABLE  2. 

[Page  371     | 

Difference  of  Latitude  and  Depart 

are  for  2°  (178°,  182 

',  358° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

300.8 

10.5 

361 

360.8 

12.6 

421 

420.8 

14.7 

481 

480.7 

16.8 

541 

540.7 

18.9 

02 

301.8 

10.5 

62 

361.8 

12.6 

22 

421.8 

14.7 

82 

481.7 

16.8 

42 

541.7 

18.9 

03 

302.8 

10.6 

63 

362.8 

12.7 

23 

422.8 

14.7 

83 

482.7 

16.8 

43 

542.7 

18.9 

04 

303.8 

10.6 

64 

363.8 

12.7 

24 

423.8 

14.8 

84 

483.7 

16.9 

44 

543.7 

19.0 

05 

304.8 

10.6 

65 

364.8 

12.7 

25 

424.8 

14.8 

85 

484.7 

16.9 

45 

544.7 

19.0 

06 

305.8 

10.7 

66 

365.8 

12.8 

26 

425.  7 

14.9 

86 

485.7 

16.9 

46 

545.7 

19.0 

07 

306.8 

10.7 

67 

366.8 

12.8 

27 

426.7 

14.9 

87 

486.7 

17.0 

47 

546.7 

19.1 

08 

307.8 

10.7 

68 

367.  8 

12.8 

28 

427.7 

14.9 

88 

487.7 

17.0 

48 

547.7 

19.1 

09 

308.8 

10.8 

69 

368.8 

12.9 

29 

428.7 

15.0 

89 

488.7 

17.0 

49 

548.7 

19.1 

10 

309.8 

10.8 

70 

369.8 
370.8 

12.9 
12.9 

30 

429.7 

15.0 

90 

489.7 

17.1 

50 

549.7 

19.2 

311 

310.8 

10.8 

371 

431 

430.7 

15.0 

491 

490.7 

17.1 

551 

550.7 

19.2 

12 

311.8 

10.9 

72 

371.8 

13.0 

32 

431.7 

15.1 

92 

491.7 

17.1 

52 

551.7 

19.2 

13 

312.8 

10.9 

73 

372.8 

13.0 

33 

432.7 

15.1 

93 

492.7 

17.2 

53 

552.7 

19.3 

14 

313.8 

10.9 

74 

373.8 

13.0 

34 

433.7 

15.1 

94 

493.7 

17.2 

54 

553.7 

19.3 

15 

314.8 

11.0 

75 

374.8 

13.1 

35 

434.7 

15.2 

95 

494.7 

17.2 

55 

554.7 

19.3 

16 

315.8 

11.0 

76 

375.8 

13.1 

36 

435.7 

15.2 

96 

495.7 

17.3 

56 

555.7 

19.4 

17 

316.8 

11.0 

77 

376.8 

13.1 

37 

436.7 

15.2 

97 

496.7 

17.3 

57 

556.7 

19.4 

18 

317.8 

11.1 

78 

377.8 

13.2 

38 

437.7 

15.3 

98 

497.7 

17.3 

58 

557.7 

19.4 

19 

318.8 

11.1 

79 

378.8 

13.2 

39 

438.7 

15.3 

99 

498.7 

17.4 

59 

558.7 

19.5 

20 

319.8 

11.2 

80 

379.8 

13.2 
13.3 

40 
441 

439.7 

15.3 

500 

499.7 

17.4 

60 

559.7 

19.5 
19.5 

321 

320.8 

11.2 

381 

380.8 

440.7 

15.4 

501 

500.7 

17.5 

561 

560.7 

22 

321.8 

11.2 

82 

381.8 

13.3 

42 

441.7 

15.4 

02 

501.7 

17.5 

62 

561.7 

19.6 

23 

322.8 

11.3 

83 

382.8 

1.3.3 

43 

442.7 

15.4 

03 

502.7 

17.5 

63 

562.7 

19.6 

24 

323.8 

11.3 

84 

383.8 

13.4 

44 

443.7 

15.5 

04 

503.7 

17.6 

64 

563.7 

19.6 

25 

324.8 

11.3 

85 

384.8 

13.4 

45 

444.7 

15.5 

05 

504.7 

17.6 

65 

564.7 

19.7 

26 

325.8 

11.4 

86 

385.8 

13.5 

46 

445.7 

15.6 

06 

505.7 

17.6 

66 

565.7 

19.7 

27 

326.8 

11.4 

87 

386.8 

13.5 

47 

446.7 

15.6 

07 

506.7 

17.7 

67 

566.7 

19.7 

28 

327.8 

n.4 

88 

387.8  1  13.5 

48 

447.7 

15.6 

08 

507.7 

17.7 

68 

567.7 

19.8 

29 

328. 8 

11.5 

89 

388.8  !  13.6 

49 

448.7 

15.7 

09 

508.7 

17.7 

69 

568.  7 

19.8 

30 

329.8 

11.5 

90 

389.8 
390.8 

13.6 

50 

449.7 
450.7 

15.7 

10 

509.7 

17.8 

70 

569.7 

19.9 

331 

330.8 

11.5 

391 

13.6 

451 

15.7 

511 

510.7 

17.8 

571 

570.7 

19.9 

32 

331.8 

11.6 

92 

391.  8  1  13.  7 

52 

451.7 

15.8 

12 

511.7 

17.8 

72 

571.7 

19.9 

33 

332.8 

11.6 

93 

392.8  '  13.7 

53 

452.7 

15.8 

13 

512.7 

17.9 

73 

572.7 

20.0 

34 

333.8 

11.6 

94 

393.  8     13.  7 

54 

453.7 

15.8 

14 

513.7 

17.9 

74 

573.6 

20.0 

35 

334.8 

11.7 

95 

394.  8     13.  8 

55 

454.7 

15.9 

15 

514.7 

17.9 

75 

574.6 

20.0 

36 

.335.  8 

11.7 

96 

395.8  j  13.8 

56 

455.7 

15.9 

16 

515.7 

18.0 

76 

575. 6 

20.1 

37 

336.8 

11.7 

97 

396.8  I  13.8 

57 

456.7 

15.9 

17 

516.7 

18.0 

77 

576.6 

20.1 

38 

337.8 

11.8 

98 

397.8  i  13.9 

58 

457.7 

16.0 

18 

517.7 

18.1 

78 

577.6 

20.1 

39 

338.8 

11.8 

99 

398.8  1  13.9 

59 

458.  7 

16.0 

19 

518.7 

18.1 

79 

578.6 

20.2 

40 

339.8 

11.9 

400 

399.8  !  13.9 

60 

459.7 

16.0 

20  1  519.7 

18.1 

80 

579.6 

20.2 

341 

340.8 

11.9 

401 

400.8  1  14.0 

461 

460.7 

16.1 

521  '■  520.  7 

18.2 

581 

580.6 

20.2 

42 

341.8 

11.9 

02 

401.8  i  14.0 

62 

461.7 

16.1 

22 

521.7 

18.2 

82 

581.6 

20.3 

43 

342.8 

12.0 

03 

402.8  1  14.0 

63 

462.7 

16.1 

23 

522.7 

18.2 

83 

582.6 

20.3 

44 

343.8 

12.0 

04 

403.8  !  14.1 

64 

463.  7 

16.2 

24 

523.7 

18.3 

84 

583.6 

20.3 

45 

344.8 

12.0 

05 

404.  8     14. 1 

65 

464.7 

16.2 

25 

524.  7 

18.3 

85 

584.6 

20.4 

46 

345.8 

12.1 

06 

405.8 

14.2 

66 

-165.7 

16.2 

26  j  525. 7 

18.4 

86 

585.6 

20.4 

47 

346.8 

12.1 

07 

406.8 

14.2 

67 

466.7 

16.3 

27  1  526.7 

18.4 

87 

586.6 

20.4 

48 

347. 8 

12.1 

08 

407.8 

14.2 

68 

467.7 

16.3 

28     527. 7 

18.4 

88 

587.6 

20.5 

49 

348.8 

12.2 

09 

408.8 

14.3 

69 

468.7 

16.4 

29     528. 7 

18.5 

89 

588.6 

20.5 

50 

349.8 

12.2 

10     409. 8 

14.3 

70 

469.7 

16.4 

30  !  529. 7 

18.5 

90 

589.6 

20.5 

351 

350.8 

12.2 

411 

410.8 

14.3 

471 

470.7 

16.4 

531 

530.7 

18.5 

591 

590.6 

20.6 

52 

351.8 

12.3 

12 

411.8 

14.4 

72 

471.  7 

16.5 

32 

531.7 

18.6 

92 

591.6 

20.6 

53 

352.8 

12.3 

13 

412.8 

14.4 

73 

472.7 

16.5 

33 

532.7 

18.6 

93 

592.6 

20.6 

54 

353.8 

12.3 

14 

413.8 

14.4 

74 

473.7 

16.5 

34 

533.7 

18.6 

94 

593.6 

20.7 

55 

354.8 

12.4 

15     414.8 

14.5 

•/5 

474.7 

16.6 

35 

534.7 

18.7 

95 

594.6 

20.7 

56 

355.8 

12.4 

16     415. 8 

14.5 

76 

475.  7 

16.6 

36 

535.7 

18.7 

96 

595.6 

20.7 

57 

356.8 

12.4 

17     416.8 

14.5 

77 

476.7 

16.6 

37 

536.  7 

18.7 

97 

596.6 

•20.8 

58 

357.8 

12.5 

18     417.8 

14.6 

78 

477.7 

16.7 

38 

537.  7 

18.8 

98 

597. 6 

20.8 

59 

358.8 

12.5 

19     418. 8 

14.6 

79 

478.7 

16.7 

39 

538.  7 

18.8 

99 

598.6 

20.8 

60 

359.8 

12.5 

20  1  419.8 

1 

14.6 

80 

479.7 

16.7 

40 

539.  7 

18.8 

600 

599.6 

20.9 

Dist. 

Dep. 

Lat. 

Dist.  1    Dep.         Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

88°  {{ 

)2°,  268' 

>     979°  ^ 

)   -' - 

. 

Page  372] 

'1 

ABLP 

I  '2. 

Difference  of  Latitude  and  Departure  for  3°  (177°,  183 

°,  357° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

'    Dep. 

Dist. 

Lat. 

Dep. 

Dist.  i     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.9 

3.2 

121 

120.8 

6.3 

181 

180.8 

9.5 

241 

240.7 

12.6 

2 

2.0 

0.1 

62 

61.9 

3.2 

22 

121.8 

6.4 

82 

181.8 

9.5 

42 

241.7 

12.7 

3 

3.0 

0.2 

63 

62.9 

3.3 

23 

122.8 

6.4 

83 

182.7 

9.6 

43 

242.7 

12.7 

4 

4.0 

0.2 

64 

63.9 

3.3 

24 

123.8 

6.5 

84 

183.7 

9.6 

44 

243.7 

12.8 

5 

5.0 

0.3 

65 

64.9 

3.4 

25 

124.8 

6.5 

85 

184.7 

9.7 

45 

244.7 

12.8 

6 

6.0 

0.3 

^ 

65.9 

3.5 

26. 

125.8 

6.6 

86 

185.7 

9.7 

46 

245.7 

12.9 

7 

7.0 

0.4 

66.9 

3.5 

27 

126.8 

6.6 

87 

186.7 

9.8 

47 

246.7 

12.9 

8 

8.0 

0.4 

68 

67.9 

3.6 

28 

127.8 

6.7 

88 

187.7 

9.8 

48 

247.7 

13.0 

9 

9.0 

0.5 

69 

68.9 

3.6 

29 

128.8 

6.8 

89 

188.7 

9.9 

49 

248.7 

13.0 

10 

10.0 

0.5 

70 

69.9 

3.7 

30 

129.8 

6.8 

90 

189.7 

9.9 

50 

249.7 

13.1 

11 

11.0 

0.6 

71 

70.9 

3.7 

131 

130.8 

6.9 

191 

190.7 

10.0 

251 

250.7 

13.1 

12 

12.0 

0.6 

72 

71.9 

3.8 

32 

131.8 

6.9 

92 

191.7 

10.0 

52 

251.7 

13.2 

13 

13.0 

0.7 

73 

72.9 

3.8 

33 

132.8 

7.0 

93 

192.7 

10.1 

53 

252.  7 

13.2 

14 

14.0 

0.7 

74 

73.9 

3.9 

34 

133.8 

7.0 

94 

193.7 

10.2 

54 

253.7 

13.3 

15 

15.0 

0.8 

75 

74.9 

3.9 

35 

134.8 

7.1 

95 

194.7 

10.2 

55 

254.7 

13.3 

16 

16.0 

0.8 

76 

75.9 

4.0 

36 

135.8 

7.1 

96 

195.7 

10.3 

56 

255.  6 

13.4 

17 

17.0 

0.9 

77 

76.9 

4.0 

37 

136.  8 

7.2 

97 

196.7 

10.3 

57 

256.6 

13.5 

18 

18.0 

0.9 

78 

77.9 

4.1 

38 

137.8 

7.2 

98 

197.7 

10.4 

58 

257.6 

13.5 

19 

19.0 

1.0 

79 

78.9 

4.1 

39 

138.8 

7.3 

99     198.7 

10.4 

59 

258.6 

13.6 

20 

20.0 

1.0 

80 

79.9 

4.2 

40 

139.8 

7.3 

200     199.7 

10.5 

60 

259.6 

13.6 

21 

21.0 

1.1 

81 

80.9 

4.2 

141 

140.8 

7.4 

201 

200.7 

10.5 

261 

260.6 

13.7 

22 

22.0 

1.2 

82 

81.9 

4.3 

42 

141.8 

7.4 

02 

201.7 

10.6 

62 

261.6 

13.7 

23 

23.0 

1.2 

83 

82.9 

4.3 

43 

142.8 

7.5 

03 

202.7 

10.6 

63 

262.6 

13.8 

24 

24.0 

1.3 

84 

83.9 

4.4 

44 

143.8 

7.5 

04 

203.7 

10.7 

64 

263.6 

13.8 

25 

25.0 

1.3 

85 

84.9 

4.4 

45 

144.8 

7.6 

05 

204.7 

10.7 

65 

264.6 

13.9 

26 

26.0 

1.4 

86 

85.9 

4.5 

46 

145.8 

7.6 

06 

205.  7 

10.8 

66 

265.  6 

13.9 

27 

27.0 

1.4 

87 

86.9 

4.6 

47 

146.8 

7.7 

07 

206.7 

10.8 

67 

266.6 

14.0 

28 

28.0 

1.5 

88 

87.9 

4.6 

48 

147.8 

7.7 

08 

207.7 

10.9 

68 

267.6 

14.0 

29 

29.0 

1.5 

89 

88.9 

4.7 

49 

148.8 

7.8 

09 

208.7 

10.9 

69 

268.6 

14.1 

30 

30.0 

1.6 

90 

89.9 
90.9 

4.7 
4.8 

50 

149.8 

7.9 

10 

209.7 

11.0 

70 

269.6 
270.6 

14.1 

31 

31.0 

1.6 

91 

151 

150.8 

7.9 

211 

210.7 

11.0 

271 

14.2 

32 

32.0 

1.7 

92 

91.9 

4.8 

52 

151.8 

8.0 

12 

211.7 

11.1 

72 

271.6 

14.2 

33 

33.0 

1.7 

93 

92.9 

4.9 

53 

152.8 

8.0 

13 

212.7 

11.1 

73 

272.6 

14.3 

34 

34.0 

1.8 

94 

93.9 

4.9 

54 

153.8 

8.1 

14 

213.7 

11.2 

74 

273.6 

14.3 

35 

35.0 

1.8 

95 

94.9 

5.0 

55 

154.8 

8.1 

15 

214.7 

11.3 

75 

274.6 

14.4 

36 

36.0 

1.9 

96 

95.9 

5.0 

56 

155.8 

8.2 

16 

215.7 

11.3 

76 

275.6 

14.4 

37 

36.9 

1.9 

97 

96.9 

5.1 

57 

156.8 

8.2 

17 

216.7 

11.4 

77 

276.6 

14.5 

38 

37.9 

2.0 

98 

97.9 

5.1 

58 

157.8 

8.3 

18 

217.7 

11.4 

78 

277.6 

14.5 

39 

38.9 

2.0 

99 

98.9 

5.2 

59 

158.  8 

8.3 

19 

218.7 

11.5 

79 

278.6 

14.6 

40 

39.9 

2.1 

100 

99.9 
100.9 

5.2 

60 

159.8 

8.4 

20 

219.7 

11.5 
11.6 

80 
281 

279.6 
280. 6 

14.7 

41 

40.9 

2.1 

101 

5.3 

161 

160.8 

8.4 

221 

220.7 

14.7 

42 

41.9 

2.2 

02 

101.9 

5.3 

62 

161.8 

8.5 

22 

221.7 

11.6 

82 

281.6 

14.8 

43 

42.9 

2.3 

03 

102.9 

5.4 

63 

162.8 

8.5 

23 

222.7 

11.7 

83 

282.6 

14.8 

44 

43.9 

2.3 

04 

103.9 

5.4 

64 

163.8 

8.6 

24 

223.7 

11.7 

84 

283.6 

14.9 

45 

44.9 

2.4 

05 

104.9 

5.5 

65 

164.8 

8.6 

25 

224.7 

11.8 

85 

284.6 

14.9 

46 

45.9 

2.4 

06 

105.9 

5.5 

66 

165.8 

8.7 

26 

225.7 

11.8 

86 

285.  6 

15.0 

47 

46.9 

2.5 

07 

106.9 

5.6 

67 

166.8 

8.7 

27 

226.7 

11.9 

87 

286.6 

15.0 

48 

47.9 

2.5 

08 

107.9 

5.7 

68 

167.8 

8.8 

28 

227.7 

11.9 

88 

287.6 

15.1 

49 

48.9 

2.6 

09 

108.9 

5.7 

69 

168.8 

8.8 

29 

228.7 

12.0 

89 

288.6 

15.1 

50 

49.9 

2.6 

10 

109.8 

5.8 

70 

169.8 
170.8 

8.9 

30 

229.7 
230.7 

12.0 

90 
291 

289.6 
290.6 

15.2 

51 

50.9 

2.7 

111 

110.8 

5.8 

171 

8.9 

231 

12.1 

15.2 

52 

51.9 

2.7 

12 

111.8 

5.9 

72 

171.8 

9.0 

32 

231.7 

12.1 

92 

291.6 

15.3 

53 

52.9 

2.8 

13 

112.8 

5.9 

73 

172.8 

9.1 

33 

232.7 

12.2 

93 

292.6 

15.3 

54 

53.9 

2.8 

14 

113.8 

6.0 

74 

173.8 

9.1 

34 

233.  7 

12.2 

94 

293.6 

15.4 

55 

54.9 

2.9 

15 

114.8 

6.0 

75 

174.8 

9.2 

35 

234.7 

12.3 

95 

294.6 

15.4 

56 

55.9 

2.9 

16 

115.8 

6-i 

76 

175.8 

9.2 

36 

235.  7 

12.4 

96 

295.  6 

15.5 

57 

•    56.9 

3.0 

17 

116.8 

6.i 

77 

176.  8 

9.3 

37 

236.7 

12.4 

97 

296.6 

15.5 

58 

57.9 

3.0 

18 

117.8 

6.2 

78 

177.8 

9.3 

38 

237.7 

12.5 

98 

297.6 

15.6 

59 

58.9 

3.1 

19 

118.8 

6.2 

79 

178.8 

9.4 

39 

238.7 

12.5 

99 

298.6 

15.6 

60 

59.9 

3.1 

20 

119.8 

6.3 

80 

179.8 

9.4 

40 

239.7 

12.6 

300 

299.6 

15.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

87°  {i 

)3°,  267' 

',  273°] 

. 

TABLE  2. 

[Page  373    | 

Difference  of  Latitude  and  Departure  for  3°  (177°,  183°,  357° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 
360.  5 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

301 

300.6 

15.7 

361 

18.9 

421 

420.4 

22.0 

481 

480.3  !  25.2 

541 

540.2 

28.3 

02 

301.6 

15.8 

62 

361.5 

19.0 

22 

421.4 

22.1 

82 

481.3 

25.2 

42 

541.2 

28.4 

03 

302.6 

15.9 

63 

362.5 

19.0 

23 

422.  4, 

22.2 

83 

482.3 

25.3 

43 

542.2 

28.4 

04 

303.5 

15.9 

64 

363.5 

19.1 

24 

423.4 

22.2 

84 

483.3 

25.3 

44 

543.2 

28.5 

05 

304.5 

16.0 

65 

364.5 

19.1 

25 

424.4 

22.3 

85 

484.3  ;  25.4 

45 

544.2 

28.5 

06 

305.5 

16.0 

66 

365.  5 

19.2 

26 

425.4 

22.3 

86 

485.3     25.4 

46 

545.2 

28.6 

07 

306.5 

16.1 

67 

366.5 

19.2 

27 

426.4 

22.4 

87 

486. 3     25. 5 

47 

546.2 

28.6 

08 

307.5 

16.1 

68 

367.5 

19.3 

28 

427.4 

22.4 

88 

487.  3     25. 5 

48 

547.2 

28.7 

09 

308.5 

16.2 

69 

368.5 

19.3 

29  '  428.4 

22.5 

89 

488.  3     25.  6 

49 

548.2 

28.7 

10 
311 

309.5 
310.  5 

16.2 
16.3 

70 

369.5 

19.4 
19.4 

30     429. 4 
431     430. 4 

22.5 

90 

489.3 
490.3 

25.6 

50 

549.  2 

28.8 

371 

370.5 

22.6 

491 

25.7 

551 

550.2 

28.8 

12 

311.5 

16.3 

72 

371.5 

19.5 

32     431. 4 

22.6 

92 

491.3  1  25.7 

52 

551.2 

28.9 

13 

312.5 

16.4 

73 

372.5 

19.5 

33     432.4 

22.  7 

93 

492.3  1  25.8 

53 

552.2 

28.9 

14 

313. 5 

16.4 

74 

373.5 

19.6 

34 

433.  4 

22.7 

94 

493.3 

25.9 

54 

553.  2 

29.0 

15 

314.5 

16.5 

75 

374.5 

19.6 

35 

434.4 

22.8 

95 

494.3 

25.9 

55 

554.2 

29.1 

16 

315.5 

16.6 

76 

375.5 

19.7 

36 

435.4 

22.8 

96 

495.3 

26.0 

56 

555.2 

29.1 

17 

316.5 

16.6 

77 

376.5 

19.8 

37 

436.4 

22.9 

97 

496.3  '  26.0 

57 

556.2 

29.2 

18 

317.5 

16.7 

78 

377.4 

19.8 

38 

437.4 

22.9 

98 

497.  3  i  26. 1 

58 

557.2 

29.2 

19 

318.5 

16.7 

79 

378.4 

19.9 

39 

438.4 

23.0 

99 

498.3     26.1 

59 

558.2 

29.3 

20 

319.5 

16.8 
16.8 

80 

379.  4 
380.4 

19.9 

40 

439.4 

23.0 

500 
501 

499.3  1  26.2 
500.3     26.2 

60 
561 

559.2 
560.2 

29.3 
29.4 

321 

320.5 

381 

20.0 

441 

440.4 

23.1 

22 

321.5 

16.9 

82 

381.4 

20.0 

42 

441.4 

23.1 

02 

501.3     26.3 

62 

561.2 

29.4 

23 

322.5 

16.9 

83 

382.4 

20.1 

43 

442.4 

23.2 

03 

502.3     26.3 

63 

562.2 

29.5 

24 

323.5 

17.0 

84 

383.4 

20.1 

44 

443.4 

23.  3 

04 

503.3     26.4 

64 

563.2 

29.5 

25 

324.5 

17.0 

85 

384.  4 

20.2 

45 

444.4 

23.3 

05 

504.3     26.4 

65 

564.2 

29.6 

26 

325.5 

17.1 

86 

385.4 

20.2 

46 

445.  4 

23.4 

06 

505.3  1  26.5 

66 

565.2 

29.6 

27 

326.5 

17.1 

87 

386.4 

20.3 

47 

446.4 

23.4 

07 

506.3     26.5 

67 

566.2 

29.7 

28 

327.5 

17.2 

88 

387.4 

20.3 

48 

447.4 

23.5 

08 

507.3  '  26.6 

68 

567.2 

29.7 

29 

328.5 

17.2 

89 

388.4 

20.4 

49 

448.4 

23.5 

09 

508.3     26.6 

69 

568.2 

29.8 

30 

329.5 

17.3 

90 

389.4 

20.4 

50 

449.3 
450.3 

23.6 

10 

509.3     26.7 

70 

569.2 

29.8 
29.9" 

331 

330.5 

17.3 

391 

390.  4 

20.5 

451 

23.6 

511  j  510.  3  i  26.  7 

571 

570.2 

32 

331.5 

17.4 

92 

391.4 

20.5 

52 

451.3 

23.  7 

12  1  511.3  '  26.8 

72 

571.2 

29.9 

33 

332.5 

17.5 

93 

392.4 

20.6 

53 

452.3 

23.7 

13 

512.3 

26.8 

73 

572.2 

30.0 

34 

333.  5 

17.5 

94 

393.4 

20.6 

54 

453.  3 

23.8 

14 

513.3 

26.9 

74 

573.2 

30.0 

35 

334.5 

17.6 

95 

394.4 

20.7 

55 

454.3 

23.8 

15 

514.3 

27.0 

75 

574.2 

30.1 

36. 

335.5 

17.6 

96 

395.4 

20.7 

56 

455.  3 

23.9 

16 

515.3 

27.0 

76 

575.2 

30.1 

37 

336.  5 

17.7 

97 

396.4 

20.8 

57 

456.3 

23.9 

17 

516.3 

27.1 

77 

576.2 

30.2 

38 

337. 5 

17.7 

98 

397.4 

20.8 

58 

457.  3 

24.0 

18 

517.3 

27.1 

78 

577.2 

30.2 

39 

338.5 

17.8 

99 

398.4 

20.9 

59 

458.3 

24.0 

19 

518.3 

27.2 

79 

578.2 

30.3 

40 

339.5 

17.8 

400 

399.  4 
400.4 

20.9 
21.0 

60 

459.  3 

24.1 

20 
521 

519.3 
520.3 

27.2 

80 

579.2 

30.3 

341 

340. 5 

17.9 

401 

461 

460.  3 

24.1 

27.3 

581 

580.2 

30.4 

42 

341.5 

17.9 

02 

401.4 

21.1 

62 

461.3 

24.2 

22  1  521.  3 

27.3 

82 

581.2 

30.4 

43 

342.5 

18.0 

03 

402.4 

21.1 

63 

462.  3 

24.2 

23     522.3 

27.4 

83 

582.2 

30.5 

44 

343.5 

18.0 

04 

403.4 

21.2 

64 

463.  3 

24.3 

24  i  523.3 

27.4 

84 

583.2 

30.5 

45 

344.5 

18.1 

05 

404.4 

21.2 

65 

564.  3 

24.4 

25  i  524.3 

27.5 

85 

584.2 

30.6 

46 

345.5 

18.1 

06 

405.4 

21.3 

66 

465.  3 

24.4 

26  1  525.3 

27.5 

86 

585. 2 

30.6 

47 

346.5 

18.2 

07 

406.4 

21.3 

67 

466.  3 

24.5 

27 

526.3 

27.6 

87 

586.2 

30.7 

48 

347.5 

18.2 

08 

407.4 

21.4 

68 

467.3 

24.5 

28 

527.3 

27.6 

88 

587.2 

30.7 

49 

348.5 

18.3 

09 

408.4 

21.4 

69 

468.3 

24.6 

29 

528.3 

27.7 

89 

588.2 

30.8 

50 

349.5 
'350.5 

18.3 
18.  4 

10 

409.4 

21.5 
21.5 

70 

469.3 

24.6 
24.7 

30 
531 

529.3 
530.3 

27.7 
27.8 

90 
591 

589.2 
590.2 

30.9 

351 

411 

410.4 

471 

470.3 

30.9 

52 

351.5 

18.4 

12 

411.4 

21.6 

72 

471.3 

24.7 

32 

531.3 

27.8 

92 

591.2 

31.0 

53 

352.5 

18.5 

13 

412.4 

21.6 

73 

472.3 

24.8 

33 

532.3 

27.9 

93 

592.2 

31.0 

54 

353.5 

18.5 

14 

413.4 

21.7 

74 

473.  3 

24.8 

34 

533.3 

27.9 

94 

593.2 

31.1 

55 

354.5 

18.6 

15 

414.4 

21.7 

75 

474.3 

24.9 

35 

534.3 

28.0 

95 

594.2 

31.1 

56 

355.5 

18.6 

16 

415.4 

21.8 

76 

475.  3 

24.9 

36 

535.  3 

28.1 

96 

595.2 

31.2 

57 

356.5 

18.7 

17 

416.4 

21.8 

77 

476.  3 

25.0 

37 

536.3 

28.1 

97 

596.2 

31.2 

58 

357.5 

18.8 

18 

417.4 

21.9 

78 

477.3 

25.0 

38 

537.3 

28.2 

98 

597.2 

31.3 

59 

358.  5 

18.8 

19 

418.4 

21.9 

79 

478.  3 

25.1 

39 

538.3 

28.2 

99 

598.2 

31.3 

60 

359.5 

18.9 

20 

419.4 

22.0 

80 

479.3 

25.1 

40 

,539.3 

28.3 

600 

599.2 

31.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

87°  (93°,  267= 

,  273°) 

Page  374J 

r 

rABLE  2. 

Difference  of  Latitude  and 

Depart! 

cirefor4°   (176°,  184 

°,  356° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.9 

4.3 

121 

120.7 

8.4 

181 

180.6 

12.6 

241 

240.4 

16.8 

2 

2.0 

0.1 

62 

61.8 

4.3 

22 

121.7 

8.5 

82 

181.6 

12.7 

42 

241.4 

16.9 

3 

3.0 

0.2 

63 

62.8 

4.4 

23 

122.7 

8.6 

83 

182.6 

12.8 

43 

242.4 

17.0 

4 

4.0 

0.3 

64 

63.8 

4.5 

24 

123.7 

8.6 

84 

183.6 

12.8 

44 

243.4 

17.0 

5 

5.0 

0.3 

65 

64.8 

4.5 

25 

124.7 

8.7 

85 

184.5 

12.9 

45 

244.4 

17.1 

6 

6.0 

0.4 

^ 

65.8 

4.6 

26 

125.7 

8.8 

86 

185.5 

13.0 

46 

245.4 

17.2 

7 

7.0 

0.5 

66.8 

4.7 

27 

126.7 

8.9 

87 

186.5 

13.0 

47 

246.4 

17.2 

8 

8.0 

0.6 

68 

67.8 

4.7 

28 

127.7 

8.9 

88 

187.5 

13.1 

48 

247.4 

17.3 

9 

9.0 

0.6 

69 

68.8 

4.8 

29 

128.7 

9.0 

89  i  188.5 

13.2 

49 

248.4 

17.4 

10 

10.0 

0.7 

70 

69.8 
70.8 

4.9 

30 

129.7 

9.1 

90 

189.5 
190. 5" 

13.3 
13.3 

50 

249.4 

17.4 

11 

11.0 

0.8 

71 

5.0 

131 

130.7 

9.1 

191 

251 

2.50.  4 

17.5 

12 

12.0 

0.8 

72 

71.8 

5.0 

32 

131.7 

9.2 

92 

191.5 

13.4 

52 

251.4 

17.6 

13 

13.0 

0.9 

73 

72.8 

5.1 

33 

132.7 

9.3 

93 

192.5 

13.5 

53 

252.4 

17.6 

14 

14.0 

1.0 

74 

73.8 

5.2 

34 

133.7 

9.3 

94 

193.5 

13.5 

54 

253.4 

17.7 

15 

15.0 

1.0 

75 

74.8 

5.2 

35 

134.7 

9.4 

95 

194.5 

13.6 

55 

254.  4 

17.8 

16 

16.0 

1.1 

76 

75.8 

5.3 

36 

135.7 

9.5 

96 

195.5 

13.7 

56 

255.4 

17.9 

17 

17.0 

1.2 

77 

76.8 

5.4 

37 

136.7 

9.6 

97 

196.5 

13.7 

57 

256. 4 

17.9 

18 

18.0 

1.3 

78 

77.8 

5.4 

38 

137.7 

9.6 

98 

197.5 

13.8 

58 

257.4 

18.0 

19 

19.0 

1.3 

79 

78.8 

5.5 

39 

138.7 

9.7 

99 

198.  5 

13.9 

59 

258.4 

18.1 

20 

20.0 

1.4 

80 

79.8 

5.6 

40 

139.  7 

9.8 

200 

199.5 
200.5 

14.0 

60 

259.  4 

18.1 
18.2 

21 

20.9 

1.5 

81 

80.8 

5.7 

141 

140.7 

9.8 

201 

14.0 

261 

260.4 

22 

21.9 

1.5 

82 

81.8 

5.7 

42 

141.7 

9.9 

02 

201.5 

14.1 

62 

261.4 

18.3 

23 

22.9 

1.6 

83 

82.8 

5.8 

43 

142.7 

10.0 

03 

202. 5 

14.2 

63 

262.4 

18.3 

24 

23.9 

1.7 

84 

83.8 

5.9 

44 

143.6 

10.0 

04 

203.5 

14.2 

64 

263.4 

18.4 

25 

24.9 

1.7 

85 

84.8 

5.9 

45 

144.6 

10.1 

05 

204.5 

14.3 

65 

264.4 

18.5 

26 

25.9 

1.8 

86 

85.8 

6.0 

46 

145.6 

10.2 

06 

205.5 

14.4 

66 

265.  4 

18.6 

27 

26.9 

1.9 

87 

86.8 

6.1 

47 

146.6 

10.3 

07  i  206.5 

14.4 

67 

266.3 

18.6 

28 

27.9 

2.0 

88 

87.8 

6.1 

48 

147.6 

10.3 

08 

207.5 

14.5 

68 

267.3 

18.7 

29 

28.9 

2.0 

89 

88.8 

6.2 

49 

148.6 

10..4 

09 

208.5 

14.6 

69 

268.3 

18.8 

30 
31 

29.9 

2.1 

90 

89.8 

6.3 
6.3 

50 
151 

149.6 

10.5 

10 

209.5 

14.6 

70 
271 

269.3 
270.3 

18.8 
18.9 

30.9 

2.2 

91 

90.8 

150.6 

10.5 

211 

210.5 

14.7 

82 

31.9 

2.2 

92 

91.8 

6.4 

52 

151.6 

10.6 

12 

211.5 

14.8 

72 

271.3 

19.0 

33 

32.9 

2.3 

93 

92.8 

6.5 

53 

1.52.  6 

10.7 

13 

212.5 

14.9 

73 

272.3 

19.0 

34 

33.9 

2.4 

94 

93.8 

6.6 

54 

153.  6 

10.7 

14 

213.  5 

14.9 

74 

273.3 

19.1 

35 

34.9 

2.4 

95 

94.8 

6.6 

55 

154.6 

10.8 

15 

214.5 

15.0 

75 

274.3 

19.2 

36 

35.9 

2.5 

96 

95.8 

6.7 

56 

155.6 

10.9 

16 

215.  5 

15.1 

76 

275.3 

19.3 

37 

36.9 

2.6 

97 

96.8 

6.8 

57 

156.6 

11.0 

17 

216.5 

15.1 

77 

276.3 

19.3 

38 

37.9 

2.7 

98 

97.8 

6.8 

58 

157.  6 

11.0 

18 

217.  5 

15.2 

78 

277.3 

19.4 

39 

38.9 

2.7 

99 

98.8 

6.9 

59 

158.6 

11.1 

19 

218.5 

15.3 

79 

278.3 

19.5 

40 

39.9 

2.8 

100 

99.8 

7.0 

60 

159.6 
160.6 

11.2 

20 

219.5 

15.  3 
lb.  4: 

80 
281 

279.3 

19.5 

41 

40.9 

2.9 

101 

100.8 

7.0 

161 

11.2 

221 

220.5 

280.3 

19.6 

42 

41.9 

2.9 

02 

101.8 

7.1 

62 

161.6 

11.3 

22 

221.5 

1.5.5 

82 

281.3 

19.7 

43 

42.9 

3.0 

03 

102.7 

7.2 

63 

162.6 

11.4 

23 

222.5 

15.6 

83 

282.3 

19.7 

44 

43.9 

3.1 

04 

103.7 

7.3 

64 

163.6 

11.4 

24 

223. 5 

15.6 

84 

283.3 

19.8 

45 

44.9 

3.1 

05 

104.7 

7.3 

65 

164.6 

11.5 

25 

224.5 

1.5.7 

85 

284.  3 

19.9 

46 

45.9 

3.2 

06 

105.7 

7.4 

66 

165.6 

11.6 

26 

225.4 

15.8 

86 

285.  3 

20.0 

47 

46.9 

3.3 

07 

106.7 

7.5 

67 

166.6 

11.6 

27 

226.4 

15.8 

87 

286.3 

20.0 

48 

47.9 

3.3 

08 

107.7 

7.5 

68 

167.  6 

11.7 

28 

227.4 

15.9 

88 

287.3 

20.1 

49 

48.9 

3.4 

09 

108.7 

7.6 

69 

168.6 

11.8 

29 

228.4 

16.0 

89 

288.3 

20.2 

50 

49.9 

3.5 

10 

109.7 

7.7 
7.7 

70 
171 

169.6 

11.9 

30 

229.4 
230.4 

16.0 

90 
291 

289.  3 

20.2 

51 

50.9 

3.6 

111 

110.7 

170.6 

11.9 

231 

16.1 

290.3 

20.3 

52 

51.9 

3.6 

12 

111.7 

7.8 

72 

171.6 

12.0 

32 

231.4 

16.2 

92 

291.  3 

20.4 

53 

52.9 

3.7 

13 

112.7 

7.9 

73 

172.6 

12.1 

33 

232.4 

16.3 

93 

292.3 

20.4 

54 

53.9 

3.8 

14 

113.7 

8.0 

74 

173.6 

12.1 

34 

233.4 

16.3 

94- 

293.3 

20.5 

55 

54.9 

3.8 

15 

114.7 

8.0 

75 

174.6 

12.2 

35 

234.4 

16.4 

95 

294.3 

20.6 

56 

55.9 

3.9 

16 

115.7 

8.1 

76 

175.6 

12.3 

36 

235.  4 

16.5 

96 

295.  3 

20.6 

57 

56.9 

4.0 

17 

116.7 

8.2 

77 

176.6 

12.3 

37 

236.4 

16.5 

97 

296.3 

20.7 

58 

57.9 

4.0 

18 

117.7 

8.2 

78 

177.6 

12.4 

38 

237.4 

16.6 

98 

297.3 

20.8 

59 

58.9 

4.1 

19 

118.7 

8.3 

79 

178.6 

12.5 

39 

238.4 

16.7 

99 

298.3 

20.9 

60 

59.9 

4.2 

20 

119.7 

8.4 

80 

179.6 

12.6 

40 

239.4 

16.7 

300 

299.3 

20.9 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

86°;  ( 

M°,  266 

°,  274°). 

tablp:  2. 

[Page  375 

Difference  of  Latitude  and  Departure  for  4°  (176°,  184 

°,  356° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

300.3 

21.0 

361 

360.1 

25.2 

421 

420.0 

29.4 

481 

479.8 

33.5 

541 

539.7 

37.7 

02 

301.3 

21.1 

62 

361.1 

25.2 

22 

421.0 

29.4 

82 

480.8 

33.6 

42 

540.7 

37.8 

03 

302.2 

21.1 

63 

362.1 

25.3 

23 

422.0 

29.5 

83 

481.8 

33.7 

43 

541.7 

37.9 

04 

.303.  2 

21.2 

64 

363.1 

25.4 

24 

423.0 

29.6 

84 

482.8 

33.7 

44 

542.7 

37.9 

05 

304.2 

21.3 

65 

364.1 

25.5 

25 

424.0 

29.6 

85 

483.8 

33.8 

45 

543.  7 

38.  0 

06 

305.  2 

21.3 

66 

365.1 

25.5 

26 

424.9 

29.7 

86 

484.8 

33.9 

46 

544.  7 

38.1 

07 

306.2 

21.4 

67 

366.1 

25.6 

27 

425.  9 

29.8 

87 

485.8 

33.  9 

47 

545.7 

.38.1 

08 

307.2 

21.5 

68 

367.1 

25.7 

28 

426.9 

29.9 

88 

486.8 

34.0 

48 

546.7 

38.2 

09 

308.2 

21.6 

69 

368.1 

25.7 

29 

427.9 

29.9 

89 

487.8 

34.1 

49 

547.7 

38.3 

10 

309.2 
310.  2 

21.6 

70 

369. 1 
370.1 

25.8 

30 

428.9 

30.0 

90 

488.8 
489.8 

34.2 
34.2 

50 
551 

548.7 
549.7 

38.3 

311 

21.7 

371 

25.9 

431 

429.9 

30.1 

491 

38.4 

12 

311.2 

21.8 

72 

371.1 

25.9 

32 

430.9 

30.1 

92 

490.8 

34.3 

52 

550.7 

38.5 

13 

312.2 

21.8 

73 

372.1 

26.0 

33 

431.9 

30.2 

93 

491.8 

34.4 

53 

551.7 

38.5 

14 

313.2 

21.9 

74 

373.1 

26.1 

34 

432.9 

30.3 

94 

492.8 

34.4 

54 

552.7 

38.6 

15 

314.2 

22.0 

75 

374.1 

26.2 

35 

433.9 

30.3 

95 

493.8 

34.5 

55 

553.6 

.38.7 

16 

315.2 

22.1 

76 

375.1 

26.2 

36 

434.9 

.30.4 

96 

494.8 

34.6 

56 

554.6 

38.7 

17 

316.2 

22.1 

77 

376.1 

26.3 

37 

435.9 

30.5 

97 

495.  8 

34.6 

57 

555.6 

38.8 

18 

317.2 

22.2 

78 

377.1 

26.4 

38 

436.9 

30.6 

98 

496.8 

34.7 

58 

556.6 

38.9 

19 

318.2 

22.3 

79 

378.1 

26.4 

39 

437.9 

30.6 

99 

497.8 

34.8 

59 

557.6 

38.9 

20 

319.2 
320.  2 

22.3 

80 

379. 1 
380.1 

26.5 

40 

438.9 
439.  9 

30.7 
30.8 

500 
501 

498.8 
499.8 

34.8 

60 

558.6 
559.  6 

39.0 

321 

22.4 

381 

26.6 

441 

34.9 

561 

39.1 

22 

321.2 

22.5 

82 

381.1 

26.6 

42 

440.9 

30.8 

02 

500.8 

35.0 

62 

560.6 

39.2 

23 

322.2 

22.5 

83 

382.1 

26.7 

43 

441.9 

30.9 

03 

501.  8 

35.  0 

63 

561.6 

39.2 

24 

323.  2 

22.6 

84 

383.1 

26.8 

44 

442.9 

31.0 

04 

502.8 

35.1 

64 

562.6 

39.3 

25 

324.2 

22.7 

85 

384.  0 

26.9 

45 

443.9 

31.0 

05 

503.8 

35.2 

65 

563.6 

39.4 

26 

325.  2 

22.7 

86 

385.0 

26.9 

46 

444.9 

31.1 

06 

504.8 

35.2 

66 

564.6 

39.4 

27 

326.2 

22.8 

87 

386.  0 

27.0 

47 

445.9 

31.2 

07 

505.8 

35.3 

67 

565.6 

39.5 

28 

327.2 

22.9 

88 

387.0 

27.1 

48 

446.9 

31.2 

08 

506.8 

35.4 

68 

566.6 

39.6 

29 

328.  2 

23.0 

89 

388.0 

27.1 

49 

447.9 

31.3 

09 

507.8 

35.5 

69 

567.6 

39.7 

30 
331 

329.2 

23.0 

90 

389.0 

27.2 
27.3 

50 
451 

448.9 

31.4 
31.5 

10 
511 

508.8 

35.6 
35.6 

70 

568.6 

39.8 

330.2 

23.1 

391 

390.  0 

449.9 

509.8 

571 

569.6 

39.8 

32 

331.2 

23.2 

92 

391.0 

27.3 

52 

450.9 

31.5 

12 

510.8 

35.7 

72 

570.6 

39.9 

33 

332.2 

23.2 

93 

392.0 

27.4 

53 

451.9 

31.6 

13 

511.8 

35.8 

73 

571.6 

40.0 

34 

333.  2 

23.3 

94 

393.0 

27.5 

54 

452.9 

31.7 

14 

512.7 

35.8 

74 

572.6 

40.0 

35 

334.2 

23.4 

95 

394.0 

27.6 

55 

453.9 

31.7 

15 

513.7 

35.9 

75 

573.6 

40.1 

36 

•  335. 2 

23.4 

96 

395.0 

27.6 

56 

454.9 

31.8 

16 

514.7 

36.0 

76 

574.6 

40.2 

37 

336.2 

23.  5 

97 

396.0 

27.7 

57 

455.9 

31.9 

17 

515.7 

36.0 

II 

575.6 

40.2 

38 

337.2 

23.6 

98 

397.0 

27.8 

58 

456.9 

31.9 

18 

516.7 

36.1 

78 

576.6 

40.3 

39 

338.2 

2.3.6 

99 

398.0 

27.8 

59 

457.9 

32.0 

19 

517.7 

36.2 

79 

577.6 

40.4 

40 

339.2 

23.7 

400 

399.0 

27.9 

60 

458.9 

32.1 

20 

518.7 

36.2 
36.3 

80 

578.6 

40.5 

341 

;wo.2 

23.8 

401 

400.0 

28.0 

461 

459. 9 

32.2 

521 

519.7 

581 

579.6 

40.5 

42 

341.2 

23.9 

02 

401.0 

28.0 

62 

460.9 

32.2 

22 

520.7 

36.4 

82 

580.6 

40.6 

43 

342.2 

23.9 

03 

402.0 

28.1 

63 

461.9 

32.3 

23 

521.7 

36.4 

83 

581.6 

40.7 

44 

343. 1 

24.0 

04 

403.0 

28.2 

64 

462.9 

32.4 

24 

522.  7 

36.5 

84 

582.6 

40.7 

45 

.344. 1 

24.1 

05 

404.0 

28.2 

65 

463.9 

32.4 

25 

523.7 

36.6 

85 

583.6 

40.8 

46 

345. 1 

24.1 

06 

405.0 

28.3 

66 

464.9 

.32.5 

26 

524.  7 

36.7 

86 

584.6 

40.9 

47 

346. 1 

24.2 

07 

406.0 

28.4 

67 

465.  8 

32.6 

27 

525.7 

36.8 

87 

585.6 

40.9 

48 

347.1 

24.3 

08 

407.0 

28.5 

68 

466.8 

32.6 

28 

526.7 

36.8 

88 

586.6 

41.0 

49 

.348. 1 

24.3 

09 

408.0 

28.5 

69 

467.8 

32.7 

29 

527.7 

36.9 

89 

587.6 

41.1 

50 

349.1 

24.4 
24.5 

10 

409.0 

28.6 

70 

468.8 

32.8 

30 
531 

528.7 
529.7 

37.0 
37.0 

90 
591 

588.6 

41.2 
41.3 

.351 

350.  1 

411 

410.0 

28.7 

471 

469.8 

32.9 

589.6 

52 

351.1 

24.6 

12 

411.0 

28.7 

72 

470.8 

32.9 

32 

530.7 

.37.1 

92 

590.6 

41.3 

53 

352. 1 

24.6 

13 

412.0 

28.8 

73 

471.8 

33.0 

33 

531.7 

37.2 

93 

591.6 

41.4 

54 

353.1 

24.7 

14 

413.0 

28.9 

74 

472.8 

33. 1 

34 

532.7 

37.2 

94 

592.6 

41.5 

55 

354. 1 

24.8 

15 

414.0 

28.9 

75 

473.8 

33.1 

35 

533.  7 

37.3 

95 

593.6 

41.5 

56 

355. 1 

24.8 

16 

415. 0 

29.0 

76 

474.8 

33.2 

36 

534.7 

.37.4 

96 

594.6 

41.6 

57 

356. 1 

24.9 

17 

416.0 

29.1 

77  1  475.  8 

33.3 

37 

535.7 

37.5 

97 

595.6 

41.7 

58 

357.1 

25.0 

18 

417.0 

29.2 

78 

476.8 

33.3 

38 

536.  7 

37.5 

98 

596.6 

41.7 

59 

358. 1 

25.0 

19 

418.0 

29.2 

79 

477.8 

33.4 

39 

537.7 

37.6 

99 

597.  6 

41.8 

60 

359.1 

25.1 

20 

419.0 

29.3 

80 

478.8 

35.5 

40 

538.7 

37.7 

600 

698.6 

41.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

i 

36°;   (94°,  266°,  274°). 

1    Page  376 

1 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  5°  (1 

75°,  185 

°,  355° 

). 

DLst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.8 

5.3 

121 

120.5 

10.5 

181 

180.  3 

15.8 

241 

240.1 

21.0 

2 

2.0 

0.2 

62 

61.8 

5.4 

22 

121.5 

10.6 

82 

181.3 

15.9 

42 

241.1 

21.1 

3 

3.0 

0.3 

63 

62.8 

5.5 

23 

122.5 

10.7 

83 

182.3 

15.9 

43 

242.1 

21.2 

4 

4.0 

0.3 

64 

63.8 

5.6 

24 

123.5 

10.8 

84 

183.3 

16.0 

44 

243.1 

21.3 

5 

5.0 

0.4 

65 

64.8 

5.7 

25 

124.5 

10.9 

85 

184.3 

16.1 

45 

244.1 

21.4 

6 

6.0 

0.5 

f 

65.7 

5.8 

26 

125.5 

11.0 

86 

185.  3 

16.2 

46 

245.1 

21.4 

7 

7.0 

0.6 

66.7 

5.8 

27 

126.5 

11.1 

87 

186.3 

16.3 

47 

246.1 

21.5 

8 

8.0 

0.7 

68 

67.7 

5.9 

28 

127.  5 

11.2 

88 

187.3 

16.4 

48 

247.1 

21.6 

9 

9.0 

0.8 

69 

68.7 

6.0 

29 

128.5 

11.2 

89 

188.3 

16.5 

49 

248.1 

21.7 

10 

10.0 

0.9 

70 

69.7 

6.1 

30 

129.5 

11.3 

90 

189.3 

16.6 

50 

249.0 

21.8 

11 

11.0 

1.0 

71 

70.7 

6.2 

131 

130.5 

11.4 

191 

190.3 

16.6 

251 

250.0 

21.9 

12 

12.0 

1.0 

72 

71.7 

6.3 

32 

131.5 

11.5 

92 

191.3 

16.7 

52 

251.0 

22.0 

13 

13.0 

1.1 

73 

72.7 

6.4 

33 

132.5 

11.6 

93 

192.3 

16.8 

53 

252.0 

22.1 

14 

13.  9 

1.2 

74 

73.7 

6.4 

34 

133.5 

11.7 

94 

193.  3 

16.9 

54 

253.0 

22.1 

15 

14.9 

1.3 

75 

74.7 

6.5 

35 

134.5 

11.8 

95 

194.  3 

17.0 

55 

254.0 

22.2 

16 

15.9 

1.4 

76 

75.7 

6.6 

36 

135.5 

11.9 

96 

195.  3 

17.1 

56 

255.0 

22.3 

17 

16.9 

1.5 

77 

76.7 

6.7 

37 

136.5 

11.9 

97 

196.3 

17.2 

57 

256.0 

22.4 

18 

17.9 

1.6 

78 

77.7 

6.8 

38 

137.5 

12.0 

98 

197.2 

17.3 

58 

257.0 

22.5 

19 

18.9 

1.7 

79 

78.7 

6.9 

39 

138.5 

12.1 

99 

198.2 

17.3 

59 

258.0 

22.6 

20 

19.9 

1.7 
1.8 

80 

79.7 

7.0 

40 

139.5 
140.5 

12.2 
12.3 

200 
201 

199.2 

17.4 

60 

259.0 

22.7 

21 

20.9 

81 

80.7 

7.1 

141 

200.2 

17.5 

261 

260.0 

22.7 

22 

21.9 

1.9 

82 

81.7 

7.1 

42 

141.5 

12.4 

02 

201.2 

17.6 

62 

261.0 

22.8 

23 

22.9 

2.0 

83 

82.7 

7.2 

43 

142.5 

12.5 

03 

202.2 

17.7 

63 

262.0 

22.9 

24 

23.9 

2.1 

84 

83.7 

7.3 

44 

143.5 

12.6 

04 

203.2 

17.8 

64 

263.  0 

23.0 

25 

24.9 

2.2 

85 

84.7 

7.4 

45 

144.4 

12.6 

05 

204.2 

17.9 

65 

264.0 

23.1 

26 

25.9 

2.3 

86 

85.7 

7.5 

46 

145.4 

12.7 

06 

205.  2 

18.0 

66 

265.0 

23.2 

27 

26.9 

2.4 

87 

86.7 

7.6 

47 

146.4 

12.8 

07 

206.2 

18.0 

67 

266.0 

23.3 

28 

27.9 

2.4 

88 

87.7 

7.7 

48 

147.4 

12.9 

08 

207.2 

18.1 

68 

267.0 

23.4 

29 

28.9 

2.5 

89 

88.7 

7.8 

49 

148.4 

13.0 

09 

208.2 

18.2 

69 

268.0 

23.4 

30 

29.9 

2.6 

90 

89.7 

7.8 

50 

149.4 
150.  4 

13.1 

10 

209.2 

18.3 

70 

269.0 

23.5 

31 

30.9 

2.7 

91 

90.7 

7.9 

151 

13.2 

211 

210.2 

18.4 

271 

270.0 

23.6 

32 

31.9 

2.8 

92 

91.6 

8.0 

52 

151. 4 

13.2 

12 

211.2 

18.5 

72 

271.0 

23.7 

33 

32.9 

2.9 

93 

92.6 

8.1 

53 

152.4 

13.3 

13 

212.2 

18.6 

73 

272.0 

23.8 

34 

33.9 

3.0 

94 

93.6 

8.2 

54 

153.4 

13.4 

14 

213.2 

18.7 

74 

273.0 

23.9 

35 

34.9 

3.1 

95 

94.6 

8.3 

55 

154.4 

13.5 

15 

214.2 

18.7 

75 

274.0 

24.0 

36 

35.9 

3.1 

96 

95.6 

8.4 

56 

155.4 

13.6 

16 

215.2 

18.8 

76 

274.9 

24.1 

37 

36.9 

3.2 

97 

96.6 

8.5 

57 

156.4 

13.7 

17 

216.2 

18.9 

77 

275.9 

24.1 

38 

37.9 

3.3 

98 

97.6 

8.5 

58 

157.4 

13.8 

18 

217.2 

19.0 

78 

276.9 

24.2 

39 

38.9 

3.4 

99 

98.6 

8.6 

59 

158. 4 

13.9 

19 

218.2 

19.1 

79 

277.9 

24.3 

40 

39.8 

3.5 

100 

99.6 

8.7 

60 

159.4 

13.9 

20 
221 

219.2 

19.2 

80 

278.9 

24.4 

41 

40.8 

3.6 

101 

100.6 

8.8 

161 

160.4 

14.0 

220.2 

19.3 

281 

279.9 

24.5 

42 

41.8 

3.7 

02 

101.6 

8.9 

62 

161.4 

14.1 

22* 

221.2 

19.3 

82 

280.9 

24.6 

43 

42.8 

3.7 

03 

102.6 

9.0 

63 

162.4 

14.2 

23 

222.2 

19.4 

83 

281.9 

24.7 

44 

43.8 

3.8 

04 

103.6 

9.1 

64 

163.4 

14.3 

24 

223.1 

19.5 

84 

282.9 

24.8 

45 

44.8 

3.9 

05 

104.6 

9.2 

65 

164. 4 

14.4 

25 

224.1 

19.6 

85 

283.9 

24.8 

46 

45.8 

4.0 

06 

105.6 

9.2 

66 

165.4 

14.5 

26 

225.1 

19.7 

86 

284.9 

24.9 

47 

46.8 

4.1 

07 

106.6 

9.3 

67 

166.4 

14.6 

27 

226.1 

19.8 

87 

285.9 

25.0 

48 

47.8 

4.2 

08 

107.6 

9.4 

68 

167.4 

14.6 

28 

227.1 

19.9 

88 

286.9 

25.1 

49 

48.8 

4.3 

09 

108.6 

9.5 

69 

168.4 

14.7 

29 

228.1 

20.0 

89 

287.9 

25.2 

50 

49.8 

4.4 

10 

109.6 

9.6 

70 

169.4 

14.8 

30 

229.1 
230. 1 

20.0 

90 

288.9 

25.3 

51 

50.8 

4.4 

111 

110.6 

9.7 

171 

170.3 

14.9 

231 

20.1 

291 

289.9 

25.4 

52 

51.8 

4.5 

12 

111.6 

9.8 

72 

171.  3 

15.0 

32 

231.1 

20.2 

92 

290.9 

25.4 

53 

52.8 

4.6 

13 

112.6 

9.8 

73 

172.  3 

15.1 

33 

232. 1 

20.3 

93 

291.9 

25.5 

54 

53.8 

4.7 

14 

113.6 

9.9 

74 

173.3 

15.2 

34 

233.1 

20.4 

94 

292.9 

25.6 

55 

54.8 

4.8 

15 

114.6 

10.0 

75 

174.3 

15.3 

35 

234.  1 

20.5 

95 

293.9 

25.7 

56 

55.8 

4.9 

16 

115.6 

10.1 

76 

175.3 

15.3 

36 

235.  1 

20.6 

96 

294.9 

25.8 

57 

56.8 

5.0 

17 

116.6 

10.2 

77 

176.3 

15.4 

37 

236.1 

20.7 

97 

295.9 

25.9 

58 

57.8 

5.1 

18 

117.6 

10.3 

78 

177.3 

15.5 

38 

237. 1 

20.7 

98 

296.9 

26.0 

59 

58.8 

5.1 

19 

118.5 

10.4 

79 

178.3 

15.6 

39 

238.  1 

20.8 

99 

297.9 

26.1 

60 

59.8 

5.2 

20 

119.5 

10.5 

80 

179.3 

15.7 

40 

239.1 

20.9 

300 

298.9 

26.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

85°  (S 

5°,  265°,  275°). 

TABLE  2. 

[Page  377 

Difference  of  Latitude  and  Departure  for 

5°  (175°,  185 

°,  355° 

)• 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat.         Dep. 

Dist. 

Lat.     1    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

299.9 

26.2 

361     359.6     31.5 

421 

419.  4  '  36.  7 

481 

479.2 

41.9 

541 

538.9 

47.2 

02 

300.8 

26.3 

62     360.6     31.6 

22 

420.  4      36.  8 

82 

480.2 

42.0 

42 

539.  9 

47.3 

03 

301.8 

26.4 

63     361.6  i  31.6 

23 

421.4     36.9 

83 

481.2 

42.1 

43 

540.9 

47.4 

04 

302.8 

26.5 

64  i  362.  6  !  31.  7 

24 

422.4     37.0 

84 

482.2 

42.2 

44 

541.9 

47.5 

05 

303.8 

26.6 

65     363.6  1  31.8 

25 

423.  4  1  37. 1 

85 

483.2 

42.3 

45 

542.9 

47.6 

06 

304.8 

26.7 

66     364.6 

31.9 

26 

424.  4     37. 1 

86 

484.1 

42.4 

46 

543.9 

47.7 

07 

305.8 

26.8 

67     365.6 

32.0 

27 

425.  4     37.  2 

87 

485.1 

42.4 

47 

544.9 

47.7 

08 

306.8 

26.9 

68     366.6 

32.1 

28 

426.4  i  37.3 

88 

486. 1 

42.5 

48 

545. 9 

47.8 

09 

307.8 

26.9 

69     367. 6 

32.2 

29 

427.4  '  37.4 

89 

487.1 

42.6 

49 

546.9 

47.9 

10 

308.8 
309.8 

27.0 

70 

368.6  1  32.3 
369.6  i  32.3 

30 

428.4     37.5 

90 

488.1 
"489.1 

42.7 

42,8 

50 
551 

547.9 

48.0 

311 

27.1 

371 

431 

429.4     37.6 

491 

548.9     48.1 

12 

310.8 

27.2 

72     370.6 

32.4 

32 

430.4     37.7 

92 

490.1 

42.9 

52 

549.  9     48.  2 

13 

311.8 

27.3 

73     371.6 

32.5 

33 

431.  3  1  37.  7 

93 

491.1 

43.0 

53 

550.  9     48.  3 

14 

312.8 

27.4 

74  1  372.6 

32.6 

34 

432.3 

37.8 

94 

492.1 

43.1 

54 

551.9     48.4 

15 

313.8 

27.5 

75 

373.6  i  32.7 

35 

433.  3 

37.9 

95 

493.1 

43.1 

55 

552.9  ,  48.4 

16 

314.8 

27.5 

76 

374.6 

32.8 

36 

434.3 

38.0 

96 

494.1 

43.2 

56 

553. 9  !  48.  5 

17 

315.8 

27.6 

77 

375.6 

32.9 

37 

435.3 

38.1 

97 

495.1 

43.3 

57 

554.9  :  48.6 

18 

316.8 

27.7 

78 

376.6 

33.0 

38 

436.3 

38.2 

98 

496.1 

43.4 

58 

555. 9     48.  7 

19 

317.8 

27.8 

79 

377.6 

33. 0 

39 

437.3 

38.3 

99 

497.1 

43.5 

59 

556.9     48.8 

20 

318.8 

27.9 

80 

378.6  i  33.1 

40 

438.3 

38.4 

500 

498.1 
499.1 

43.6 

60 

557.9     48.8 

321 

"319.  8 

28.0 

381 

379.5  I  33.2 

441 

439.3  1  38.4 

501 

43.7 

561 

558.8  ;  48.9 

22 

320.8 

28.1 

82 

380.5 

33.3 

42 

440.3  ;  38.5 

02  :  500. 1 

43.8 

62 

559.8     49.0 

23 

321.  8 

28.2 

83 

381.  5 

33.4 

43 

441.3  !  38.6 

03 

501.1 

43.  8 

63 

560.  8  i  49. 1 

24 

322.  8 

28.2 

84 

382.5 

33.5 

44 

442. 3  I  38.  7 

04 

502.1 

43.9 

64 

561.  8  1  49.  2 

25 

323.8 

28.3 

85 

383.5 

33.6 

45 

443.3  1  38.8 

05 

503.1 

44.0 

65 

562.  8  j  49.  3 

26 

324.8 

28.4 

86 

384.5 

33.7 

46 

444.3     38.9 

06 

504. 1 

44.1 

66 

563.8  ,  49.4 

27 

325.8 

28.5 

87 

385.5 

33.7 

47 

445.3  {  39.0 

07 

505.1 

44.2 

67 

564.  8  i  49.  5 

28 

326.  7 

28.6 

88 

386.5 

33.8 

48 

446. 3     39. 1 

08 

506.1 

44.3 

68 

565.8  1  49.6 

29 

327.  7 

28.7 

89 

387.5 

33. 9 

49 

447.  3  :  39. 1 

09 

507.1 

44.4 

69 

566.  8  1  49.  7 

30 

328.7 

28.8 

90 

388.  5 

34.0 

50 

448.3  1  39.2 

10 

508.1 

44.5 

70 

567.  8  [  49.  7 

331 

329.  7 

28.9 

391 

389.5 

34.1 

451 

449.3  i  39.3 

511 

509.0 

44.5 

571 

568.8  1  49.8 

32 

330.7 

28.9 

92 

390.5 

34.2 

52 

450.3     39.4 

12 

510.0 

44.6 

72 

569.8  1  49.9 

33 

331.  7 

29.0 

93 

391.5 

34.3 

53 

451.3  [  39.5 

13 

511.0 

44.7 

73 

570.  8  i  50.  0 

34 

332.7 

29.1 

94 

392.5 

34.3 

54 

452.  3     39.  6 

14 

512.0 

44.8 

74 

571.8 

50.1 

35 

333.  7 

29.2 

95 

393.5 

34.4 

55 

453. 3     39.  7 

15 

513.0 

44.9 

75 

572.8 

50.2 

36 

.334.7 

29.3 

96 

394.5 

34.5 

56 

454. 3     39.  8 

16 

514.0 

45.0 

76 

573.8 

50.3 

37 

335.7 

29.4- 

97 

395. 5 

34.6 

57 

455. 3     39. 8 

17 

515.0 

45.1 

77 

574.8 

50.4 

38 

336.7 

29.5 

98 

396.5 

34.7 

58 

456.3  ;  39.9 

18 

516.0 

45.2 

78 

575.8 

50.4 

39 

337.7 

29.6 

99 

397.5 

34.8 

59 

457.3  i  40.0 

19 

517.0 

45.2 

79 

576.8  i  50.5 

40 
341 

338.7 
339.7 

29.6 

400 

398.5 

34.9 

60 

458.2 

40.1 
40.2 

20 
521 

518.0 
519.0 

45.3 

80 

577.8  1  50.6 
578.8  1  50.7 

29.7 

401 

399.5 

35.0 

461 

459.2 

45.4 

581 

42 

340.7 

29.8 

02 

400.5 

35.0 

62 

460.2  1  40.3 

22 

520.0 

45.5 

82 

579.8  !  50.8 

43 

341.7 

29.9 

03 

401.5 

35.1 

63 

46i.2 

40.4 

23 

521.0 

45.6 

83 

580.8 

50.9 

44 

342.7 

30.0 

04 

402.5 

35.2 

64 

462.2 

40.4 

24 

522.0 

45.7 

84 

581.8 

50.9 

45 

343.7 

30.1 

05 

403.5 

35.3 

65 

463.2 

40.5 

25 

523.0 

45.8 

85 

582.8 

51.0 

46 

344.7 

30.2 

06 

404.5 

35.4 

66 

464.2 

40.6 

26 

524.0 

45.9 

86 

583.  8 

51.1 

47 

345.  7 

30.3 

07 

405.4 

35.5 

67 

465.2 

40.7 

27 

525. 0 

45.9 

87 

584.8 

51.2 

48 

346.7 

30.3 

08 

406.4 

35.6 

68 

466.  2 

40.8 

28 

526.0 

46.0 

88 

585.8 

51.3 

49 

347.7 

30.4 

09 

407.4 

35.7 

69 

467.2 

40.9 

29 

527.0 

46.1 

89 

586.8 

51.4 

50 

348.7 

30.5 

10 

408.4 

35.7 

70 

468.2 
469.2 

41.0 

30 

528.0 
529. 0 

46.2 

90 

587.8 

51.5 

351 

349.7 

30.6 

411 

409.4  j  35.8 

471 

41.1 

531 

46.3 

591 

588.7 

51.6 

52 

350.7 

30.7 

12 

410.4  1  35.9 

72     470. 2 

41.1 

32 

530. 0 

46.4 

92 

589.7 

51.6 

53 

351.  7 

30.8 

13 

411.4  '  36.0 

73     471. 2 

41.2 

33 

531.0 

46.5 

93 

590.7 

51.7 

54 

352.6 

30.9 

14 

412.4  i  36.1 

74     472. 2 

41.3 

34 

532. 0 

46.6 

94 

591.7 

51.8 

55 

353.6 

30.9 

15 

413.4     36.2 

75 

473.2 

41.4 

35 

533. 0 

46.6 

95 

592.7 

51.9 

56 

354.6 

31.0 

16 

414.4     36.3 

76 

474.2 

41.5 

36 

533.9 

46.7 

96 

593.7 

52.0 

57 

355.6 

31.1 

17 

415.4  1  36.4 

77 

475.2 

41.6 

37 

534.  9 

46.8 

97 

594.7 

52.1 

58 

356.6 

31.2 

18 

416.4  [  36.4 

78 

476.2 

41.7 

38 

535. 9 

46.9 

98 

595.  7 

52.2 

59 

357.6 

31.3 

19 

417.4  [  36.5 

79 

477.2 

41.8 

39 

536.9 

47.0 

99 

596.7 

52.3 

60 

358.6 

31.4 

20 

418.4     36.6 

1 

80 

478.2 

41.8 

40 

537.9 

47.1 

600 

597.7 

52.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     1    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

85°  (95°,  265°,  275°) 

1 

Page  378] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  6°  (174°,  186 

°,  354° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
25.2 

1 

1.0 

0.1 

61 

60.7 

6.4 

121 

120.3 

12.6 

181 

180.0 

18.9 

241 

239.7 

2 

2.0 

0.2 

62 

61.7 

6.5 

22 

121.3 

12.8 

82 

181.0 

19.0 

42 

240.7 

25.3 

3 

3.0 

0.3 

63 

62.7 

6.6 

23 

122.3 

12.9 

83 

182.0 

19.1 

43 

241.7 

25.4 

4 

4.0 

0.4 

64 

63.6 

6.7 

24 

123.3 

13.0 

84 

183.0 

19.2 

44 

242.7 

25.5 

5 

5.0 

0.5 

65 

64.6 

6.8 

25 

124.3 

13.1 

85 

184.0 

19.3 

45 

243.7 

25.6 

6 

6.0 

0.6 

1? 

65.6 

6.9 

26 

125.  3 

13.2 

86 

185. 0 

19.4 

46 

244.7 

25.7 

7 

7.0 

0.7 

66.6 

7.0 

27 

126.3 

13.3 

87 

186.0 

19.5 

47 

245.  6 

25.8 

8 

8.0 

0.8 

68 

67.6 

7.1 

28 

127.3 

13.4 

88 

187.0 

19.7 

48 

246.6 

25.9 

9 

9.0 

0.9 

69 

68.6 

7.2 

29 

128.3 

13.5 

89 

188.0 

19.8 

49 

247.6 

26.0 

10 

9.9 

1.0 

70 

69.6 

7.3 

30 
131 

129.3 
130.3 

13.6 

90 

189.0 
190.0 

19.9 

50 
251 

248.6 
249.6 

26.1 

11 

10.9 

1.1 

71 

70.6 

7.4 

13.7 

191 

20.0 

26.2 

12 

11.9 

1.3 

72 

71.6 

7.5 

32 

131.3 

13.8 

92 

190.9 

20.1 

52 

250.  6 

26.3 

13 

12.9 

1.4 

73 

72.6 

7.6 

33 

132.3 

13.9 

93  i  191.9 

20.2 

53 

251.6 

26.4 

14 

13.9 

1.5 

74 

73.6 

7.7 

34 

133.3 

14.0 

94 

192.9 

20.3 

54 

252.6 

26.6 

15 

14.9 

1.6 

75 

74.6 

7.8 

35 

134.3 

14.1 

95 

193.9 

20.4 

55 

253.6 

26.7 

16 

15.9 

1.7 

76 

75.6 

7.9 

36 

135.3 

14.2 

96 

194.9 

20.5 

56 

254.6 

26.8 

17 

16.9 

1.8 

77 

76.6 

8.0 

37 

136.2 

14.3 

97 

195.  9 

20.6 

57 

255.6 

26.9 

18 

17.9 

1.9 

78 

77.6 

8.2 

38 

137.2 

14.4 

98 

196.9 

20.7 

58 

256. 6 

27.0 

19 

18.9 

2.0 

79 

78.6 

8.3 

39 

138.2 

14.5 

99 

197.9 

20.8 

59 

257.6 

27.1 

20 

19.9 

2.1 

80 

79.6 

8.4 

40 

139.  2 

14.6 

200 
201 

198.9 

20.9 

60 

258.  6 
259.6 

27.2 

21 

20.9 

2.2 

81 

80.6 

8.5 

141 

140.2 

14.7 

199.9 

21.0 

261 

27.3 

22 

21.9 

2.3 

82 

81.6 

8.6 

42 

141.2 

14.8 

02 

200.9 

21.1 

62 

260.6 

27.4 

23 

22.9 

2.4 

83 

82.5 

8.7 

43 

142.2 

14.9 

03 

201.9 

21.2 

63 

261.6 

27.5 

24 

23.9 

2.5 

84 

83.5 

8.8 

44 

143.2 

15.1 

04 

202.9 

21.3 

64 

262.6 

27.6 

25 

24.9 

2.6 

85 

84.5 

8.9 

45 

144.2 

15.2 

05 

203.9 

21.4 

65 

263.5 

27.7 

26 

25.9 

2.7 

86 

85.5 

9.0 

46 

145.2 

15.3 

06 

204.9 

21.5 

66 

264.5 

27.8 

27 

26.9 

2.8 

87 

86.5 

9.1 

47 

146.2 

15.4 

07 

205.  9 

21.6 

67 

265.  5 

27.9 

28 

27.8 

2.9 

88 

87.5 

9.2 

48 

147.2 

15.5 

08 

206.9 

21.7 

68 

266.5 

28.0 

29 

28.8 

3.0 

89 

88.5 

9.3 

49 

148.2 

15.6 

09 

207.9 

21.8 

69 

267.5 

28.1 

30 

29.8 

3.1 
3.2 

90 

89.5 

9.4 

50 
151 

149.2 

15.7 

10 

208.8 

22.0 

70 

268.5 
269.5 

28.2 

31 

30.8 

91 

90.5 

9.5 

150.2 

15.8 

211 

209.8 

22.1 

271 

28.3 

32 

31.8 

3.3 

92 

91.5 

9.6 

52 

151.2 

15.9 

12 

210.8 

22.2 

72 

270.  5 

28.4 

33 

32.8 

3.4 

93 

92.5 

9.7 

53 

152.  2 

16.0 

13 

211.8 

22.3 

73 

271.5 

28.5 

34 

33.8 

3.6 

94 

93.5 

9.8 

54 

153.2 

16.1 

14 

212.8 

22.4 

74 

272.5 

28.6 

35 

34.8 

3.7 

95 

94.5 

9.9 

55 

154.2 

16.2 

15 

213.8 

22.5 

75 

273.5 

28.7 

36 

35.8 

3.8 

96 

95.5 

10.0 

56 

155.1 

16.3 

16 

214.8 

22.6 

76 

274.5 

28.8 

37 

36.8 

3.9 

97 

96.5 

10.1 

57 

156.1 

16.4 

17 

215.8 

22.7 

•77 

275.5 

29.0 

38 

37.8 

4.0 

98 

97.5 

10.2 

58 

157.1 

16.5 

18 

216.8 

22.8 

78 

276.5 

29.1 

39 

38.8 

4.1 

99 

98.5 

10.3 

59 

158.1 

16.6 

19 

217.8 

22.9 

79 

277.5 

29.2 

40 
41 

39.8 

4.2 

100 

99.5 

10.5 

60 

159.1 
160. 1 

16.7 

20 

218.8 
219.8 

23.0 
23.1 

80 
281 

278.5 
279.5 

29.3 
29.4 

40.8 

4.3 

101 

100.4 

10.6 

161 

16.8 

221 

42 

41.8 

4.4 

02 

101.4 

10.7 

62 

161.1 

16.9 

22 

220.8 

23.2 

82 

280.5 

29.5 

43 

42.8 

4.5 

03 

102.4 

10.8 

63 

162.1 

17.0 

23 

221.8 

23.3 

83 

281.4 

29.6 

44 

43.8 

4.6 

04 

103.4 

10.9 

64 

163.1 

17.1 

24 

222.8 

23.4 

84 

282.4 

29.7 

45 

44.8 

4.7 

05 

104.4 

11.0 

65 

164.1 

17.2 

25 

223.8 

23.5 

85 

283.  4 

29.8 

46 

45.7 

4.8 

06 

105.4 

11.1 

66 

165.1 

17.4 

26 

224.8 

23.6 

86 

284.4 

29.9 

47 

46.7 

4.9 

07 

106.4 

11.2 

67 

166.1 

17.5 

27 

225.8 

23.7 

87 

285.4 

30.0 

48 

47.7 

5.0 

08 

107.4 

11.3 

68 

167.1 

17.6 

28 

226.8 

23.8 

88 

286.4 

30.1 

49 

48.7 

5.1 

09 

108.4 

11.4 

69 

168.1 

17.7 

29 

227.7 

2.3.9 

89 

287.4 

30.2 

50 

49.7 

5.2 

10 

109.4 

11.5 

70 

169.1 

17.8 

30 

228.7 

24.0 
24.1 

90 
291 

288.4 

30.3 

51 

50.7 

5.3 

111 

110.4 

11.6 

171 

170.1 

17.9 

231 

229.7 

289.4 

30.4 

52 

51.7 

5.4 

12 

111.4 

11.7 

72 

171.1 

18.0 

32 

230.7 

24.3 

92 

290.4 

30.5 

53 

52.7 

5.5 

13 

112.4 

11.8 

73 

172.1 

18.1 

33 

231.  7 

24.4 

93 

291.4 

30.6 

54 

53.7 

5.6 

14 

113.4 

11.9 

74 

173.0 

18.2 

34 

232.7 

24.5 

94 

292.4 

30.7 

55 

54.7 

5.7 

15 

114.4 

12.0 

75 

174.0 

18.3 

35 

233.  7 

24.6 

95 

293.  4 

30.8 

56 

55.7 

5.9 

16 

115.4 

12.1 

76 

175.0 

18.4 

36 

234.  7 

24.7 

96 

294.4 

30.9 

57 

56.7 

6.0 

17 

116.4 

12.2 

77 

176.0 

18.5 

37 

2.35.  7 

24.8 

97 

295.4 

31.0 

58 

57.7 

6.1 

18 

117.4 

12.3 

78 

177.0 

18.6 

38 

236.  7 

24.9 

98 

296.4 

31.1 

59 

58.7 

6.2 

19 

118.3 

12.4 

79 

178.0 

18.7 

39 

237.  7 

25.0 

99 

297.4 

31.3 

60 

59.7 

6.3 

20 

119.3 

12.5 

80 

179.0 

18.8 

40 

238.7 

25.1 

300 

298.4 

31.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

84°  (£ 

►6°,  264= 

,  276°) 

TABLE  2. 

[Page  379    | 

Difference  of  Latitude  and  Departure  fpr 

6°  (174°,  186° 

,  354°) 

Dlst. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

299.3 

31.5 

361 

359.0 

37.7 

421 

418.7 

44.0 

481 

478.4 

50.3 

541 

538.0 

56.  5 

02 

300.3 

31.6 

62 

360.0 

37.8 

22 

419.7 

44.1 

82 

479.4 

50.4 

42 

539.  0 

56.6 

03 

301.3 

31.7 

63 

361.0 

37.9 

23 

420.7 

44.2 

83 

480.  4 

50.5 

43 

540.0 

56.7 

04 

302.3 

31.8 

64 

362.0 

38.0 

24 

421.7 

44.3 

84 

481.3 

50.6 

44 

541.0 

56.8 

05 

303.3 

31.9 

65 

363.  0 

38.1 

25 

422.7 

44.4 

85 

482.3 

50.7 

45 

542.  0 

56.9 

06 

304.3 

32.0 

66 

364.  0 

38.3 

26 

423.7 

44.5 

86 

483.  3 

50.8 

46 

543.0 

57.0 

07 

305.3 

32.1 

67 

365.  0 

38.4 

27 

424.7 

44.6 

87 

484.3 

50.9 

47 

544.0 

57.1 

08 

306.3 

32.2 

68 

366.0 

38.5 

28 

425.  7 

44.7 

88 

485.  3 

51.0 

48 

545.0 

57.2 

09 

307.3 

32.3 

69 

367.0 

38.6 

29 

426.6 

44.8 

89 

486.  3 

51.1 

49 

546.0 

57.3 

10 

308.3 

32.4 

70 

368.0 
369.0 

38.7 
38.8 

30 
431 

427.6 
428.6 

44.9 

45.0 

90 
491 

487.3 

51.2 

50 
551 

547.0 
548.0 

57.4 
57. 5 

311 

309.3 

32.5 

371 

488.  3 

51.3 

12 

310.  3 

32.6 

72 

370. 0 

38.9 

32 

429.6 

45.2 

92 

489.3 

51.4 

52 

549.0 

57.6 

13 

311.3 

32.7 

73 

371.0 

39.0 

33 

430.6 

45.3 

93 

490.  3 

51.5 

53 

550.  0 

57.7 

14 

312.3 

32.8 

74 

371.9 

39.1 

34 

431.6 

45.4 

94  !  491.3 

51.6 

54 

551.0 

57.9 

15 

313.3 

32.9 

75 

372.9 

39.2 

35 

432.6 

45.  5 

95  i  492.3 

51.7 

55 

552.0 

58.0 

16 

314.  3 

33.0 

76 

373.9 

39.3 

36 

433.6 

45.6 

96 

493.3 

51.8 

56 

553.  0 

58.1 

17 

315.3 

33.1 

77 

374.9 

39.4 

37 

434.6 

45.7 

97 

494.3 

51.9 

57 

554.0 

58.2 

18 

316.3 

33.2 

78 

375.9 

39.5 

38 

435.  6 

45.8 

98 

495.3 

52.0 

58 

555.  0 

58.3 

19 

317.3 

33.3 

79 

376.9 

39.6 

39 

436.  6 

45.9 

99 

496.3 

52.1 

59 

556. 0 

58.4 

20 

318.2 

33.4 

80 

377.9 

39.7 

40 

437.6 

46.0 
46.1 

500 

497.3 

52.3 

60 

556.9 

58.5 
58.6 

321 

319.2 

33.6 

381 

378.9 

39.8 

441 

438.6 

501  1  498.3 

52.4 

561 

557.9 

22 

320.2 

33.7 

82 

379.  9 

39.9 

42 

439.6 

46.2 

02 

499.3 

52.5 

62 

558.9 

58.7 

23 

321.2 

33.8 

83 

380.9 

40.0 

43 

440.6 

46.3 

03 

500.2 

52.6 

63 

559.9 

58.8 

24 

322.2 

33.9 

84 

381. 9 

40.1 

44 

441.6 

46.4 

04 

501.2 

52.7 

64 

560.9 

59.0 

25 

323.2 

34.0 

85 

382.9 

40.2 

45 

442.6 

46.5 

05 

502.2 

52.8 

65 

561.9 

59.1 

26 

324.2 

34.1 

86 

383.9 

40.3 

46 

443.6 

46.6 

06 

503.2 

52.9 

66 

562.9 

59.2 

27 

325.2 

34.2 

87 

384. 9 

40.5 

47 

444.5 

46.7 

07 

504.2 

53.0 

67 

563.9 

59.3 

28 

326.2 

34.3 

88 

385.9 

40.6 

48 

445.  5 

46.8 

08 

505.  2 

53.1 

68 

564.9 

59.4 

29 

327.2 

34.4 

89 

386.9 

40.7 

49 

446.5 

46.9 

09 

506.2 

53.2 

69 

565.9 

59.5 

30 

328.2 

34.5 

90 
391 

387.9 

40.8 

50 

447.5 

47.0 

10 

507.2 

53.3 

70 
571 

566.9 

59.6 

331 

329.2 

34.6 

388.9 

40.9 

451 

448.5 

47.1 

511 

508.2 

53.4 

567.9 

59.7 

32 

330.2 

34.7 

92 

389.  9 

41.0 

52 

449.5 

47.2 

12 

509.2 

53.5 

72 

568.9 

59.8 

33 

331.2 

34.8 

93 

390.  8 

41.1 

53 

450.5 

47.3 

13 

510.2 

53.6 

73 

569.9 

59.9 

34 

332.2 

34.9 

94 

391.8 

41.2 

54 

451.  5 

47.5 

14 

511.2 

53.7 

74 

570.9 

60.0 

35 

333.2 

35.0 

95 

392.  8 

41.3 

55 

452.5 

47.6 

15 

512.2 

53.8 

75 

571.9 

60.1 

36 

334.2 

35.1 

96 

393.8 

41.4 

56 

453. 5 

47.7 

16 

513.2 

53.9 

76 

572.9 

60.2 

37 

335.2 

35.2 

97 

394.8 

41.5 

57 

454.6 

47.8 

17 

514.2 

54.0 

77 

573.9 

60.3 

38 

336.1 

35.3 

98 

395.8 

41.6 

58 

455.5 

47.9 

18 

515.2 

54.1 

78 

574.9 

60.4 

39 

•337. 1 

35.4 

99 

396.8 

41.7 

59 

456.5 

48.0 

19 

516.2 

54.2 

79 

575.8 

60.5 

40 

338.1 
339.1 

35.  5 
35.6 

400 
401 

397.8 
398.8 

41.8 
41.9 

60 

457.5 

48.1 

20 

517.2 
518.1 

54.3 

80 

576.8 

60.6 

341 

461 

458.  5 

48.2 

521 

54.5 

581 

577.8 

60.7 

42 

340.1 

35.7 

02 

399.8 

42.0 

62 

459.  5 

48.3 

22 

519.1 

54.6 

82 

578.8 

60.8 

43 

341.1 

35.8 

03 

400.8 

42.1 

63 

460*5 

48.4 

23 

520.1 

54.7 

83 

579.8 

60.9 

44 

342.1 

36.0 

04 

401.8 

42.2 

64 

461.  5 

48.  5 

24 

521.1 

54.8 

84 

580.8 

61.1 

45 

343.1 

36.1 

05 

402.8 

42.3 

65 

462.5 

48.6 

25 

522.1 

54.9 

85 

581.8 

61.2 

46 

344.1 

36.2 

06 

403.  8 

42.4 

66 

463.4 

48.7 

26 

523. 1 

55.0 

86 

582.8 

61.3 

47 

345.1 

36.3 

07 

404.8 

42.5 

67 

464.4 

48.8 

27 

524.1 

55.1 

87 

583.8 

61.4 

48 

346.1 

36.4 

08 

405.8 

42.6 

68 

465.  4 

48.9 

28 

525.1 

55.2 

88 

584.8 

61.5 

49 

347.1 

36.5 

09 

406.8 

42.7 

69 

466.4 

49.0 

29 

526.1 

55.3 

89 

585.8 

61.6 

50 
351 

348.1 
349.1 

36.6 
36.7 

10 

407.8 

42.9 
43.  0 

70 

467.4 

49.1 

30 
531 

527.1 

55.4 

90 

586.8 

61.7 

411 

408.7 

471 

468.4 

49.2 

528.1 

55.5 

591 

587.8 

61.8 

52 

350.1 

36.8 

12 

409.7 

43.1 

72 

469.4 

49.3 

32 

529.1 

55.6 

92 

588.8 

61.9 

53 

351.1 

36.9 

13 

410.7 

43.2 

73 

470.4 

49.4 

33 

530. 1 

55.7 

93 

589.8 

62.0 

54 

352.1 

37.0 

14 

411.7 

43.3 

74 

471.4 

49.5 

34 

531.1 

55.8 

94 

590.  8 

62.1 

55 

353.1 

37.1 

15 

412.7 

43.4 

75 

472.4 

49.6 

35 

532.1 

55.  9 

95 

591.8 

62.2 

56 

354.0 

37.2 

16 

413.7 

43.5 

76 

473.4 

49.8 

36 

533. 1 

56.0 

96 

592.8 

62.3 

57 

355.0 

37.3 

17 

414.7 

43.6 

77 

474.4 

49.9 

37 

534. 1 

56.1 

97 

593.  8 

62.4 

58 

356.  0 

37.4 

18 

. 415. 7 

43.7 

78 

475.4 

50.0 

38 

535. 1 

56.2 

98 

594.7 

62.5 

59 

357.0 

37.5 

19 

416.7 

43.8 

79 

476.4 

50.1 

39 

536.1 

56.3 

99 

595.7 

62.6 

60 

358.0 

37.6 

20 

417.7 

43.9 

80 

477.4 

50.2 

40 

537. 1 

56.4 

600 

596.7 

62.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

84°  ( 

96°,  264 

°,  276° 

). 

Page  380] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  7°  (17 

•3°,  187° 

,  353°) 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.5 

7.4 

121 

120.1 

14.7 

181 

179.  7 

22.1 

241 

239.2 

29.4 

2 

2.0  1 

0.2 

62 

61.5 

7.6 

22 

121.1 

14.9 

82 

180.6 

22.2 

42 

240.2 

29.5 

3 

3.0 

0.4 

63 

62.5 

7.  7 

23 

122.1 

15.0 

83 

181.6 

22.3 

43 

241.2 

29.6 

4 

4.0 

0.5 

ft4 

63.5 

7.8 

24 

123.1 

15.1 

84 

182.6 

22.4 

44 

242.2 

29.7 

5 

5.0 

0.6 

65 

64.5 

7.9 

25 

124.1 

15.2 

85 

183.6 

22.5 

45 

243.  2 

29.9 

6 

6.0 

0.7 

66 

65.5 

8.0 

26 

125.1 

15.4 

86 

184.6 

22.7 

46 

244.2 

30.0 

7 

6.9 

0.9 

*7 

66.5 

8.2 

27 

126.1 

15.5 

87 

185.6 

22.8 

47 

245.  2 

30.1 

8 

7.9 

1.0 

68 

67.5 

8.3 

28 

127.0 

15.6 

88 

186.6 

22.9 

48 

246.2 

30.2 

9 

8.9 

1.1 

69 

68.5 

8.4 

29 

128.0 

15.7 

89 

187.6 

23.0 

49 

247.1 

30.3 

10 

9.9 
10.9 

1.2 

70 

69.5 

8.5 

8.7 

30 

129.0 

15.8 

90 

188.6 

23.2 
23.3 

50 

248.1 

30.5 
30.6 

11 

1.3 

71 

70.5 

131 

130.0 

16.0 

191 

189.6 

251 

249.1 

12 

11.9 

1.5 

72 

71.5 

8.8 

32 

131.  0 

16.1 

92 

190.6 

23.4 

52 

250.1 

30.7 

13 

12.9 

1.6 

73 

72.5 

8.9 

33 

132.0 

16.2 

93 

191.6 

23.5 

53 

251.1 

30.8 

14 

13.9 

1.7 

74 

73.4 

9.0 

34 

133.  0 

16.3 

94 

192.6 

23.6 

54 

252.1 

31.0 

15 

14.9 

1.8 

75 

74.4 

9.1 

35 

134. 0 

16.5 

95 

193.5 

23.8 

55 

253.1 

31.1 

16 

15.9 

1.9 

76 

75.4 

9.3 

36 

135.0 

16.6 

96 

194.5 

23.9 

56 

254.1 

31.2 

17 

16.9 

2.1 

77 

76.4 

9.4 

37 

136.0 

16.7 

97 

195.5 

24.0 

57 

255. 1 

31.3 

18 

17.9 

2.2 

78 

77.4 

9.5 

38 

137.0 

16.8 

98 

196.5 

24.1 

58 

256.1 

31.4 

19 

18.9 

2.3 

79 

78.4 

9.6 

39 

138.0 

16.9 

99 

197.5 

24.3 

59 

257.1 

31.6 

20 
21 

19.9 
20.8 

2.4 
2.6 

80 

79.4 

9.7 

40 

139.0 

17.1 

200 
201 

198.5 

24.4 

60 

258.1 
259.1 

31.7 

81 

80.4 

9.9 

141 

139.9 

17.2 

199.  5 

24.5 

261 

31.8 

22 

21.8 

2.7 

82 

81.4 

10.0 

42 

140.9 

17.3 

02 

200.5 

24.6 

62 

260.0 

31.9 

23 

22.8 

2.8 

83 

82.4 

10.1 

43 

141.9 

17.4 

03 

201.5 

24.7 

63 

261.0 

32.1 

24 

23.8 

2.9 

84 

83.4 

10.2 

44 

142.9 

17.5 

04 

202.5 

24.9 

64 

262.0 

32.2 

25 

24.8 

3.0 

85 

84.4 

10.4 

45 

143.9 

17.7 

05 

203.5 

25.0 

65 

263.0 

32.3 

26 

25.8 

3.2 

86 

85.4 

10.5 

46 

144.9 

17.8 

06 

204.5 

25.1 

66 

264.0 

32.4 

27 

26.8 

3.3 

87 

86.4 

10.6 

47 

145.9 

17.9 

07 

205.5 

25.2 

67 

265.0 

32.5 

28 

27.8 

3.4 

88 

87.3 

10.7 

48 

146.9 

18.0 

08 

206.4 

25.3 

68 

266.0 

32.7 

29 

28.8 

3.5 

89 

88.3 

10.8 

49 

147.9 

18.2 

09 

207.4 

25.5 

69 

267.0 

32.8 

30 

29.8 

3.7 

3.8 

90 

89.3 

11.0 

50 

148.9 

18.3 

10 

208.4 

25.6 

70 

268.0 

32.9 

31 

30.8 

91 

90.3 

11.1 

151 

149.9 

18.4 

211 

209.4 

25.7 

271 

269.0 

33.0 

32 

31.8 

3.9 

92 

91.3 

11.2 

52 

150.9 

18.5 

12 

210.4 

25.8 

72 

270.0 

33.1 

33 

32.8 

4.0 

93 

92.3 

11.3 

53 

151.9 

18.6 

13 

211.4 

26.0 

73 

271.0 

33.3 

34 

33.7 

4.1 

94 

93.3 

11.5 

54 

152.9 

18.8 

14 

212.4 

26.1 

74 

272.0 

3.3.4 

35 

34.7 

4.3 

95 

94.3 

11.6 

55 

153.8 

18.9 

15 

213.4 

26.2 

75 

273.0 

33.5 

36 

35.7 

4.4 

96 

95.3 

11.7 

56 

154.8 

19.0 

16 

214.4 

26.3 

76 

273.9 

33.6 

37 

36.7 

4.5 

97 

96.3 

11.8 

57 

155.8 

19.1 

17 

215.4 

26.4 

77 

274.9 

33.8 

38 

37.7 

4.6 

98 

97.3 

11.9 

58 

156.8 

19.3 

18 

216.4 

26.6 

78 

275.9 

33.9 

39 

38.7 

4.8 

99 

98.3 

12.1 

59 

157.8 

19.4 

19 

217.4 

26.7 

79 

276.9 

34.0 

40 
41 

39.7 

4.9 

100 

99.3 

12.2 

60 

158.8 

19.5 

20 

218.4 

26.8 

80 

277.9 

34.1 

40.7 

5.0 

101 

100.2 

12.3 

161 

159.8 

19.6 

221 

219.4 

26.9 

281 

278.9 

34.2 

42 

41.7 

5.1 

02 

101.2 

12.4 

62 

160.8 

19.7 

22 

220.  3 

27.1 

82 

279.9 

34.4 

43 

42.7 

5.2 

03 

102.2 

12.6 

63 

161.8 

19.9 

23 

221.3 

27.2 

83 

280.9 

34.5 

44 

43.7 

5.4 

04 

103.2 

12.7 

64 

162.8 

20.0 

24 

222.3 

27.3 

84 

281.9 

34.6 

45 

44.7 

5.5 

05 

104.2 

12.8 

65 

163.8 

20.1 

25 

223.3 

27.4 

85 

282.9 

34.7 

46 

45.7 

5.6 

06 

105.2 

12.9 

66 

164.8 

20.2 

26 

224  3 

27.5 

86 

283.9 

34.9 

47 

46.6 

5.7 

07 

106.2 

13.0 

67 

165.  8 

20.4 

27 

225.3 

27.7 

87 

284.9 

35.0 

48 

47.6 

5.8 

08 

107.2 

13.2 

68 

166.7 

20.5 

28 

226.3 

27.8 

88 

285.  9 

35.1 

49 

48.6 

6.0 

09 

108.2 

13.3 

69 

167.7 

20.6 

29 

227.3 

27.9 

89 

286.8 

35.2 

50 

49.6 

6.1 

10 

109.2 

13.4 

70 

168.7 

20.7 

30 

228.3 

28.0 

90 

287.8 

35.3 

51 

50.6 

6.2 

111 

110.2 

13.5 

171 

169.7 

20.8 

231 

229.3 

28.2 

291 

288.8 

35.5 

52 

51.6 

6.3 

12 

111.2 

13.6 

72 

170.7 

21.0 

32 

230.  3 

28.3 

92 

289.8 

35.6 

53 

52.6 

6.5 

13 

112.2 

13.8 

73 

171.7 

21.1 

33 

231.3 

28.4 

93 

290.8 

35.7 

54 

53.6 

6.6 

14 

113.2 

13.9 

74 

172.7 

21.2 

34 

232.  3 

28.5 

94 

291.8 

35.8 

55 

54.6 

6.7 

15 

114.1 

14.0 

75 

173.  7 

21.3 

35 

233.2 

28.6 

95 

292.8 

36.0 

56 

55.6 

6.8 

16 

115. 1 

14.1 

76 

174.7 

21.4 

36 

234.  2 

28.8 

96 

293.8 

36.1 

57 

56.6 

6.9 

17 

116.1 

14.3 

77 

175.  7 

21.6 

37 

235.  2 

28.9 

97 

294.8 

36.2 

58 

57.6 

7.1 

18 

117.1 

14.4 

78 

176.7 

21.7 

38 

236.2 

29.0 

98 

295.8 

36.3 

59 

58.6 

7.2 

19 

IS.l 

14.5 

79 

177.7 

21.8 

39 

237.  2 

29.1 

99 

296.8 

36.4 

60 

59.6 

7.3 

20 

ip..l 

14. 6       80 

178.7 

21.9 

40 

238.2 

29.2 

300 

297.8 

36.6 

Dist. 

Dep. 

Lat.   JDist. 

1  ^ep. 

Lat.      Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

/ 

83°  ( 

97°,  263°,  277° 

). 

TABLE 

2. 

[Page 

381 

Difference  of 

Latitude  and  Departure  for 

7°  (173°,  187 

°,  353° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

801 

298.7 

36.7 

361 

858.  3 

44.0 

421 

417.9 

51.3 

481 

477.4 

58.6 

541 

537.  0 

65.9 

02 

299.7 

36.8 

62 

859.  3 

44.1 

22 

418.8 

51.4 

82 

478.4 

58.7 

42 

537.9 

•  66.0 

08 

300.7 

36.9 

63 

360.  8 

44.2 

28 

419.8 

51.5 

83 

479.4 

58.8 

48 

588.9 

66.2 

04 

301.7 

37.0 

64 

861.3 

44.4 

24 

420.8 

51.7 

84 

480.4 

59.0 

44 

589.  9 

66.3 

05 

302.7 

87.2 

65 

862.8 

44.5 

25 

421.8 

51.  8 

85 

481.4 

59.1 

45 

540.9 

66.4 

06 

303.7 

37.3 

66 

363.  3 

44.6 

26 

422.8 

51.9 

86 

482.4 

59.2 

46 

541. 9 

66.6 

07 

304.7 

37.4 

67 

364.  3 

44.7 

27 

428.  8 

52.0 

87 

488.4 

59.4 

47 

542.  9 

66.7 

08 

305.  7 

37.5 

68 

365.2 

44.8 

28 

424.8 

52.2 

88 

484.3 

59.  5 

48 

543.9 

66.8 

09 

306.7 

37.7 

69 

366.2 

45.0 

29 

425.8 

52.3 

89 

485.3 

59.6 

49 

544.9 

66.9 

10 
811 

307.7 
308.7 

37.8 

70 

367.2 

45.1 
45.2 

80 

426.8 

52.4 

90 

486.3 
487.8 

59.7 
59.8 

50 

545.  9 

67.0 

37.9 

371 

368.2 

431 

427.8 

52.5 

491 

551 

546.  9 

67.1 

12 

309.7 

88.0 

72 

369.2 

45.3 

82 

428.8 

52.6 

92 

488.3 

59.9 

52 

547.9 

67.2 

18 

810.7 

38.1 

73 

370.  2 

45.5 

33 

429.8 

52.8 

93 

489.3 

60.1 

53 

548.  9 

67.4 

14 

311.7 

38.8 

74 

371.2 

45.6 

34 

430.8 

52.9 

94 

490.3 

60.2 

54 

549.9 

67.5 

15 

312.6 

88.4 

75 

372.2 

45.7 

35 

431.7 

58.0 

95 

491.3 

60.3 

55 

550.  8 

67.6 

16 

313.6 

88.5 

76 

373.2 

45.8 

36 

432.7 

58.1 

96 

492.3 

60.5 

56 

551.  8 

67.8 

17 

314.6 

88.6 

77 

374.2 

45.9 

37 

433.7 

53.3 

97 

493.3 

60.6 

57 

552.8 

67.9 

18 

315.6 

88.7 

78 

375.2 

46.1 

38 

434.7 

58.4 

98 

494.3 

60.7 

58 

558.8 

68.0 

19 

316.6 

38.9 

79 

876.2 

46.2 

39  !  435. 7 

58.5 

99 

495.3 

60.8 

59 

554.8 

68.1 

20 
821 

317.6 

39.0 
39.1 

80 

877.2 

46.8 

40 

486.7 
437.7 

5.3.6 
58.7 

500 
501 

496.8 
497.2 

61.0 
61.1 

60 

555.  8 

68.3 

318.6 

881 

878.1 

46.4 

441 

561 

556.  8 

68.4 

22 

319.6 

89.2 

82 

879.1 

46.5 

42  !  438.  7 

58.9 

02 

498.2 

61.2 

62 

557.  8 

68.5 

28 

320.6 

89.4 

83 

880.1 

46.7 

43 

439.7 

54.0 

08 

499.2 

61.3 

63 

558.  8 

68.6 

24 

321.6 

89.5 

84 

881.1 

46.8 

44 

440.7 

54.1 

04 

500.  2 

61.4 

64 

559.  8 

68.7 

25 

322.6 

39.6 

85 

882.1 

46.9 

45 

441.7 

54.2 

05 

501.2 

61.  5 

65 

560.8 

68.9 

26 

823.  6 

39.7 

86 

383.1 

47.0 

46 

442.7 

54.3 

06 

502.2 

61.0 

66 

561.  8 

69.0 

27 

324.6 

89.8 

87 

384.1 

47.2 

47 

44.3.7 

54.5 

07 

503.2 

61.8 

67 

562.8 

69.1 

28 

325.  5 

40.0 

88 

385. 1 

47.8 

48 

444.7 

54.6 

08 

504.2 

61.9 

68 

563.8 

69.2 

29 

326. 5 

40.1 

89 

886.1 

47.4 

49 

445.  6 

54.7 

09 

505.  2 

62.0 

69 

564.8 

69.3 

30 

327.5 

40.2 

90 

387.1 

47.5 

50 

446.6 
447.6 

54.8 

10 
511 

506.2 
507.2 

62.1 
62.8" 

70 
571 

565.8 
566.7 

69.4 

381 

828.  5 

40.8 

391 

888.1 

47.6 

451 

55.0 

69.6 

32 

329.  5 

40.5 

92 

889.1 

47.8 

52 

448.6 

55.1 

12 

508.2 

62.4 

72 

567.7 

69.7 

33 

330.5 

40.6 

93 

390.1 

47.9 

53 

449.6 

55.2 

18 

509.2 

62.5 

73 

568.7 

69.8 

34 

881.5 

40.7 

94 

891.1 

48.0 

54 

450.  6 

55.3 

14 

510.2 

62.6 

74 

569.7 

69.9 

35 

882.5 

40.8 

95 

892.0 

48.1 

55 

451.6 

55.4 

15 

511.1 

62.7 

75 

570.  7 

70.1 

36 

^33.5 

40.9 

96 

393.  0 

48.3 

56 

452.6 

55.6 

16 

512.1 

62.9 

76 

571.7 

70.2 

37 

334.5 

41.1 

97 

894.0 

48.4 

57 

453.6 

55.7 

17 

518.1 

68.0 

77 

572.  7 

70.8 

38 

335.5 

41.2 

98 

895.0 

48.5 

58 

454.6 

55.8 

18 

514.1 

63.1 

78 

573.7 

70.4 

39 

886.  5 

41.3 

99 

396.0 

48.6 

59 

455.6 

55.9 

19 

515.1 

63.2 

79 

574.7 

70.5 

40 

337.5 

41.4 

400 

397.0 
398.0 

48.7 
48.9 

60 

456.6 
457.6 

56.1 
56.2 

20 

516.1 

63.4 
63.5 

80 
581 

575.  7 

70.7 

341 

838.  4 

41.6 

401 

461 

521 

517.1 

576.7 

70.8 

42 

839.4 

41.7 

02 

399.0 

49.0 

62 

458^5 

56.3 

22 

518.1 

63.  6 

82 

577.6 

70.9 

43 

840.4 

41.8 

03 

400.0 

49.1 

68 

459. 5 

56.4 

23 

519.1 

68.7 

88 

578.6 

71.0 

44 

841.4 

41.9 

04 

401.0 

49.2 

64 

460. 5 

56.5 

24 

520. 1 

63.8 

84 

579.6 

71.2 

45 

842.4 

42.0 

05 

402.0 

49.4 

65 

461.5 

56.7 

25 

521.1 

64.0 

85 

580.  6 

71.3 

46 

343.4 

42.2 

06 

403.0 

49.5 

66 

462.  5 

56.8 

26 

522.  1 

64.1 

86 

581.6 

71.4 

47 

344.4 

42.8 

07 

404.0 

49.6 

67 

463.  5 

56.9 

27 

523. 1 

64.2 

87 

582. 6 

71.5 

48 

845.4 

42.4 

08 

405.0 

49.7 

68 

464.5 

57.0 

28 

524.1 

64.3 

88 

583.6 

71.6 

49 

846.4 

42.5 

09 

405.9 

49.8 

69 

465.  5 

57.2 

29 

525.0 

64.  5 

89 

584.  6 

71.8 

50 

847.4 

42.6 

10 
411 

406.9 
407.9 

50.0 

70 

466.  5 
467.5 

57.3 
57.  4 

30 
581 

526.0 
'527. 0 

64.6 
64.7 

90 
591 

585.  6 

71.9 

351 

348.4 

42.8 

50.1 

471 

586.  6 

72.0 

52 

349.4 

42.9 

12 

408.9 

50.2 

72 

468.  5 

57.5 

32 

528.  0 

64.8 

92 

587.  6 

72.1 

53 

850.4 

48.0 

13 

409.9 

50.3 

78 

469.5 

57.6 

38 

529.  0 

64.9 

93 

588.  6 

72.2 

54 

851.4 

43.1 

14 

410.9 

50.4 

74 

470.5 

57.8 

84 

580.  0 

65.1 

94 

589.6 

72.4 

55 

852.  3 

48.8 

15 

411.9 

50.6 

75 

471.5 

57.9 

85 

581.0 

65.2 

95 

590.6 

72.5 

56 

858.3 

43.4 

16 

412.9 

50.7 

76 

472.4 

58.0 

36 

582.  0 

65.8 

96 

591.  5 

72.6 

57 

354.3 

43.5 

17 

413.9 

50.8 

77 

473.4 

58.1 

37 

533.0 

65.4 

97 

592.5 

72.7 

58 

355.3 

43.6 

18 

414.9 

50.9 

78 

474.4 

58.2 

38 

534.  0 

65.6 

98 

598.5 

72.9 

59 

356.3 

43.7 

19 

415.9 

51.1 

79 

475.4 

58.4 

39 

585.0 

65.7 

99 

594. 5 

7.3.0 

60 

357.3 

43.9 

20 

416.9 

51.2 

80 

476.4 

58.5 

40 

536.  d" 

65.8 

600 

595.  5 

73. 1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.  " 

Lat. 

Dist. 

Dep. 

Lat. 

88°  (97°,  263^ 

,  277°) 

. 

Page  382] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  8°  (172",  188 

°,  352°) . 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.1 

61 

60.4 

8.5 

121 

119.8 

16.8 

181 

179.2 

25.2 

241 

238.7 

33.5 

2 

2.0 

0.3 

62 

61.4 

8.6 

22 

120.8 

17.0 

82 

180.2 

25.3 

42 

239.6 

33.7 

3 

3.0 

0.4 

63 

62.4 

8.8 

23 

121.8 

17.1 

83 

181.2 

25.5 

43 

240.6 

33.8 

4 

4.0 

0.6 

64 

63.4 

8.9 

24 

122.8 

17.3 

84 

182.2 

25.6 

44 

241.6 

34.0 

5 

5.0 

0.7 

65 

64.4 

9.0 

25 

123.8 

17.4 

85 

183.2 

25.7 

45 

242.6 

.34.1 

6 

5.9 

0.8 

66 

65.4 

9.2 

26 

124.8 

17.5 

86 

184.2 

25.9 

46 

243.6 

34.2 

7 

6.9 

1.0 

«7 

66.3 

9.3 

27 

125.8 

17.7 

87 

185.2 

26.0 

47 

244.6 

34.4 

8 

7.9 

1.1 

68 

67.3 

9.5 

28 

126.8 

17.8 

88 

186.2 

26.2 

48 

245.6 

34.5 

9 

8.9 

1.3 

69 

68.3 

9.6 

29 

127.7 

18.0 

89 

187.2 

26.3 

49 

246.6 

34.7 

10 

9.9 

1.4 

70 

69.3 

9.7 

30 

128.7 

18.1 

90 

188.2 

26.4 

50 

247.6 

34.8 

11 

10.9 

1.5 

71 

70.3 

9.9 

131 

129.7 

18.2 

191 

189.1 

26.6 

251 

248.6 

34.9 

12 

11.9 

1.7 

72 

71.3 

10.0 

32 

130.7 

18.4 

92 

190.1 

26.7 

52 

249.5 

35.1 

13 

12.9 

1.8 

73 

72.3 

10.2 

33 

131.7 

18.5 

93 

191.1 

26.9 

53 

250.5 

35.2 

14 

13.9 

1.9 

74 

73.3 

10.3 

34 

132.7 

18.6 

94 

192.1 

27.0 

54 

251.5 

35.3 

15 

14.9 

2.1 

75 

74.3 

10.4 

35 

133.7 

18.8 

95 

193.1 

27.1 

55 

252.5 

35.5 

16 

15.8 

2.2 

76 

75.3 

10.6 

36 

134.7 

18.9 

96 

194.1 

27.3 

56 

253.5 

35.6 

17 

16.8 

2.4 

77 

76.3 

10.7 

37 

135.7 

19.1 

97 

195.1 

27.4 

57 

254.5 

35.8 

18 

17.8 

2.5 

78 

77.2 

10.9 

38 

136.7 

19.2 

98 

196.1 

27.6 

58 

255.5 

35.9 

19 

18.8 

2.6 

79 

78.2 

11.0 

39 

137.7 

19.3 

99 

197.1 

27.7 

59 

256.5 

36.0 

20 

19.8 

2.8 

80 

79.2 

11.1 

40 
141 

138.6 
139.6 

19.5 

200 

198.1 

27.8 

60 

257.5 

36.2 

21 

20.8 

2.9 

81 

80.2 

11.3 

19.6 

201 

199.0 

28.0 

261 

258.5 

36.3 

22 

21.8 

3.1 

82 

81.2 

11.4 

42 

140.6 

19.8 

02 

200.0 

28.1 

62 

259.5 

36.5 

23 

22.8 

3.2 

83 

82.2 

11.6 

43 

141.6 

19.9 

03 

201.0 

28.3 

63 

260.4 

36.6 

24 

23.8 

3.3 

84 

83.2 

11.7 

44 

142.6 

20.0 

04 

202.0 

28;  4 

64 

261.4 

36.7 

25 

24.8 

3.5 

85 

84.2 

11.8 

45 

143.6 

20.2 

05 

203.0 

28.5 

65 

262.4 

36.9 

26 

25.7 

3.6 

86 

85.2 

12.0 

46 

144.6 

20.3 

06 

204.0 

28.7 

66 

263.4 

37.0 

27 

26.7 

3.8 

87 

86.2 

12.1 

47 

145.6 

20.5 

07 

205.0 

28.8 

67 

264.4 

37.2 

28 

27.7 

3.9 

88 

87.1 

12.2 

48 

146.6 

20.6 

08 

206.0 

28.9 

68 

265.4 

37.3 

29 

28.7 

4.0 

89 

88.1 

12.4 

49 

147.5 

20.7 

09 

207.  0 

29.1 

69 

266.4 

37.4 

30 
31 

29.7 

4.2 
4.3 

90 

89.1 

12.5 

50 

148.5 

20.9 

10 
211 

208.0 

29.2 

70 
271 

267.4 
268.4 

37.6 
37.7 

30.7 

91 

90.1 

12.7 

151 

149.5 

21.0 

208.9 

29.4 

32 

31.7 

4.5 

92 

91.1 

12.8 

52 

150.5 

21.2 

12 

209.9 

29.5 

72 

269.4 

37.9 

33 

32.7 

4.6 

93 

92.1 

12.9 

53 

151.5 

21.3 

13 

210.9 

29.6 

73 

270.3 

38.0 

34 

33.7 

4.7 

94 

93.1 

13.1 

54 

152.5 

21.4 

14 

211.9 

29.8 

74 

271.3 

38.1 

35 

34.7 

4.9 

95 

94.1 

13.2 

55 

153.5 

21.6 

15 

212.9 

29.9 

75 

272.3 

38.3 

36 

35.6 

5.0 

96 

95.1 

13.4 

56 

154.  5 

21.7 

16 

213.9 

30.1 

76 

273.3 

38.4 

37 

36.6 

5.1 

97 

96.1 

13.5 

57 

155.5 

21.9 

17 

214.9 

30.2 

77 

274.3 

38.6 

38 

37.6 

5.3 

98 

97.0 

13.6 

58 

156.5 

22.0 

18 

215.9 

30.3 

78 

275.3 

38.7 

39 

38.6 

5.4 

99 

98.0 

13.8 

59 

157.5 

22.1 

19 

216.9 

30.5 

79 

276.3 

38.8 

40 

39.6 

5.6 
5.7 

100 

99.0 

13.9 
14.1 

60 

158.4 
159.4 

22.3 

20 

217.9 

30.6 

80 
281 

277. 3 
278.3 

39.0 

41 

40.6 

101 

100.0 

161 

22.4 

221 

218.8 

30.8 

39.1 

42 

41.6 

5.8 

02 

101.0 

14.2 

62 

160.4 

22.5 

22 

219.8 

30.9 

82 

279.3 

39.2 

43 

42.6 

6.0 

03 

102.0 

14.3 

63 

161.4 

22.7 

23 

220.8 

31.0 

83 

280.2 

39.4 

44 

43.6 

6.1 

04 

103.0 

14.5 

64 

162.4 

22.8 

24 

221.8 

31.2 

84 

281.2 

39.5 

45 

44.6 

6.3 

05 

104.0 

14.6 

65 

163.4 

23.0 

25 

222.8 

31.3 

85 

282.2 

39.7 

46 

45.6 

6.4 

06 

105.0 

14.8 

66 

164.4 

23.1 

26 

223.8 

31.5 

86 

283.2 

39.8 

47 

46.5 

6.5 

07 

106.0 

14.9 

67 

165.4 

23.2 

27 

224.8 

31.6 

87 

284.2 

39.9 

48 

47.5 

6.7 

08 

106.9 

15.0 

68 

166.4 

23.4 

28 

225.8 

31.7 

88 

285.2 

40.1 

49 

48.5 

6.8 

09 

107.9 

15.2 

69 

167.4 

23.5 

29 

226.8 

31.9 

89 

286.2 

40.2 

50 
51 

49.5 

7.0 
7.1 

10 

108.9 

15.3 

70 

168.3 

23.7 

30 

227.8 

32.0 

90 

287.2 

40.4 

50.5 

111 

109.9 

15.4 

171 

169.3 

23.8 

231 

228.8 

32.1 

291 

288.2 

40.5 

52 

51.5 

7.2 

12 

110.9 

15.6 

72 

170.3 

23.9 

32 

229.7 

32.3 

92 

289.2 

40.6 

53 

52.5 

7.4 

13 

111.9 

15.7 

73 

171.3 

24.1 

33 

230.7 

32.4 

93 

290.1 

40.8 

54 

53.5 

7.5 

14 

112.9 

15.9 

74 

172.3 

24.2 

34 

231.7 

32.6 

94 

291.1 

40.9 

55 

54.5 

7.7 

15 

113.9 

16.0 

75 

173.3 

24.4 

35 

232.7 

32.7 

95 

292.1 

41.1 

56 

55.5 

7.8 

16 

114.9 

16.1 

76 

174.3 

24.5 

36 

233.7 

32.8 

96 

293.1 

41.2 

57 

56.4 

7.9 

17 

115.9 

16.3 

77 

175.3 

24.6 

37 

234.7 

33.0 

97 

294.1 

41.3 

58 

57.4 

8.1 

18 

116.9 

16.4 

78 

176.3 

24.8 

38 

235.7 

33. 1 

98 

295.1 

41.5 

59 

58.4 

8.2 

19 

117.8 

16.6 

79 

177.3 

24.9 

39 

236.7 

33.3 

99 

296.1 

41.6 

60 

59.4 

8.4 

20 

118.8 

16.7 

80 

178.2 

25.1 

40 

237.7 

33.4 

300 

297.1 

41.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

82°  ({ 

)8°,  262< 

',  278° 

. 

TABLE  2. 

[Page  383    | 

Difference  of  Latitude  and  Departure  for  8°  (172°,  188°,  352' 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     1    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

298.0 

41.9 

361 

357.5 

50.2 

421 

416.9 

58.6 

481 

476.3 

66.9 

541 

535.7 

75.2 

U2 

299.0 

42.0 

62 

358.5 

50.4 

22 

417.9 

58.7 

82 

477.3 

67.1 

42 

536.7 

75.4 

03 

300.0 

42.2 

63 

359.  4 

50.5 

23 

418.9 

58.9 

83 

478.3 

67.2 

43 

537.  7 

75.5 

04 

301.0 

42.3 

64 

360.  4 

50.7 

24 

419.8 

59.0 

84 

479.3 

67.4 

44 

538.7 

75.7 

05 

302.0 

42.5 

65 

361.4 

50.8 

25 

420.8 

59.2 

85 

480.3 

67.5 

45 

539.7 

75.8 

06 

303.0 

42.6 

66 

362.4 

50.9 

26 

421.8 

59.3 

86 

481.2 

67.6 

46 

540.6 

75.9 

07 

304.0 

42.7 

67 

363.  4 

51.1 

27 

422.8 

59.4 

87 

482.2 

67.8 

47 

541.6 

76.1 

08 

305.  0 

42.9 

68 

364.4 

51.2 

28 

423.8 

59.6 

88 

483.2 

67.9 

48 

542.6 

76.2 

09 

306.  0 

43.0 

69 

365.  4 

51.4 

29 

424.8 

59.7 

89 

484.2 

68.1 

49 

543.6 

76.4 

10 

307.0 

43.1 

70 

366.4 

51.5 
51.6 

30 

425.8 
426.8 

59.8 

90 

485.2 

68.2 

50 

544.6 
545.6 

76.5 

311 

307.9 

43.3 

371 

367.4 

431 

60.0 

491 

486.2 

68.3 

551 

76.6 

12 

308.9 

43.4 

72 

368.4 

51.8 

32 

427.8 

60.1 

92 

487.2 

68.5 

52 

546.6 

76.8 

13 

309.9 

43.6 

73 
74 

369.3 

51.9 

33 

428.8 

60.3 

93 

488.2 

68.6 

53 

547.6 

76.9 

14 

310.9 

43.7 

370.3 

52.1 

34 

429.8 

60.4 

94 

489.2 

68.8 

54 

548.6 

77.1 

15 

311.9 

43.8 

75 

371.3 

52.2 

35 

430.  7 

60.6 

95 

490.2 

68.9 

55 

549.6 

77.2 

16 

312.9 

44.0 

76 

372.3 

52.3 

36 

431.7 

60.7 

96 

491.2 

69.0 

56 

550.6 

77.4 

17 

313.9 

44.1 

77 

373.3 

52.5 

37 

432.7 

60.8 

97 

492.1 

69.2 

57 

551.5 

77.5 

18 

314.9 

44.3 

78 

374.3 

52.6 

38 

433.7 

61.0 

98 

493. 1 

69.3 

58 

552.5 

77.6 

19 

315.9 

44.4 

79 

375.3 

52.7 

39 

434.7 

61.1 

99 

494.1 

69.5 

59 

553.5 

77.8 

20 
321 

316.9 

44.5 

80 

376.3 

52.9 
53.0 

40 
441 

435.7 

61.2 

500 
501 

495.1 
496.1 

■69.6 

60 

554.5 

77.9 

317.9 

44.7 

381 

377.3 

436.7 

61.4 

69.7 

561 

555.5 

78.1 

22 

318.8 

44.8 

82 

378.3 

53.2 

42 

437.7 

61.5 

02 

497.1 

69.9 

62 

556.5 

78.2 

23 

319.8 

45.0 

83 

379.2 

53.3 

43 

438.  7 

61.7 

03 

498.1 

70.0 

63 

557.5 

78.3 

24 

320.8 

45.1 

84 

380.2 

53.4 

44 

439.7 

61.8 

04 

499.1 

70.2 

64 

558.  5 

78.5 

25 

321.8 

45.2 

85 

.381.  2 

53.6 

45 

440.6 

61.9 

05 

500.1 

70.3 

65 

559.5 

78.6 

26 

322.8 

45.4 

86 

382.2 

53.7 

46 

441.6 

62.1 

06 

501.0 

70.4 

66 

560.5 

78.8 

27 

323.8 

45.5 

87 

383.2 

53.9 

47 

442.6 

62.2 

07 

502.0 

70.6 

67 

561.5 

78.9 

28 

324.8 

45.7 

88 

384.2 

54.0 

48 

443.6 

62.4 

08 

503.0 

70.7 

68 

562.5 

79.0 

29 

325.8 

45.8 

89 

385.2 

54.1 

49 

444.6 

62.5 

09 

504.0 

70.8 

69 

563.5 

79.1 

30 
331 

326.8 

327.8 

45.9 

90 

386.2 
387.2 

54.3 

50 

445.6 
446.6 

62.6 
62.8 

10 

505.0 

70.9 

70 
571 

564.5 

79.3 

46.1 

391 

54.4 

451 

511 

506.0 

71.1 

565.4 

79.4 

32 

328.7 

46.2 

92 

388.2 

54.6 

52 

447.6 

62.9 

12 

507.0 

71.2 

72 

566.4 

79.6 

33 

329.7 

46.3 

93 

389.1 

54.7 

53 

448.6 

63.0 

13 

508.0 

71.4 

73 

567.4 

79.7 

34 

330.7 

46.5 

94 

390.1 

54.8 

54 

449.6 

63.2 

14 

509.0 

71.5 

74 

568.4 

79.8 

35 

331.7 

46.6 

95 

391.1 

55.0 

55 

450.  5 

63.3 

15 

510.0 

71.6 

75 

569.4 

80.0 

36 

332.7 

46.8 

96 

392.1 

55.1 

56 

451.5 

63.5 

16 

510.9 

71.8 

76 

570.4 

80.1 

37 

*333. 7 

46.9 

97 

393.1 

55.3 

57 

452.5 

63.6 

17 

511.9 

71.9 

77 

571.4 

80.2 

38 

334.7 

47.0 

9$ 

394.1 

55.4 

58 

453.  5 

63.7 

18 

512.9 

72.0 

78 

572.4 

80.4 

39 

335.7 

47.2 

99 

395.1 

55.5 

59 

454.5 

63.9 

19 

513.9 

72.2 

79 

573.4 

80.5 

40 
341 

336.  7 

47.3 

400 

396.1 

55.7 

55.8 

60 

455.5 
456.5 

64.0 

20 

514.9 

72.3 

80 

574.4 

80.6 

337.7 

47.5 

401 

397.1 

461 

64.2 

521 

515.9 

72.4 

581 

575.4 

80.8 

42 

338.6 

47.6 

02 

398.1 

56.0 

62 

457.5 

64.3 

22 

516.9 

72.6 

82 

576.4 

80.9 

43 

339.6 

47.7 

03 

399.1 

56.1 

63 

45S.  5 

64.4 

23 

517.9 

72.8 

83 

577.4 

81.1 

44 

340.6 

47.9 

04 

400.0 

56.2 

64 

459.5 

64.6 

24 

518.9 

73.0 

84 

578.4 

81.3 

45 

341.6 

48.0 

05 

401.0 

56.4 

65 

460.4 

64.7 

25 

519.9 

73.1 

85 

579.4 

81.4 

46 

342.6 

48.2 

06 

402.0 

56.5 

66 

461.4 

64.9 

26 

520.9 

73.2 

86 

580.3 

81.6 

47 

343.6 

48.3 

07 

403.0 

56.6 

67 

462.4 

65.0 

27 

521.8 

73.4 

87 

581.3 

81.7 

48 

344.6 

48.4 

08 

404.0 

56.8 

68 

463.4 

65.1 

28 

522.8 

73.5 

88 

582.3 

81.8 

49 

345.6 

48.6 

09 

405.0 

56.9 

69 

464.4 

65.3 

29 

523.8 

73.7 

89 

583.3 

82.0 

50 
351 

346.6 

48.7 
48.9 

10 
411 

406.  0 

407.  0 

57.1 

70 

465.4 
466.4 

65.4 
65.6 

30 
531 

524.8 
525.  8 

73.8 

90 

584.3 

82.1 

347.6 

57.2 

471 

73.9 

591 

585.3 

82.2 

52 

348.5 

49.0 

12 

408.0 

57.3 

72 

467.4 

65.7 

32 

526.8 

74.1 

92 

586.3 

82.4 

53 

349.5 

49.1 

13 

409.0 

57.5 

73 

468.4 

65.8 

33 

527.8 

74.2 

93 

587.3 

82.5 

54 

350. 5 

49.3 

14 

409.9 

57.6 

74 

469.4 

66.0 

34 

528.8 

74.3 

94 

588.3 

82.6 

55 

351.5 

49.4 

15 

410.9 

57.8 

75 

470.4 

66.1 

35 

529.8 

74.5 

95 

589.3 

82.8 

56 

352.5 

49.5 

16 

411.9 

57.9 

76 

471.3 

66.2 

36 

530.8 

74.6 

96 

590.3 

83.0 

57 

353.5 

49.7 

17 

412.9 

58.0 

77 

472.3 

66.4 

37 

531.7 

74.7 

97 

591.2 

83.1 

58 

354.5 

49.8 

18 

413.9 

58.2 

78 

473.3 

66.5 

38 

532.7 

74.9 

98 

592.2 

83.2 

59 

355.5 

50.0 

19 

414.9 

58.3 

79 

474.3 

66.7 

39 

533.7 

75.0 

99 

593.2 

83.3 

60 

356.5 

50.1 

20 

415.9 

58.5 

80 

475.3 

66.8 

40 

534.7 

75.1 

600 

594.2 

83.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

82°  (98°,  262°,  278°).                                                                           1 

Page  384] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  9°  (171°,  189°,  351° 

• 

Dist. 
1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1.0 

0.2 

61 

60.2 

9.5 

121 

119.5 

18.9 

181 

178.8 

28.3 

241 

238.  0 

37.7 

2 

2.0 

0.3 

62 

61.2 

9.7 

22 

120.  5 

19. 1 

82 

179.8 

28.5 

42 

239.0 

37.9 

3 

3.0 

0.5 

63 

62.2 

9.9 

23 

121.5 

19.2 

83 

180.7 

28.6 

43 

240.0 

38.0 

4 

4.0 

0.6 

64 

63.2 

10.0 

24 

122.5 

19.4 

84 

181.7 

28.8 

44 

241.0 

38.2 

5 

4.9 

0.8 

65 

64.2 

10.2 

25 

123.5 

19.6 

85 

182.7 

28.9 

45 

242.0 

38.3 

6 

5.9 

0.9 

66 

65.2 

10.3 

26 

124.4 

19.7 

86 

183.7 

29.1 

46 

243.0 

38.5 

7 

6.9 

1.1 

«7 

66.2 

10.5 

27 

125.4 

19.9 

87 

184.7 

29.3 

47 

244.0 

38.6 

8 

7.9 

1.3 

68 

67.2 

10.6 

28 

126.4 

20.0 

88 

185.7 

29.4 

48 

244.9 

38.8 

9 

8.9 

1.4 

69 

68.2 

10.8 

29 

127.4 

20.2 

89 

186.7 

29.6 

49 

245.9 

39.0 

10 
11 

9.9 
10.9 

1.6 

70 

69.1 

11.0 
11.1 

30 
131 

128.4 
129.4 

20.3 
20.  5 

90 

187.7 

29.7 

50 

246.9 
247.  9 

39.1 

1.7 

71 

70.1 

191 

188.6 

29.9 

251 

39.3 

12 

11.9 

1.9 

72 

71.1 

11.3 

32 

130.4 

20.6 

92 

189.6 

30.0 

52 

248.9 

.39.4 

13 

12.8 

2.0 

73 

72.1 

11.4 

33 

131.4 

20.8 

93 

190.6 

30.2 

53 

249.9 

39.6 

14 

13.8 

2.2 

74 

73.1 

11.6 

34 

132.  4 

21.0 

94 

191.6 

30.3 

54 

250.9 

39.7 

15 

14.8 

2.3 

75 

74.1 

11.7 

35 

133.  3 

21.1 

95 

192.6 

30.5 

55 

251.9 

39.9 

16 

15.8 

2.5 

76 

75.1 

11.9 

36 

134.3 

21.3 

96 

193.6 

30.7 

56 

252.8 

40.0 

17 

16.8 

2.7 

77 

76.1 

12.0 

37 

135.3 

21.4 

97 

194.6 

30.8 

57 

253.8 

40.2 

18 

17.8 

2.8 

78 

77.0 

12.2 

38 

136.3 

21.6 

98 

195.6 

31.0 

58 

254.8 

40.4 

19 

18.8 

3.0 

79 

78.0 

12.4 

39 

137.3 

21.7 

99 

196.5 

31.1 

59 

255. 8 

40.5 

20 
21 

19.8 
20.7 

3.1 

80 

•  79.0 

12.5 
12.7 

40 

138.3 

21.9 

200 

197.5 

31.3 

60 

256.8 

40.7 

3.3 

81 

80.0 

141 

139.3 

22.1 

201 

198.5 

31.4 

261 

257.8 

40.8 

22 

21.7 

3.4 

82 

81.0 

12.8 

42 

140.3 

22.2 

02 

199.5 

31.6 

62 

258.8 

41.0 

23 

22.7 

3.6 

83 

82.0 

13.0 

43 

141.2 

22.4 

03 

200.5 

31.8 

63 

259.8 

41.1 

24 

23.7 

3.8 

84 

83.0 

13.1 

44 

142.2 

22.5 

04 

201.5 

31.9 

64 

260.7 

41.3 

25 

24.7 

3.9 

85 

84.0 

13.3 

45 

143.2 

22.7 

05 

202.5 

32.1 

65 

261.7 

41.5 

26 

25.7 

4.1 

86 

84.9 

13.5 

46 

144.2 

22.8 

06 

203.5 

32.2 

66 

262.7 

41.6 

27 

26.7 

4.2 

87 

85.9 

13.6 

47 

145.2 

23.0 

07 

204.5 

32.4 

67 

263.7 

41.8 

28 

27.7 

4.4 

88 

86.9 

13.8 

48 

146.2 

23.2 

08 

205.4 

32.5 

68 

264.7 

41.9 

29 

28.6 

4.5 

89 

87.9 

13.9 

49 

147.2 

23.3 

09 

206.4 

32.7 

69 

265.  7 

42.1 

30 

29.6 

4.7 

90 

88.9 
89.9 

14.1 
14.2 

50 
151 

148.2 

23.5 
23.6 

10 

207.4 

32.9 

70 
271 

266.7 

42.2 
42.4 

31 

30.6 

4.8 

91 

149. 1 

211 

203. 4 

33.0 

267.7 

32 

31.6 

5.0 

92 

90.9 

14.4 

52 

150.1 

2.3.8 

12 

209.4 

33.2 

72 

268.7 

42.6 

33 

32.6 

5.2 

93 

91.9 

14.5 

53 

151.1 

23.9 

13 

210.4 

33.3 

73 

269.6 

42.7 

34 

33.6 

5.3 

94 

92.8 

14.7 

54 

•152. 1 

24.1 

14 

211.4 

33.5 

74 

270.6 

42.9 

35 

34.6 

5.5 

95 

93.8 

14.9 

55 

153.1 

24.2 

15 

212.4 

33.6 

75 

271.6 

43.0 

36 

35.6 

5.6 

96 

94.8 

15.0 

56 

15+.  1 

24.4 

16 

213.3 

33.8 

76 

272.6 

43.2 

37 

36.5 

5.8 

97 

95.8 

15.2 

57 

155.1 

24.6 

17 

214.3 

33.9 

77 

273.6 

43.3 

38 

37.5 

5.9 

98 

96.8 

15.3 

58 

156.1 

24.7 

18 

215.3 

34.1 

78 

274.6 

43.5 

39 

38.5 

6.1 

99 

97.8 

15.5 

59 

157.0 

24.9 

19 

216.3 

34.3 

79 

275.6 

43.6 

40 
41 

39.5 
40.5 

6.3 
6.4 

100 
101 

98.8 
99.8 

15.6 
15.  8^ 

60 
161 

158.0 
159.0" 

25.0 

20 

217.3 

34.4 

80 

276.6 
277.  5 

43.8 
44.0 

25.2 

221 

218.3 

34.6 

281 

42 

41.5 

6.6 

02 

100.7 

16.0 

62 

160.0 

25.3 

22 

219.3 

34.7 

82 

278.5 

44.1 

43 

42.5 

6.7 

03 

101.7 

16.1 

63 

161.0 

25.5 

23 

220.  3 

34.9 

83 

279.5 

44.3 

44 

43.5 

6.9 

04 

102.7 

16.3 

64 

162.0 

25.7 

24 

221.2 

35.0 

84 

280.5 

44.4 

45 

44.4 

7.0 

05 

103.7 

16.4 

65 

163.0 

25.8 

25 

222.2 

35.2 

85 

281.5 

44.6 

46 

45.4 

7.2 

06 

104.7 

16.6 

66 

164.0 

26.0 

26 

223.  2 

35.4 

86 

282. 5 

44.7 

47 

46.4 

7.4 

07 

105.7 

16.7 

67 

164.9 

26.1 

27 

224.2 

35.5 

87 

283.5 

44.9 

48 

47.4 

7.5 

08 

106.7 

16.9 

68 

165.9 

26.3 

28 

225.2 

35.7 

88 

284.5 

45.1 

49 

48.4 

7.7 

09 

107.7 

17.1 

69 

166.9 

26.4 

29 

226.2 

35.8 

89 

285.4 

45.2 

'•50 

49.4 

7.8 

10 

108.6 
109.6 

17.2 
17.4 

70 
171 

167.9 
168.9 

26.6 
26.8 

30 
231 

227.2 

228.2 

36.0 

90 

286.4 

45.4 

51 

50.4 

8.0 

111 

36.1 

291 

287.4 

45.5 

52 

51.4 

8.1 

12 

110.6 

17.5 

72 

169.9 

26.9 

32 

229.1 

36.3 

92 

288.4 

45.7 

53 

52.  3 

8.3 

13 

111.6 

17.7 

73  j  170.9 

27.1 

33 

230.  1 

36.4 

93 

289.4 

45.8 

54 

53.3 

8.4 

14 

112.6 

17.8 

74     171.9 

27.2 

34 

231.1 

36.6 

94 

290.4 

46.0 

55 

54.3 

8.6 

15 

113.6 

18.0 

75     172.8 

27.4 

35 

232.1 

36.8 

95 

291.4 

46.1 

56 

55.3 

8.8 

16 

114.6 

18.1 

76     173. 8 

27.5 

36 

233.  1 

36.9 

96 

292.4 

46.3 

57 

56.3 

8.9 

17 

115.6 

18.  3* 

77     174.8 

27.7 

37 

234. 1 

37.1 

97 

293.  3 

46.5 

58 

57.3 

9.1 

18 

116.5 

18.5 

78  1  175.8 

27.8 

38 

235. 1 

37.2 

98 

294.3 

46.6 

59 

58.3 

9.2 

19 

117.5 

18.6 

79 

176.8 

28.0 

39 

236.  1 

37.4 

99 

295.  3 

46.8 

60 

59.3 

9.4 

20 

118.5 

18.8 

80 

177.8 

28.2 

40 

237.0 

37.  5 
Lat. 

300 

296.3 

46.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1     Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

81°  (99°,  261°,  279° 

). 

TABLE  S 

[Page  385    | 

Difference  of  Latitude  and  Departure  for 

9°  (171°,  189 

%  351° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep.l 

301 

297.3 

47.1 

361 

356.  6 

56.5 

421 

415.8 

65.9 

481 

475.1 

75.2 

541 

534.4 

84.6 

02 

298.3 

47.2 

62 

357.  5 

56.7 

22 

416.8 

66.0 

82 

476.1 

75.3 

42 

535.4 

84.7 

03 

299.3 

47.4 

63 

358.  5 

56.8 

23 

417.8 

66.  2 

83 

477.1 

75.5 

43 

536.  3 

84.9 

04 

300.  3 

47.6 

64 

359.  5 

56.9 

24 

418.8 

66.3 

84 

478.0 

75.  6 

44 

537.3 

85.1 

05 

301.2 

47.7 

65 

360.5 

57.1 

25 

419.8 

66.5 

85 

479.0 

75.8 

45 

538.3 

85.3 

06 

302.2 

47.9 

66 

361.5 

57.3 

26 

420.8 

66.6 

86 

480.0 

75.9 

46 

539.3 

85.4 

07 

303.2 

48.0 

67 

362.5 

57.4 

27 

421.7 

66.8 

87 

481.0 

76.1 

47 

540.3 

85.6 

08 

304.2 

48.2 

68 

363.  5 

57.6 

28 

422.7 

67.0 

88 

482.0 

76.2 

48 

541.  3 

85.7 

09 

305.2 

48.3 

69 

364.5 

57.7 

29 

423.7 

67.1 

89 

483.0 

76.4 

49 

542.3 

85.9 

10 

306.2 

48.5 
48.7 

70 

365.4 

57.9 
58.1 

30 
431 

424.7 

67.3 

90 
491 

484.0 
485.0 

76.5 

76.7 

50 
551 

543.  3 
544.3 

86.0 

311 

307.2 

371 

366.4 

425.7 

67.4 

86.2 

12 

308.2 

48.8 

72 

367.4 

58.2 

32 

426.7 

67.6 

92 

485.9 

76.8 

52 

545.2 

86.3 

13 

309.1 

49.0 

73 

368.  4 

58.4 

33 

427.7 

67.7 

93 

486.9 

77.0 

53 

546.  2 

86.5 

14 

310.1 

49.1 

74 

369.4 

58.5 

34 

428.7 

67.9 

94 

487.9 

77.1 

54 

547.2 

86.6 

15 

311.1 

49.3 

75 

370.4 

58.7 

35 

429.6 

68.1 

95 

488.  9 

77.3 

55 

548.2 

86.8 

16 

312.1 

49.4 

76 

371.4 

58.8 

36 

430.6 

68.2 

96 

589.9 

77.5 

56 

549.2 

87.0 

17 

313.1 

49.6 

77 

372.4 

59.0 

37 

431.  6 

68.4 

97 

490.9 

77.  7 

57 

550.2 

87.1 

18 

314.1 

49.8 

78 

373.3 

59.  1 

38 

432.  6 

68.5 

98 

491.9 

77.9 

58 

551.  2 

87.3 

19 

315.1 

49.9 

79 

374.3 

59.3 

39 

433.6 

68.7 

99 

492.9 

78.0 

59 

552.  2 

87.4 

20 

316.1 

50.1 

80 
381 

375.3 

59.5 

40 

434.6 

68.8 

500 
501 

493.8 
4914.8 

78.2 
78.4" 

60 
561 

553.1 
554. 1 

87.6 
87.7 

321 

317.0 

50.2 

376.  3 

59.6 

441 

435.6 

69.0 

22 

318.0 

50.4 

82 

377.  3 

59.8 

42 

436.6 

69.1 

02 

495.8 

78.5 

62 

555. 1 

87.9 

23 

319.0 

50.5 

83 

378.3 

59.9 

43 

437.5 

69.3 

03 

496.8 

78.7 

63 

556.1 

88.0 

24 

320.0 

50.7 

84 

379.3 

60.1 

44 

438.5 

69.5 

04 

497.8 

78.8 

64 

557.1 

88.2 

25 

321.0 

50.8 

85 

380.3 

60.2 

45 

439.  5 

69.6 

05 

498.8 

79.0 

65 

558.1 

88.3 

26 

322.0 

51.0 

86 

381.2 

60.4 

46 

440.5 

69.8 

06 

499.8 

79.1 

66 

559.1 

88.5 

27 

323.0 

51.2 

87 

382.2 

60.5 

47 

441.5 

69.9 

07 

500.8 

79.2 

67 

560.1 

88.6 

28 

324.  0 

51.3 

88 

383.2 

60.7 

48 

442.5 

70.1 

08 

501.7 

79.4 

68 

561.0 

88.8 

29 

324.9 

51.5 

89 

384.2 

60.9 

49 

443.5 

70.2 

09 

502.  7 

79.5 

69 

562.0 

88.9 

30 
331 

325.  9 

51.7 

90 
391 

385.2 
386.2 

61.0 

50 

444.5 
445.  4 

70.4 

10 

503.7 
504.7 

79.7 

79.8 

70 
571 

563.0 
564.0 

89.1 

326.9 

51.8 

61.2 

451 

70.6 

511 

89.2 

32 

327.9 

51.9 

92 

387.2 

61.3 

52 

446.4 

70.7 

12 

505.  7 

80.1 

72 

565.0 

89.4 

33 

328.9 

52.1 

93 

388.2 

61.5 

53 

447.4 

70.9 

13 

506.7 

80.2 

73 

566. 0 

89.5 

34 

329.9 

52.3 

94 

389.1 

61.6 

54 

448.4 

71.0 

14 

507.7 

80.3 

74 

567.0 

89.7 

.35 

330.  9 

52.4 

95 

390.1 

61.8 

55 

449.4 

71.2 

15 

508.7 

80.5 

75 

568.0 

89.9 

36 

331.9 

52.6 

96 

391. 1 

62.0 

56 

450.4 

71.3 

16 

509.6 

80.6 

76 

568.9 

90.1 

37 

S32.8 

52.7 

97 

392.1 

62.1 

57 

451.4 

71.5 

17 

510.6 

80.8 

77 

569.9 

90.2 

38 

333.8 

52.9 

98 

393.1 

62.3 

58 

452.4 

71.7 

18 

511.6 

80.9 

78 

570. 9 

90.3 

39 

334.8 

53.0 

99 

394.1 

62.4 

59 

453.3 

71.8 

19 

512.6 

81.1 

79 

571.9 

90,5 

40 
341 

335.8 

53.2 

400 

395. 1 

62.6 

60 

454.  3 

72.0 

20 

513. 6 

81.3 

80 

572.9 

90.7 

336.  8 

53.3 

401 

396.1 

62.7 

461 

455.3 

72.1 

521 

514.6 

81.4 

581 

573.9 

90.9 

42 

337.8 

53.5 

02 

397.0 

62.9 

62 

456.3 

72.3 

22 

515.  6 

81.6 

82 

574.9 

91.0 

43 

338.8 

53.7 

03 

398.0 

63.0 

63 

457.3 

72.4 

23 

516.6 

81.8 

83 

575.9 

91.2 

44 

339.  8 

53:8 

04 

399.0 

63.2 

64 

458.  3 

72.6 

24 

517.6 

81.9 

84 

576.9 

91.3 

45 

340.8 

54.0 

05 

400.0 

63.4 

65 

459.3 

72.7 

25 

518.6 

82.1 

85 

577.9 

91.5 

46 

341.7 

54.1 

06 

401.0 

63.5 

66 

460.  3 

72.9 

26 

519.  5 

82.3 

86 

578.8 

91.7 

47 

342.7 

54.3 

07 

402.0 

63.7 

67 

461.2 

73.1 

27 

520. 5 

82.4 

87 

579.8 

91.8 

48 

343.7 

54.4 

08 

403.0 

63.8 

68 

462.2 

73.2 

28 

521.5 

82.6 

88 

580.8 

92.0 

49 

344.7 

54.6 

09 

404.0 

64.0 

(59 

463.2 

73.4 

29 

522.5 

82.7 

89 

581.8 

92.1 

50 
351 

345.  7 
346.7 

54.8 

10 

405.0 

64.1 

70 

464.2 

73.5 

30 

523.5 

82.9 

90 

582.8 

92.2 

54.9 

411 

405.9 

64.3 

471 

465.  2 

73.7 

531 

524. 5 

83.1 

591 

583.8 

92.4 

52 

347.7 

55.1 

12 

406.9 

64.5 

72 

466.2 

73.8 

32 

525. 5 

83.2 

92 

584.8 

92.5 

53 

348.7 

55.2 

13 

407.9 

64.6 

73 

467.2 

74.0 

33 

526.5 

83.4 

93 

585.  7 

92.7 

54 

349.6 

55.4 

14 

408.9 

64.8 

74 

468.2 

74.2 

34 

527.5 

83.5 

94 

586.7 

92.9 

55 

350.6 

55.5 

15 

409.9 

64.9 

75 

469.2 

74.3 

35 

528.4 

83.7 

95 

587.7 

93.1 

56 

351.6 

55.7 

16 

410.9 

65.1 

76 

470.1 

74.5 

36 

529.4 

83.8 

96 

588.7 

93.2 

57 

352.6 

55.9 

17 

411.9 

65.2 

77 

471.1 

74.6 

37 

530.  4 

84.0 

97 

589.7 

93.4 

58 

353.6 

56.0 

18 

412.9 

65.4 

78 

472.1 

74.8 

38 

531.4 

84.1 

98 

590.7 

93.5 

59 

354.6 

56.2 

19 

413.8 

65.6 

79 

473.1 

74.9 

39 

532.4 

84.3 

99 

591.7 

93.7 

60 

355.6 

56.3 

20 

414.8 

65.7 

80 

474.1 
Dep. 

75.0 

40 

533.4 

84.4 

600 

592.6 

93.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

81°  {{ 

)9°,  261' 

',  279° 

. 

22489—03- 


-25 


Page  386 

TABLE  2. 

Difftreiue  of  Latitude  and  Departure  for  10°  (170°,  190°,  350° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

60.1 

10.6 

121 

119.2 

21.0 

181 

178.  3 

31.4 

241 

237.3 

41.8 

2 

2.0 

0.3 

62 

61.1 

10.8 

22 

120.1 

21.2 

82 

179.2 

31.6 

42 

238.3 

42.0 

3 

3.0 

0.5 

63 

62.0 

10.9 

23 

121.1 

21.4 

83 

180.2 

31.8 

43 

239.3 

42.2 

4 

3.9 

0.7 

64 

63.0 

11.1 

24 

122.1 

21.5 

84 

181.2 

32.0 

44 

240.3 

42.4 

5 

4.9 

0.9 

65 

64.0 

11.3 

25 

123.1 

21.7 

85 

182.2 

32.1 

45 

241.3 

42.5 

6 

5.9 

1.0 

.66 

65.0 

11.5 

26 

124.1 

21.9 

86 

183.  2 

32.3 

46 

242.3 

42.7 

7 

6.9 

1.2 

•67 

66.0 

11.6 

27 

125.1 

22.1 

87 

184.2 

32.5 

47 

243.2 

42.9 

8 

7.9 

1.4 

68 

67.0 

11.8 

28 

126.1 

22.2 

88 

185.1 

32.6 

48 

244.2 

43.1 

9 

8.9 

1.6. 

69 

68.0 

12.0 

29 

127.0 

22.4 

fe9 

186.1 

32.8 

49 

245.2 

43.2 

10 
11 

9.8 

1.7 

70 
71 

68.9 

12.2 
12.3 

30 
131 

128.0 
129.0 

22.6 
22.7 

90 
191 

187.1 
18'8. 1 

33.0 

50 
251 

246.2 
247.2 

43.4 
43.6 

10.8 

1.9 

69.9 

33.2 

12 

11  8 

2.1 

72 

70.9 

12.5 

32 

130.0 

22.9 

92 

189.1 

33.3 

52 

248.2 

43.8 

13 

12.8 

2.3 

73 

71.9 

12.7 

33 

131.0 

23.1 

93 

190.1 

33.5 

53 

249.2 

43.9 

14 

13.8 

2.4 

74 

72.9 

12.8 

34 

132.0 

23.3 

94 

191.1 

33.7 

54 

250.1 

44.1 

15 

14.8 

2.6 

75 

73.9 

1.3.0 

35 

132.9 

23.4 

95 

192.0 

33. 9 

55 

251.1 

44.3 

16 

15.8 

2.8 

76 

74.8 

1.3.2 

36 

133.9 

23.6 

96 

193.0 

34.0 

56 

252.1 

44.5 

17 

16.7 

3.0 

77 

75.8 

13.4 

37 

134.9 

23.8 

97 

194.0 

34.2 

57 

253.1 

44.6 

18 

17.7 

3.1 

78 

76.8 

13.5 

38 

135.9 

24.0 

98 

195.0 

34.4 

58 

254.1 

44.8 

19 

18.7 

3.3 

79 

77.8 

13.7 

39 

136.9 

24.1 

99 

196.0 

34.6 

59 

255.1 

45.0 

20 
21 

19.7 
20.7 

3.5 

80 

78.8 

13.9 

40 

137.  9 

24.3 

200 

197.0 
197.9 

34.7 
34.9 

60 
261 

256.1 
257.0 

45.1 
45.3 

3.6 

81 

79.  8 

14.1 

141 

138.9 

24.5 

201 

22 

21.7 

3.8 

82 

80.8 

14.2 

42 

139.8 

24.7 

02 

198.9 

35.1 

62 

258.0 

45.5 

23 

22.7 

4.0 

83 

81.7 

14.4 

43 

140.8 

24.8 

03 

199.9 

35.3 

63 

259.0 

45.7 

24 

23.6 

4.2 

84 

82.7 

14.6 

44 

141.8 

25.0 

04 

200.9 

.35.4 

64 

260.0 

45.8 

25 

24.6 

•  4.3 

85 

83.7 

14.8 

45 

142.8 

25.2 

05 

201.9 

35.6 

65 

261.0 

46.0 

26 

25.6 

4.5 

86 

84.7 

14.9 

46 

143.8 

25.4 

06 

202.9 

35.8 

66 

262.0 

46.2 

27 

26.6 

4.7 

87 

85.7 

15.1 

47 

144.8 

25.5 

07 

203.9 

35.9 

67 

262.  9 

46.4 

28 

27.6 

4.9 

88 

86.7 

15.3 

48 

145.8 

25.7 

08 

204.8 

36.1 

68 

263.9 

46.5 

29 

28.6 

5.0 

89 

87.6 

15.5 

49 

146.7 

25.9 

09 

205.  8 

36.3 

69 

264.9 

46.7 

30 
31 

29.5 
30.5 

5.2 

90 

88.6 

15.6 
15.8 

50 

147.7 

148.7 

26.0 
26.2 

10 
211 

206.8 

36.5 

70 

265.9 

46.9 

6.4 

91 

89.6 

151 

207.8 

36.6 

271 

266.9 

47.1 

32 

31.5 

5.6 

92 

90.6 

16.0 

52 

149.7 

26.4 

12 

208.8 

36.8 

72 

267.9 

47.2 

33 

32.5 

5.7 

93 

91.6 

16.1 

53 

150.  7 

26.6 

13 

209.8 

37.0 

73 

268.9 

47.4 

34 

33.5 

5.9 

94 

92.6 

16.3 

.    54 

151.7 

26.7 

14 

210.7 

37.2 

74 

269.8 

47.6 

35 

34.5 

6.1 

95 

93.6 

16.5 

55 

152.6 

26.9 

15 

211.7 

37.3 

75 

270.8 

47.8 

36 

35.5 

6.3 

96 

94.5 

16.7 

56 

153.6 

27.1 

16 

212.7 

37.5 

76 

271.8 

47.9 

37 

36.4 

6.4 

97 

95.5 

16.8 

57 

154.  6 

27.3 

17 

213.7 

37.7 

77 

272.8 

48.1 

38 

37.4 

6.6 

98 

96.5 

17.0 

58 

155. 6 

27.4 

18 

214.7 

37.9 

78 

273.8 

48.3 

39 

38.4 

6.8 

99 

97.5 

17.2 

59 

156.6 

27.6 

19 

215.7 

38.0 

79 

274.8 

48.4 

40 

39.4 

6.9 

7.1 

100 
101 

98.5 

17.4 
17.5 

60 

157.6 
158.6 

27.8 

20 

216.7 

38.2 

80 

275.7 

48.6 

41 

40.4 

99.5 

161 

28.0 

221 

217.6 

38.4 

281 

276.7 

48.8 

42 

41.4 

7.3 

02 

100.5 

17.7 

62 

159.5 

28.1 

22 

218.6 

38.5 

82 

277.7 

49.0 

43 

42.3 

7.5 

03 

101.4 

17.9 

63 

160.5 

28.3 

23 

219.6 

38.7 

83 

278.7 

49.1 

44 

43.3 

7.6 

04 

102.4 

18.1 

64 

161.5 

28.5 

24 

220.6 

38.9 

84 

279.7 

49.3 

45 

44.3 

7.8 

05 

103. 4 

18.2 

65 

162. 5 

28.7 

25 

221.6 

39.1 

85 

280.7 

49.5 

46 

45.3 

8.0 

06 

104.4 

18.4 

66 

163.5 

28.8 

26 

222.6 

39.2 

86 

281.7 

49.7 

47 

46.3 

8.2 

07 

105.4 

18.6 

67 

164.5 

29.0 

27 

223.6 

39.4 

87 

282.6 

49.8 

48 

47.3 

8.3 

08 

106.4 

18.8 

68 

165.4 

29.2 

28 

224.5 

39.6 

88 

283.6 

50.0 

49 

48.3 

8.5 

09 

107.3 

18.9 

69 

166.4 

29.3 

29 

225.5 

39.8 

89 

284.6 

50.2 

50 

49.2 

8.7 

10 

108.3 
109. 3~ 

19.1 

70 

167.4 

29.5 

30 

226.5 
227.5 

39.9 

90  . 

285.6 

50.4 
50.5 

51 

50.2 

8.9 

ni 

19.3 

171 

168.4 

29.7 

231 

40.1 

291 

286.6 

52 

51.2 

9.0 

12 

110.3 

19.4 

72 

169.4 

29.9 

32 

228.5 

40.3 

92 

287.6 

50.7 

53 

52.2 

9.2 

13 

111.3 

19.6 

73 

170.4 

30.0 

33 

229.5 

40.5 

93 

288.5 

50.9 

54 

53.2 

9.4 

14 

112.  3 

19.8 

74 

171.4 

30.2 

34 

230.4 

40.6 

94 

289. 5 

51.1 

55 

54.2 

9.6 

15 

113.3 

20.0 

75 

172.3 

30.4 

35 

231.4 

40.8 

95 

290.  5 

51.2 

56 

55.1 

9.7 

16 

114.2 

20.1 

76 

173.3 

30.6 

36 

232.4 

41.0 

96 

291.5 

51.4 

57 

56.1 

9.9 

17 

115.  2 

20.3 

77 

174.  S 

30.7 

37 

233.  4 

41.2 

97 

292.5 

51.6 

58 

57.1 

10.1 

18 

116.2 

20.5 

78 

175.3 

30.9 

38 

234.4 

41.3 

98 

293.5 

51.7 

59 

58. 1 

10.2 

19 

117.2 

20.7 

79 

176.3 

31.1 

39 

235.  4 

41.5 

99 

294.5 

51.9 

60 

59.1 

1 

10.4 

20 

118.2 

20.8 

80 

177.3 

31.3 

40 

236.4 

41.7 

300 

295.4 

52.1 

Dist. 

Dep. 

Lat. 

DLst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

80°  (100°,  260°,  280°). 

TABLE  27 

[Page  387 

Difference  of  Latitude  and  Departure  for  10°  (170°,  190°,  350' 

') 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

296.  4 

52.3 

361 

.355.  5 

62.7 

421 

414.6 

73.1 

481 

473.7 

83.5 

541 

532.8 

93.9 

02 

297.4 

52.5 

62- 

356.  5 

62.9 

22 

415.6     73.3 

82 

474.7 

83.7 

42 

533.8 

94.1 

03 

298.4 

52.6 

63 

357.  5 

63.0 

23 

416.6  1  73.5 

83 

475.  7 

83.9 

43 

534.8 

94.3 

04 

299.4 

52.8 

64 

358.  5 

63.2 

24 

417.6 

73.6 

84 

476.6 

84.1 

44 

535.  7 

94.5 

05 

300.4 

53.  0 

65 

359.5 

63.4 

25 

418.5 

73.8 

85 

477.6 

84.2 

45 

536.7 

94.6 

06 

301.4 

53. 1 

66 

360. 4 

63.6 

26 

419.5 

74.0 

86 

478.6 

84.4 

46 

537.  7 

94.8 

07 

302.  3 

53.  3 

67 

361.4 

63.7 

27 

420.5 

74.2 

87 

479.6 

84.6 

47 

538.  7 

95.0 

08 

303.  3 

53.5 

68 

362.4 

63.9 

28 

421.5 

74.3 

88 

480.6 

84.7 

48 

539.  7 

95.1 

09 

304.  3 

53.7 

69 

363.  4 

64.1 

29 

422.  5 

74.5 

89 

481.  6 

84.9 

49 

540.7 

95.3 

10 

305.  3 

306.  3 

53.8 

70 

364. 4  . 

64.3 
64.4 

30 
431 

423.5 
424.  5 

74.7 

90 

482.6 
483.  5 

85.1 

50 

541.  6 
542.6 

95.5 

311 

54.0 

371 

365.4 

74.9 

491 

85.2 

551 

95.6 

12 

307.3 

54.2 

72 

366.4 

64.6 

32 

425.4     75.0 

92 

484.  5 

85.4 

52 

543.  6 

95.8 

13 

308.  2 

54.3 

73 

367.  3 

64.8 

3S 

426.4     75.2 

93 

485.  5 

85.6 

53 

544.  6 

96.0 

14 

309.  2 

54.5 

74 

368.  3 

65.0 

34 

427.4  1  75.4 

94 

486.5 

85.8 

54 

545.6 

96.2 

15 

310.2 

54.7 

75 

369.3 

65.1 

35 

428.4     75.5 

95 

487.5 

85.9 

55 

546.6 

96.3 

16 

311.  2 

54.9 

76 

370.3 

65.3 

36 

429. 4  ;  75.  7 

96 

488.5 

86. 1 

56 

547.  5 

96.* 

17 

312.2 

55.1 

77 

371.3 

65.5 

3t 

430.4  i  75.9 

97 

489.4 

86.3 

57 

548.5 

96.7 

18 

313.2 

55.2 

78 

372.3 

65.6 

38 

431.3     76.1 

98 

490.4 

86.5 

58 

549. 5 

96.9 

19 

314.2 

55.  4 

79 

373.2 

65.8 

39 

432.3     76.2 

99 

491.4 

86.6 

59 

550.5 

97.0 

20 
321 

315. 1 

55.6 

55.8 

80 
381 

374.2 
375.  2 

66.0 

40 

433.3 

76.4 
76.6 

500 
501 

492.4 
493.4 

86.8 
87.0 

60 

551.5 

97.2 
97.4 

316. 1 

66.2 

441 

434. 3 

561 

552.  5 

22 

317.1 

55.9 

82 

376.2 

66.3 

42 

435.3     76.8 

02 

494.4 

87.2 

62 

553.5 

97.6 

23 

318.1 

56.1 

83 

377.2 

66.5 

43 

436.3  i  76.9 

03 

495.  3 

87.3 

63 

554.4 

97.7 

24 

319.1 

56.3 

84 

378.2 

66.7 

44 

437.3  1  77.1 

04 

496.  3 

87.5 

64 

555.  4 

97. 9 

25 

320.1 

56.4 

85 

379.  2 

66.9 

45 

438.2     77.3 

05 

497.  3 

87.7 

65 

556.4 

98.1 

26 

321.0 

56.6 

86 

380. 1 

67.0 

46 

439.2 

77.5 

06 

498.3 

87.9 

66 

557.4 

98.3 

27 

322.0 

56.8 

87  i  381.1 

67.2 

47 

440.2 

77.6 

07 

499.3 

88.0 

67 

558.4 

98.4 

28 

323.0 

57.0 

88 

382. 1 

67.4 

48 

441.2 

77.8 

08 

500.3 

88.2 

68 

559.4 

98.6 

29 

324.0 

57.1 

89 

383.1 

67.6 

49 

442.2 

78.0 

09 

501.3 

88.4 

69 

560.3 

98.8 

30 

325. 0 
326.0 

57.3 

90 

384. 1 

67.7 

50 

443.2 

78.2 

10 

502.2 

88.6 

70 

561.3 

99.0 

331 

57.5 

391 

385.1 

67.9 

451 

444.2 

78.3 

511 

503.2 

88.7 

571 

562.3 

99.1 

32 

327.0 

57.7 

92 

386.0 

68.1 

52 

445.1 

78.5 

12 

504.2 

88.9 

72 

563.3 

99.3 

33 

327.9 

57.8 

93 

387.0 

68.2 

53 

446.1 

78.7 

13 

505.2 

89.1 

73 

564.3 

99.5 

34 

328.9 

58.0 

94 

388.0 

68.4 

54 

447.1 

78.8 

14 

506.2 

89.2 

74 

565.3 

99.6 

35 

329.9 

58.2 

95 

389.  0 

68.6 

55 

448.1 

79.0 

15 

507.2 

89.4 

75 

566.3 

99.8 

36 

530.9 

58.4 

96 

390.0 

68.8 

56 

449.1 

79.2 

16 

508.2 

89,6 

76 

567.2 

100.0 

37 

331.9 

58.5 

97 

391.0 

68.9 

57 

450.1 

79.4 

17 

509.1 

89.8 

77 

568.2 

100.2 

38 

332.9 

58.7 

98 

392.0 

69.1 

58 

451.0 

79.5 

18 

510.1 

89.9 

78 

569.2 

100.3 

39 

333.9 

58.9 

99 

392.9 

69.3 

59 

452.0 

79.7 

19 

511.1 

90.1 

79 

570.2 

100.5 

40 

334.8 

59.1 
59.2 

400 
401 

393. 9 

69.5 
69.6 

60 
461 

453.0 

79.9 

20 

512.1 
513. 1 

90.3 
90.5 

80 
581 

571.2 
572.  2" 

100.7 
100.9 

341 

335.  8 

394.9 

454.0 

80.1 

^521" 

42 

336.8 

59.4 

02 

395.9 

69.8 

62 

455.  0 

80.2 

22 

514.1 

90.6 

82 

573.2 

101.0 

43 

837.8 

59.6 

03 

396.  9 

70.0 

63 

456.0 

80.4 

23 

515.1 

90.8 

83 

574.1 

101.2 

44 

338.8 

59.8 

04 

397.9 

70.2 

64 

457.0 

80.6 

24 

516.0 

91.0 

84 

575.1 

101.4 

45 

339.8 

59.9 

05 

398.9 

70.3 

65 

457.9 

80.8 

25 

517.0 

91.2 

85 

576.1 

101.6 

46 

340.7 

60.1 

06 

399.8 

70.5 

66 

458.9 

80.9 

26 

518.0 

91.3 

86 

577.1 

101.7 

47 

341.7 

60.3 

07 

400.8 

70.7 

67 

459.9 

81.1 

27 

519. 0 

91.5 

87 

578.1 

101.9 

48 

342.7 

60.4 

08 

401.8 

70.9 

68 

460.9 

81.3 

28 

520.0 

91.7 

88 

579.1 

102.1 

49 

343.7 

60.6 

09 

402.8 

71.0 

69 

461.9     81.5 

29 

521.0 

91.9 

89 

580.0 

102.3 

50 
351 

344  7 

60.8 

10 

403.8 

71.2 

70 
471 

462.9 
463.8 

81.6 
81.8 

30 

521.9 

92.0 

90 
591 

581.0 

102.4 

345.7 

61.0 

411 

404.8 

71.4 

531      522. 9 

92.2 

582.0 

102.6 

52 

346.7 

61.1 

12 

405.  7 

71.6 

72 

464.8 

82.0 

32 

523.9 

92.4 

92  . 

583.0 

102.8 

53 

347.6 

61.3 

13 

406.7 

71.7 

73 

465.  8 

82.1 

33 

524.9 

92.5 

93 

584.0 

102.9 

54 

348.6 

61.5 

14 

407.7 

71.9 

74 

466.8 

82.3 

34 

525. 9 

92.7 

94 

585.0 

103.1 

55 

349.6 

61.7 

15 

408.7 

72.1 

75 

467.8 

82.5 

35 

526.9 

92.9 

95 

586.0 

103.  3 

56 

350.  6 

61.8 

16 

409.7 

72.2 

76 

468.8 

82.7 

36 

527.  9 

93.1 

96 

586.9 

103.5 

57 

351.6 

62.0 

17 

410.7 

72.4 

77 

469.8 

82.8 

37 

528.8 

93.2 

97 

587.9 

103.6 

•58 

352.  6 

62.2 

18 

411.7 

72.  6 

78 

470.7 

83.0 

38 

529.8 

93.4 

98 

588.9 

103.8 

59 

353.  5 

62  4 

19 

412.6 

72.8 

79 

471.7 

83.2 

39 

530.8 

93.6 

99 

589.9 

104.0 

60 

354.5 
Dep. 

62.5 

20 

413.6 

72.9 

80 

472.7 

83.4 

40 

531.  8 

93.8 

600 

590.9 

104.2 

Dist. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  j     Dep. 

Lat. 

Dist. 

Dep. 

Lat.' 

1 

^0°  (100°,  260°,  280° 

)• 

Page  388] 

TABLE  '2. 

Difference  of  Latitude  and  Depart 

ure  for  11°  (169°,  191°,  349 

'). 

Dist. 

Lat. 

1   Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

;   Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.9 

11.6 

121 

118.8 

23.1 

181 

177.7 

34.5 

241 

236.6 

46.0 

2 

2.0 

0.4 

62 

60.9 

11.8 

22 

119.8 

23.3 

82 

178.7 

34,7 

42 

237.6 

46.2 

3 

2  9 

0.6 

63 

61.8 

12.0 

23 

120.7 

23.5 

83 

179.6 

34.9 

43 

238.5 

46.4 

4 

3.9 

0.8 

64 

62.8 

12.2 

24 

121.7 

23.7 

84 

180.  6 

35.1 

44 

239.5 

46.6 

5 

4.9 

1.0 

65 

63.8 

12.4 

25  1  122.7 

23.9 

85 

181.6 

35.  3 

45 

240.5 

46.7 

6 

5.9 

1.1 

M 

64.8 

12.6 

26     123. 7 

24.0 

86 

182.6 

35.5 

46 

241.5 

46.9 

7 

6.9 

1.3 

65.8 

12.8 

27  1  124.  7 

24.2 

87 

183.6 

3.5.7 

47 

242.5 

47.1 

8 

7.9 

1.5 

68 

66,8 

13.0 

28 

125.6 

24.4 

88 

184.5 

35.9 

48 

243.4 

47.3 

9 

8.8 

1.7 

69 

67.7 

13.2 

29 

126.6 

24.6 

89 

185.5 

36.1 

49 

244.4 

47.5 

10 

9.8 

1.9 

70 

68.7 

13.4 

30 

127.6 

24.8 

90 

186.5 

36.3 

50 

245.4 

47.7 

11 

10.8 

2.1 

71 

69.7 

13.5 

131 

128. 6 

25.0 

191 

187.5 

36.4 

251  :  246.4 

47.9 

12 

11.8 

2.3 

72 

70.7 

13.7 

32 

129.6 

25.2 

92 

188.5 

36.6 

52  1  247.4 

48.1 

13 

12.8 

2.5 

73 

71.7 

13.9 

33 

130.6 

25.4 

93 

189.5 

36.8 

53  i  248.4 

48.3 

14 

13.7 

2.7 

74 

72.6 

14.1 

34 

131. 5 

25.6 

94 

190.4 

37.0 

54 

249.3 

48.5 

15 

14.7 

2.9 

75 

73.6 

14.3 

35 

132.5 

25.8 

95 

191.4 

37.2 

55 

250.3 

48.7 

*6 

15.7 

3.1 

76 

74.6 

14.5 

36 

133.5 

26.0 

96 

192.4 

37.4 

56 

251.3 

48.8 

17 

16.7 

3.2 

77 

75.6 

14.7 

37 

134.5 

26.1 

97 

193.4 

37.6 

57 

252.3 

49.0 

18 

17.7 

3.4 

78 

76.6 

14.9 

38 

135.5 

26.3 

98 

194.4 

37.8 

58 

253.3 

49.2 

19 

18.7 

3.6 

79 

77.5 

15.1 

39 

136.4 

26.5 

99 

195.3 

.38.0 

59 

254.2 

49.4 

20 

19.6 

3.8 

80 

78.5 

15.3 

40 

137.4 

26.7 

20a 

196.3 

38.2 

60 

2.55. 2 

49.6 

21 

20.6 

4.0 

81 

79.5 

15.5 

141 

138.4 

26.9 

201 

1«7.3 

38.4 

261 

256. 2 

49.8 

22 

21.6 

4.2 

82 

80.5 

15.6 

42 

139.4 

27.1 

02 

198.3 

38.5 

62 

257.2 

50.0 

23 

22.6 

4.4 

83 

81.5 

15.8 

43 

140.4 

27.3 

03 

199.3 

38.7 

63 

258.2 

50.2 

-24 

23.6 

4.6 

84 

82.5 

16.0 

44 

141  4 

27.5 

04 

200.3 

38.9 

64 

259.1 

50.4 

25 

24.5 

4.S 

85 

83.4 

16.2 

45 

142.3 

27.7 

05 

201.2 

39.1 

65 

260.1 

50.6 

26 

25.5 

5.0 

86 

84.4 

16.4 

46 

143.3 

27.9 

06 

202.2 

39.3 

66 

261.1 

50.8 

27 

26.5 

5.2 

87 

85.4 

16.6 

47 

144.3 

28.0 

07 

203.  2 

39.5 

67 

262.1 

50.9 

28 

27.5 

5.3 

88 

86.4 

16.8 

48 

145.3 

28.2 

08 

204.2 

39.7 

68 

263.1 

51.1 

29 

28.5 

5.5 

89 

87.4 

17.0 

49 

146.3 

28.4 

09 

205.2 

39.9 

69 

264.1 

51.3 

30 

29.4 

5.7 

90 

88.3 

17.2 

50 

147.2 

28.6 

10  '  206. 1 

40.1 
40.  3 

70 

265.0 

51.5 
51.7 

31 

30.4 

5.9 

91 

89.3 

17.4 

151 

148.2 

28.8 

211     207. 1 

271 

266.0 

32 

31.4 

6.1 

92 

90.3 

17.6 

52 

149.2 

29.0 

12 

208.1 

40.5 

72 

267.0 

51.9 

33 

32.4 

6.3 

93 

91.3 

17.7 

53 

150.2 

29.2 

13 

209.1 

40.6 

73 

268.0 

52.1 

34 

33.4 

6.5 

94 

92.3 

17.9 

54 

151.  2 

29.4 

14 

210.1 

40.8 

74 

269.0 

52.3 

35 

34.4 

6.7 

95 

93.3 

18.1 

55 

152.2 

29.6 

15  1  211.0 

41.0 

75 

269.9 

52.5 

36 

35.3 

6.9 

96 

94.2 

18.3 

56 

153.1 

29.8 

16 

212.0 

41.2 

76 

270.9 

52.7 

37 

36.3 

7.1 

97 

95.2 

18.6 

57 

154.1 

30.0 

17 

213.0     41.4 

77 

271.9 

52.9 

38 

37.3 

7.3 

98 

96.2 

18.7 

58 

155.1 

30.1 

18 

214.0     41.6 

78 

272.9 

53.0 

39 

38.3 

7.4 

99 

97.2 

18.9 

59 

156. 1 

30.3 

19 

215.0  1  41.8 

79 

273.9 

53.2 

40 

39.3 

7.6 

100 

98.2 

19. 1 

60 

157.1 

30.5 

20 

216.0  1  42.0 

80 

274.9 

53.  4 

41 

40.2 

7.8 

101 

99.1 

19.3 

161 

158. 0 

30.7 

221 

216.9     42.2 

281 

275.8 

53.6 

42 

41.2 

8.0 

02 

100.1 

19.5 

62 

159.0 

30.9 

22 

217.9  ;  42.4 

82 

276.8 

53.8 

43 

42.2 

8.2 

03 

101. 1 

19.7 

63 

160.0 

31.1 

23 

218.9  :  42.6 

83 

277.8 

64.0 

44 

43.2 

8.4 

04 

102.1 

19.8 

64 

161.0 

31.3 

24 

219.  9     42.  7 

84 

278.8 

54.2 

45 

44.2 

8.6 

05 

103. 1 

20.0 

65 

162.0 

31.5 

25 

220.9  \  42.9 

85 

279.8 

54.4 

46 

45.2 

8.8 

06 

104.1 

20.2 

66 

163.0 

31.7 

26 

221.8  1  4.3.1 

86 

280.7 

54.6 

47 

46.1 

9.0 

07 

105.0 

20.4 

67 

163.9 

31.9 

27 

222.8 

43.  3 

87 

281.7 

54.8 

48 

47.1 

9.2 

08 

106.  X)' 

20.6 

68 

164.9 

32.1 

28 

223.8 

43.  5 

88 

282.7 

55.0 

49 

48.1 

9.3 

09 

107.0 

20.8 

69 

165. 9 

32.2 

29 

224.8 

43.7 

89 

283.7 

66.1 

50 

49.1 

9.5 

10 

108.0 

21.0 

70 

166.9 

32.4 

30 

225.8 

43.9 

90 
291 

284.7 

56.3 

51 

50.1 

9.7 

111 

109.0 

21.2 

171 

167.9 

32.6 

231 

226.8 

44.1 

285.7 

65.5 

52 

51.0 

9.9 

12 

109. 9 

21.4 

72 

168.8 

32.8 

32 

227.7 

44.3 

92 

286  6 

55.7 

53 

52.0 

10.1 

13 

110.9 

21.6 

73 

169.8 

33.0 

33 

228.7 

44.5 

93 

287.6 

56.9 

54 

53.0 

10.3 

14 

111.9 

21.8 

74 

170.8 

33.2 

34 

229.  7  1  44.  6 

94 

288.6 

66.1 

55 

54.0 

10.5 

15 

112.9 

21.9 

75 

171.8 

33.4 

35 

230.7     44.8 

95 

.  289.  6 

66.3 

56 

55.0 

10.7 

16 

113.9 

22.1 

76 

172.8 

33.6 

36 

231.  7  1  45.  0 

96 

290.6 

56.5 

57 

56.0 

10.9 

17 

114.9 

22.3 

77 

173.7 

33.8 

37 

232.6  i  45.2 

97 

291.5 

56.7 

58 

56.9 

11.1 

18 

115.8 

22.5 

78 

174.7 

34.0 

38 

233.6  i  45.4 

98 

292.5 

56.9 

59 

57.9 

11.3 

19 

116.8 

22.7 

79 

175.7 

34.2 

39 

234.6     45.6 

99 

293.5  : 

57.1 

60 

58.9 

11.4 

20 

117.8 

22.9 

80 

176.7 

34.3 

40 

235.6 

45.8 

300 

294.5 

67.2 

Dlst. 

Dep, 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.    1 

Lat. 

Dist. 

Dep. 

Lat. 

7 

9°  (101°,  259' 

',■281°). 

TABLE  2. 

[Page  389 

Difference  of  Latitude  and  Departure  for  11°  (169°,  191 

°,  349° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

295.4 

57.4 

361 

354.3 

68.9 

421 

413.2 

80.3 

481 

472.1 

91.8 

541 

531.0 

103.2 

02 

296.4 

57.6 

62 

355.  3 

69.1 

22 

414.2 

80.5 

82 

473.1 

92.0 

42 

532.0 

103.4 

03 

297.4 

57.8 

63 

356.  3 

69.3 

23 

415.2 

80.7 

83 

474.1 

92.2 

43 

533.0 

103.  6 

04 

298.4 

58.0 

64 

357.  3 

69.5 

24 

416.2 

80.9 

84 

475.1 

92.4 

44 

534.0 

103.8 

05 

299.4 

58.2 

65 

358.3 

69.6 

25 

417.2     81.1 

85 

476. 1 

92.6 

45 

535. 0 

104.0 

06 

300.3 

58.4 

66 

359.  2 

69.8 

26 

418.1  j  81.3 

86 

477.0 

92.8 

46 

535.9 

104.2 

07 

301.3 

58.6 

67 

360.2 

70.0 

27 

419.1  1  81.5 

87 

478.0 

93.0 

47 

536.9 

104.4 

08 

302.3 

58.8 

68 

361.2 

70.2 

28 

420.1   i  81.7 

88 

479.0 

93.2 

48 

537.9 

104.6 

09 

303.3 

59.0 

69 

362.2 

70.4 

29 

421.1  1  81.9 

89 

480.0 

93.3 

49 

538. 9 

104.8 

10 
311 

304.3 
305.3 

59.2 

70 

363.  2 
364.1 

70.6 

30 

422.1  1  82.1 

90 
491 

481.0 

93.5 

50 

539.9 
540.8 

105.0 

59.3 

371 

70.8 

431 

423.0  1  82.2 

481.9 

93.6 

551 

105.  1 

12 

306.2 

59.5 

72 

365.1 

71.0 

32 

424.0 

82.4 

92 

482.9 

93.8 

52 

541.8 

105.3 

13 

307.2 

59.7 

73 

366. 1 

71.2 

33 

425.  0 

82.6 

93 

483.9 

94.0 

53 

542.8 

105.5 

14 

308.2 

59.9 

74 

367.1 

71.4 

34 

426.0 

82.8 

94 

484.9 

94.2 

54 

543.8 

105.7 

15 

309.2 

,60.1 

75 

368.1 

71.6 

35 

427.0 

83.0 

95 

485.9 

94.4 

55 

544.8 

105.  9 

16 

310.2 

60.3 

76 

369.1 

71.7 

36 

428.0 

83.2 

96 

486.9 

94.6 

56 

545.8 

106.1 

17 

311.1 

60.5 

77 

370.0 

71.9 

37 

428.9 

83.4 

97 

487.8 

94.8 

57 

546.7 

106.3 

18 

312.1 

60.7 

78 

371.0 

72.1 

38 

429.9 

83.6 

98 

488.8 

95.0 

58 

547.7 

106.5 

19 

313.1 

60.9 

79 

372.0 

72.3 

39 

430.9 

83.8 

99 

489.8 

95.2 

59 

548.7 

106.7 

20 
321 

314.1 
315.1 

61.1 

80 
381 

373.0 

72.5 

40 

431.9 
432.9 

84.0 
84.1 

500 
501 

490.8 
491.8 

95.4 

60 

549.7 
550.  T 

106.9 
107.1 

61.3 

374.0 

72.7 

441 

95.6 

561 

22 

316.1 

61.4 

82 

374.9 

72.9 

42 

433.  8 

84.3 

02 

492.7 

95.8 

62 

551.6 

107.2 

23 

317.0 

61.6 

83 

375.9 

73.1 

43 

434.8 

84.5 

03 

493.7 

96.0 

63 

552.6 

107.4 

24 

318.0 

61.8 

84 

376.9 

73.3 

44 

435.8 

84.7 

04 

494.7 

96.2 

64 

553.6 

107.6 

25 

319.0 

62.0 

85 

377.9 

73.5 

45 

436.8 

84.9 

05 

495.7 

96.4 

65. 

554.6 

107.8 

26 

320.0 

62.2 

86 

378.9 

73.7 

46 

437.8 

85.1 

06 

496.7 

96.6 

66 

555.6 

108.0 

27 

321.0 

62.4 

87 

379.9 

73.8 

47 

438.8 

85.3 

07 

497.7 

96.8 

67 

556.6 

108.2 

28 

321.9 

62.6 

88 

380.8 

74.0 

48 

439.7 

85.5 

08 

498.6 

97.0 

68 

557.6 

108.4 

29 

322.9 

62.8 

89 

381.8 

74.2 

49 

440.7 

85.7 

09 

499.6 

97.2 

69 

558.6 

108.6 

30 

323.9 

63.0 

90 

382.  8 

74.4 

50 

441.7 

85.9 

10 

500.6 

97.3 

70 
571 

559.5 
560.5 

108.8 

331 

324.9 

63.2 

391 

383.8 

74.6 

451 

442.7 

86.1 

511 

501.6 

97.5 

109.0 

32 

325.  9 

63.4 

92 

384.8 

74.8 

52 

443.7 

86.2 

12 

502.6 

97.6 

72 

561.5 

109.1 

33 

326.8 

63.5 

93 

385.7 

75.0 

53 

444.6 

86.4 

13 

503.5 

97.8 

73 

562.5 

109.3 

34 

327.  8 

63.7 

94 

386.7 

75.2 

54 

445.6 

86.6 

14 

504.5 

98.0 

74 

563.5 

109.5 

35 

328.8 

63.9 

95 

387.7 

75.4 

55 

446.6 

86.8 

15 

505.5 

98.2 

75 

564.5 

109.7 

36 

329.8 

64.1 

96 

388.7 

75.6 

56 

447.6 

87.0 

16 

506.5 

98.4 

76 

565.4 

109.9 

37 

330.8 

64.3 

97 

389.7 

75.8 

57 

448.6 

87.2 

17 

507.5 

98.6 

77 

566.4 

110.1 

38 

331.8 

64.5 

98 

390.7 

75.9 

58 

449.6 

87.4 

18 

508.5 

98.8 

78 

567.4 

110.3 

39 

332.7 

64.7 

99 

391.6 

76.1 

59 

450.5 

87.6 

19 

509.4 

99.0 

79 

568.3 

110.5 

40 

333.7 

64.9 

400 
401 

392.  6 
393.6 

76.3 

60 

451.5 

87.8 

20 

510.4 
511.4 

99.2 

80 

569.3 
570.3 

110.7 

341 

334.7 

65.1 

76.5 

46] 

452.5 

88.0 

521 

99.4 

581 

110.9 

42 

335.7 

65.3 

02 

394.6 

76.7 

62 

453.5 

88.2 

22 

512.4 

99.6 

82 

571.3 

111.1 

43 

336.7 

65.5 

03 

395.  6 

76.9 

63 

454.5 

88.3 

23 

513.4 

99.8 

83 

572.3 

111.3 

44 

337.6 

65.6 

04 

396.5 

77.1 

64 

455. 4 

88.5 

24 

514.3 

100.0 

84 

573.2 

111.5 

45 

338.6 

65.8 

05 

397.5 

77.3 

65 

456.4 

88.7 

25 

515.3 

100.2 

85 

574.2 

111.7 

46 

339.6 

66.0 

06 

398.5 

77.5 

66 

457.4 

88.9 

26 

516.3 

100.4 

86 

575.  2 

111.8 

47 

340.6 

66.2 

07 

399.5 

77.7 

67 

458.4 

89.1 

27 

517.3 

100.6 

87 

576.2 

112.1 

48 

341.6 

66.4 

08 

400.5 

77.9 

68 

459.4 

89.3 

28 

518.3 

100.8 

88 

577.  2 

112.3 

49 

342.  6 

66.6 

09 

401.5 

78.1 

69 

460.4 

89.5 

29 

519.3 

101.0 

89 

578.2 

112.4 

50 
351 

343.5 

66.8 

10 

402.4 
403.4 

78.2 
78.4 

70 
471 

461.  3 
462.3 

89.7 

30 

520.2 

101.2 

90 

579.1 

112.6 

344.5 

67.0 

411 

89.9 

531 

521.2 

101.4 

591 

580. 1 

112.8 

52 

345.5 

67.2 

12 

404.4 

78.6 

72 

463.3 

90.1 

32 

522.2 

101.6 

92 

581.1 

113.0 

53 

346.5 

67.4 

13 

405.4 

78.8 

73 

464.3 

90.3 

33 

523.2 

101.7 

93 

582.1 

113.2 

54 

347. 5 

67.5 

14 

406.4 

79.0 

74 

465.3 

90.4 

34 

524.2 

101.8 

94 

583.1 

113.3 

55 

348.4 

67.7 

15 

407.3 

79.2 

75 

466.2 

90.6 

35 

525.1 

102.0 

95 

584.0 

113.5 

56 

349.4 

67.9 

16 

408.3 

79.4 

76 

467.2 

90.8 

36 

526.1 

102.2 

96 

585.0 

113.7 

57 

350.  4 

68.1 

17 

409.3 

79.6 

77 

468.2 

91.0 

37 

527.1 

102.4 

97 

586.0 

113.9 

58 

351.4 

68.3 

18 

410.3 

79.8 

78 

469.2 

91.2 

38 

528.1 

102.6 

98 

587.0 

114.1 

59 

352.4 

68.5 

19 

411.3 

80.0 

79 

470.2 

91.4 

39 

529.1 

102.8 

99 

588.0 

114.3 

60 

353.4 

68.7 

20 

412.3 

80.1 

80 

471.1 

91.6 

40 

530.1 

103.0 

600 

589.0 

114.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1     Dep. 

Lat. 

D:st. 

Dep. 

Lat. 

79°  (101°,  259°,  281°). 

Page  390] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  12° 

(168°,  192°,  348°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.7 

12.7 

121 

118.4 

25.2 

181 

177.0 

37.6 

241 

235.7 

50.1 

2 

2.0 

0.4 

62 

60.6 

12.9 

22 

119.3 

25.4 

82 

178.0 

37.8 

42 

236.7 

50.3 

3 

2.9 

0.6 

63 

61.6 

13.1 

23 

120.3 

25.6 

83 

179.0 

38.0 

43 

237.7 

50.5 

4 

3.9 

0.8 

64 

62.6 

13.3 

24 

121.3 

25.8 

84 

180.0 

38.3 

44 

238.7 

50.7 

5 

4.9 

1.0 

65 

63.6 

13.5 

25 

122.3 

26.0 

85 

181.0 

38.5 

45 

239.6 

50.9 

6 

5.9 

1.2 

6/ 

64.6 

13.7 

26 

123.2 

26.2 

86 

181.9 

38.7 

46 

240.6 

51.1 

7 

6.8 

1.5 

65.5 

13.9 

27 

124.2 

26.4 

87 

182.9 

38.9 

47 

24L6 

51.4 

8 

7.8 

1.7 

68 

66.5 

14.1 

28 

125.  2 

26.6 

88 

183.9 

39.1 

48 

242.6 

51.6 

9 

8.8 

1.9 

69 

67.5 

14.3 

29 

126.2 

26.8 

89 

184.9 

39.3 

49 

243.6 

51.8 

10 
11 

9.8 
10.8 

2.1 
2.3 

70 

68.5  1  14.6 

30 
131 

127.2 

27.0 
27.2 

90 
191 

185.8 
186.8 

39.5 

50 

244.  5 
245.5 

52.0 
52.2 

71 

69.4 

14.8 

128.1 

39.7 

251 

12 

11.7 

2.5 

72 

70.4 

15.0 

32 

129.1 

27.4 

92 

187.8 

39.9 

52 

246.5 

52.4 

13 

12.7 

2.7 

73 

71.4 

15.2 

33 

130.1 

27.7 

93 

188.8 

40.1 

53 

247.5 

52.6 

14 

13.7 

2.9 

74 

72.4 

15.4 

34 

131.1 

27.9 

94 

189.8 

40.3 

54 

248.4 

52.8 

15 

14.7 

3.1 

75 

73.4 

15.6 

35 

132.0 

28.1 

95 

190.7 

40.5 

55 

249.4 

53.0 

16 

15.7 

3.3 

76 

74.3 

15.8 

36 

133.0 

28.3 

96 

191.7 

40.8 

56 

250.4 

53.2 

17 

16.6 

3.5 

77 

75.3 

16.0 

37 

134.0 

28.5 

97 

192.7 

41.0 

57 

251.4 

53.4 

18 

17.6 

3.7 

78 

76.3 

16.2 

38 

135.0 

28.7 

98 

193.7 

41.2 

58 

252.4 

53.6 

19 

18.6 

4.0 

79 

77.3 

16.4 

39 

136.0 

28.9 

99 

194.7 

41.4 

59 

253.3 

53.8 

20 

21 

19.6 

4.2 

80 

78.3 

16.6 

40 

136.9 

29.1 
29.3 

200 
201" 

195.6 
196.6 

41.6 
41.8 

60 
261 

254.3 

54.1 

20.5 

4.4 

81 

79.2 

16.8 

141 

137.9 

255.  3 

54.3 

22 

21.5 

4.6 

82 

80.2 

17.0 

42 

138.9 

29.5 

02 

197.6 

42.0 

62 

256.3 

54.5 

23 

22.5 

4.8 

83 

81.2 

17.3 

43 

139.9 

29,7 

03 

198.6 

42.2 

63 

257.3 

54.7 

24 

23.5 

5.0 

84 

82.2 

17.5 

44 

140.9 

29.9 

04 

199.5 

42.4 

64 

258.2 

54.9 

25 

24.5 

5.2 

85 

83.1 

17.7 

45 

141.8 

30.1 

05 

200.5 

42.6 

65 

259.2 

55.1 

26 

25.4 

5.4 

86 

84.1 

17.9 

46 

142.8 

30.4 

06 

201.5 

42.8 

66 

260.2 

55.3 

27 

26.4 

5.6 

87 

85.1 

18.1 

47 

143.8 

30.6 

07 

202.5 

43.0 

67 

261.2 

55.5 

28 

27.4 

5.8 

88 

86.1 

18.3 

48 

144.8 

30.8 

08 

203.5 

43.2 

68 

262.1 

55.7 

29 

28.4 

6.0 

89 

87.1 

18.5 

49 

145.7 

31.0 

09 

204.4 

43.5 

69 

263.1 

55.9 

30 

29.3 

6.2 

90 

88.0 

18.7 

50 

146.7 

31.2 

10 

205.4 
206.4 

43.7 
43.9 

70 

264.1 

56.1 

31 

30.3 

6.4 

91 

89.0 

18.9 

151 

147.7 

31.4 

211 

271 

265.1 

56.3 

32 

31.3 

6.7 

92 

90.0 

19.1 

52 

148.7 

31.6 

12 

207.4 

44.1 

72 

266.1 

56.6 

33 

32.3 

6.9 

93 

91.0 

19.3 

53 

149.7 

31.8 

13 

208.3 

44.3 

73 

267.0 

56.8 

34 

33.3 

7.1 

94 

91.9 

19.5 

54 

150.6 

32.0 

14 

209.3 

44.5 

74 

268.0 

57.0 

35 

34.2 

7.3 

95 

92.9 

19.8 

55 

151.6 

32.2 

15 

210.  3 

44.7 

75 

269.0 

57.2 

36 

35.2 

7.5 

96 

93.9 

20.0 

56 

152.6 

32.4 

16 

211.3 

44.9 

76 

270.0 

57.4 

37 

36.2 

7.  7 

97 

94.9 

20.2 

57 

153.6 

32.6 

17 

212.  3 

45.1 

77 

270.9 

57.6 

38 

37.2 

7.9 

98 

95.9 

20.4 

58 

154.  5 

32.9 

18 

213.  2 

45.3 

78 

271.9 

57.8 

39 

38.1 

8.1 

99 

96.8 

20.6 

59 

155.  5 

33.1 

19 

214.2 

45.  5 

79 

272.9 

58.0 

40 

39.1 

8.3 

100 

97.8 

20.8 

60 

156.5 

33.3 

20 

215.2 
216.2 

45.7 
45.9 

80 
281 

273.9 
274.  9 

58.2 
58.4 

41 

40.1 

8.5 

101 

98.8 

21.0 

161 

157.5 

33.5 

221 

42 

41.1 

8.7 

02 

99.8 

21.2 

62 

158.5 

33.7 

22 

217.1 

46.2 

82 

275.8 

58.6 

43 

42.1 

8.9 

03 

100.7 

21.4 

63 

159.4 

33.9 

23 

218.1 

46.4 

83 

276.8 

58.8 

44 

43.0 

i9.1 

04 

101.7 

21.6 

64 

160.4 

34.1 

24 

219.1 

46.6 

84 

277.8 

59.0 

45 

44.0 

'9.4 

05 

102.7 

21.8 

65 

161.4 

34.3 

25 

220.1 

46.8 

85 

278.8 

59.3 

46 

45.0 

9.6 

oS 

103.7 

22.0 

66 

162.4 

34.5 

26 

221.1 

47.0 

86 

279.8 

59.5 

47 

46.0 

9.8 

07 

104.7 

22.2 

67 

163.4 

34.7 

27 

222.0 

47.2 

87 

280.7 

59.7 

48 

47.0 

10.0 

08 

105.7 

22.5 

68 

164.3 

34.9 

28 

223.0 

47.4 

88 

281.7 

59.9 

49 

47.9 

10.2 

09 

106.6 

22.7 

69 

165.3 

35.1 

29 

224.0 

47.6 

89 

282.7 

60.1 

50 

48.9 

10.4 

10 

107.6 

22.9 

70 

166.3 

35.3 
35.6 

30 
231 

225.0 
226.0 

47.8 
48.0 

90 
291 

283.7 

60.3 

51 

49.9 

10.6 

111 

108.6 

23.1 

171 

167.3 

284.6 

60.5 

52 

50.9 

10.8 

12 

109.6 

23.3 

72 

168.2 

35.8 

32 

226.9 

48.2 

92 

285.  6 

60.7 

53 

51.8 

11.0 

13 

110.5 

23.5 

73 

169.2 

36.0 

33 

227.9 

48.4 

93 

286.6 

60.9 

54 

52.8 

11.2 

14 

111.5 

23.7 

74 

170.2 

36.2 

34 

228.9 

48.7 

94 

287.6 

61.1 

55 

53.8 

11.4 

15 

112.5 

23.9 

75 

171.2 

36.4 

35 

229.9 

48.9 

95 

288.6 

61.3 

56 

54.8 

11.6 

16 

113.  5 

24.1 

76 

172.2 

36.6 

36 

230.8 

49.1 

96 

289.5 

61.5 

57 

55.8 

11.9 

17 

114.4 

24.3 

77 

173.1 

36.8 

37 

231.8 

49.3 

97 

290.5 

61.7 

58 

56.7 

12.1 

18 

115.  4 

24.5 

78 

174.1 

37.0 

38 

232.8 

49.5 

98 

291.5 

62.0 

59 

57.7 

12.3 

19 

116.4 

24.7 

79 

175.1 

37.2 

39 

233.  8 

49.7 

99 

292.5 

62.2 

60 

58.7 

12.5 

20 

117.4 

24.9 

80 

176.1 

37.4 

40 

234.8 

49.9 

300 

293.4 

62.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lit. 

Dist. 

Dep. 

Lat. 

1 

'8°  (1 

32°,  258 

=,.282°). 

TABLE  2. 

[Page  391 

Difference  of  Latitude  and  Departure  for  12°  ( 

168°,  192°,  348 

°)- 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.      j    Dep. 

Dist. 

Lat. 

Dep. 

301 

294.4 

62.6 

361 

353. 1 

75.0 

421 

411.8 

87.5 

481 

470.5 

100.0 

541 

529.2 

112.5 

02 

295.  4 

62.8 

62 

354. 1 

75.2 

22 

412.8 

87.7 

82 

471.5 

100.2 

42 

530.2 

112.7 

03 

296.4 

63.0 

63 

355. 1 

75.4 

23 

413.8 

87.9 

83 

472.5 

100.4 

43 

531.1 

112.9 

04 

297.4 

63.2 

64 

356.0 

75..  7 

24 

414.7 

88.1 

84 

473.4 

100.6 

44 

532. 1 

113.1 

05 

298.3 

63.4 

65 

357.  0 

75.9 

25 

415.  7 

88.3 

85 

474.4 

100.8 

45 

533.1 

113.3 

0(5 

299.  3 

63.6 

66 

358.  0 

76.1 

26 

416.7 

88.6 

86 

475.4 

101.0 

46 

534. 1 

113.5 

07 

300.  3 

63.8 

67 

359.  0 

76.3 

1    27 

417.7 

88.8 

87 

476.4 

101.  2 

47 

535.1 

113.7 

08 

301.3 

64.0 

68 

360.  0 

76.5 

28 

418.6 

89.0 

88 

477.3 

101.4 

48 

536.0 

113.9 

09 

302.  2 

64.2 

69 

360.  9 

76.7 

29 

419.6 

89.2 

89 

478.3 

101.6 

49 

537.0 

114.1 

10 
311 

303.  2 

304.  2 

64.4 

70 
371 

361.9 

76.9 
77.1 

30 

420.6 
421.6 

89.4 
89.6 

90 
491 

479.3 

101.9 

50 

538.  0 
538.9 

114.4 
114.6 

64.6 

362.9 

1  431 

480.3 

102.1 

551 

12 

305.2 

64.8 

72 

363.9 

77.3 

32 

422.6 

89.8 

92 

481.2 

102.3 

52 

539.  9 

114.3 

13 

306.  2 

65.1 

73 

364.8 

77.5 

33 

423.5  ;  90.0 

93 

482.2 

102.5 

53 

540.9 

115.0 

14 

307. 1 

65.3 

74 

365.8 

77.7 

34 

424.5  i  90.2 

94 

483.2 

102.7 

54 

541.9 

115.2 

15 

308.1 

65.5 

75 

366.8 

77.9 

35 

425.5     90.4 

95 

484.2 

102.9 

55 

542.9 

115.4 

16 

309.1 

65.7 

76 

367.8 

78.2 

36 

426.5     90.6 

96 

485.2 

103.1 

56 

543.  8 

115.6 

17 

310.  1 

65.9 

77 

368.8 

78.4 

37 

427.5  .  90.8 

97 

486.1 

103.3 

57 

544.  8 

115.8 

18 

311.  1 

66.1 

78 

369.7 

78.6 

38 

428.4     91.0 

98 

487.1 

103.5 

58 

545. 8 

116.0 

19 

312.0 

66.3 

79 

370.7 

78.8 

39 

429.4     91.3 

99 

488.1 

103.8 

59 

546.8 

116.2 

20 

313. 0 

66.5 

80 

371.7 

79.0 

40 

430.4     91.5 

500 

489.1 

104.0 

60 

547.8 

116.4 

321 

314.0 

66.7 

381 

372.7 

79.2 

441 

431.4     91.7 

501 

490.0 

104.2 

561 

548.7 

116.6 

22 

315.0 

66.9 

82 

373.  7 

79.4 

42 

432.3  i  91.9 

02 

491.0 

104.4 

62 

549.7 

116.8 

23 

315.9 

67.1 

83 

374.6 

79.6 

43 

433.  3     92. 1 

03 

492.0 

104.6 

63 

550.7 

117.0 

24 

316.9 

67.3 

84 

375.6 

79.8 

44 

434.3  '  92.3 

04 

493.0 

104.8 

64 

551.7 

117.2 

25 

317.9 

67.6 

85 

376.6 

80.0 

45 

435.  3     92.  5 

05 

494.0 

105.0 

65 

552.7 

117.4 

26 

318.9 

67.8 

86 

377.6 

80.2 

46 

436.  3     92.  7 

06 

495.  0 

105.2 

66 

553.  7 

117.6 

27 

319.9 

68.0 

87 

378.5 

80.4 

47 

437.2  !  92.9 

07 

495.9 

105.4 

67 

554.6 

117.8 

28 

320.8 

68.2 

88 

379.  5 

80.7 

48 

438.2  !  9.3.1 

08 

496.9 

105.  6 

68 

555.6 

118.0 

29 

321.8 

68.4 

89 

380.  5 

80.9 

49 

439.2  i  93.3 

09 

497.9 

105.  8 

69 

556.6 

118.2 

30 
331 

322.  8 
323.8 

68.6 

90 

381.5 
382.5 

81.1 
81.3 

50 

440.2 

93.5 
93.7 

10 

498.9 

106.0 
106.  2 

70 
571 

557.5 

118.5 
118.7 

68.8 

391 

451 

441.1 

511 

499.8 

558.5 

32 

324.7 

69.0 

92 

383.4 

81.5 

52 

442.1 

93.9 

12 

500.8 

106.4 

72 

559.  5 

118.9 

33 

325.7 

69.2 

93 

384.4 

81.7 

53 

443.1 

94.1 

13 

501.8 

106.6 

73 

560.5 

119.1 

34 

326.7 

69.4 

94 

385.4 

81.9 

54 

444.1 

9'4.4 

14 

502.8 

106.8 

74 

561.5 

119.3 

35 

327.7 

69.6 

95 

386.4 

82.1 

55 

445. 1 

94.6 

15 

503.7 

107.0 

75 

562.  4 

119.5 

36 

328.7 

69.8 

96 

387.  3 

82.3 

56 

446.0 

94.8 

16 

504.7 

107.2 

76 

563.4 

119.7 

37 

'329. 6 

70.0 

97 

388.3 

82.5 

57 

447.0 

95.0 

17 

505.7 

107.4 

77 

564.  4 

119.  9 

38 

330.6 

70.3 

98 

389.3 

82.7 

58  1  448.0 

95.2 

18 

506.  7 

107.6 

78 

565.4 

120.1 

39 

331.6 

70.5 

99 

390.3 

82.9 

59  j  449.0 

95.4 

19 

507.7 

107.8 

79 

566,4 

120.3 

40 

332.6 
333.  5 

70.7 

400 

391.3 
392.2 

83.1 

60 

450.  0 
450.  9 

95.6 
95.  8 

20 
521 

508.7 
509.  6 

108.1 

80 

567.4 

120.6 
120.  8 

341 

70.9 

401 

83.4 

461 

108.3 

581 

568.3 

42 

334.  5 

71.1 

02 

393.  2 

83.6 

62 

451.9 

96.0 

22 

510.6 

108.5 

82 

569.3 

121.0 

43 

335.5 

71.3 

03 

394.  2 

83.8 

63 

452.9 

96.2 

23 

511.6 

108.7 

83 

570. 3 

121.2 

44 

386.5 

71.5 

04 

395.2 

84.0 

64     453.9 

96.5 

24 

512.5 

108.9 

84 

571.2 

121.4 

45 

337.5 

71.7 

05 

396.2 

84.2 

65 

454.8 

96.7 

25 

513.5 

109.2 

85 

572.2 

121.6 

46 

338. 4 

71.9 

06 

397. 1 

84.4 

66 

455.  8 

96.9 

26 

514.5 

109.4 

86 

573.2 

121.8 

47 

339.4 

72.1 

07 

398.1 

84.6 

67 

456.  8 

97.1 

27 

515. 5 

109.6 

87 

574.2 

122.0 

48 

340.4 

72.3 

08 

399. 1 

84.8 

68  i  457.8 

97.3 

28 

516.  5 

109.8 

88 

575.2 

122.2 

49 

341.4 

72.5 

09 

400.1 

85.0 

69  1  458.8 

97.5 

29 

517.5- 

110.0 

89 

576.2 

122.4 

50 

342.4 

72.7 

10 
411 

401.0 
402.0 

85.2 
85.  4" 

70  i  459.  7 

97.7 

30 

518.  4 
519.4 

110.2 

90 
591 

577.1 

122.  6 
122.8 

351 

343.  3 

73.0 

471     460. 7 

97.9 

531 

110.4 

578.1 

52 

344.3 

73.2 

12 

403.0 

85.6 

72  !  461. 7 

98.1 

32 

520.  4 

110.6 

92 

579.1 

123.0 

53 

345.  3 

73.4 

13 

404.0 

85.8 

73  .  462.  7 

98.3 

33 

521.  3 

110.8 

93 

580.0 

123.2 

54 

346.3 

73.6 

14 

405.  0 

86.1 

74     463.6 

98.5 

34 

522.3 

111.0 

94 

581.0 

123.4 

55 

347.2 

73.8 

15 

405.  9 

86.3 

75     464.6 

98.7 

35 

523.3 

111.2 

95 

582.0 

123.6 

56 

.348.  2 

74.0 

16 

406.  9 

86.5 

76 

465.6 

98.9 

36 

524.3 

111.4 

96 

583.0 

123.9 

57 

349.2 

74.2 

17 

407.9 

86.7 

77 

466.6 

99.1 

37 

525.3 

111.6 

97 

584.0 

124.1 

58 

350.  2 

74.4 

18 

408.  9 

86.9 

78 

467.6 

99.4 

38 

526.2 

111.8 

98 

584.  9 

124.  3 

59 

.351.2 

74.6 

19 

409.8 

87.1 

79 

468.5 

99.6 

39 

527.2 

112.0 

99 

585.9 

124.5 

60 

352.1 

74.8 

20 

410.8 

87.3 

80 

469.5 

99.8 

40 

528.2 

112.3 

600 

586.9 

124.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Di.st. 

Dep. 

Lat. 

7 

8°    (102°,  258°,  282° 

)• 

Page  392] 

TABLE 

(  2. 

Difference  of  Latitude  and  Departure  for 

13°  (167°,  193 

°,  347° 

). 

Dist. 

J^t. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.2 

61 

59.4 

13.7 

121 

117.9 

27.2 

181 

176.4 

40.7 

241 

234.8 

54.2 

2 

1.9 

0.4 

62 

60.4 

13.9 

22 

118.9 

27.4 

82 

177.3 

40.9 

42 

235.8 

54.4 

3 

2.9 

0.7 

63 

61.4 

14.2 

23 

119.8 

27.7 

83 

178.3 

41.2 

43 

236.8 

54.7 

4 

3.9 

0.9 

64 

62.4 

14.4 

24 

120.8 

27.9 

84. 

179.3 

41.4 

44 

237.7 

54.9 

5 

4.9 

1.1 

65 

63.3 

14.6 

25 

121.8 

28.1 

85 

180.3 

41.6 

45 

238.7 

55.1 

6 

5.8 

1.3 

1? 

64.3 

14.8 

26 

122.8 

28.3 

86 

181.2 

41.8 

46 

239.7 

55.3 

7 

6.8 

1.6 

65.3 

15.1 

27 

123.7 

28.6 

87 

182.2 

42.1 

47 

240.7 

55.6 

8 

7.8 

1.8 

68 

66.3 

15.3 

28 

124.7 

28.8 

88 

183.2 

42.3 

48 

241.6 

55.8 

9 

8.8 

2.0 

69 

67.2 

15.5 

29 

125.7 

29.0 

89 

184.2 

42.5 

49 

242.6 

56.0 

10 

9.7 
10.7 

2.2 

70 

68.2 

15.7 

30 

126.7 

29.2 
29.5 

90 

185.1 

42.7 

50 

243.6 
244.6 

56.  2 

11 

2.5 

71 

69.2 

16.0 

131 

127.6 

191 

186.1 

43.0 

251 

56.5 

12 

11.7 

2.7 

72 

70.2 

16.2 

32 

128.6 

29.7 

92 

187.1 

43.2 

52 

245.5 

56.7 

13 

12.7 

2.9 

73 

71.1 

16.4 

33 

129.6 

29.9 

93 

188.1 

43.4 

53 

246.5 

56.9 

14 

13.6 

3.1 

74 

72.1 

16.6 

34 

130.6 

30.1 

94 

189.0 

43.6 

54 

247.5 

57.1 

15 

14.6 

3.4 

75 

73.1 

16.9 

35 

131.5 

30.4 

95 

190.0 

43.9 

55 

248.5 

57.4 

16 

15.6 

3.6 

76 

74.1 

17.1 

36 

132.5 

30.6 

96 

191.0 

44.1 

56 

249.4 

57.6 

17 

16.6 

3.8 

77 

75.0 

17.3 

37 

133.5 

30.8 

97 

192.0 

44.3 

57 

250.4 

57.8 

18 

17.5 

4.0 

78 

76.0 

17.5 

38 

134.5 

31.0 

98 

192.9 

44.5 

58 

251.4 

58.0 

19 

18.5 

4.3 

79 

77.0 

17.8 

39 

135.4 

31.3 

99 

193.9 

44.8 

59 

252.4 

58.3 

20 

19.5 

4.5 

80 

77.9 

18.0 

40 

136.4 

31.5 

200 

194.9 

45.0 

60 
261 

253.  3 
254.3 

58.5 
58.7 

21 

20.5 

4.7 

81 

78.9 

18.2 

141 

137.4 

31.7 

201 

195.8 

45.2 

22 

21.4 

4.9 

82 

79.9 

18.4 

42 

138.4 

31.9 

02 

196.8 

45.4 

62 

255.3 

58.9 

23 

22.4 

5.2 

83 

80.9 

18.7 

43 

139.3 

32.2 

03 

197.8 

45.7 

63 

256.3 

59.2 

24 

23.4 

5.4 

84 

81.8 

18.9 

44     140. 3 

32.4 

04 

198.8 

45.9 

64 

257.2 

59.4 

25 

24.4 

5.6 

85 

82.8 

19.1 

45     141. 3 

32.6 

05 

199.7 

46.1 

65 

258.2 

59.6 

26 

25.3 

5.8 

86 

83.8 

19.3 

46 

142.3 

32.8 

06 

200.7 

46.3 

66 

259.2 

59.8 

27 

26.3 

6.1 

87 

84.8 

19.6 

47 

143.2 

33.1 

07 

201.7 

46.6 

67 

260.2 

60.1 

28 

27.3 

6.3 

88 

85.7 

19.8 

48 

144.2 

3.3.3 

08 

202.7 

46.8 

68 

261.1 

60.3 

29 

28.3 

6.5 

89 

86.7 

20.0 

49 

145.2 

33.5 

09 

203.  6 

47.0 

69 

262.1 

60.5 

30 

29.2 

6.7 

90 
91 

87.7 

20.2 

50 
151 

146.2 

33.7 

10 

204.6 
205.6 

47.2 
47.5 

70 

263.1 
264.1 

60.7 
61.0 

31 

30.2 

7.0 

88.7 

20.5 

147.1 

34.0 

211 

271 

32 

31.2 

7.2 

92 

89.6 

20.7 

52 

148.1 

34.2 

12 

206.6 

47.7 

72 

265.0 

61.2 

33 

32.2 

7.4 

93 

90.6 

20.9 

53 

149.1 

34.4 

13 

207.5 

47.9 

73 

266.0 

61.4 

34 

33.1 

7.6 

94 

91.6 

21.1 

54 

150.1 

34.6 

14 

208.5 

48.1 

74 

267.0 

61.6 

35 

34.1 

7.9 

95 

92.6 

21.4 

55 

151.0 

34.9 

15 

209.5 

48.4 

75 

268.0 

61.9 

36 

35.1 

8.1 

96 

93.5 

21.6 

56 

152.0 

35.1 

16 

210.5 

48.6 

76  !  268.9 

62.1 

37 

36.1 

8.3 

97 

94.5 

21.8 

57 

153.0 

35.3 

17 

211.4 

48.8 

77 

269.9 

62.3 

38 

37.0 

8.5 

98 

95.5 

22.0 

58 

154.0 

35.5 

18 

212.4 

49.0 

78 

270.9 

62.5 

39 

38.0 

8.8 

99 

96.5 

22.3 

59 

154.9 

35.8 

19 

213.4 

49.3 

79 

271.8 

62.8 

40 

39.0 

9.0 

100 

97.4 

22.5 

60 

155.9 

36.0 

20 
221 

214.  4 

49.5 

80 

272.8 

63.0 

41 

39.9 

9.2 

101 

98.4 

22.7 

161 

156.9 

36.2 

215.3 

49.7 

281 

273.8 

63.2 

42 

40.9 

9.4 

02 

99.4 

22.9 

62 

157.8 

36.4 

22 

216.3 

49.9 

82 

274.8 

63.4 

43 

41.9 

9.7 

03, 

100.4 

23.2 

63 

158.8 

36.7 

23 

217.3 

50.2 

83 

275.7 

63.7 

44 

42.9 

9.9 

04 

101.3 

23.4 

64 

159.8 

36.9 

24 

218.3 

50.4 

84 

276.7 

63.9 

45 

43.8 

10.1 

05 

102.3 

23.6 

65 

160.8 

37.1 

25 

219.2 

50.6 

85 

277.7 

64.1 

46 

44.8 

10.3 

06 

103.3 

23.8 

66 

161.7 

37.3 

26 

220.2 

50.8 

86 

278.7 

64.3 

47 

45.8 

10.6 

07 

104.3 

24.1 

67 

162.7 

37.6 

27 

221.2 

51.1 

87 

279.6 

64.6 

48 

46.8 

10.8 

08 

105.2 

24.3 

68 

163.7 

.37.8 

28 

222.2 

51.3 

88 

280.6 

64.8 

49 

47.7 

11.0 

09 

106.2 

24.5 

69 

164.7 

38.0 

29 

223.1 

51.5 

89 

281.6 

65.0 

50 

48.7 

11.2 

10 

107.2 

24.7 

70 

165.  6 
166.6 

38.2 
38.5 

30 
231 

224.1 

51.7 

90 

282.6 

65.2 

51 

49.7 

11.5 

111 

108.2 

25.0 

171 

225.1 

52.0 

291 

283. 5 

65.5 

52 

50.7 

11.7 

12 

109.1 

25.2 

72 

167.6 

38.7 

32 

226.1 

52.2 

92 

284.5 

65.7 

53 

51.6 

11.9 

13 

110.1 

25.4 

73 

168.6 

38.9 

33 

227.0 

52.4 

93 

285. 5 

65.9 

54 

52.6 

12.1 

14 

111.1 

25.6 

74 

169.5 

39.1 

34 

228.0 

52.6 

94 

286.5 

66.1 

55 

53.6 

12.4 

15 

112.1 

25.9 

75 

170.5 

39.4 

35 

229.0 

52.9 

95 

287.4 

66.4 

56 

54.6 

12.6 

16 

113.0 

26.1 

76 

171.5 

39.6 

36 

230.0 

53.1 

96 

288.4 

66.6 

57 

55.5 

12.8 

17 

114.0 

26.3 

77 

172.5 

39.8 

37 

230.9 

53.3 

97 

289.4 

66.8 

58 

56.5 

13.0 

18 

115.0 

26.5 

78 

173.4 

40.0 

38 

231.  9 

53.5 

98 

290.4 

67.0 

59 

57.5 

13.3 

19 

116.0 

26.8 

79 

174.4 

40.3 

39 

232.9 

53.8 

99 

291.3 

67.3 

60 

58.5 

13.5 

20 

116.9 

27.0 

80 

175.4 

40.5 

40 

233.8 

54.0 

300 

292.3 

67.5 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

11°  (103°,  257 

°,  283° 

)• 

TABLE 

2. 

[Page  393     ] 

Difference  of  Latitude  and  Departure  for  13°  (167°,  193°,  347° 

)■ 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

301 

293.3 

67.7 

361 

351.8 

81.2 

421 

410.2 

94.7 

481     468.  7  '  108.  2 

541 

527.2 

121.7 

02 

294.3 

67.9 

62 

352.7 

81.4 

22 

411.2 

94.9 

82     469.  7    108.  4 

42 

528.1 

121.9 

03 

295.  2 

68.1 

63 

353.7 

81.6 

23 

412.2 

95.1 

83  ;  470.  6    108.  6 

43 

529.1 

122.1 

04 

296.2 

68.4 

64 

354.  7 

81.9 

24 

413.1 

95.3 

84  1  471.6    108.8 

44 

530.1 

122.3 

05 

297.2 

68.6 

65 

355.  6 

82.1 

25 

414.1 

95.6 

85  :  472.6 

109.0 

45 

531. 1 

122.5 

06 

298.2 

68.8 

66 

356.  6 

82.3 

26 

415.1 

95.8 

86  i  473.  6 

109.3 

46 

532.0 

122.8 

07 

299.1 

69.0 

67 

357.6 

82.5 

27 

416.1 

96.0 

87     474. 5 

109.5 

47 

533.0 

123.0 

08 

300.1 

69.3 

68 

358.6 

82.8 

28 

417.0 

96.2 

88     475. 5 

109.7 

48 

534.0 

123.  2 

09 

301. 1 

69.5 

69 

359.5 

83.0 

29 

418.0 

96.5 

89     476. 5 

109.9 

49 

535.0 

123.4 

10 

302.1 

69.7 

70 

360.5 
361.5 

83.2 

30 

419.0 

96.7 

90  1  477.5  1110.1 

50 

535.9 

123.7 

311 

303.0 

69.9 

371 

83.4 

431 

420.0 

96.9 

491     478.4    110.4 

551 

536.  9 

123.9 

12 

304.0 

70.2 

72 

362.5 

83.7 

32 

420.9 

97.1 

92     479.4    110.6 

52 

537.9 

124.1 

13 

305.0 

70.4 

73 

363.  4 

83.9 

33 

421.9 

97.4 

93  !  480.  4  !  110. 9 

53 

538.9 

124.4 

14 

306.0 

70.6 

74 

364.4 

84.1 

34 

422.9 

97.6 

94  '  481.4  '111.1 

54 

539.8 

124.6 

15 

306.9 

70.8 

75 

365.4 

84.3 

35 

423.9 

97.8 

95  1  482.  3  i 111. 3 

55 

540.8 

124.9 

16 

307.9 

71.1 

76 

366.4 

84.6 

36 

424.8 

98.0 

96  !  483.3    111.5 

56 

541.8 

125. 1 

17 

308.9 

71.3 

77 

367.3 

84.8 

37 

425.8 

98.3 

97 

484.3     111.8 

57 

542.8 

125.3 

18 

309.9 

71.5 

78 

368.3 

85.0 

38 

426.8 

98.5 

98 

485.  3  1  112.  0 

58 

543.7 

125.5 

19 

310.8 

71.7 

79 

369.3 

85.2 

39 

427.8 

98.7 

99     486. 2  ! 112. 2 

59 

544.7 

125.8 

20 
321 

311.  8 

72.0 
72.2 

80 
381 

370.3 

85.5 

40 

428.7 

98.9 

500 

487.2 
488.2 

112.4 

60 

545.7 

126.0 

312.8 

371.2 

85.7 

441 

429.7 

99.2 

501 

112.6 

561 

546.7 

126.2 

22 

313.8 

72.4 

82 

372.2 

85.9 

42 

430.7 

99.4 

02     489.2     112.9 

62 

547.6 

126.4 

23 

314.7 

72.6 

83 

373.2 

86.1 

43 

431.6 

99.6 

03     490. 1     113. 1 

63 

548.6 

126.7 

24 

315.7 

72.9 

84 

374.2 

86.4 

44 

432.6 

99.8 

04     491.1 

113.3 

64 

549.6 

126.9 

25 

316.7 

73.1 

85 

375.1 

86.6 

45 

433.6 

100.1 

05     492. 1 

113.5 

65 

550.6 

127.1 

26 

317.6 

73.3 

86 

376.1 

86.8 

46 

434.6 

100.3 

06     493. 1 

113.8 

66 

551.5 

127.3 

27 

318.6 

73.5 

87 

377. 1 

87.0 

47 

435.5 

100.5 

07  1  494.0 

114.0 

67 

552.5 

127.6 

28 

319.6 

73.8 

88 

378.1 

87.3 

48 

436.5 

100.7 

08     495.0 

114.2 

68 

553. 5 

127.8 

29 

320.6 

74.0 

89 

379.0 

87.5 

49 

437.5 

101.0 

09     496.0 

114.5 

69 

554.5 

128.0 

30 

321.5 
322.5 

74.2 
74.4 

90 
391 

380. 0 

87.7 

50 

438.5 

101.2 

10 

496.9 
497. 9 

114.7 

70 

555.4 
556.4 

128.3 
128.5 

331 

381.0 

87.9 

451 

439.4 

101.4 

511 

114.9 

571 

32 

323.5 

74.7 

92 

382.0 

88.2 

52 

440.4 

101.6 

12 

498.9 

115.1 

72 

557.4 

128.7 

33 

324.5 

74.9 

93 

382.9 

88.4 

53 

441.4 

101.9 

13 

499.9 

115.4 

73 

558.4 

128.9 

34 

325.4 

75.1 

94 

383.9 

88.6 

54 

442.4 

102.1 

14  !  500.8 

115. 6 

74 

559.3 

129.2 

35 

326.4 

75.3 

95 

384.9 

88.8 

55 

443.3 

102.3 

15  i  501.8 

115.8 

75 

560.3 

129.4 

36 

.  327. 4 

75.6 

96 

385.9 

89.1 

56 

444.3 

102.5 

16  i  502.  8 

116.0 

76 

561.3 

129.6 

37 

■  328. 4 

75.8 

97 

386.8 

89.3 

57 

445.3 

102.8 

17     503. 8 

116.3 

77 

562.3 

129.8 

38 

329.3 

76.0 

98 

387.8 

89.5 

58 

446.3 

103.0 

18 

504.7 

116.5 

78 

563.  2 

130.0 

39 

330.3 

76.2 

99 

388.8 

89.7 

59 

447. 2 

103.2 

19 

505.7 

116.7 

79 

564.2 

130.2 

40 

331.3 
332.3 

76.5 

400 

389.8 
390.  7 

90.0 

60 

448.2 
449.  2 

103.4 
103.  7 

20 

506.7 

116.9 

80 

565.2 
566.2 

130.4 

341 

76.7 

401 

90.2 

461 

521 

507.7  :117.2 

581 

130.7 

42 

333.2 

76.9 

02 

391.  7 

90.4 

62 

450.2 

103.9 

22 

508.6  1117.5 

82 

567.1 

131.0 

43 

334.2 

77.1 

03 

392.7 

90.6 

63 

451.1 

104.1 

23 

509.  6  i  117.  7 

83 

568.1 

131.  2 

44 

335.2 

77.4 

04 

393.  6 

90.8 

64 

452. 1 

104.3 

24 

510.6    117.9 

84 

569.1 

131.4 

45 

336.2 

77.6 

05 

394.  6 

91.1 

65 

453. 1 

104.6 

25 

511.6    118.1 

85 

570.1 

131.6 

46 

337.1 

77.8 

06 

395. 6 

91.3 

66 

454.1 

104.8 

26 

512.5     118.3 

86 

571.0 

131.8 

47 

338.1 

78.0 

07 

396.6 

91.5 

67 

455.0 

105.0 

27 

513.5    118.5 

87 

572.0 

132.0 

48 

339. 1 

78.3 

08 

397.  5 

91.7 

68 

456.0 

105.2 

28 

514.5    118.7 

88 

573.0 

132.  3 

49 

340.1 

78.5 

09 

398.  5 

92.0 

69 

457.0 

105.5 

29 

515.5  ,119.0 

89 

573.9 

132.5 

50 

341.0 

78.7 

10 

399.5 

92.2 

70 

458.0 

105.  7 

30 

516.4 

119.2 

90 

574.9 

132.8 

351 

342.0 

78.9 

411 

400.5 

92.4 

471 

458.9 

105. 9 

531 

517.4 

119.4 

591 

575.9 

133.0 

52 

343.0 

79.2 

12 

401.4 

92.6 

72 

459.  9 

106.1 

32 

518.4 

119.6 

92 

576.9 

133.2 

53 

344.0 

79.4 

13 

402.4 

92.9 

73 

460.9 

106.4 

33 

519.4 

119.9 

93 

577.8 

133.4 

54 

344.9 

79.6 

14 

403.4 

93.1 

74 

461.9 

106.6 

34 

520.3    120.1 

94 

578.8 

133.6 

55 

345.9 

79.8 

15 

404.4 

93.3 

75 

462.8 

106.8 

35 

521.  3  i  120.  3 

95 

579.8 

133.  8 

56 

346.9 

80.1 

16 

405.3 

93.5 

76 

463.8 

107.0 

36 

522.  3  !  120. 5 

96 

580.8 

134.0 

57 

347. 9 

80.3 

17 

406.3 

93.8 

77 

464.8 

107.3 

37 

523.3 

120.8 

97 

581.7 

134.3 

58 

348.8 

80.5 

18 

407.3 

94.0 

78 

465.8 

107.5 

38 

524.2 

121.0 

98 

582.7 

134.5 

59 

349.8 

80.7 

19 

408.3 

94.2 

79 

466.7 

107.7 

39 

525.2 

121.2 

99 

583.7 

134.8 

60 

350.8 

81.0 

20 

409.2 

94.4 

80 

467.7 

107.9 

40 

526.2 

121.5 

600 

584.6 

135.0 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.    1    Lat. 

Dist. 

Dep. 

Lat. 

77°  (1 

03°,  257 

°,  283° 

)• 

Page  394] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  14°  (166°,  194 

°,  346° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1   0 

0.2 

61 

59.2 

14.8 

121 

117.4 

29.3 

181 

175.6 

43.8 

241 

233.8 

58.3 

2 

1.9 

0.5 

62 

60.2 

15.0 

22 

118.4 

29.5 

82 

176.6 

44.0 

42 

234.8 

58.5 

3 

2.9 

0.7 

63 

61.1 

15.2 

23 

119.3 

29.8 

83 

177.6 

44.3 

43 

235.8 

58.8 

4 

3.9 

1.0 

64 

62.1 

15.5 

24 

120.3 

30.0 

84 

178.5 

44.5 

44 

236.8 

59.0 

5 

4.9 

1.2 

65 

63.1 

15.7 

25 

121.3 

30.2 

85 

179.5 

44.8 

45 

237.7 

59.3 

6 

5.8 

1.5 

66 

(54.0     16.0 

26 

122.3 

30.5 

86 

180.5 

45.0 

46 

238.7 

59.5 

7 

6.8 

1.7 

t7 

65.0  1  16.2 

27 

123.2 

30.7 

87 

181.4 

45.2 

47 

239.  7 

59.8 

8 

7.8 

1.9 

68 

66.0     16.5 

28 

124.2 

31.0 

88 

182.4 

45.5 

48 

240.6 

60.0 

9 

8.7 

2.2 

69 

67. 0  !  16.  7 

29 

125.2 

31.2 

89 

183.4 

45.7 

49 

241.6 

60.2 

10 
11 

9.7 
10.7 

2.4 

70 

67.9  1  16.9 

30 

126.1 

31.4 
31.7 

90 
191 

184.4 

46.0 
46.2 

50 

251 

242.  6 
243.5 

60.5 

2.7 

71 

68.9 

17.2 

131 

127.1 

185. 3 

60.7 

12 

11.6 

2.9 

72 

69.9 

17.4 

32 

128.1 

31.9 

92 

186.3 

46.4 

52 

244.5 

61.0 

13 

12.6 

3.1 

73 

70.8 

17.7 

33 

129.0 

32.2 

93 

187.3 

46.7 

53 

245. 5 

61.2 

14 

13.6 

3.4 

74 

71.8 

17.9 

34 

130.0 

32.4 

94 

188.2 

46.9 

54 

246.5 

61.4 

15 

14.6 

3.6 

75 

72.8 

18.1 

35 

131. 0 

32.7 

95 

189.  2 

47.2 

55 

247.4 

61.7 

16 

15.5 

3.9 

76 

73.7 

18.4 

36 

132.0 

32.9 

96 

190.2 

47.4 

56 

248.4 

61.9 

17 

16.5 

4.1 

77 

74.7 

18.6 

37 

132.9 

33.1 

97 

191.1 

47.7 

57 

249.4 

62.2 

18 

17.5 

4.4 

78 

75.7 

18.9 

38 

133.9 

33.4 

98 

192.1 

47.9 

58 

250.3 

62.4 

19 

18.4 

4.6 

79 

76.7 

19.1 

39 

134.9 

33.6 

99 

193.1 

48.1 

59 

251.3 

62.7 

20 

19.4 

4.8 

80 

77.6 

19.4 

40 

135.8 

33.9 

200 

194.1 

48.4 

60 

252.3 

62.9 

21 

20.4 

5.1 

81 

78.6 

19.6 

141 

136.8 

34.1 

201 

195.0" 

48.6 

261 

253.2 

63.1 

22 

21.3 

5.3 

82 

79.6 

19.8 

42 

137.8 

34.4 

02 

196.0 

48.9 

62 

254.2 

63.4 

23 

22.3 

5.6 

83 

80.5 

20.1 

43 

138.8 

34.6 

03 

197.0 

49.1 

63 

255.  2 

63.6 

24 

23.3 

5.8 

84 

81.5 

20.3 

44 

139.  7 

34.8 

04 

197.9 

49.4 

64 

256.2 

63.9 

25 

24.3 

6.0 

85 

82.5 

20.6 

45 

140.7 

35.1 

05 

198.9 

49.6 

65 

257.1 

64.1 

26 

25.2 

6.3 

86 

83.4 

20.8 

46 

141.7 

35.3 

06 

199.9 

49.8 

66 

258. 1 

64.4 

27 

26.2 

6.5 

87 

84,4 

21.0 

47 

142.6 

35.6 

07 

200.9 

50.1 

67 

259.1 

64.6 

28 

27.2 

6.8 

88 

85.4 

21.3 

48 

143.6 

35.8 

08 

201.8 

50.3 

68 

260.0 

64.8 

29 

28.1 

7.0 

89 

86.4 

21.5 

49 

144.6 

36.0 

09 

202.8 

50.6 

69 

261.0 

65.1 

30 

29.1 

7.3 

90 

87.3 

21.8 

50 

145.5 

36.3 

10 

203.8 
204.7 

50.8 

70 

262.0 

65.3 

31 

30.1 

7.5 

91 

88.3 

22.0 

151 

146.5 

36.5 

211 

51.0 

271 

'263.  0 

65.6 

32 

31.0 

7.7 

92 

89.3 

22.3 

52 

147.5 

36.8 

12 

205.7 

51.3 

72 

263.9 

65.8 

33 

32.0 

8.0 

93 

90.2 

22.5 

53 

148.  5 

37.0 

13 

206.7 

51.5 

73 

264.9 

66.0 

34 

33.0 

8.2 

94 

91.2 

22.7 

54 

149.4 

37.3 

14 

207.6 

51.8 

74 

265.9 

66.3 

35 

34.0 

8.5 

95 

92.2 

23.0 

55 

150.4 

37.5 

15 

208.6 

52.0 

75 

266.8 

66.5 

36- 

34.9 

8.7 

96 

93.1  1  23.2 

56 

151.  4 

37.7 

16 

209.6 

52.3 

76 

267.8 

66.8 

37 

35.9 

9.0 

97 

94.1  !  23.5 

57 

152.3 

38.0 

17 

210.6 

52.5 

77 

268.8 

67.0 

38 

36.9 

9.2 

98 

95.1  i  23.7 

58 

153.  3 

38.2 

18 

211.5 

52.7 

78 

269.7 

67.3 

39 

37.8 

9.4 

99 

96.1     24.0 

59 

154.3 

.  .38.  5 

19 

212.  5 

53.0 

79 

270.7 

67.5 

40 

38.8 

9.7 

100 

97.0     24.2 

60 

155.2 

38.7 

20 

213.  5 

53.2 

80 

271.7 

67.7 
68.0 

41 

39.8 

9.9 

101 

98.0  j  24.4 

161 

156.  2 

38.9 

221 

214.4 

53.5 

281 

272.7 

42 

40.8 

10.2 

02 

99.  0  '  24.  7 

62 

157.  2 

39.2 

22 

215.4 

53.7 

82 

273.6 

68.2 

43 

41.7 

10.4 

03 

99.9  1  24.9 

63 

158.2 

39.4 

23 

216.4 

53. 9 

83 

274.6 

68.5 

44 

42.7 

10.6 

04 

100.9  !  25.2 

64 

159.1 

39.7 

24 

217.3 

54.2 

84 

275.  6 

68.7 

45 

43.7 

10.9 

05 

101.9     25.4 

65 

160.1 

39.9 

25 

218.3 

54.4 

85 

276.5 

68.9 

46 

44.6 

11.1 

06 

102. 9     25. 6 

66 

161.1 

40.2 

26 

219.3 

54.7 

86 

277.5 

69.2 

47 

45.6 

11.4 

07 

103.8     25.9 

67 

162.0 

40.4 

27 

220.3 

54.9 

87 

278.5 

69.4 

48 

46.6 

11.6 

08 

104. 8     26. 1 

68 

163.0 

40.6 

28 

221.2 

55.2 

88 

279.4 

69.7 

49 

47.5 

11.9 

09 

105.  8     26.  4 

69 

164.0 

40.9 

29 

222.2 

55.4 

89 

280.4 

69.9 

50 

48.5 

12.1 

10 

106.7  1  26.6 

70 

165.0 
165.9 

41.1 

30 

223.2 

55.6 

90 

281.4 

282.4 

70.2 
70. 4 

51 

49.5 

12.3 

111 

107.  7     26. 9 

171 

41.4 

231 

224.1 

55. 9 

291 

52 

50.5 

12.6 

12 

108.  7     27. 1 

72 

166.9 

41.6 

32 

225. 1 

56.1 

92 

283.3 

70.6 

53 

51.4 

12.8 

13 

109. 6     27. 3 

73 

167.9 

41.9 

33 

226.1 

56.4 

93 

284.  3 

70.9 

54 

52.4 

13.1 

14 

110.6  1  27.6 

74 

168.8 

42.1 

34 

227.0 

56.6 

94 

285.  3 

71.1 

55 

53.4 

13.3 

15 

111.6 

27.8 

75 

169.8 

42.3 

35 

228.0 

56.9 

95 

286.2 

71.4 

56 

54.3 

13.5 

16 

112,6 

28.1 

76 

170.8 

42.6 

36 

229.0 

57.1 

96 

287.2 

71.6 

57 

55.3 

13.8 

17 

113.5 

28.3 

77 

171.7 

42.8 

37 

230.  0 

57.3 

97 

288.2 

71.9 

58 

56.3 

14.0 

18 

114. 5 

28.5 

78 

172.7 

43.1 

38 

230.  9 

57.6 

98 

289.1 

72.1 

59 

57.2 

14.3 

19 

115.5 

28.8 

79 

173.7 

43.3 

39 

231.9 

57.8 

99 

290.1 

72.3 

60 

58.2 

14.5 

20 

116.4 

29.0 

80 

174.7 

43.5 

40 

232.9 

58.1 

300 

291.1 

72.6 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

■6°  (1 

04°,  256°,.  284° 

). 

TABLE 

J  2. 

[Page  395 

Difference  of  Latitude  and  Departure  for  14°  (166°,  194 

°,  346° 

)• 

Dist. 
301 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

292.0 

72.8 

361 

350.  2 

87.3 

421 

408.5 

101.8 

481 

466.7 

116.3 

541 

525.  0 

130.9 

02 

293.0 

73.0 

62 

351.  2 

87.6 

22 

409.4 

102.1 

82 

467.7 

116.6 

42 

525.  9 

131.2 

03 

294.0 

73.3 

63 

352.  2 

87.8 

23 

410.4 

102.3 

83 

468.6 

116.8 

43 

526. 9 

131.4 

04 

294.9 

73.5 

64 

353.  2 

88.0 

24 

411.4 

102.6 

84 

469.6 

117.1 

44 

527.  9 

131.6 

05 

295.9 

73.8 

65 

354.1 

88.3 

25 

412.3 

102.8 

85 

470.6 

117.3 

45 

528.  8 

131.9 

06 

296.9 

74.0 

66 

355. 1 

88.5 

26 

413.3 

103.0 

86 

471.5     117.6 

46 

52a.  8 

132. 1 

07 

297.8 

74.2 

67 

356. 1 

88.8 

27 

414.3 

103.3 

87 

472.5 

117.8 

47 

530.8 

132.  3 

08 

298.8 

74.5 

68 

357.0 

89.0 

28 

415.3 

103.5 

88 

473.5 

118.0 

48 

531.  7 

132.6 

09 

299.8 

74.7 

69 

358.0 

89.2 

29 

416.2 

103.8 

89 

474.5 

118.3 

49 

532.  7 

132.8 

10 
311 

300.8 

75.0 

70 

359.0 
359.9 

89.5 

30 
431 

417.2 

104.0 

90 

475.4 

118.5 

50 
551 

533.  7 
534.6 

133.0 
133.3 

301.  7 

75.2 

371 

89.7 

418.2 

104.2 

491 

476.4 

118.8 

12 

302.7 

75.5 

72 

360.9 

90.0 

32 

419.1 

104.  5 

92 

477.4 

119.0 

52 

535. 6 

133.6 

13 

303.7 

75.7 

73 

361.9 

90.2 

33 

420.1 

104.7 

93 

478.3 

119.2 

53 

536.6 

133.8 

14 

304.6 

7S.9 

74 

362.9 

90.5 

34 

421.1 

105.0 

94 

479.3 

119.5 

54 

537.5 

134.0 

15 

305.6 

76.2 

75 

363.8 

90.7 

35 

422.0 

105.  2 

95 

480.3 

119.7 

55 

538.5 

134.  3 

16 

306.6 

76.4 

76 

364.8 

90.9 

36 

423.0 

105.5 

96 

481.3 

120.0 

56 

539.5 

134.  5 

17 

307.6 

76.7 

77 

365.8 

91.2 

37 

424.0 

105.7 

97 

482.2 

120.2 

57 

540.  5 

134.8 

18 

308.5 

76.9 

78 

366.7 

91.4 

38 

425.0 

105. 9 

98 

483.2 

120.4 

58 

541.4 

135.  0 

19 

309.5 

77.2 

79 

367.  7  * 

91.7 

39     425. 9 

106.2 

99 

484.2 

120.7 

59 

542.4 

135.  2 

20 
321 

310.5 

77.4 

80 

368.7 

91.9 

40 

426.9 

106.4 

500 
501 

485.1 
486.1 

121.0 

60 

543.4 
544.  3 

135.  5 
135.  7 

311.4 

77.6 

381 

369. 6 

92.2 

441 

427.9 

106.7 

121.2 

561 

22 

312.4 

77.9 

82 

370.6 

92.4 

42 

428.8 

106.9 

02 

487.1 

121.4 

62 

545.  3 

135.9 

23 

313. 4 

78.1 

83 

371.6 

92.6 

43 

429.8 

107.1 

03 

488.0 

121.7 

63 

546.3 

136.2 

24 

314.3 

78.4 

84 

372. 6 

92.9 

44 

430.8 

107.4 

04 

489.0 

122.0 

64 

547.2 

136.  5 

25 

315.  3 

78.6 

85 

373.5 

93.1 

45 

431.7 

107.6 

05 

490.0 

122.1 

65 

548.2 

136.6 

26 

316.  3 

78.8 

86 

374.  5 

93.4 

46     432. 7 

107.9 

06 

491.0 

122.4 

66 

549.2 

136.9 

27 

317.  3 

79.1 

87 

375. 5 

93.6 

47 

433.  7 

108.1 

07 

491.9 

122.6 

67 

550.1 

137.1 

28 

318.2 

79.3 

88 

376.  4 

93.8 

48 

434.7 

108.4 

08 

492.9 

122.9 

68 

551.1 

137.4 

29 

319.2 

79.6 

89 

377.4 

94.1 

49 

435.6 

108.6 

09 

493.9 

123.1 

69 

552.1 

137.6 

30 
331 

320.2 

79.8 

90 

378.4 

94.3 
94.6 

50 
451 

436.6 
437.6 

108.8 
109.1 

10 
511 

494.  9 

495.  8 

123.  4 

70 

553.1 
554.0 

137.9 
138.1 

321.1 

80.1 

391 

379.4 

123.6 

571 

32 

322. 1 

80.3 

92 

380.3 

94.8 

52  !  438.5 

109.3 

12 

496.8 

123.  8 

72 

555.  0 

138.  3 

33 

323. 1 

80.5 

93 

381.  3 

95.1 

53  1  439.5 

109.6 

13 

497.8 

124.1 

73 

556.0 

138.6 

34 

324.  0 

80.8 

94 

382.  3 

95.  3 

54     440.5 

109.8 

14 

498.7 

124.3 

74 

557.0 

138.  8 

35 

325.  0 

81.0 

95 

383.  2 

95.  5 

55 

441.5 

110.1 

15 

499.  7 

124.6 

75 

557.9 

139.1 

36 

■  326. 0 

81.3 

96 

384.  2 

95.8 

56 

442.4 

110.3 

16 

500.7 

124.8 

76 

558.9 

139.3 

37 

327.  0 

81.5 

97 

385.2 

96.0 

57 

443.4 

110.5 

17 

501.7 

125.0 

77 

559.9 

139.5 

38 

327.  9 

81.7 

98 

386. 1 

96.3 

58 

444.4 

110.8 

18 

502.6 

125.3 

78 

560.9  I  139.8 

39 

328.9 

82.0 

99 

387. 1 

96.5 

59 

445.  3 

111.0 

19 

503.6 

125.6 

79 

561.8     140.0 

40 
341 

329.9 

82.2 

400 

388.1 

96.7 
97.0 

60  1  446.  3 
461  i  447.  3 

111.3 

20 
521 

504.  6 
505.5 

12.5.  8 
126. 0 

80 
581 

562.8  i  140.3 

330.8 

82.5 

401 

389.1 

111.5 

563.8 

140.5 

42 

331.8 

82.7 

02 

390. 0 

97.2 

62 

448.2 

111.7 

22 

506. 5 

126.2 

82 

564.7 

140.8 

43 

332.8 

83.0 

03 

391.0 

97.5 

63 

449.2 

112.0 

23 

507.5 

126.5 

83 

565.7 

141.0 

44 

333.7 

83.2 

04 

392.0 

97.7 

64 

450.2 

112.2 

24 

508.  4 

126.8 

84 

566.7 

141.3 

45 

334.7 

83.4 

05 

392.9 

98.0 

65 

451.  2 

112.5 

25 

509.  4 

127.0 

85 

567.6 

141.5 

46 

335.  7 

83.7 

06 

393.9 

98.2 

66 

452. 1 

112.7 

26 

510.4 

127.2 

86 

568. 6 

141.8 

47 

336.  7 

83.9 

07 

394.9 

98.4 

67 

453.1 

113.0 

27 

511.4 

127.5 

87 

569. 6 

142.0 

48 

337.6 

84.2 

08 

395.8 

98.7 

68 

454.1 

113.2 

28 

512.  3 

127.8 

88 

570.  6 

142.3 

49 

338. 6 

84.4 

09 

396.8 

98.9 

69 

455.  0 

113.4 

29 

513.3 

128.0 

89 

571. 5 

142.5 

50 
351 

339.6 
340.5 

84.7 
84.9 

10 
411 

397. 8 

99.2 

70 

456.0 
457.0 

113.7 
113.9 

30 
531 

514.3 
515.3 

128.2 
128.5 

90 
591 

572.5 

142.8 

398.8 

99.4 

471 

573.5  1  143.0 

52 

341.5 

85.1 

12 

399.7 

99.7 

72 

457.9 

114.2 

32 

516.2 

128.8 

92 

574.4  1  143.3 

53 

342.5 

85.4 

13 

400.  7 

99.9 

73 

458. 9 

114.4 

33 

517.2 

129.0 

93 

575.4  j  143.5 

54 

343.  5 

85.6 

14 

401.7 

100.1 

74 

459.  9 

114.6 

34 

518.  2 

129.2 

94 

576.4  '  143.8 

55 

344.4 

85.9 

15 

402.6 

100.4 

75 

460.9 

114.9 

35 

519.  1 

129.4 

95 

577.3  i  144.0 

56 

345.4 

86.1 

16 

403.  6 

100.6 

76 

461.8 

115.1 

36 

520.1 

129.7 

96 

578.3  ;  144.2 

57 

346.  4 

86.3 

17 

404.6 

100.9 

77  i  462.8 

115.4 

37 

521.1 

129.9 

97 

579.3     144.5 

58 

347.3 

86.6 

18 

405.  5 

101.1 

78 

463.8 

115.6 

38 

522. 1 

130.  2 

98 

580.3     144.7 

59 

348.  3 

86.8 

19 

406.  5 

101.3 

79 

464.7 

115.  9 

39 

523.  0 

130.  4 

99 

581.2     144.9 

60 

349.3 

87.1 

20 

407.  5 

101.6 

80 

465.7 

116.1 

40 

524.  0 

130.6 

600 

582.2     145.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1     Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.         Lat. 

76°  (104°,  256 

°,  284° 

)• 

1    Page  396] 

TABLE 

2. 

Difference  of  Latitude  and  Departure  for  15°  (165°,  195° 

,  345°) 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.9 

15.8 

121 

116.9 

31.3 

181 

174.8 

46.8 

241 

232.8 

62.4 

2 

1.9 

0.5 

62 

59.9 

16.0 

22 

117.8 

31.6 

82 

175.8 

47.1 

42 

233.  8 

62.6 

3 

2.9 

0.8 

63 

60.9 

16.3 

23 

118.8 

31.8 

83 

176.  8 

47.4 

43 

234.7 

62.9 

4 

3.9 

1.0 

64 

61.8 

16.6 

24 

119.8 

32.1 

84 

177.7 

47.6 

44 

235.7 

63.2 

5 

4.8 

1.3 

65 

62.8 

16.8 

25 

120.7 

32.4 

85 

178.7 

47.9 

45 

236.7 

63.4 

6 

5.8 

1.6 

66 

63.8 

17.1 

26 

121.7 

32.6 

86 

179.7 

48.1 

46 

237.6 

63.7 

7 

6.8 

1.8 

•67 

64.7 

17.3 

27 

122.7 

32.9 

87 

180.6 

48.4 

47 

238.6 

63.9 

8 

7.7 

2,1 

68 

65.7 

17.6 

28 

123.6 

33.1 

88 

181.6 

48.7 

48 

239.5 

64.2 

9 

8.7 

2.3 

69 

66.6 

17.9 

29 

124.6 

33.4 

89 

182.6 

48.9 

49 

240.5 

64.4 

10 

9.7 

2.6 

2.8 

70 
71 

67.6 

18.1 

30 

125.6 

33.6 

90 
191 

183.5 
184.5 

49.2 

50 

241.5 
242.4 

64.7 
65.0 

11 

10.6 

68.6 

18.4 

131 

126.5 

33.9 

49.4 

251 

12 

11.6 

3.1 

72 

69.5 

18.6 

32 

127.5 

34.2 

92 

185.5 

49.7 

52 

243.4 

65.2 

13 

12.6 

3.4 

73 

70.5 

18.9 

33 

128.5 

34.4 

93 

186.4 

50.0 

53 

244.4 

65.5 

14 

13.5 

3.6 

74 

71.5 

19.2 

34 

129.4 

34.7 

94 

187.4 

50.2 

54 

245.3 

65.7 

15 

14.5 

3.9 

75 

72.4 

19.4 

35 

130.4 

34.9 

95 

188.4 

50.5 

55 

246.3 

66.0 

16 

15.5 

4.1 

76 

73.4 

19.7 

36 

131.4 

35.2 

96 

189.3 

50.7 

56 

247.3 

66.3 

17 

16.4 

4.4 

77 

74.4 

19.9 

37 

132.3 

35.5 

97 

190.3 

51.0 

57 

248.2 

66.5 

18 

17.4 

4.7 

78 

75.3 

20.2 

38 

133.3 

35.7 

98 

191.3 

51.2 

58 

249.2 

66.8 

19 

18.4 

4.9 

79 

76.3 

20.4 

39 

134.3 

36.0 

99 

T92.2 

51.5 

59 

250.2 

67.0 

20 

19.3 

5.2 

80 

77.3 

20.7 

40 

135.2 

36.2 

200 

193.2 

51.8 

60 

251.1 
252.1 

67.3 
67.6 

21 

20.3 

5.4 

81 

78.2 

21.0 

141 

136.2 

36.5 

201 

194.2 

52.0 

261 

22 

21.3 

5.7 

82 

79.2 

21.2 

42 

137.2 

36.8 

02 

195.1 

52.3 

62 

253.1 

67.8 

23 

22.2 

6.0 

83 

80.2 

21.5 

43 

138. 1 

37.0 

03 

196.1 

52.5 

63 

254.0 

68.1 

24 

23.2 

6.2 

84 

81.1 

21.7 

44 

139. 1 

37.3 

04 

197.0 

52.8 

64 

255.0 

68.3 

25 

24.1 

6.5 

85 

82.1 

22.0 

45 

140.1 

37.5 

05 

198.0 

53.1 

65 

256.0 

68.6 

26 

25.1 

6.7 

86 

83.1 

22.3 

46 

141.0 

37.8 

06 

199.0 

53.3 

66 

256.9 

68.8 

27 

26.1 

7.0 

87 

84.0 

22.5 

47 

142.0 

38.0 

07 

199.9 

53.6 

67 

257.  9 

69.1 

28 

27.0 

7.2 

88 

85.0 

22.8 

48 

143.0 

38.3 

08 

200.9 

53.8 

68 

258.9 

69.4 

29 

28.0 

7.5 

89* 

86.0 

23.0 

49 

143.9 

38.6 

09 

201.  9 

54.1 

69 

259.8 

69.6 

30 

29.0 

7.8 

90 

86.9 

23.3 

50 

144.9 

38.8 

10 

202.8 

54.4 

70 

260.8 

69.9 

31 

29.9 

8.0 

91 

87.9 

23.6 

151 

145.9 

39.1 

211 

203.8 

54.6 

271 

261.8 

70.1 

32 

30.9 

8.3 

92 

88.9 

23.8 

52 

146.8 

39.3 

12 

204.8 

54.9 

72 

262.7 

70.4 

33 

31.9 

8.5 

93 

89.8 

24.1 

53 

147.8 

39.6 

13 

205.7 

55.1 

73 

263.7 

70.7 

34 

32.8 

8.8 

94 

90.8 

24.3 

54 

148.8 

39.9 

14 

206.7 

55.4 

74 

264.7 

70.9 

35 

33.8 

9.1 

95 

91.8 

24.6 

55 

149.7 

40.1 

15 

207.7 

55.6 

75 

265.6 

71.2 

36 

34.8 

9.3 

96 

92.7 

24.8 

56 

150.7 

40.4 

16 

208.6 

55.9 

76 

266.6 

71.4 

37 

35.7 

9.6 

97 

93.7 

25.1 

57 

151.7 

40.6 

17 

209.6 

56.2 

77 

267.6 

71.7 

38 

36.7 

9.8 

98 

94.7 

25.4 

58 

152.6 

40.9 

18 

210.6 

56.4 

78 

268.5 

72.0 

39 

37.7 

10.1 

99 

95.6 

25.6 

59 

153.6 

41.2 

19 

211.5 

56.7 

79 

269.5 

72.2 

40 

38.6 

10.4 

100 

96.6 

25.9 

60 

154.5 

41.4 

20 

212.5 

56.9 

80 

281 

270.5 

72.5 

41 

39.6 

10.6 

101 

97.6 

26.1 

161 

155. 5 

41.7 

221 

213.5 

57.2 

271.4 

72.7 

42 

40.6 

10.9 

02 

98.5 

26.4 

62 

156.5 

41.9 

22 

214.4 

57.5 

82 

272.4 

73.0 

43 

41.5 

11.1 

03 

99.5 

26.7 

63 

157.4 

42.2 

23 

215.4 

57.7 

83 

273.4 

73.2 

44 

42.5 

11.4 

04 

100.5 

26.9 

64 

158.4 

42.4 

)J^ 

216.4 

58.0 

84 

274.3 

73.5 

45 

43.5 

11.6 

05 

101.4 

27.2 

65 

159.4 

42.7 

'-^5 

217.3 

58.2 

85 

275.  3 

73.8 

46 

44.4 

11.9 

06 

102.4 

27.4 

66 

160.3 

43.0 

26 

218.3 

58.5 

86 

276.3 

74.0 

47 

45.4 

12.2 

07 

103.4 

27.7 

67 

161.3 

43.2 

27 

219.3 

58.8 

87 

277.2 

74.3 

48 

46.4 

12.4. 

08 

104.3 

28.0 

68 

162.3 

43.5 

28 

220.2 

59.0 

88 

278.2 

74.5 

49 

47.3 

12.7 

09 

105.3 

28.2 

69 

163.2 

43.7 

29 

221.2 

59.3 

89 

279.2 

74.8 

50 
51 

48.3 

12.9 

10 

106.3 

28.5 

70 
171 

164.2 

44.0 

30 

222.2 

59.5 

90 

280.1 

75.1 

49.3 

13.2 

111 

107.2 

28.7 

165.2 

44.3 

231 

223.1 

59.8 

291 

281.1 

75.3 

52 

50.2 

13.5 

12 

108.2 

29.0 

72 

166.1 

44.5 

32 

224.1 

60.0 

92 

282.1 

75.6 

53 

51.2 

13.7 

13 

109.1 

29.2 

73 

167.1 

44.8 

33 

225.1 

60.3 

93 

283.0 

75.8 

54 

52.2 

14.0 

14 

110.1 

29.5 

74 

168.1 

45.0 

34 

226.0 

60.6 

94 

284.0 

76.1 

55 

53.1 

14.2 

15 

111.1 

29.8 

75 

169.0 

45.3 

35 

227.0 

60.8 

95 

284.9 

76.4 

56 

54.1 

14.5 

16 

112.0 

30.0 

76 

170.0 

45.6 

36 

228.0 

61.1 

96 

285.  9 

76.6 

57 

55.1 

14.8 

17 

113.0 

30.3 

77 

171.0 

45.8 

37 

228.9 

61.3 

97 

286.9 

76.9 

58 

56.0 

15.0 

18 

114.0 

30.5 

78 

171.9 

46.1 

38 

229.9 

61.6 

98 

287.8 

77.1 

59 

57.0 

15.3 

19 

114.9 

30.8 

79 

172.9 

46.3 

39 

230.  9 

61.9 

99 

288.8 

77.4 

60 

58.0 

15.5 

20 

115.9 

31.1 

80 

173.9 

46.6 

40 

231.8 

62.1 

300 

289.8 

77.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

75°  (105°,  25, 

>°,  285< 

')• 

TABLE  2. 

[Page  397 

Difference  of  Latitude  and  Departure  for 

15°  (165°,  195 

°,  345° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

290.  7 

77.9 

361 

348.7 

93.4 

421 

406.6 

109.0 

481 

464.6 

124.5 

541 

522.6 

140.0 

02 

291.7 

78.2 

62 

349.  6 

93.7 

22 

407.6 

109.2 

82 

465.6 

124.8 

42 

523.5 

140.3 

03 

292.7 

78.4 

63 

350.  6 

94.0 

23 

408.6 

109.  5 

83 

466.5 

125.  0 

43 

524.5 

140.5 

04 

293.6 

78.7 

64 

351.6 

94.2 

24 

409.  5 

109.7 

84 

467.5 

125.  3 

44 

525.5 

140.8 

05 

294.6 

78.9 

65 

352.  5 

94.5 

25 

410.  5 

110.0 

85 

468.5 

125.  6 

45 

526.4 

141.1 

06 

295.6 

79.2 

66 

353.5 

94.7 

26 

411.5 

110.3 

86 

469.  4 

125.  8 

46 

527.  4 

141.4 

07 

296.5 

79.5 

67 

354.  5 

95.0 

27 

412.4 

110.5 

87 

470.4 

126.1 

47 

528. 4 

141.6 

08 

297.5 

79.7 

68 

355.  4 

95.3 

28 

413.4 

110.8 

88 

471.4 

126.4 

48 

529.3 

141.9 

09 

298.4 

80.0 

69 

356.4 

95.5 

29 

414.4 

111.0 

89 

472.3 

126.6 

49 

530.  3 

142.1 

10 
311 

299.4 
300.4 

80.2 

70 

357.  4 
358.3 

95.8 
96.0 

30 
431 

415.3 
416.3 

111.3 

90 

473.3 

126.9 

50 
551 

531.  3 

532.  2 

142.4 

80.5 

371 

111.6 

491 

474.  3 

127.1 

142.6 

12 

301.3 

80.8 

72 

359.3 

96.3 

32 

417.3 

111.8 

92 

475.2 

127.4 

52 

533.  2 

142.9 

13 

302.  3 

81.0 

73 

360.3 

96.5 

33 

418.2 

112.1 

93 

476.2 

127.6 

53 

534.2 

143.1 

14 

303.3 

81.3 

74 

361.2 

96.8 

34 

419.2 

112.3 

94 

477.2 

127.9 

54 

535.1 

143.4 

15 

304.2 

81.5 

75 

362.2 

97.1 

35 

420.  2  i  112.  6 

95 

478.1 

128.1 

55 

536.1 

143.7 

16 

305.2 

81.8 

76 

363.2 

97.3 

36 

421.1  [112.9 

96 

479.1 

128.4 

56 

537. 1 

143.9 

17 

306.2 

82.1 

77 

364.1 

97.6 

37 

422.1     113.1 

97 

480.1 

128.6 

57 

538.  0 

144.2 

18 

307. 1 

82.3 

78  1  365. 1 

97.8 

38 

423.1     113.4 

98 

481.0 

128.9 

58 

539. 0 

144.4 

19 

308.1 

82.6 

79  i  366. 1 

98.1 

39 

424.0    113.6 

99 

482.0 

129.1 

59 

540.  0 

144.7 

20 

309. 1 

82.8 

80 

367.0 

98.4 

40 

425.0    113.9 

500 

483.0 
483.9 

129.4 
129.7 

60 

540.  9 

144.9 

321 

310.  0 

83.1 

381 

368.0 

98.6 

441 

426.0    114.1 

501 

561 

541.9 

145.2 

22 

311.0 

83.3 

82 

369.0 

98.9 

42 

426.9 

114.4 

02 

484.9 

129.9 

62 

542.9 

145.4 

23 

312.0 

83.6 

83 

369.  9 

99.1 

43 

427.9 

114.7 

03 

485.9 

130.  2 

63 

.543.8 

145.7 

24 

312.9 

83.9 

84 

370.9 

99.4 

44 

428.8 

114.9 

04 

486.8 

130.4 

64 

544.8 

146.0 

25 

313.9 

84.1 

85 

371.9 

99.6 

45 

429.8 

115.  2 

05 

487.8 

130.7 

65 

545.8 

146.2 

26 

314.9 

84.4 

86  1  372.  8 

99.9 

46 

4.30.  8 

115.4 

06 

488.8 

131.0 

66 

546.7 

146.5 

27 

315.8 

84.6 

87 

373.8 

100.2 

47 

431.7 

115.  7 

07 

489.7 

131.2 

67 

547.7 

146.7 

28 

316.8 

84.9 

88 

374.8 

100.4 

48 

432.7 

116.0 

08 

490.7 

131.5 

68 

548.  7 

147.0 

29 

317.8 

85.1 

89 

375.7 

100.7 

49 

433.  7 

116.2 

09 

491.7 

131.7 

69 

549.6 

147.2 

30 

318.7 

85.4 

90 

376.7 

100.9 

50 

434.6 

116.  5 

10 

492.6 
493.6 

132. 0 

70 

550.6 

147.5 

331 

319.7 

85.7 

391 

377.7 

101.2 

451 

435.  6 

116.  7 

511 

132.3 

571 

551.6 

147.8 

32 

320.  7 

85.9 

92 

378.6 

101.5 

52 

436.6 

117.0 

12 

494.5 

132.  5 

72 

552.5 

148.0 

33 

321.6 

86.2 

93 

379.6 

101.7 

53 

437.5 

117.3 

13 

495.5 

132.8 

73 

553.5 

148.3 

34 

322.6 

86.5 

94 

380.6 

102.0 

54 

438.  5 

117.5 

14 

496.5 

133. 0 

74 

554.4 

148.5 

35 

323.6 

86.7 

95 

381.5 

102.2 

55 

439.5 

117.8 

15 

497.4 

133.3 

75 

555.4 

148.8 

36 

324.  5 

87.0 

96 

382.  5 

102.5 

56 

440.4 

118.0 

16 

498.4 

133.5 

76 

556.4 

149.0 

37 

325.  5 

87.2 

97 

383.  4 

102.8 

57 

441.4 

118.3 

17 

499.4 

133.8 

77 

557.3 

149.3 

38 

326.5 

87.5 

98 

384.4 

103.0 

58 

442.4 

118.5 

18 

500.3 

134.0 

78 

558.3 

149.  5 

39 

327.  4 

87.7 

99 

385.4 

103:3 

59 

443.3 

118.8 

19 

501.3 

134.3 

79 

559.  3 

149.8 

40 

328.4 

88.0 

400 

386.3 

103.5 
T03.8 

60 

444.3 

119.1 

20 

502.  3 

134.6 

80 

560.2 

150.1 

341 

329.  4 

88.3 

401 

387.3 

461 

445.3 

119.3 

521 

503.2 

134.8 

581 

561.2 

150.3 

42 

330.  3 

88.5 

02 

388.3 

104.1 

62 

446.2 

119.6 

22 

504.2 

135.1 

82 

562.2 

150.6 

43 

331.  3 

88.8 

03 

389.2 

104.3 

63 

447.2 

119.8 

23 

505.  2 

135.  3 

83 

563. 1 

150.8 

44 

332.  3 

89.0 

04 

390.  2 

104.6 

64 

448.2 

120.1 

24 

506. 1 

135.  6 

84 

564. 1 

151.1 

45 

333. 2 

89.3 

05 

391.2 

104.8 

65 

449.1 

120.4 

25 

507. 1 

135.  9 

85 

565. 1 

151.4 

46 

334.  2 

89.6 

06 

392. 1 

105. 1 

66 

450. 1 

120.6 

26 

508. 1 

136.1 

86 

566.  0 

151.6 

47 

335.2 

89.8 

07 

393.1 

105.  3 

67 

451. 1 

120.9 

27 

509.0 

136. 4 

87 

567.0 

151.9 

48 

336.1 

90.1 

08 

394. 1 

105.  6 

68 

452.  0 

121.1 

28 

510.0 

136. 6 

88 

568.0 

152.2 

49 

337.1 

t)0.3 

09 

395.  0 

105.9 

69 

453.0 

121.  4 

29 

511.0 

136.9 

89 

568.9 

152.4 

50 
351 

338.1 

90.6 

10 

396.0 

106.1 

70 

454.0 

121.7 

30 

511.9 

137.2 
137.4 

90 

569.9 

152.7 

339. 0 

90.9 

411 

397.  0 

106.4 

471 

454.  9 

121.9 

531 

512.9 

591 

570.9 

153. 0 

52 

340.0 

91.1 

12 

397.9 

106.6 

72 

455.  9 

122.2 

32 

513.  9 

137.  7 

92 

571.8 

153.2 

53 

340.9 

91.4 

13 

398.9 

106.9 

73 

456.9 

122.4 

33 

514.8 

137.  9 

93 

572.8 

153.5 

54 

341.  9 

91.6 

14 

399.9 

107.2 

74 

457.8 

122.7 

34 

515.  8 

138.2 

94 

573.8 

153.7 

55 

342.9 

91.9 

15 

400.8 

107.4 

75 

458.8 

122.9 

35 

516.  8 

138.4 

95 

574.7 

154.0 

56 

343.8 

92.1 

16 

401.8 

107.7 

76 

459.  8 

123.2 

36 

517.  7 

138.  7 

96 

575.  7 

154.  2 

57 

344.8 

92.4 

17 

402.  8 

107.9 

77 

460.7 

123.5 

37 

518.  7 

139.0 

97 

576.7 

154.5 

58 

345.8 

92.7 

18 

403.7 

108.2 

78 

461.7 

123.7 

38 

519.7 

139.2 

98 

577.6 

154.8 

59 

346.7 

92.9 

19 

404.7 

108.5 

79 

462.7 

124.0 

39 

520.6 

139.  5 

99 

578.6 

155.0 

60 

347.7 

93.2 

20 

405.7 

108.7 

80 

463.6 

124.2 

40 

521.6 

139.7 

600 

579.5 

155.3 

Dist. 

Dep. 

Lav. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

"i 

'5°  (1 

[)5°,  255°,  285°; 

. 

Page  398] 

TABLE  2. 

difference  of  Latitude  and  Departure  for  16°  ( 

L64°,  196°,  344= 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
66.4 

1 

1.0 

0.3 

61 

58.  6     16.  8 

121      116.3 

33.4 

181 

174.0 

49.9 

241 

231.7 

2 

1.9 

0.6 

62 

59.6     17.1 

22  1  117.3 

33.6 

82 

174.9 

50.2 

42 

232.  6 

66.7 

3 

2.9 

0.8 

63 

60.6      17.4 

23 

118.2 

33.9 

83 

175.  9 

50.4 

43 

233.  6 

67.0 

4 

3.8 

1.1 

64 

61.5 

17.6 

24 

119.2 

34.2 

84 

176.9 

50.7 

44 

234.5 

67.3 

6 

4.8 

1.4 

65 

62.5 

17.9 

25 

120.2 

34.5 

85 

177.8 

51.0 

45 

235.5 

67.5 

6 

5.8 

1.7 

^6 

63.4 

18.2 

26 

121.1 

34.7 

86 

178.8 

51.3 

46 

236.5 

67.8 

7 

6.7 

1.9 

67 

64.4 

18.5 

27 

122.1 

35.0 

87 

179.8 

51.5 

47 

237. 4 

68.1 

•  8 

7.7 

2.2 

68 

65.4 

18.7 

28 

123.0 

35.3 

88 

180.7 

51.8 

48 

238.  4 

68.4 

9 

8.7 

2.5 

69 

66.3 

19.0 

29 

124.0 

35.6 

89 

181.  7 

52.1 

49 

239.4 

68.6 

10 
11 

9.6 

2.8 

70 

67.3 

19.3 

30 

125.0 
125.9 

35.8 

90 

182.6 

52.4 

50 
251 

240.  3 
241.3 

68.9 
69.  2 

10.6 

3.0 

71 

68.2 

19.6 

131 

36.1 

191 

183.6 

52.6 

12 

11.5 

3.3 

72 

69.2 

19.8 

32 

126.9     36.4 

92 

184.6 

52.9 

52 

242.2 

69.5 

13 

12.5 

3.6 

73 

70.2 

20.1 

33 

127.8  1  .36.7 

93 

185.5 

53.2 

53 

243.  2 

69.7 

14 

13.5 

3.9 

74 

71.1 

20.4 

34 

128.8     36.9 

94 

186.  5 

53.5 

54 

244.2 

70.0 

15 

14.4 

4.1 

75 

72.1 

20.7 

35 

129.8     37.2 

95 

187.4 

53.7 

55 

245. 1 

70.3 

16 

15.4 

4.4 

76 

73.1 

20.9 

36 

130.7  1  37.5 

96 

188.4 

54.0 

56 

246.1 

70.6 

17 

16.3 

4.7 

77 

74.0 

21.2 

37 

131.7     37.8 

97 

189.4 

54.3 

57 

247.0 

70.8 

18 

17.3 

5.0 

78 

75.0 

21.5 

38 

132.7     38.0 

98 

190.3 

54.6 

58 

248.0 

71.1 

19 

18.3 

5.2 

79 

75.9 

21.8 

39 

133.6  1  38.3 

99 

191.3 

54.9 

59 

249.0 

71.4 

20 

19.2 

5.5 

80 
81 

76.9 

22.1 

40 

134.6 

38.6 

200 
201 

192.3 
193.2 

55.1 
55.4 

60 
261 

249.9 
250.9 

71.7 

21 

20.2 

5.8 

77.9 

22.3 

141 

135.5 

38.9 

71.9 

22 

21.1 

6.1 

82 

78.8 

22.6 

42 

136.5 

39.1 

02 

194.2 

55.7 

62 

251.9 

72.2 

23 

22.1 

6.3 

83 

79.8 

22.9 

43 

137.5 

39.4 

03 

195.1 

56.0 

63 

252.8 

72.5 

24 

23.1 

6.6 

84 

80.7 

23.2 

44 

138.4 

39.7 

04 

196.1 

56.2 

64 

253.8 

72.8 

25 

24.0 

6.9 

85 

81.7 

23.4 

45 

139.4 

40.0 

05 

197.1 

56.5 

65 

254.7 

73.0 

26 

25.0 

7.2 

86 

82.7 

23.7 

46 

140.3 

40.2 

06 

198.0 

56.8 

66 

255.7 

73.3 

27 

26.0 

7.4 

87 

83.6 

24.0 

47 

141.3 

40.5 

07 

199.0 

57.1 

67 

256.  7 

73.6 

28 

26.9 

7.7 

88 

84.6 

24.3 

48 

142.3 

40.8 

08 

199.9 

57.3 

68 

257.6 

73.9 

29 

27.9 

8.0 

89 

85.6 

24.5 

49 

143.2 

41.1 

09 

200.9 

57.6 

69 

258.6 

74.1 

30 

28.8 

8.3 

90 

86.5 
87.5 

24.8 

50 

144.2 
145.  2 

41.3 
41.6 

10 

201.9 

57.9 

70 

259.5 
260.5 

74.4 

31 

29.8 

8.5 

91 

25.1 

151 

211 

202.8 

58.2 

271 

74.7 

32 

30.8 

8.8 

92 

88.4 

25.4 

52 

146.1 

41.9 

12 

203.8 

58.4 

72 

261.5 

75.0 

33 

31.7 

9.1 

93 

89.4 

25.6 

53 

147.1 

42.2 

13 

204.7 

58.7 

73 

262.4 

75.2 

34 

32.7 

9.4 

94 

90.4 

25.9 

54 

148. 0 

42.4 

14 

205.7 

59.0 

74 

263.4 

75.5 

35 

33.6 

9.6 

95 

91.3 

26.2 

55 

149.0 

42.7 

15 

206.7 

59.3 

75 

264.3 

75.8 

36 

34.6 

9.9 

96 

92.3 

26.5 

56 

150.0 

43.0 

16 

207.6 

59.5 

76 

265.3 

76.1 

37 

35.6 

10.2 

97 

93.2 

26.7 

57 

150.9 

43.3 

17 

208.6 

59.8 

77 

266.3 

76.4 

38 

36.5 

10.5 

98 

94.2 

27.0 

58 

151.9 

43.6 

18 

209.6 

60.1 

78 

267.2 

76.6 

39 

37.5 

10.7 

99 

95.2 

27.3 

59 

152.8 

43.8 

19 

210. 5 

60.4 

79 

268.2 

76.9 

40 

38.5 

11.0 

100 

96.1 

27.6 

60 

153.  8 
154.8 

44.1 
44.4' 

20 
221 

211.5 

60.6 

80 

269.2 

77.2 

41 

39.4 

11.3 

101 

97.1 

27.8 

161 

212.4 

60.9 

281 

270.1 

77.5 

42 

40.4 

11.6 

02 

98.0 

28.1 

62 

155.  7 

44.7 

22 

213.4 

61.2 

82 

271.1 

77.7 

43 

41.3 

11.9 

03 

99.0 

28.4 

63 

156. 7     44.  9 

23 

214. 4 

61.5 

83 

272.0 

78.0 

44 

42.3 

12.1 

04 

100.0 

28.7 

64 

157.6  1  45.2 

24 

215. 3 

61.7 

84 

273.0 

78.3 

45 

43.3 

12.4 

05 

100.9 

28.9 

65  !  158.6  !  45.5 

25 

216.3 

62.0 

85 

274.0 

78.6 

46 

44.2 

12.7 

06 

101.9 

29.2 

66  1  159.6 

45.8 

26 

217.2 

62.3 

86 

274.9 

78.8 

47 

45.2 

13.0 

07 

102.9 

29.5 

67 

160.5 

46.0 

27 

218.2 

62.6 

87 

275.9 

79.1 

48 

46.1 

13.2 

08 

103.  8 

29.8 

68 

161.5 

46.3 

28 

219.2 

62.8 

88 

276.  8 

79.4 

49 

47.1 

13.5 

09 

104.8 

30.0 

69 

162.5 

46.6 

29 

220.1 

63.1 

89 

277.8 

79.7 

50 

48.1 

13.8 
14.1 

10 
111 

105.  7  1  30.  3  1 

70 

163.4 
164.4 

46.9 

30 

221.1 
222.1 

63.4 
63.7 

90 
291 

278.8 
279.7 

79.9 
80. 2 

51 

49.0 

106.7 

30.6 

171 

47-1 

231 

52 

50.0 

14.3 

12 

107.7 

30.9 

72 

165.3 

47.4 

32 

223.0 

63.9 

92 

280.7 

80.5 

53 

50.9 

14.6 

13 

108.6 

31.1 

73 

166.  3 

47.7 

33 

224.0 

64.2 

93 

281.6 

80.8 

54 

51.9 

14.9 

14 

109.6 

31.4 

74 

167.3 

48.0 

34 

224.9 

64.5 

94 

282.6 

81.0 

55 

52.9 

15.2 

15 

110.5 

31.7 

75 

168.2 

48.2 

35 

225.9 

64.8 

95 

283.  6 

81.3 

56 

53.8 

15.4 

16 

111.5 

32.0 

76 

169.2 

48.5 

36 

226.9 

65.1 

96 

284.5 

81.6 

57 

54.8 

15.7 

17 

112.5 

32.2 

77 

170.1 

48.8 

37 

227.8 

65.3 

97 

285.  5 

81.9 

58 

55.8 

16.0 

18 

113.4 

32.5 

78 

171.1 

49.1 

38 

228.8 

65.6 

98 

286.5 

82.1 

59 

56.7 

16.3 

19 

114.4 

32.8 

79 

172.1 

49.3 

39 

229.7 

65.9 

99 

287.4 

82.4 

60 

57.7 

16.5 

20 

115.4 

33.1 

80 

173.0 

49.6 

40 

230.7 

66.2 

300 

288.4 

82.7 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

ri°  (106°,  254°,  286° 

). 

TABLE  2. 

[Page 

399 

Difference  of  Latitude  and  Departure  for  16°  (164°,  196°,  344' 

)■ 

Dist. 

Lat. 

Dep. 

Dist. 

1     Lat. 

Dep. 

Dist. 

1     Lat. 

Dep. 
116.0 

1  Dist. 
481 

Lat. 

Dep. 
132.5 

Dist. 

Lat. 

Dep. 

301 

289.3 

82.9 

361 

347.0 

99.5 

421 

404.7 

462.4 

541 

520.1 

149.1 

02 

290.3 

83.2 

62 

348.0 

99.7 

22 

405.6 

116.3 

82  1  463.3 

132.8 

42 

521.0 

149.4 

03 

291.2 

83.5 

68 

348.  9 

100.0 

23 

406.6 

116.  6 

83  1  464.3 

133.1 

43 

522.0 

149.7 

04 

292.2 

83.8 

64 

349.9 

100.  3 

24 

407.6 

116.8 

84  i  465.2 

133.4 

44 

523.0 

150.  0 

05 

293.2 

84.0 

65 

350.8 

100.6 

25 

408.5 

117.1 

85  i  466.2 

133.  6 

45 

523.9 

150.2 

06 

294.1 

84.3 

66 

351.8 

100.8 

26 

409.5 

117.4 

86  (  467.2 

133.  9 

46 

524.9 

150.4 

07 

295. 1 

84.6 

67 

352.8 

101.1 

27 

410.4 

117.7 

87  1  468. 1 

134.2 

47 

525.9 

150.7 

08 

296.0 

84.9 

68 

353.7 

101.4 

28 

411.4 

117.9 

88     469.1 

134.5 

48 

526.  8 

151.0 

09 

297.0 

85.1 

69 

354.7 

101.7 

29 

412.4 

118.2 

89  j  470. 1 

134.  8 

49 

527.8 

151.3 

10 

298.0 

85.4 

70 

355.  6 

356.  6 

101.  9 
102.2 

30 
431 

413.  3 
414.3 

118.  5 

90  1  471.0 

135.0 
135.3 

50 
551 

528.7 
529.7 

151.6 
151.9 

311 

298.9 

85.7 

371 

118.8 

491 

472.0 

12 

299.9 

86.0 

72 

357.6 

102.5 

32 

415.2 

119.  0 

92 

472.9 

135.  6 

52 

530.6 

152.2 

13 

300.9 

86.2 

73 

358.5 

102.8 

33  1  416.2 

119.  3 

93 

473.  9 

135.  9 

53 

531.6 

152.  5 

14 

301.8 

86.5 

74 

359.5 

103.  1 

34     417.2 

119.6 

94 

474.9 

136.  2 

54 

532.6 

152.8 

15 

302.8 

86.8 

75 

360.4 

103.3 

35  i  418. 1 

119.9 

95 

475.  8 

136.4 

55 

533.  5 

153.0 

16 

303.7 

87.1 

76 

361.4 

103.6 

36     419. 1 

120.1 

96 

476.8 

136.  7 

56 

534.5 

153.2 

17 

304.7 

87.3 

77 

362.4 

103.9 

37  1  420.0 

120.4 

97 

477.7 

137.0 

57 

535. 4 

153.  5 

18 

305.7 

87.6 

78 

363.3 

104.2 

38  1  421.0 

120.7 

98 

478.7 

137.3 

58 

536.4 

153.8 

19 

306. 6 

87.9 

79 

364.3 

104.4 

39  i  422.0 

121.0 

99 

479.7 

137.  5 

59 

537.4 

154. 1 

20 
321 

307.6 
308.5 

88.2 
88.4 

80 
381 

365.3 
366.2 

104.7 
105.  0 

40 

441 

422.9 

121.2 
121.  5 

500 
501 

480.  6  '  137. 8 
481.6    138.1 

60 

538.3 

154.4 
154.  7 

423.  9 

561 

539.3 

22 

309.5 

88.7 

82 

367.2 

105.3 

42  i  424.9 

121.8 

02 

482. 6    138.  3 

62 

540.3 

154.9 

23 

310.5 

89.0 

83 

368.1 

105. 5 

43 

425.8 

122.1 

03 

483. 5    138.  6 

63 

541.2 

155.2 

24 

311.4 

89.3 

84 

369.1 

105.8 

44 

426.8 

122.3 

04  ,  484.5     138.9 

64 

542.2 

155.4 

25 

312.  4 

89.5 

85 

370.1 

106.1 

45 

427.7 

122.6 

05  [  485.  4     139.  2 

65 

543.1 

155.7 

26 

313.3 

89.8 

86 

371.0 

106.4 

46 

428.7 

122.9 

06     4^6. 4    139. 4 

66 

544.1 

156.0 

27 

314.3 

90.1 

87 

372.0 

106.6 

47 

429.7 

123.  2 

07     487.  3  i  139.  7 

67 

545.1 

156.3 

28 

315.  3 

90.4 

88 

372.9 

106.9 

48 

430.6 

123.4 

08 

488.  3    140. 0 

68 

546.0 

156.6 

29 

316.2 

90.6 

89 

373.9 

107.2 

49 

431.6 

123.  7 

09 

489.3  !l40.3 

69 

547.0 

156.9 

30 
331 

317.2 
318.2 

90.9 
91.2 

90 
391 

374. 9 
375.8 

107.5 
107.7 

50 
451 

432.6 
433.5 

124.0 
124.3 

10 
511 

490.2 

140.6 

70 

547.9 
548.  9" 

157.1 

491.2 

140.8 

571 

157.3 

32 

319.1 

91.5 

92 

376.8 

108.0 

52 

434.5 

124.6 

12 

492.1 

141.1 

72 

549.8 

157.6 

33 

320.1 

91.8 

93 

377.8 

108.3 

53 

435.4 

124.8 

13 

493.1 

141.4 

73 

550.8 

157.9 

34 

321.0 

92.0 

94 

378. 7  1 108.  6 

54 

436.  4 

125. 1 

14 

494.1  jl41.7 

74 

551.8 

158.2 

35 

322.0 

92.3 

95 

379.7 

108.8 

55 

437.  4 

125.4 

15 

495.0  !l41.9 

75 

552.7 

158.4 

36 

323.0 

92.6 

96 

380.6 

109.1 

56 

438.3 

125.7 

16 

496.0 

142.2 

76 

553.7 

158.7 

37 

323.9 

92.9 

97 

381.6 

109.4 

57 

439.  3 

125.  9 

17 

496.9 

142.5 

77 

554.6 

159.0 

38 

324.9 

93.1 

98 

382.6 

109.7 

58 

440.2 

126.2 

18 

497.9 

142.8 

78 

555.6 

159.3 

39 

325.  8 

93.4 

99 

383.5 

109.9 

59 

441.2 

126.5 

19 

498.9 

143.0 

79 

556.5 

159.5 

40 
341 

326.  8 

93.7 

400 

384.5 

110.2 

60 

442.2 
443.1 

126.8 
127.0 

20 
521" 

499.8 

143.3 

80 

557.5 

159.  8 

327.8 

94.0 

401 

385.4 

110.5 

461 

500.8 

143.6 

581 

558.4 

160.1 

42 

328.7 

94.2 

02 

386.  4 

110.8 

62 

444.1 

127.  3 

22 

501.7 

143.9 

82 

559.4 

160.4 

43 

329.7 

94.5 

03 

387.4 

111.0 

63 

445.0 

127.6 

23 

502.7 

144.1 

83 

560.4 

160.6 

44 

330.7 

94.8 

04 

388.3    111.3 

64 

446.  0 

127.9 

24 

503.7 

144.4 

84 

561.3 

161.0 

45 

331.6 

95.1 

05 

389.3     111.6 

65 

447.0 

128.1 

25 

504.6 

144.7 

85 

562.3 

161.3 

46 

332.  6 

95.3 

06 

390.2  1111.9 

66 

447.9 

128.4 

26 

505.6 

145.  0 

86 

563.2 

161.6 

47 

333.  5 

95.6 

07 

391.2 

112.1 

67 

448.9 

128.7 

27 

506.  6 

145.3 

87 

564.2 

161.8 

48 

334.5 

95.9 

08 

392.2 

112.4 

68 

449.8 

129.0 

28 

507.5 

145.6 

88 

565.2 

162.1 

49 

335. 5 

96.2 

09 

393.1 

112.7 

69 

450.  8 

129.2 

29 

508.  5 

145.  8 

89 

566.1 

162.4 

50 
351 

336.4 

96.4 
96.7 

10 
411 

394.1 
395.1" 

113.0 

70 
471" 

451.8 
452.7 

129.5 
129.8 

30 
531 

509.4 

146.1 
146.4 

90 
591 

567.1 
568.1 

162.7 

337.  4 

113.3 

510.4 

162.9 

52 

338.3 

97.0 

12 

396.0 

113.5 

72 

453.  7 

130. 1 

32 

511.4 

146.7 

92 

569.0 

163.  2 

53 

339.  3 

97.3 

13 

397.0 

113.  8 

73 

454.  7 

130.3 

33 

512.  3 

146.9 

93 

570.0 

163.  5 

54 

340.  3 

97.5 

14 

397.  9 

114.1 

74 

455.6 

130.6 

34 

513.  3 

147.2 

94 

571.0 

163.8 

55 

341.2 

97.8 

15 

398.9 

114.4 

75 

456.6 

130.9 

35 

514.3 

147.5 

95 

571.9 

164.0 

56 

342.  2 

98.1 

16 

399.  9 

114.6 

76 

457.5 

131.2 

36 

515.  2 

147.8 

96 

572.9 

164.3 

57 

343. 1 

98.4 

17 

400.8 

114.9 

77 

458.5 

131.4 

37 

516.2 

148.0 

97 

573.9 

164.6 

58 

344.1 

98.6 

18 

401.8 

115.  2 

78 

459.5 

131.7 

38 

517.2 

148.2 

98 

574.8 

164.9 

59 

345. 1 

98.9 

19 

402.7 

115.5 

79 

460.4 

132.0 

39 

518.1 

148.5 

99 

575.8 

165.1 

60 

346.0 

99.2 

20 

403.7 

115.8 

80 

461.4 

132.3 

40 

519.1 

148.8 

600 

576.8 

165.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Di.st. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

•4°  (106°,  254 

=,  286° 

). 

Page  400 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  1 

7°  (163°,  197 

=,  343° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.3 

17.8 

121 

115.7 

35.4 

181 

173.1 

52.9 

241 

230.5 

70.5 

2 

1.9 

0.6 

62 

59.3 

18.1 

22 

116.7 

35.7 

82 

174.0 

53.2 

42 

231.4 

70.8 

3 

2.9 

0.9 

63 

60.2 

18.4 

23 

117.6 

36.0 

83 

175.0 

53.5 

43 

232.4 

71.0 

4 

3.8 

1.2 

64 

61.2 

18.7 

24 

118.6 

36.3 

84 

176.0 

53.8 

44 

2.33.  3 

71.3 

5 

4.8 

1.5 

65 

62.2 

19.0 

25 

119.5 

36.5 

85 

176.9 

54.1 

45 

234.3 

71.6 

6 

5.7 

1.8 

^6 

63.1 

19.3 

26 

120.5 

36.8 

86 

177.9 

54.4 

46 

235.3 

71.9 

7 

6.7 

2.0 

64.1 

19.6 

27 

121.5 

37.1 

87 

178.  8 

54.7 

47 

236.  2 

72.2 

8 

7.7 

2.3 

68 

65.0 

19.9 

28 

122.4 

37.4 

88 

179.8 

55.0 

48 

237.2 

72.5 

9 

8.6 

2.6 

69 

66.0 

20.2 

29 

123.4 

37.7 

89 

180.7 

55.3 

49 

238.1 

72.8 

10 
11 

9.6 
10.5 

2.9 

70 

66.9 

20.5 

30 

124.3 

38.0 
38.3 

90 

181.7 

55.6 
55.  8 

50 
251 

239.1 
240.0 

73.1 

3.2 

71 

67.9 

20.8 

131 

125.3 

191 

182.7 

73.4 

12 

11.5 

3.5 

72 

68.9 

21.1 

32 

126.2  :  38.6 

92 

183. 6 

56.1 

52 

241.0 

73.7 

13 

12.4 

3.8 

73 

69.8 

21.3 

33 

127.2  i  38.9 

93 

184.6 

56.4 

53 

241.9 

74.0 

14 

13.4 

4.1 

74 

70.8 

21.6 

34 

128.1 

39.2 

94 

185.5 

56.7 

54 

242.9 

74.3 

15 

14.3 

4.4 

75 

71.7 

21.9 

35 

129.1 

39.5 

95 

186.5 

57.0 

55 

243.9 

74.6 

16 

15.3 

4.7 

76 

72.7 

22.2 

36 

130.1 

39.8 

96 

187.4 

57.3 

56 

244.8 

74.8 

17 

16.3 

6.0 

77 

73.6 

22.5 

37 

131.0 

40.1 

97 

188.4 

57.6 

57 

245.  8 

75.1 

18 

17.2 

5.3 

78 

74.6 

22.8 

38 

132.0 

40.3 

98 

189.3 

57.9 

58 

246.  7 

75.4 

19 

18.2 

5.6 

79 

75.5 

23.1 

39 

132.9 

40.6 

99 

190.3 

58.2 

59 

247.7 

75.7 

20 

19.1 

5.8 
6.1 

80 

76.5 

23.4 

40 

133.9 

40.9 

200 

191.3 

58.5 

60 

248.6 

76.0 
76.3 

21 

20.1 

81 

77.5 

23.7 

141 

]34.8 

41.2 

201 

192.2 

58.8 

261 

249.6 

22 

21.0 

6,4 

82 

78.4 

24.0 

42 

135.8 

41.5 

02 

193.2 

59.1 

62 

250.6 

76.6 

23 

22.0 

6.7 

83 

79.4 

24.3 

43 

136.8 

41.8 

03 

194.1 

59.4 

63 

251.5 

76.9 

24 

23.0 

7.0 

84 

80.3 

24.6 

44 

137.  7 

42.1 

04 

195.1 

59.6 

64 

252. 5 

77.2 

25 

23.9 

7.3 

85 

81.3 

24.9 

45 

138.7 

42.4 

05 

196.0 

59.9 

65 

253.4 

77.5 

26 

24.9 

7.6 

86 

82.2 

25.1 

46 

139.6 

42.7 

06 

197.0 

60.2 

66 

254.4 

77.8 

27 

25.8 

7.9 

87 

83.2 

25.4 

47 

140.6 

43.0 

07 

198.0 

60.5 

67 

255.  3 

78.1 

28 

26.8 

8.2 

88 

84.2 

25.7 

48 

141.5 

43.3 

08 

198.9 

60.8 

68 

256.3 

78.4 

29 

27.7 

8.5 

89 

85.1 

26.0 

49 

142.5 

43.6 

09 

199.9 

61.1 

69 

257.  2 

78.6 

30 

28.7 

8.8 

90 

86.1 

26.3 

50 

143.4 
144.4 

43.9 

10 

200.8 

61.4 

61.  7' 

70 
271 

258.2 

78.9 

31 

29.6 

9.1 

91 

87.0 

26.6 

151 

44.1 

211 

201.8 

259.2 

79.2 

32 

30.6 

9.4 

92 

88.0 

26.9 

52 

145.4 

44.4 

12 

202.7 

62.0 

72 

260.1 

79.5 

33 

31.6 

9.6 

93 

88.9 

27.2 

53 

146.3 

44.7 

13 

203.7 

62.3 

73 

261.1 

79.8 

34 

32.5 

9.9 

94 

89.9 

27.5 

54 

147.3 

45.0 

14 

204.6 

62.6 

74 

262.0 

80.1 

35 

33.5 

10.2 

95 

90.8 

27.8 

55 

148.2 

45.3 

15 

205.6 

62.9 

75 

263.0 

80.4 

36 

34.4 

10.5 

96 

91.8 

28.1 

56 

149.2 

45.6 

16 

206.6 

63.2 

76 

263.9 

80.7 

37 

35.4 

10.8 

97 

92.8 

28.4 

57 

150.1 

45.9 

17 

207.5 

63.4 

77 

264.9 

81.0 

38 

36.3 

11.1 

98 

93.7 

28.7 

58 

151.1 

46.2 

18 

208.5 

63.7 

78 

265.9 

81.3 

39 

37.3 

11.4 

99 

94.7 

28.9 

59 

152.1 

46.5 

19 

209.4 

64.0 

79 

266.8 

81.6 

.4a 

38.3 

11.7 

100 
101 

95.6 
96.6 

29.2 
29.5 

60 
161 

153.0 
154.0 

46.8 

20 

210.4 
211.3 

64.3 

80 

267.8 

81.9. 

41 

39.2 

12.0 

47.1 

221 

64.6 

281 

268.7 

82.2 

42 

40.2 

12.3 

02 

97.5 

29.8 

62 

154.9 

47.4 

22 

212.3 

64.9 

82 

269.7 

82.4 

43 

41.1 

12.6 

03 

98.5 

30.1 

63 

155. 9 

47.7 

23 

213.3 

65.2 

83 

270.6 

82.7 

44 

42.1 

12.9 

04 

99.5 

30.4 

64 

156.8 

47.9 

24 

214.2 

65.5 

84 

271.6 

83.0 

45 

43.0 

13.2 

05 

100.4 

30.7 

65 

157.8 

48.2 

25 

215.2 

65.8 

85 

272.5 

83.3 

46 

44.0 

13.4 

06 

101.4 

31.0 

66 

158.7 

48.5 

26 

216.1 

66.1 

86 

273. 5 

83.6 

47 

44.9 

13.7 

07 

102.3 

31.3 

67 

159.7 

48.8 

27 

217.1 

66.4 

87 

274.5 

83.9 

48 

45.9 

14.0 

08 

103.3 

31.6 

68 

160.7 

49.1 

28 

218.0 

66.7 

88 

275.4 

84.2 

49 

46.9 

14.3 

09 

104.2 

31.9 

69 

161.6 

49.4 

29 

219.0 

67.0 

89 

276.4 

84.5 

50 

47.8 

14.6 

10 

105.2 

32.2 

70 

162.6 

49.7 

30 

220.0 

67.2 

90 

277.3 
278.3 

84.8 
85.1 

51 

48.8 

14.9 

111 

106.1 

32.5 

171 

163.5 

50.0 

231 

220.9 

67.5 

291 

52 

49.7 

15.2 

12 

107.1 

32.7 

72 

164.5 

50.3 

32 

221.9 

67.8 

92 

279.2 

85.4 

53 

50.7 

15.5 

13 

108.1 

33.0 

73 

165.4 

50.6 

33 

222.8 

68.1 

93 

280.2 

85.7 

54 

51.6 

15.8 

14 

109.0 

33.3 

74 

166.4 

50.9 

34 

223.8 

68.4 

94 

281.2 

86.0 

55 

52.6 

16.1 

15 

110.0 

33.6 

75 

167.4 

51.2 

35 

224.7 

68.7 

95 

282.1 

86.2 

56 

53.6 

16.4 

16 

110.9 

33.9 

76 

168.3 

51.5 

36 

225.7 

69.0 

96 

283.1 

86.5 

57 

54.5 

16.7 

17 

111.9 

34.2 

77 

169.3 

51.7 

37 

226.6 

69.3 

97 

284.0 

86.8 

58 

55.5 

17.0 

18 

112.8 

34.5 

78 

170.2 

52.0 

38 

227.6 

69.6 

98 

285.0 

87.1 

59 

56.4 

17.2 

19 

113.8 

34.8 

79 

171.2 

52.3 

39 

228.6 

69.9 

99 

285.9 

87.4 

60 

57.4 

17.5 

20 

114.8 

35.1 

80 

172.1 

52.6 

40 

229.5 

70.2 

300 

286.9 

87.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

73°  (1 

07°,  253°,  287° 

)• 

TABLE  2. 

[Page  401 

Difference  of  Latitude  and  Departure  for  17°  (163°,  197°,  343°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist.        Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

287.8 

88.0 

361 

345.  2 

105.5 

421 

402.  6     123. 1 

481      460.0 

140.6 

541 

517.3 

158.2 

02 

288.8 

88.3 

62 

346.1 

105.8 

22 

403.5 

123.4 

82  '  460.9 

140.9 

42 

518.3 

158.5 

03 

289.7 

88.6 

63 

347. 1 

106.1 

23 

404.5 

123.  7 

83  1  461.9 

141.2 

43 

519.2 

158.8 

04 

290.7 

88.9 

64 

348.1 

106.4 

24 

405.  4 

124.0 

84 

462.8 

141.5 

44 

520.2 

159.1 

05 

291.6 

89.2 

65 

349.  0 

106.7 

25 

406.4 

124.3 

85 

463.8 

141.8 

45 

521.2 

159.  3 

06 

292.6 

89.5 

66 

350.  0 

107.0 

26 

407.  3 

124.6 

86 

464.7 

142.1 

46 

522.1 

159.6 

07 

293.5 

89.8 

67 

350.  9 

107.3 

27 

408.3 

124.8 

87 

465.  7 

142.  3 

47- 

523.  1 

159.  9 

08 

294.5 

90.1 

68 

351.  9 

107.6 

28 

409.3 

125.1 

88 

466.7 

142.6 

48 

524.0 

160.2 

09 

295.  5 

90.3 

69 

352.  8 

107.9 

29 

410.2 

125.  4 

89 

467.6 

142.9 

49 

1  525.0 

160.5 

10 
311 

296.4 
297.4 

90.6 

70 

353.  8 

108.2 

30 

411.2 
412.1 

125.7 

90 

468.6 

143.  2 

50 

1  526.0 

160.8 
161.1 

90.9 

371  i  354.8 

108.5 

431 

126.0 

491 

469.5 

143.  5 

551 

526.  9 

12 

298.3 

91.2 

72     355.7 

108.8 

32 

413.1 

126.3 

92 

470.5 

143.8 

52 

527.9 

161.4 

13 

299.3 

91.5 

73  !  356.  7 

109.1 

33 

414.0 

126.6 

93 

471.4 

144.1 

53  i  528.8 

161.7 

14 

300.2 

91.8 

74 

357.  6 

109.4 

34  '  415.0 

126.9 

94 

472.4 

144.4 

54  i  529.8 

162.0 

]5 

301.2 

92.1 

75 

358.6 

109.6 

35     416.0 

127.2 

95 

473.4 

144.7 

55 

530.8 

162.3 

16 

302.2 

92.4 

76 

359.  5 

109.9 

36     416.9 

127.5 

96 

474.3 

145.  0 

56 

531.7 

162.6 

17 

303. 1 

92.7 

77 

360. 5 

110.2 

37  i  417.9  1127.8 

97 

475.  3 

145.3 

57 

532.7 

162.9 

18 

304.1 

93.0 

78 

361.4 

110.5 

.38  ;  418.8  1128.1 

98 

476.2 

145.  6 

58     533.6 

163.2 

19 

305.0 

93.3 

79 

362.4 

110.8 

39     419. 8    128. 4 

99 

477.2 

145.  9 

59  i  534.6 

163.  5 

20 

306.  0 
306.9 

93.6 

80 
381 

363.4 

111.1 

40  1  420.  7     128.  6 

500 

478.1 
479. 1 

146.2 

60  1  535.5 
561     536.5 

163.8 

321 

93.9 

364.3 

111.4 

441  i  421. 7  : 128. 9 

501 

146.5 

164.1 

22 

307.9 

94.1 

82 

365.3 

111.7 

42 

422.  7  !  129. 2 

02 

480.1 

146.8 

62     537.5 

164.4 

23 

308.8 

94.4 

83 

366.2 

112.0 

43 

423.  6  1  129. 5 

03 

481.0 

147.1 

63  i  538.4 

164.6 

24 

309.8 

94.7 

84 

367.2 

112.3 

44 

424.6    129.8 

04 

482.0 

147.4 

64  :  5,39.4 

164.8 

25 

310.8 

95.0 

85 

368. 1 

112.  6 

45 

425.5    130.1 

05 

482.9 

147.7 

65     540.3 

165.1 

26 

311.7 

95.3 

86 

369.1 

112.9 

46 

426.5 

130.4 

06 

483.  9 

148.0 

66     541.3 

165.4 

27 

312.7 

95.6 

87 

370.1 

113.2 

47 

427.4 

130.7 

07 

484.8 

148.3 

67     542.2 

165.7 

28 

313.6 

95.9 

88 

371.0 

113.4 

48 

428.4 

131.0 

08 

485.  8 

148.6 

68     543.2 

166. 0 

29 

314.6 

96.2 

89 

372.0 

113.7 

49 

429.3 

131.  3 

09 

486.7 

148.9 

69     544.1 

166.4 

30 

315.  5 

316.  5 

96.5 

90 

372.9 
373.9 

114.0 

50 

430.3 
431.  3 

131.6 

10 

487.7 

149.1 

70 

545. 1 
546.1 

166.7 

331 

96.8 

391 

114.3 

451 

131.9 

511 

488.7 

149.4 

571 

167.0 

32 

317.5 

97.1 

92 

374.8 

114.6 

52 

432.2 

132.2 

12 

489.6 

149.7 

72  !  547.0 

167.2 

33 

318.4 

97.4 

93 

375.  8 

114.9 

53 

433.2 

132.4 

13 

490.6 

150.0 

73  !  548.0 

167.5 

34 

319.4 

97.7 

94 

376.  7 

115.2 

54 

434.1 

132.7 

14 

491.5 

150.  2 

74 

548.  9 

167.8 

35 

320.3 

97.9 

95 

377.7 

115.5 

55 

435.1 

133.  0 

15 

492.5 

150.  5 

75 

549.9 

168.1 

36 

321.  3 

98.2 

96 

378.  7 

115.8 

56 

436.0 

133.3 

16 

493.4 

150.  8 

76 

550.  8 

168.4 

37 

322.2 

98.5 

97 

379.6 

116.1 

57 

437.0 

133.6 

17 

494.4 

151.1 

77 

551.  8 

168.7 

38 

323.  2 

98.8 

98 

380.6 

116.4 

58 

4.38.  0 

133. 9 

18 

495.  3 

151.4 

78 

552.7 

169.0 

39 

324.2 

99.1 

99 

.381.5 

116.7 

59 

438.  9 

134.2 

19 

496.3 

151.7 

79 

553.7 

169.3 

40 

325. 1 
326.1 

99.4 
99.  7 

400 

382.  5 
383.4 

117.0 
117.  2 

60  i  439.9 
461     440. 8 

f34.5 
134.8 

20 
521 

497.2 

152.0 

80 

554.6 

169.6 

341 

401 

498.2 

152.3 

581 

555.6 

169.9 

42 

327.0 

100.0 

02 

384.4 

117.5 

62     441. 8 

135.1 

22 

499.2 

152.6 

82 

556.  5 

170.2 

43 

328.0 

100.3 

03 

385.  4 

117.8 

63  i  442.  7 

135.  4 

23 

500.1 

152. 9 

83 

557.5 

170.5 

44 

328.9 

100.6 

04 

386.3 

118.1 

64  !  443.  7 

135.7 

24 

501.1 

153.2 

84 

558.4 

170.8 

45  i 

329.9 

100.9 

05     387. 3 

118.4 

65     444.6 

136.0 

25 

502.0 

153.5 

85 

559.4 

171.1 

46  ' 

330.8 

101.2 

06  1  388.  2 

118.7 

66     445.6 

136.2 

26 

503.0 

153.  8 

86 

560.4 

171.3 

47 

331.8 

101.5 

07  !  389.2 

119.0 

67  1  446.6 

136.5 

27 

503.  9 

154.1 

87 

561.3 

171.6 

48 

332.8 

101.8 

08     390.  1 

119.3 

68  i  447.5 

136.  8 

28 

504.  9 

154.  4 

88 

562.3 

171.9 

49 

333.7 

102.0 

09     391. 1 

119.6 

69     448. 5 

137.1 

29 

505.  9 

154.  7 

89 

563.2 

172.2 

50 
351 

334.7 
335.  6 

102.  3 

10  ! 

392.0 
393.0 

119.9 

70 

449.4 
450.4 

137.4 

30 
531 

506.  8 

155.  0 

90 
591 

564.2 

172.5 

172.8 

102.  6 

411  i 

120.2 

471 

137.  7 

507.8 

155.  3 

565. 1 

52 

336.6 

102.9 

12  1  394.  0 

120.5 

72 

451.  3 

138.0 

32 

508.7 

155.6 

92 

566.1 

173. 1 

53 

337.5 

103.  2 

13     394.9 

120.8 

73 

452.  3 

138.3 

33 

509.  7 

155.  9 

93 

567.1 

173. 4 

54 

338.  5 

103.5 

14 

395.  9 

121.0 

74 

453.  3 

138.6 

34 

510.6 

156.  2 

94 

568.0 

173.7 

55 

339.5 

103.8 

15 

396.  8 

121.3 

75 

454.  2 

138.9 

35 

511.6 

156.  5 

95 

569.  0 

174.0 

56 

340.4 

104.1 

16 

397.8 

121.6 

76 

455.  2 

139.2 

36 

512.6 

156.  8 

96 

569.9 

174.  3 

57 

341.4 

104.4 

17 

398.  7 

121.9 

77 

456. 1 

139.5 

37 

513.  5 

157. 1 

97 

570.9 

174.6 

58 

342.3 

104.7 

18 

399.  7 

122.2 

78 

457. 1 

139.8 

38 

514.  5 

157.3 

98 

571.8 

174.9 

59 

343.  3 

105.  0 

19     400.7  1 

122.5 

79 

458.  0 

140.0 

39 

515. 4 

157.  6 

99 

572.8 

175.  2 

60 

344.2 

105.3 

20     401. 6 

122.8 

80 

459.0 

140.3 

40 

516.4 

157.9 

600 

573.8 

175.  4 

Dist. 

Dep. 

Lat. 

Dist.        Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.         Lat.    | 

Dist. 

Dep. 

Lat. 

^3°  (107°,  253°,  287° 

)• 

22489—03- 


-26 


Page  402] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  18°  (162°,  198 

°,  342° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

1.0 

0.3 

61 

58.0 

18.9 

121 

115.1 

37.4 

181 

172.1 

55.9 

241 

229.2 

74.5 

2 

1.9 

0.6 

62 

59.0 

19.2 

22 

116.0 

37.7 

82 

173.1 

56.2 

42 

230.2 

74.8 

3 

2.9 

0.9 

63 

59.9 

19.5 

23 

117.0 

38.0 

83 

174.0 

56.6 

43 

231.1 

75.1 

4 

3.8 

1.2 

64 

60.9 

19.8 

24 

117.9 

38.  3 

84 

175.  0 

56.9 

44 

232.1 

75.4 

5 

4.8 

1.5 

«5 

61.8 

20.1 

25 

118.9 

38.6 

85 

175.9 

57.2 

45 

233.0 

75.7 

6 

5.7 

1.9 

66 

62.8 

20.4 

26 

119.8 

38.9 

86 

176.9 

57.5 

46 

234.  0 

76.0 

7 

6.7 

2.2 

67 

63.7 

20.7 

27 

120.8 

39.2 

87 

177.8 

57.8 

47 

234.9 

76.3 

8 

7.6 

2.5 

68 

64.7 

21.0 

28  i  121.7 

.39.6 

88 

178.8 

58.1 

48 

2.35.  9 

76.6 

9 

8.6 

2.8 

69 

65.6 

21.3 

29  1  122. 7 

39.9 

89 

179.7 

58.4 

49 

236.8 

76.9 

10 
11 

9.5 
10.5 

3.1 
3.4 

70 
71 

66.6 

21.6 
21.9 

30 

123.6 
124.6 

40.2 
40.5 

90 
191 

180.7 
181.7 

58.7 

50 

237.  8 

238.  7 

77.3 

67.5 

131 

59.0 

251 

77.6 

12 

11.4 

3.7 

72 

68.5 

22.2 

32 

125.5 

40.8 

92 

182.6 

59.3 

52 

239.7 

77.9 

13 

12.4 

4.0 

73 

69.4 

22.6 

33 

126.  5 

41.1 

93 

183.6 

59.6 

53 

240.6 

78.2 

14 

13.3 

4.3 

74 

70.4 

22.9 

34 

127.4 

41.4 

94 

184.5 

59.9 

54 

241.6 

78.5 

15 

14.3 

4.6 

75 

71.3 

23.2 

35 

128.4 

41.7 

95 

185. 5 

60.3 

55 

242.5 

78.8 

16 

15.2 

4.9 

76 

72.3 

23.5 

36 

129.  3 

42.0 

96 

186.4 

60.6 

56 

243.  5 

79.1 

17 

16.2 

5.3 

77 

73.2 

23.8 

37 

130.  3 

42.3 

97 

187.4 

60.9 

57 

244.4 

79.4 

18 

17.1 

5.6 

78 

74.2 

24.1 

38 

131.2 

42.6 

98 

188.  3 

61.2 

58 

245.4 

79.7 

19 

18.1 

5.9 

79 

75.1 

24.4 

39 

132.2 

43.0 

99 

189.3 

61.5 

59 

246.  3 

80.0 

20 

19.0 
20.0 

6.2 
6.  5 

80 
81 

76.1 

24.7 

40 

133.1 

43.3 

200 

190.2 

61.8 

60 

247.  3 
248.2 

80.3 
80.7 

21 

77.0 

25.0 

141 

134.1 

43:  6 

201 

191.2 

62.1 

261 

22 

20.9 

6.8 

82 

78.0 

25.3 

42 

135.1 

43.9 

02 

192.1 

62.4 

62 

249.2 

81.0 

23 

21.9 

7.1 

83 

78.9 

25.6 

43 

136.0 

44.2 

03 

193.1 

62.7 

63 

250.1 

81.3 

24 

22.8 

7.4 

84 

79.9 

26.0 

44 

137.0 

44.5 

04 

194.  0 

63.0 

64 

251.1 

81.6 

25 

23.8 

7.7 

85 

80.8 

26.3 

45 

137.9 

44.8 

05 

195.  0 

63.3 

65 

252.0 

81.9     . 

26 

24.7 

8.0 

86 

81.8 

26.6 

46 

138.9 

45.1 

06 

195.9 

63.7 

66 

253.0 

82.2 

27 

25.7 

8.3 

87 

82.7 

26.9 

47 

139.  8 

45.4 

07 

196.  9 

64.0 

67 

253.  9 

82.5 

28 

26.6 

8.7 

88 

83.7 

27.2 

48 

140.8 

45.7 

08 

197.8 

64.3 

68 

254.  9 

82.8 

29 

27.6 

9.0 

89 

84.6 

27.5 

49 

141.7 

46.0 

09 

198.8 

64.6 

69 

255.  8 

83.1 

30 

28.5 

9.3 

90 
91 

85.6 

27.8 

50 

142.7 

46.4 

10 

199.7 
^200.7 

64.9 

70 

256.8 

83.4 
83.7 

31 

29.5 

9.6 

86.5 

28.1 

151 

143.6 

46.7 

211 

65.2 

271 

257.  7 

32 

30.4 

9.9 

92 

87.5 

28.4 

52 

144.6 

47.0 

12 

201.6 

65.5 

72 

258.7 

84.1 

33 

31.4 

10.2 

93 

88.4 

28.7 

53 

145.  5 

47.3 

13 

202.6 

65.8 

73 

259.6 

84.4 

34 

32.3 

10.5 

94 

89.4 

29.0 

54 

146.5 

47.6 

14 

203.  5 

66.1 

74 

260.6 

84.7 

35 

33.3 

10.8 

95 

90.4 

29.4 

55 

147.4 

47.9 

15 

204.5 

66.4 

75 

261.5 

85.0 

36 

34.2 

11.1 

96 

91.3 

29.7 

56 

148.4 

48.2 

16 

205.  4 

66.7 

76 

262.  5 

85.3 

37 

35.2 

11.4 

97 

92.3 

30.0 

57 

149.  3 

48.5 

17 

206.4 

67.1 

77 

263.4 

85.6 

38 

36.1 

11.7 

98 

93.2 

30.3 

58 

150.  3 

48.8 

18 

207.  3 

67.4 

78 

264.4 

85.9 

39 

37.1 

12.1 

99 

94.2 

30.6 

59 

551.2 

49.1 

19 

208.  3 

67.7 

79 

265.3 

86.2 

40 

38.0 

12.4 
12.7 

100 

95.1 

30.9 
31.2 

60 

152.2 
153. 1 

49.4 

20 

209.2 
210.2 

68.0 

80 

266.3 

86.5 

41 

39.0 

101 

96.1 

161 

49.8 

221 

68.3 

281 

267.2 

86.8 

42 

39.9 

13.0 

02 

97.0 

31.5 

62 

154. 1 

50.1 

22 

211.1 

68.6 

82 

268.2 

87.1 

43 

40.9 

13.3 

03 

98.0 

31.8 

63 

155.  0 

50.4 

23 

212.1 

68.9 

83 

269.1 

87.5 

44 

41.8 

13.6 

04 

98.9 

32.1 

64 

156.0 

50.7 

24 

213.  0 

69.2 

84 

270.1 

87.8 

45 

42.8 

13.9 

05 

99.9 

.32.4 

65 

156.9 

51.0 

25 

214.0 

69.5 

85 

271.1 

88.1 

46 

43.7 

14.2 

06 

100.8 

32.8 

66 

157.  9 

51.3 

26 

214.9 

69.8 

86 

272.0 

88.4 

47 

44.7 

14.5 

07 

101.8 

33.1 

67 

158.  8 

51.6 

27 

215. 9 

70.1 

87 

273.0 

88.7 

48 

45.7 

14.8 

08 

102.7 

33.4 

68 

159.  8 

51.9 

28 

216.8 

70.5 

88 

273.9 

89.0 

49 

46.6 

15.1 

09 

103.  7 

33.  7 

69 

160.7 

52.2 

29 

217.8 

70.8 

89 

274.9 

89.3 

50 
51 

47.6 

15.5 

10 

104.6 

34.0 

70 

161.  7 

52.5 

52.8 

30 
231 

218.7 

71.1 

90 

275.8 

89.6 

48.5 

15.8 

111 

105.6 

34.3 

171 

162.6 

219.7 

71.4 

291 

276.8 

89.9 

52 

49.5 

16.1 

12 

106.5 

34.6 

72 

163.6 

53.2 

32 

220.6 

71.7 

92 

277.7 

90.2 

53 

50.4 

16.4 

13 

107.5 

34.9 

73 

164.  5 

53.5 

33 

221.6 

72.0 

93 

278.7 

90.5 

54 

51.4 

16.7 

14 

108.4 

35.2 

74 

165.  5 

53.8 

34 

222.  5 

72.3 

94 

279.  6 

90.9 

55 

52.3 

17.0 

15 

109.4 

35.5 

75 

166.4 

54.1 

35 

223.  5 

72.6 

95 

280.6 

91.2 

56 

53.3 

17.3 

16 

110.3 

35.8 

76 

167.4 

54.4 

36 

224.4 

72.9 

96 

281.5 

91.5 

57 

54.2 

17.6 

17 

111.3 

36.2 

77 

168.3 

54.7 

37 

225.  4 

73.2 

97 

282.  5 

91.8 

58 

55.2 

17.9 

18 

112.2 

36.5 

78 

169.3 

55.0 

38 

226.4 

73.5 

98 

283.4 

92.1 

59 

56.1 

18.2 

19 

113.  2     36.  8 

79 

170.2 

55.3 

39 

227.3 

73.9 

99 

284.4 

92.4 

60 

57.1 

18.5 

20 

114.1 

37.1 

80 

171.2 

55.6 

40 

228.3 

74.2 

300 

285.3 

92.7 

Dist. 

Dep.' 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

^2°  (1 

}8°,  252°,  288° 

)• 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  18°  (162°,  198°,  342°). 


[Page  403 


341 
42 
43 
44 
45 
46 


Lat. 


286.3 
287.2 
288.2 
289.1 
290.1 
291.0 
292.  0 
292.9 
293.9 
294.8 


295.8 
296.7 
297.7 
298.6 
299.6 
300.5 

301.  5 

302.  4 

303.  4 
304.3 

305.  3 

306.  2 

307.  2 
308.2 
309.1 
310. 1 
311.0 
312.  0 
312.9 
313.9 


Dep. 


314.  8 

315.  8 
316.7 
317.7 
318.6 
319.6 
320.5 
321.5 
322.4 
323.4 


324.3 
325. 3 
326.2 
327.2 
328. 1 
329.1 


93.0 
93.3 
93.7 
94.0 
94.3 
94.6 
94.9 
95.2 
95.5 

96.1 

96.4 

96.7 

97.0 

97.4 

97.7 

98.0 

98.  3 

98.6 

98^ 

99.2 

99.5 

99.8 

100.1 

100.4 

100.7 

101. 1 

101.4 

101.7 

102.0 

102.3 

102.6 

102.9 

103.2 

103.5 

103.8 

104.1 

104.5 

104.8 

105.1 


Dist. 


361 
62 
63 
64 
65 
66 
67 
68 
69 
70 


47 

330.0 

48 

331.0 

49 

331.9 

50 

332.9 

351 

333.8 

52 

334.8 

53 

335.7 

54 

336.7 

55 

337.6 

56 

338.6 

57 

339.5 

58 

340.5 

59 

341.4 

60 

342.4 

Dist. 

Dep. 

105.4 

105.  7 
106.0 

106.  3 
106.6 
106.9 
107.2 
107.5 
107.9 
108.2 
108.  5 
108.8 
109.1 
109.4 
109.7 
110.0 
110.  3 
110.6 
110.9 
111.3 


Lat.       Dist. 


371 

72 
73 
74 
75 
76 
77 
78 
79 
80 


381 

82 
83 
84 
85 
86 
87 
88 
89 
90 


391 
92 
93 
94 
95 
96 
97 
98 
99 

400 


401 
02 
03 
04 
05 
06 
07 
08 
09 
10 


411 
12 
13 
14 
15 
16 
17 
18 
19 
20 


Lat. 


343.  3 
344.3 
345.  2 
346.2 
347.1 
348.1 

349.  0 

350.  0 
350.  9 

^1.9 

352.  9' 

353.  8 

354.  8 
355.7 
356.7 
357.6 
358.6 
359.5 
360.5 
361.4 


362.4 
363.  3 
364.3 
365.2 
366.2 
367. 1 
368.1 
369.0 
370.0 
370.9 


371.9 
372.8 
373.  8 
374.7 
375.  7 
376.6 
377.6 
378. 5 
379.  5 
380.4 


Dep. 


111.6 
111.9 
112.2 
112.5 
112.8 
113.1 
113.4 
113.7 
114.0 
114.3 


114.7 
115.0 
115.3 
115.6 
115.9 
116.2 
116.5 
116.8 
117.1 
117.Jl^ 
117.7 
118.1 
118.4 
118.7 
119.0 
119.  3 
119.6 
119.9 
120.2 
120.5 


Dist. 


381.4 
382.3 
383.  3 
384.2 
385.2 
386.1 
387. 1 
388.0 
389.0 
389.9 
390.  9 
391.8 
392.8 
393.  7 
394.7 
395.  6 
396.6 
397.5 
398. 5 
399.5 


Dep. 


120.8 
121.1 
121.5 
121.8 
122.1 
122.4 
122.7 
123.0 
123.  3 
123.  6 
123.9 
124.2 
124.5 
124.9 
125.2 
125.  5 
125.  8 
126.1 
126.4 
126^ 
127.0 
127.3 
127.6 
127.9 
128.  3 
128.6 
128.9 
129.2 
129.5 
129.8 


Lat.   Dist 


421 
22 
23 
24 
25 
26 
27 
28 
29 
30 


431 
32 
33 
34 
35 
36 
37 
38 
39 
40 


441 
42 
43 
44 
45 
46 
47 
48 
49 
50 


451 
52 
53 
54 
55 
56 
57 
58 
59 
60^ 

461 
62 
63 
64 
65 
66 
67 
68 
69 

JO 

471 
72 
73 
74 
75 
76 
77 
78 
79 
80 


lAt. 


400.4 
401.4 
402.3 
403.  3 
404.2 
405.2 
406.1 
407.1 
408.0 
409^0 
"409.  9 
410.9 
411.8 
412.8 
413.7 
414.7 
415.6 
416.6 
417.5 
418.5 


Dep. 


130.1 
130.4 
130.  7 
131.0 
131.3 
131.7 
132.0 
132.3 
132.6 
132.9 


133.2 
133.5 
133.8 
134.1 
134.4 
134.7 
135.1 
135.4 
135.7 
136.0 


419.4 
420.4 
421.3 
422.3 
423.2 
424.2 
425. 1 
426. 1 
427.0 
428.0 
428.  9 
429.9 
430.8 
431.8 
432.7 
433.7 
434.6 
435.6 
436. 5 
437.  5 


448.0 
448.9 

449.  9 

450.  8 
451.8 
452.7 
453.7 
454.6 
455. 6 
456.5 


Dep. 


136.3 
136.6 
136.9 
137.2 
137.  5 
137.  8 
138.1 
138.4 
138.8 
139. 1 


139.4 
139.7 
140.0 
140.  3 
140.6 
140.9 
141.2 
141.5 
141.8 
142.2 


142.5 
142.8 
143.1 
143. 4 
143.7 
144.0 

144.  3 
144.6 
144.9 

145.  2 


145.6 
145.  9 
146.2 
146.5 
146.8 
147.1 
147.4 
147.7 
148.0 
148.3 


Lat.   Dist, 


Dist. 


481 

82 
83 
84 
85 
86 
87 
88 
89 
90 


491 
92 
93 
94 
95 
96 
97 
98 
99 
500 
501 
02 
03 
04 
05 
06 
07 
08 
09 
10 


Lat. 


457.5 
458.5 
459.4 
460.4 
461.  3 
462.3 
463.2 
464.2 
465. 1 
466.1 


Dep.      Dist 


467.0 
468.0 
468.9 
469.8 
470.8 
471.7 
472.7 
473. 6 
474.6 
475.5 


476 

477, 

478, 

479 

480, 

481, 

482.2 

483.2 

484.1 

485.1 


511 
12 
13 
14 
15 
16 
17 
18 
19 
20 


521 
22 
23 
24 
25 
26 
27 
28 
29 
30 


486.0 
487.0 
487.9 
488.9 
489.8 
490.8 
491.7 
492.7 
493.6 
494.6 


531 
32 
33 
34 
35 
36 
37 
38 
39 
40 


495.5 
496.  5 
4^^7.4 
498.4 
499.  3 
500.3 
501.2 
502.2 
503. 1 
504.1 
505. 0' 
506. 0 
506.  9 
507. 9 
508.  8 
509.8 
510.7 
511.7 

512.  6 

513.  6 


Dep. 


148.6 
148.9 

149.  3 
149.6 
149.9 
150.2 

150.  5 
150.8 
151. 1 
15L4 

151.  7 
152.0 
152.3 

152.  6 

153.  0 
153.3 
153. 6 
153.9 
154.2 
154.5 


154.8 
155.1 
155.  4 

155.  7 
156.1 

156.  4 

156.  7 

157.  0 

157.  3 
157^ 
157. 9 

158.  2 
158.  5 

158.  8 

159.  1 
159.  4 
159.7 
160.0 
160.3 
160.^ 
161. 0 
161.3 
161.6 
161.9 
162.2 
162.5 
162.9 
163.2 
163.5 
163.  8 


164.1 
164.4 
164.7 
165.  0 
165.3 
165.  6 
165.  9 
166.2 
166.5 
166.9 


541 
42 
43 
44 
45 
46 
47 
48 
49 
50 

551 
52 
53 
54 
55 
56 
57 
58 
59 
60 


561 
62 
63 
64 
65 
66 
67 
68 
69 
70 


571 
72 
73 
74 
75 
76 
77 
78 
79 
80 


581 
82 
83 
84 
85 
86 
87 
88 
89 
90 


591 
92 
93 
94 
95 
96 
97 
98 
99 

600 


Lat.      Dist. 


Lat. 


514.5 
515. 5 
516.  4 
517.4 

518.  3 

519.  3 
520.2 
521.2 
522.1 

523. 1 

524.  0 

525.  0 
525.  9 
526.9 
527.8 
528.8 
529.7 
530.7 
531.  6 

^2^6_ 
533.5 
534.5 
535. 4 
536.4 
537. 3 
538.3 

539. 2 
540.  2 
541.1 
542.1 


543.0 
544.  0 

544.  9 

545.  9 

546.  8 
.547.8 

548.  7 

549.  7 

550.  6 
551.6 

552.  5 

553.  5 
554. 4 
555.4 
556.3 

557.  3 

558.  2 
559.2 
560.1 
561.1 


562.  0 

563.  0 
563.  9 
564.9 
565.  8 
566.8 

567.  7 

568.  7 

569.  6 
570.6 


Dep. 


Dep. 

167.2 

167.  5 
167.9 
168.2 

168.  5 
168.8 
169.1 
169.4 
169.7 
170^0^ 
170.  3 
170.6 
170.9 
171.2 
171.5 
171.8 
172.1 
172.4 
172.7 
173.0 
173.3 
173.  6 
173.9 
174.2 
174.6 
174.9 
175.2 
175.5 
175.8 
176.1 
176.  4" 
176.7 
177.0 
177.3 
177.6 
178.0 
178.3 
178.6 
178.9 
179^ 
179.  5 
179.8 
180.1 
180.4 
180.7 
181.1 
181.4 
181.7 
182.0 
182.^ 

182.  7 
183.0 
183.3 

183.  6 
183.9 
184.2 
184.5 
184.8 
185. 1 
185. 4 

Lat. 


72°  (108,  252°,  288°). 


Page  404] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  19°  (161°,  199 

°,  341°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.3 

61 

57.7 

19.9 

121 

114.4 

39.4 

181 

171.1 

58.9 

241 

227.9 

78.5 

2 

1.9 

0.7 

62 

58.6 

20.2 

22 

115.4 

39.7 

82 

172.1 

59.3 

42 

228.8 

78.8 

3 

2.8 

1.0 

63 

59.6 

20.5 

23 

116.  3 

40.0 

83 

173.0 

59.6 

43 

229.8 

79.1 

4 

3.8 

1.3 

64 

60.5 

20.8 

24 

117.2 

40.4 

84 

174.0 

59.9 

44 

230.  7 

79.4 

5 

4.7 

1.6 

65 

61.5 

21.2 

25 

118.2 

40.7 

85 

174.9 

60.2 

45 

231.  7 

79.8 

6 

5.7 

2.0 

«6 

62.4 

21.5 

26 

119.1 

41.0 

86 

175.9 

60.6 

46 

232.6 

80.1 

7 

6.6 

2.3 

67 

63.3 

21.8 

27 

120.1 

41.3 

87 

176.8 

60.9 

47 

233.5 

80.4 

8 

7.6 

2.6 

68 

64.3 

22.1 

28 

121.0 

41.7 

88 

177.8 

61.2 

48 

234.5 

80.7 

9 

8.5 

2.9 

69' 

65.2 

22.5 

29 

122.0 

42.0 

89 

178.7 

61.5 

49 

235.4 

81.1 

10 

9.5 

3.3 

70 

66.2 

22.8 

30 

122.9 
123.9 

42.3 

90 

179.6 

61.9 

50 
251 

236.4 
237.3 

81.4 
81.7 

11 

10.4 

3.6 

71 

67.1 

23.1 

131 

42.6 

191 

180.6 

62.2 

12 

11.3 

3.9 

72 

68.1 

23.4 

32 

124.8 

43.0 

92 

181.5 

62.5 

52 

238.3 

8gi0 

13 

12.3 

4,2 

73 

69.0 

23.8 

33 

125.8 

43.3 

93 

182.5 

62.8 

53 

239.2 

8^.4 

14 

13.2 

.4.6 

74 

70.0 

24.1 

34 

126.7 

43.6 

94 

183.4 

63.2 

54 

240.2 

82.7 

15 

14.2 

4.9 

75 

70.9 

24.4 

35 

127.6 

44.0 

95 

184.4 

63.5 

55 

241.1 

83.0 

16 

15.1 

5.2 

76 

71.9 

24.7 

36 

128.6 

44.3 

96 

185.  3 

63.8 

56 

242.1 

83.3 

17 

16.1 

5.5 

77 

72.8 

25.1 

37 

129.5 

44.6 

97 

186.3 

64.1 

57 

243.0 

83.7 

18 

17.0 

5.9 

78 

73.8 

2.5.4 

38 

130. 5 

44.9 

98 

187.2 

64.5 

58 

243.9 

84.0 

19 

18.0 

6.2 

79 

74.7 

25.7 

39 

131.4 

45.3 

99 

188.2 

64.8 

59 

244.9 

84.3 

20 

18.9 

6.5 

80 

75.6 

26.0 

40 

132.4 

45.6 
45.9 

200 

189.1 
190.0 

65.1 

60 

245.8 
246.8 

84.6 

21 

19.9 

6.8 

81 

76.6 

26.4 

141 

133.  3 

201 

65.4 

261 

85.0 

22 

20.8 

7.2 

82 

77.5 

26.7 

42 

134.3 

46.2 

02 

191.0 

65.8 

62 

247.7 

85.3 

23 

21.7 

7.5 

83 

78.5 

27.0 

43 

135.2 

46.6 

03 

191.9 

66.1 

63 

248.7 

85.6 

24 

22.7 

7.8 

84 

79.4 

27.3 

44 

136.2 

46.9 

04 

192.9 

66.4 

64 

249. 6 

86.0 

25 

23.6 

8.1 

85 

80.4 

27.7 

45 

137.1 

47.2 

05 

193.8 

66.7 

65 

250.6 

86.3 

26 

24.6 

8.5 

86 

81.3 

28.0 

46 

138.0 

47.5 

06 

194.8 

67.1 

66 

251.5 

86.6 

27 

25.5 

8.8 

87 

82.3 

28.3 

47 

139.0 

47.9 

07 

195.7 

67.4 

67 

252.5 

86.9 

28 

26.5 

9.1 

88 

83.2 

28.7 

48 

139.9 

48.2 

08 

196.7 

67.7 

68 

253.  4 

87.3 

29 

27.4 

9.4 

89 

84.2 

29.0 

49 

140.9 

48.5 

09 

197.6 

68.0 

69 

254.3 

87.6 

30 

28.4 

9.8 

90 

85.1 

29.3 

50 

141.8 

48.8 

10 
211 

198.6 
199.  5 

68.4 

68.  7 

70 

271 

255.3 
256.2 

87.9 

31 

29.3 

10.1 

91 

86.0 

29.6 

151 

142.8 

49.2 

88.2 

32 

30.3 

10.4 

92 

87.0 

30.0 

52 

143.7 

49.5 

12 

200.4 

69.0 

72 

257.2 

88.6 

33 

31.2 

10.7 

93 

87.9 

30.3 

53 

144.7 

49.8 

13 

201.4 

69.3 

73 

258.1 

88.9 

34 

32.1 

11.1 

94 

88.9 

30.6 

54 

145.6 

50.1 

14 

202.3 

69.7 

74 

259.1 

89.2 

35 

33.1 

11.4 

95 

89.8 

30.9 

55 

146.6 

50.5 

15 

203.3 

70.0 

75 

260.0 

89.5 

36 

34.0 

11.7 

96 

90.8 

31.3 

56 

147.5 

50.8 

16 

204.2 

70.3 

76 

261.0 

89.9 

37 

35.0 

12.0 

97 

91.7 

31.6 

57 

148.4 

51.1 

17 

205. 2 

70.6 

77 

261.9 

90.2 

38 

35.9 

12.4 

98 

92.7 

31.9 

58 

149.4 

51.4 

18 

206.1 

71.0 

78 

262.9 

90.5 

39 

36.9 

12.7 

99 

93.6 

32.2 

59 

150.  3 

51.8 

19 

207.1 

71.3 

79 

263.8 

90.8 

40 

37.8 

13.0 

100 

94.6 

32.6 

60 

151.3 

52.1 

20 

208.0 

71.6 
72.0 

80 

264.7 

91.2 

41 

38.8 

13.3 

101 

95.5 

32.9 

161 

152.2 

52.4 

221 

209.0 

281 

265.7 

91.5 

42 

39.7 

13.7 

02 

96.4 

33.2 

62 

153.2 

52.7 

22 

209.9 

72.3 

82 

266.  6 

91.8 

43 

40.7 

14.0 

03 

97.4 

33.5 

63 

154. 1 

53.1 

23 

210.9 

72.6 

83 

267.6 

92.1 

44 

41.6 

14.3 

04 

98.3 

33.9 

64 

155. 1 

53.4 

24 

211.8 

72.9 

84 

268.  5 

92.5 

45 

42.5 

14.7 

05 

99.3 

34.2 

65 

156.0 

53.7 

25 

212.7 

73.3 

85 

269.5 

92.8 

46 

43.5 

15.0 

06 

100.2 

34.5 

66 

157.  0 

54.0 

26 

213.7 

73.6 

86 

270.4 

93.1 

47 

44.4 

15.3 

07 

101.2 

34.8 

67 

157.9 

54.4 

27 

214.6 

73.9 

87 

271.4 

93.4 

48 

45.4 

15.6 

08 

102.1 

35.2 

68 

158.8 

54.7 

28 

215.6 

74.2 

88 

272.3 

93.8 

49 

46.3 

16.0 

09 

103.1 

35.5 

69 

159.8 

55.0 

29 

216.5 

74.6 

89 

273.  3 

94.1 

50 

47.3 

16.3 

10 

104.0 

35.8 

70 

160.7 

55.3 

30 

217.5 
218.4 

74.9 
75.2 

90 
291 

274.2 
275.1 

94.4 
94.7 

51 

48.2 

16.6 

111 

105. 0 

36.1 

171 

161.7 

55.7 

231 

52 

49.2 

16.9 

12 

105.  9 

36.  5 

72 

162.6 

56.0 

32 

219.4 

75.5 

92 

276.1 

95.1 

53 

50.1 

17.3 

13 

106.8 

36.8 

73 

163.6 

56.3 

33 

220.  3 

75.9 

93 

277.0 

95.4 

54 

51.1 

17.6 

14 

107.8 

37.1 

74 

164.5 

56.6 

34 

221.3 

76.2 

94 

278.0 

95.7 

55 

52.0 

17.9 

15 

108.7 

37.4 

75 

165.  5 

57.0 

35 

222.2 

76.5 

95 

278.9 

96.0 

56 

52.9 

18.2 

16 

109.7 

37.8 

76 

166.4 

57.3 

36 

223.  1 

76.8 

96 

279.9 

96.4 

57 

53.9 

18.6 

17 

110.6 

38.1 

77 

167.4 

57.6 

37 

224.1 

77.2 

97 

280.8 

96.7 

58 

54.8 

18.9 

18 

111.6 

38.4 

78 

168.3 

58.0 

38 

225.  0 

77.5 

98 

281.8 

97.0 

59 

55.8 

19.2 

19 

112.5 

38.7 

79 

169.2 

58.3 

39 

226.0 

77.8 

99 

282.7 

97.3 

60 

56.7 

19.5 

20 

113.5 

39.1 

80 

170.2 

58.6 

40 

226.9 

78.1 

300 

283.7 

97.7 
Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

■1°  (1 

09°,  251 

°,  289° 

)• 

TABLE  '2. 

[Page  405 

Difference  of  Latitude  and 

Departure  for  19°  (161°,  199 

°,  341° 

)• 

Dlst. 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

284.6 

98.0 

361 

341.3 

117.  5 

421 

398.1 

137.0 

481 

454.  8 

156.6 

541 

511.5 

176.1 

02 

285.5 

98.3 

62 

342.3 

117.8 

22 

399.0 

137.4 

82 

455.  7 

156.9 

42 

512.4 

176.4 

03 

286.5 

98.6 

63 

343.2 

118.2 

23 

400.0 

137.  7 

83 

456.7 

157.  2 

43 

513.  4 

176.8 

04 

287.4 

99.0 

64 

344.2 

118.5 

24 

400.9 

138.0 

84 

457.6 

157.  6 

44 

514.3 

177.1 

05 

288.  4 

99.3 

65 

345.1 

118.8 

25 

401.8 

138.4 

85 

458.6 

157.9 

45 

515.  3 

177.4 

06 

289.3 

99.6 

66 

346.1 

119.1 

26 

402.8 

138.7 

86 

459.  5 

158.  2 

46 

516.  2 

177.7 

07 

290.3 

99.9 

67 

347.  0 

119.5 

27 

403.  7 

139.0 

87 

460.5 

158.  5 

47 

517.2 

178.1 

08 

291.2 

100.  3 

68 

348.0 

119.8 

28 

404.7 

139.  3 

88 

461.4 

158.  9 

48 

518.1 

178.4 

09 

292.2 

100.6 

69 

348.9 

120.1 

29 

405.  6 

139.7 

89 

462.4 

159.2 

49 

519.1 

178.7 

10 
311 

293.1 
294. 1 

100.9 
101.2 

70 
371 

349.8 

120.4 

30 
431 

406.6 
407.5 

140.0 

90 
491 

463.3 
464.3 

159.5 

50 
551 

520.0 
521.0 

179.0 
179.4 

350.8 

120.8 

140.3 

159.8 

12 

295.  0 

101.6 

72 

351.7 

121.1 

32 

408.  5 

140.6 

92 

465.2 

160.^2 

52 

521.9 

179.  7 

13 

295.9 

101.9 

73 

352.7 

121.4 

33 

409.4 

141.0 

93 

466.1 

160.  5 

53 

522.8 

180.0 

14 

296.9 

102.2 

74 

353.6 

121.7 

34 

410.4 

141.  3 

94 

467.1 

160.8 

54 

523.  8 

180.3 

15 

297.8 

102.5 

75 

354.6 

122.1 

35 

411.3 

141.6 

95 

468.0 

161.1 

55 

524.7 

180.7 

16 

298.8 

102.9 

76 

355.5 

122.4 

36 

412.2 

141.9 

96 

469.0 

161.5 

56 

525.7 

181.0 

17 

299.7 

103.2 

77 

356.5 

122.7 

37 

413.2 

142.3 

97 

469.9 

161.  8 

57 

526.6 

181.3 

18 

300.7 

103.5 

78 

357.  4 

123.  0 

38 

414.1 

142.6 

98 

470.9 

162.1 

58 

527.6 

181.6 

19 

301.6 

103. 8 

79 

358.4 

123.4 

39 

415.1 

142.9 

99 

471.8 

162.4 

59 

528.  5 

182.0 

20 
321 

302.6 
303.  5 

104.2 
104. 5" 

80 

359.3 

123.7 
124.  0' 

40 
441 

416.0 

143.2 
143.  6' 

500 

472.8 
473.7 

162.8 

60 

529.  5 

530.  4" 

182.3 
182.6 

381 

360.  2 

417.0 

501 

163.1 

561 

22 

304.5 

104.8 

82 

361.2 

124.4 

42 

417.9 

143.9 

02 

474.7 

163.4 

62 

531.4 

182.9 

23 

305.4 

105.1 

83 

362. 1 

124.7 

43 

418.9 

144.2 

03 

475.  6 

163.7 

63 

532.3 

183.3 

24 

306.3 

105.5 

84 

363.1 

125.0 

44 

41§.8 

144.5 

04 

476.  5 

164.1 

64 

533.2 

183.  6 

25 

307.3 

105.8 

85 

364.  0 

125.  3 

45 

420.8 

144.9 

05 

477. 5 

164.4 

65 

534.2 

183.  9 

26 

308.2 

106.1 

86 

365.  0 

125.  7 

46 

421.7 

145.2 

06 

478.4 

164.7 

66 

535.  1 

184.2 

27 

309.2 

106.  4 

87 

365.  9 

126.0 

47 

422.6 

145.5 

07 

479.4 

165.0 

67 

536.  1 

184.6 

28 

310.1 

106.8 

88 

366.  9 

126.3 

48 

423.  6 

145.8 

08 

480.3 

165.4 

68 

537.  0 

184.  9 

29 

311.1 

107.1 

89 

367.8 

126.6 

49 

424.  5 

146.2 

09 

481.2 

165.7 

69 

538.  0 

185.2 

30 
331 

312.0 

107.4 

90 

368.8 
369.  7 

127.0 

50 

425.  5 
426.4 

146.5 

10 

482.2 
483.1 

166.1 

70 

538.9 

185.  6 
185.  9 

313.0 

107.7 

391 

127.3 

451 

146.8 

511 

166.4 

571 

539.9 

32 

313.9 

108.1 

.92 

370.6 

127.6 

52 

427.4 

147.1 

12 

484.1 

166.7 

72 

540.8 

186.2 

33 

314.9 

108.4 

93 

371.6 

127.9 

53 

428.  3 

147.5 

13 

485.  0 

167.0 

73 

541.7 

186.  5 

34 

315.  8 

108.7 

94 

372.  5 

128.3 

54 

429.3 

147.8 

14 

486.0 

167.4 

74 

542.  7 

186.  9 

35 

316.7 

109.1 

95 

373.5 

128.  6 

55 

430.  2 

148.1 

15 

486.9 

167.7 

75 

543.  6 

187.2 

36 

317.7 

109.4 

96 

374.4 

128.9 

56 

431.2 

148.4 

16 

487.9 

168. 0 

76 

.544.  6 

187.  5 

37 

318.6 

109.7 

97 

375.4 

129.2 

57 

432. 1 

148.8 

17 

488.8 

168.3 

77 

545.  5 

187.  8 

38 

319.6 

110.0 

98 

376.  3 

129.6 

58 

433.  0 

149.1 

18 

489.7 

168.7 

78 

546.  5 

188.2 

39 

320.5 

110.4 

99 

377.3 

129.9 

59 

434.0 

149.4 

19 

490.7 

169.  0 

79 

547.4 

188.  5 

40 
341 

321.  5 

110.7 

400 

378.2 

130.2 

60 

434.9 

149.7 
150.1 

20 
521 

491.6 
492.6 

169.  3 
169.  6 

80 
581 

548.4 
549.  3 

188.8 
189.1 

322.4 

111.0 

401 

379.2 

130.5 

461 

435.9 

42 

323.4 

111.3 

02 

380. 1 

130.9 

62 

436.8 

150.4 

22 

493.5 

170.0 

82 

550. 3 

189.  5 

43 

324.3 

111.7 

03 

381.0 

131.2 

63 

437.8 

150.7 

23 

494.5 

170.  3 

83 

551.  2 

189.8 

44 

325.3 

112.0 

04 

382.0 

131.5 

64 

438.7 

151.0 

24 

495.4 

170.6 

84 

552.2 

190.1 

45 

326.  2 

112.3 

05 

382.9 

131.8 

65 

439.7 

151.4 

25 

496.4 

170.9 

85 

553.1 

190.4 

46 

327.1 

112.  6 

06 

383.9 

132.  2 

66 

440.6 

151.7 

26 

497.3 

171.2 

86 

554. 1 

190.  8 

47 

328.1 

113.0 

07 

384.8 

132.5 

67 

441.6 

152.0 

27 

498.  3 

171.6 

87 

555.  0 

191.1 

48 

329.0 

113.3 

08 

385.  8 

132.8 

68 

442.5 

152.4 

28 

499.2 

171.9 

88 

555.  9 

191.4 

49 

330.  0 

113.6 

09 

386.  7 

133.1 

69 

443.4 

152.7 

29 

500.1 

172.2 

89 

556.  9 

191.7 

50 

330.9 
331.9 

113.9 
114.  3 

10 
411 

387.7 
388.6 

133.5 

70 

444.4 
445.3 

153. 0 

30 
531 

501.1 
502.  0 

172.5 

90 

557.8 
558.8 

192.1 
192.  4 

351 

133.8 

471 

153.3 

172.9 

591 

52 

332.8 

114.6 

12 

389.6 

134.1 

72 

446.3 

153.7 

32 

503.  0 

173.2 

92 

559.7 

192.7 

53 

333.8 

114.9 

13 

390.5 

134.4 

73 

447.2 

154.0 

33 

503.  9 

173.5 

93 

560.7 

193.  0 

54 

334.7 

115.2 

14 

391.4 

134.8 

74 

448.2 

154.3 

34 

504.9 

173.8 

94 

561.6 

193.4 

55 

335.  7 

115.6 

15 

392.4 

135.1 

75 

449.1 

154.6 

35 

505.  8 

174.2 

95 

562.6 

193.7 

56 

336.  6 

115.9 

16 

393.  3 

135.  4 

76 

450.1 

155.0 

36 

506.  8 

174.  5 

96 

563.  5 

194.0 

57 

337.  5 

116.2 

17 

394.  3 

135.  7 

77 

451.0 

155.3 

37 

507.  7 

174.8 

97 

564.5 

194.  3 

58 

338.5 

116.5 

18 

395.2 

136.1 

78 

452.0 

155.6 

38 

508.  7 

175. 1 

98 

565.  4 

194.7 

59 

339.4 

116.9 

19 

396.2 

136.4 

79 

452.9 

155.9 

39 

509.  6 

175.  5 

99 

566.4 

195.  0 

60 

340.4 

117.2 

20 

397.1 

136.7 

80 
Dist. 

453.  8 

156.3 

40 

510.6 

175.  8 

600 

567.3 

195.  3 

Dist. 

Dep. 

Lat'. 

Dist. 

Dep. 

Lat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

71°  (1 

09°,  251 

°,  289°). 

Page  406] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  20°  (160°,  20C 

°,  340° 

). 

DIst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep.    1 

1 

0.9 

0.3 

61 

57.3 

20.9 

121 

113.7 

41.4 

181 

170.1 

61.9 

241 

226.5       82.4 

2 

1.9 

0.7 

62 

58.3 

21.2 

22 

114.6 

41.7 

82 

171.0 

62.2 

42 

227.4  j     82.8 

3 

2.8 

1.0 

63 

59.2 

21.5 

23 

115.6 

42.1 

83 

172.0 

62.6 

43 

228. 3  1     83. 1 

4 

3.8 

1.4 

64 

60.1 

21.9 

24 

116.5 

42.4 

84 

172.9 

62.9 

44 

229.3  i     83.5 

5 

4.7 

1.7 

65 

61.1 

22.2 

25 

117.5 

42.8 

85 

173.8 

63.3 

45 

230.  2 

83.8 

6 

5.6 

2.1 

66 

62.0 

22.6 

26 

118.4 

43.1 

86 

174.8 

63.6 

46 

231.2 

84.1 

7 

6.6 

2.4 

•  67 

63.0 

22.9 

27 

119.3 

43.4 

87 

175.7 

64.0 

47 

232.1 

84.5 

8 

7.5 

2.7 

68 

63.9 

23.3 

28 

120.  3 

43.8 

88 

176.7 

64.3 

48 

233. 0 

84.8 

9 

8.5 

3.1 

69 

64.8 

23.6 

29 

,121.2 

44.1 

89 

177.6 

64.6 

49 

234.0  !     85.2 

10 
11 

9.4 
10.3 

3.4 

70 

65.8 

23.9 

30 
131 

122.2 
123.1 

44.5 

90 

178.  5 

65.0 

50 
251 

234.9  1     85.5 
235.9  j     85.8 

3.8 

71 

66.7 

24.3 

44.8 

191 

179.5 

65.3 

12 

11.3 

4.1 

72 

67.7 

24.6 

32 

124.0 

45.1 

92 

180.4 

65.7 

52 

236.8  !     86.2 

13 

12.2 

4.4 

73 

68.6 

25.0 

33 

125.  0 

45.5 

93 

181.4 

66.0 

53 

237.7 

86.5 

14 

13.2 

4.8 

74 

69.5 

25.  3 

34 

125.9 

45.8 

94 

182.3 

66.4 

54 

238.7 

86.9 

15 

14.1 

5.1 

75 

70.5 

25.7 

35 

126.9 

46.2 

95 

183.  2 

66.7 

55 

239.6 

87.2 

16 

15.0 

5.5 

76 

71.4 

26.0 

36 

127.8 

46.5 

96 

184.2 

67.0 

56 

240.6 

87.6 

17 

16.0 

5.8 

77 

72.4 

26.3 

37 

128.7 

46.9 

97 

185.1 

67.4 

57 

241.5 

87.9 

18 

16.9 

6.2 

78 

73.3 

26.7 

38 

129.7 

47.2 

98 

186.1 

67.7 

58 

242.4 

88.2 

.  19 

17.9 

6.5 

79 

74.2 

27.0 

39 

130.6 

47.5 

99 

187.0 

68.1 

59 

243.4 

88.6 

'  20 

18.8 
19.7 

6.8 
7.2 

80 

75.2 
76.1 

27.4 
27.7 

40 
141 

131.6 
132.  5 

47.9 
48.2 

200 

187.9 
188.  9 

68.4 

60 

244.3 

88.9 

21 

81 

201 

68.7 

261 

245.  3 

89.3 

22 

20.7 

.  7.5 

82 

77.1 

28.0 

42 

133.4 

48.6 

02 

189.8 

69.1 

62 

246.  2 

89.6 

23 

21.6 

7.9 

83 

78.0 

28.4 

43 

134.4 

48.9 

03 

190.8 

69.4 

63 

247.1 

90.0 

24 

22.6 

8.2 

84 

78.9 

28.7 

44 

135.  3 

49.3 

04 

191.7 

69.8 

64 

248.1 

90.3 

25 

23.5 

8.6 

85 

79.9 

29.1 

45 

136.3 

49.6 

05 

192.6 

70.1 

65 

249.0 

90.6 

26 

24.4 

8.9 

86 

80.8 

29.4 

46 

137.2 

49.9 

06 

193.6 

70.5 

66 

250.  0 

91.0 

27 

25.4 

9.2 

87 

81.8 

29.8 

47 

138.1 

50.3 

07 

194.5 

70.8 

67 

250.9 

91.  3 

28 

26.3 

9.6 

88 

82.7 

30.1 

48 

139.1 

50.6 

08 

195.  5 

71.1 

68 

251.8 

91.7 

29 

27.3 

9.9 

89 

83.6 

30.4 

49 

140.0 

51.0 

09 

■196.  4 

71.5 

69 

252.8 

92.0 

30 

28.2 

10.3 

90 

84.6 

85.5 

30.8 
31.1 

50 

140.9 

51.3 

10 

197.3 
198.3 

71.8 
72.2 

70 
271 

253.7 
254.7 

92.3 
92.7 

31 

29.1 

10.6 

91 

151 

141.9 

51.6 

211 

32 

30.1 

10.9 

92 

86.5 

31.5 

52 

142.8 

52.0 

12 

199.2 

72.5 

72 

255.6 

93.0 

33 

31.0 

11.3 

93 

87.4 

31.8 

53 

143.8 

52.3 

13 

200.2 

72..9 

73 

256.5 

93.4 

34 

31.9 

11.6 

94 

88.3 

32.1 

54 

144.7 

52.7 

14 

201.1 

73.2 

74 

257.5 

93.7 

35 

32.9 

12.0 

95 

89.3 

32.5 

55 

145.7 

53.0 

15 

202.0 

73.5 

75 

258.4 

94.1 

36 

33.8 

12.3 

96 

90.2 

32.8 

56 

146.6 

53.4 

16 

203.0 

73.9 

76 

259.4 

94.4 

37 

34.8 

12.7 

97 

91.2 

33.2 

57 

147.5 

53.7 

17 

203.9 

74.2 

77 

260.3 

94.7 

38 

35.7 

13.0 

98 

92.1 

33.5 

58 

148.6 

54.0 

18 

204.9 

74.6 

78 

261.2 

95.1 

39 

36.6 

13.3 

99 

93.0 

33.9 

59 

149.4 

54.4 

19 

205.8 

74.9 

79 

262.2 

95.4 

40 

37.6 

13.7 

100 

94.0 

34.2 

60 
161 

150.4 
151.3 

54.7 

20 
221 

206.7 

207.7 

75.2 
75.6 

80 

28  r 

263.1 
264.1 

95.8 

41 

38.5 

14.0 

101 

94.9 

34.5 

55.1 

96.1 

42 

39.5 

14.4 

02 

95.8 

34.9 

62 

152.2 

55.4 

22 

208.6 

75.9 

82 

265. 0 

96.4 

43 

40.4 

14.7 

03 

96.8 

35.2 

63 

153.2 

55.7 

23 

209.6 

76.3 

83 

265.  9       96.  8  1 

44 

41.3 

15.0 

04 

97.7 

35.6 

64 

154. 1 

56.1 

24 

210.  5 

76.6 

84 

266.9 

97.1 

45 

42.3 

15.4 

05 

98.7 

35.9 

65 

155. 0 

56.4 

25 

211.4 

77.0 

85 

267.8 

97.5 

46 

43.2 

15.7 

06 

99.6 

36.3 

66 

156.0 

56.8 

26 

212.4 

77.3 

86 

268.8 

97.8 

47 

44.2 

16.1 

07 

100.5 

36.6 

67 

156.9 

57.1 

27 

213.  3 

77.6 

87 

269.7 

98.2 

48 

45.1 

16.4 

08 

101.5 

36.9 

68 

157.9 

57.5 

28 

214.2 

78.0 

88 

270.6 

98.5 

49 

46.0 

16.8 

09 

102.4 

37.3 

69 

158.8 

57.8 

29 

215.2 

78.3 

89 

271.6 

98.8 

50 

47.0 

17.1 

10 

103.4 

37.6 
38.0 

70 

159.7 

58.1 

30 

216.1 
217.1 

78.7 

90 

272.5 

99.2 
99.5 

51 

47.9 

17.4 

111 

104.3 

171 

160.7 

58.5 

231 

79.0 

291 

273.5 

52 

48.9 

17.8 

12 

105.  2 

38.3 

72 

161.6 

58.8 

32 

218.0 

79.3 

92 

274.4 

99.9 

53 

49.8 

18.1 

13 

106.2 

38.6 

73 

162.  6 

59.2 

33 

218.9 

79.7 

93 

275.  3 

100.2 

54 

50.7 

18.5 

14 

107.1 

39.0 

74 

163.5 

59.5 

34 

219.  9 

80.0 

94 

276.  3 

100.  6 

55 

51.7 

18.8 

15 

108.1 

39.3 

75 

164.4 

59.9 

35 

220.8 

80.4 

95 

277.2 

100.9 

56 

52.6 

19.2 

16 

109.0 

39.7 

76 

165.4 

60.2 

36 

221.8 

80.7 

96 

278.1 

101.2 

57 

53.6 

19.5 

17 

109.9 

40.0 

77 

166.3 

60.5 

37 

222.7 

81.1 

97 

279.1 

101.6 

58 

54.5 

19.8 

18 

110.9 

40.4 

78 

167.3 

60.9 

38 

223.6 

81.4 

98 

280.0 

101.9 

59 

55.4 

20.2 

19 

111.8 

40.7 

79 

168.2 

61.2 

39 

224.6 

81.7 

99 

281.0 

102.  3 

60 

56.4 

20.5 

20 

112.8 

41.0 

80 

169.1 

61.6 

40 

225.5 

82.1 

300 

281.9 

102.6 

Dlst. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

70°  (110°,  250 

%  290° 

)■ 

1 

TABLE  2. 

[Page 

407 

Difference  of  Latitude  and  Departure  for  20°  (160°,  20C 

)°,  340= 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist.       Lat. 

Dep. 

Dist. 
481 

Lat.     i 

j 

Dep. 

Dist. 

Lat.     j 

Dep. 

301 

282,9 

103.  0 

361 

339.2 

123.5 

421     395. 6 

144.0 

452.0 

164.5 

541 

508.4 

185.0 

02 

283.8 

103.3 

62 

340.2 

123.8 

22     396. 6 

144.3 

82 

453.0 

164.8 

42 

509.3 

185.4 

03 

284.7 

103.6 

63 

341.1 

124.2 

23 

397.  5 

144.7 

83 

453.9 

165.2 

43 

510.3 

185.7 

04 

285.  7 

104.0 

64 

342.1 

124.5 

24 

398.  4 

145.  0 

84 

454.8 

165.5 

44 

511.2 

186.0 

05 

286.6 

104.3 

65 

343.0 

124.8 

25 

399.4 

145.  4 

85 

455.8 

165.9 

45 

512.1 

186.4 

06 

287.6 

104.7 

66 

343.9 

125.2 

26 

400.3 

145.7 

86 

456.7 

166.3 

46 

513.1 

186.8 

07 

288.5 

105.  0 

67 

344.9 

125.5 

27 

401.3 

146.1 

87 

457.7 

166.6 

47 

514.0 

187.1 

08 

289.4 

105.4 

68 

345.8 

125.  9 

28 

402.2 

146.4 

88 

458.6 

166.9 

48 

515.0 

187.4 

09 

290.4 

105.  7 

69 

346.8 

126.2 

29 

403. 1 

146.7 

89 

459.5 

167.3 

49 

515.9 

187.8 

10 

291.3 

106.0 
106.4 

70 
371 

347.7 
348.6 

126.6 
126.9 

30 
431 

404.1 
405.0 

147.1 
147.4 

90 
191^ 

460.5 

167.7 

50 

516.8 

188.2 

311 

292.3 

461.4 

168.0 

551 

517.8 

188.5 

12 

293.2 

106.7 

72 

349.6 

127.2 

32 

406.0 

147.8 

92 

462.4 

168.3 

52 

518.7 

188.8 

13 

294.1 

107.1 

73 

350.5 

127.6 

33 

406.9 

148.1 

93 

463.3 

168.6 

53 

519.7 

189.1 

14 

395.1 

107.4 

74 

351.5 

127.9 

34 

407.8 

148.4 

94 

464.2 

168.9 

54 

520.  6 

189.4 

15 

296.0 

107.7 

75 

352.4 

128.3 

35 

408.8 

148.8 

95 

465.2 

169.3 

55 

521.5 

189.8 

16 

297.0 

108.1 

76 

353. 3  i 128. 6 

36 

409.7 

149.1 

96 

466.1 

169.6 

56 

522.5 

190.2 

17 

297.9 

108.4 

77 

354.  3 

129.0 

37 

410.7 

149.5 

97 

467.0 

170.0 

57 

523.  4 

190.  5 

18 

298.8 

108.8 

78 

355.  2 

129.3 

38 

411.6 

149.8 

98 

468.0 

170.  3 

58 

524.  4 

190.8 

19 

299.8 

109.1 

79 

356.  2 

129.6 

39 

412.5 

150.2 

99 

468.9 

170.7 

59 

525.3 

191.2 

20 

300.  7 
301.6 

109.  5 

80 

357. 1 

130.0 
130.  3 

40 
441 

413.5 
414.4 

150.5 

500 
501 

469.9 
470.8 

171.0 

60 
561 

526.2 

191.6 

321 

109.8 

381 

358.  0 

150.8 

171.3 

527.2 

191.9 

22 

302.6 

110.1 

82 

359. 0 

130.7 

42 

415.4 

151.2 

02 

471.7 

171.7 

62 

528. 1 

192.2 

23 

303.5 

110.5 

83 

359.9 

131.0 

43 

416.3 

151.  5 

03 

472.7 

172.0 

63 

.529.0 

192.  5 

24 

304.5 

110.8 

84 

360.8 

131.3 

44 

417.2 

151.9 

04 

473.6 

172.4 

64 

530.0 

192.9 

25 

305.  4 

111.2 

85 

361.  8 

131.7 

45 

418.2 

152.2 

05 

474.5 

172.7 

65 

530.9 

193.2 

26 

306.3 

111.5 

86 

362.  7 

132.0 

46 

419.1 

152.5 

06 

475.4 

173.0 

66 

531.8 

193.6 

27 

307.3 

111.8 

87 

363.  7 

132.4 

47 

420.0 

152.9 

07 

476.4 

173.  4 

67 

532.8 

193.9 

28 

308.2 

112.2 

88 

364.  6 

132.7 

48 

421.0 

153.2 

08 

477.3 

173.7 

68 

533.  7 

194.2 

29 

309.2 

112.5 

89 

365. 5 

133. 1 

49 

421.9 

153.  6 

09 

478.3 

174.1 

69 

534.  7 

194.6 

30 

310. 1 

112.9 

90 

366.  5 

133.4 

50 
451 

422.9 

153.9 

10 
511 

479.2 

174.4 

70 

535.  6 

195.0 

331  i  311.0 

113.  2 

391 

367.4 

133.7 

423.8 

154.  3 

480.2 

174.8 

571 

536.  6 

195.3 

32     312.0 

113.6 

92 

368.4 

134.1 

52 

424.7 

154.  6 

12 

481.1 

175.1 

72 

537. 5 

195.6 

33 

312.9 

113.9 

93 

369.3 

134.4 

53 

425.7 

154.9 

13 

482.1 

175.4 

73 

538.5 

195.9 

34 

313.9 

114.2 

94 

370.2 

134.8 

54 

426.6 

155.3 

14 

483. 0 

175.8 

74 

539.4 

196.3 

35 

314.8 

114.6 

95 

371.2 

135. 1 

55 

427.  6  i 155. 6 

15 

484.0 

176.1 

75 

540.  3 

196.6 

36  t  315. 7 

114.9 

96 

372.1 

135.  4 

56 

428.5    156.0 

16 

484.9 

176.5 

76 

541.  3 

197.0 

37 

316.7 

115.3 

97 

373.1 

135.  8 

57 

429.4    156.3 

17 

485.8 

176.8 

77 

542.2 

197.3 

38 

317.6 

115.6 

98 

374.0 

136.1 

58 

430.4    156.7 

18 

486.8 

177.2 

78 

543.  2 

197.7 

39 

318.6 

116.0 

99 

374.9 

136.5 

59 

431.3  ,157.0 

19 

487.7 

177.5 

79 

544.1 

198.0 

40 

319.5 

116.3 

400 
401 

375.9 

136.8 

60 

432.3 
433.2 

157.4 

20 

488.7 
489. 6 

177.9 

80 

545.0 

198.4 

341     320.4 

116.6 

376.8 

137.2 

461 

157.7 

521 

178.2 

581 

546.0 

198.7 

42  !  321.4 

117.0 

02 

377.8 

137.5 

62 

434. 1     158. 0 

22 

490.5 

178.5 

82 

546.9 

199.0 

43 

322.3 

117.3 

03 

378.7 

137.8 

63 

435.1 

158.  4 

23 

491.5 

178.9 

83 

547.9 

199.4 

44 

323.  3 

117.7 

04 

379.6 

138.2 

64 

436.0 

158.7 

24 

492.4 

179.2 

84 

548.  8 

199.  8 

45 

324.2 

118.0 

05 

380.6 

138.5 

65 

437.0 

159.0 

25 

493.4 

179.6 

85 

549.8 

200.1 

46 

325.1 

118.4 

06 

381.5 

138.9 

66 

437.9 

159.4 

26 

494.3 

179.9 

86 

550.  7 

200.4 

47 

326.1 

118.7 

07 

382.5 

139.2 

67 

438.  8 

159.7 

27 

495.3 

180.2 

87 

551.7 

200.8 

48 

327.  0 

119.0 

08 

383.4 

139.6 

68 

439.8 

160.1 

28 

496.2 

180.6 

88 

552. 6 

201.2 

49 

328.0 

119.4 

09 

384.3 

139.9 

69 

440.7 

160.4 

29 

497.1 

181.0 

89 

553. 5 

201.5 

50 

328.9 
329.8 

119.7 
120.1 

10 
411 

385.3 
386.2 

140.2 

70 
471 

441.7 
442.6 

160.8 
161.1 

30 
531 

498.1 

181.3 

90 

554. 4 

201.8 

351 

140.6 

499.0 

181.6 

591 

555.4 

202.1 

52 

330.8 

120.4 

12 

387.2 

1 40.  9 

72 

443.5 

161.4 

32 

499.9 

181.9 

92 

556.3 

202.4 

53 

331.7 

120.7 

13 

388.1 

141.3 

73 

444.5 

161.8 

33 

500.9 

182.3 

93 

557.3 

202.8 

54 

332.7 

121.1 

14 

389.0 

141.6 

74 

445.4 

162.1 

34 

501.8 

182.6 

94 

558.  2 

203.2 

55 

333.6 

121.4 

15 

390.0 

141.9 

75  1  446.4 

162.5 

35 

502.7 

183.0 

95 

559. 1 

203. 5 

56 

334.5 

121.8 

16 

390.9 

142.3 

76     447.3 

162.8 

36 

503.7 

183.  3 

96 

560.0 

203.  8 

57 

335.5 

122.1 

17 

391.9 

142.6 

77     448.2 

163.2 

37 

504.6 

183.7 

97 

561.  0 

204.2 

58 

336. 4 

122.5 

18 

392.8 

143.0 

78  '  449.2 

163.  5 

38 

505. 5 

184.0 

98 

561. 9 

204.6 

59 

337.4 

122.8 

19 

393.  7 

143.3 

79     450. 1 

163.  8 

39 

506. 5 

184.3 

99 

562.9 

204.9 

60 

338.3 

123.1 

20 

394.7 

143.7 

80     451. 1 

164.2 

40     507.4 

184.7 

600 

563.8 

205.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Di.st.       Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

70°  (110°,  250°,  290°). 

Page  408] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  21°  (159°,  201 

°,  339° 

). 

Dist 
1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep.   iDlst.       Lat.        Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

0.9 

0.4 

61 

56.9 

21.9  1  121  1  113.0     43.4 

181 

169.0 

64.9 

241 

225.0 

86.4 

2 

1.9 

0.7 

62 

57.9 

22.2 

22  1  113.9  j  43.7 

82 

169.9 

65.2 

42 

225.9 

86.7 

3 

2.8 

1.1 

63 

58.8 

22.6 

23     114.8  1  44.1 

83 

170.8 

65.6 

43 

226.9 

87.1 

4 

3.7 

1.4 

64 

59.7 

22.9 

24      115.8  1  44.4 

84 

171.8 

65.9 

44 

227.8 

87.4 

5 

4.7 

1.8 

65 

60.7 

23.3 

25      116.7  j  44.8 

85 

172.  7 

66.3 

45 

228.7 

87.8 

6 

5.6 

2.2 

i? 

61.6 

23.7 

26     117.6     45.2 

86 

173.6 

66.7 

46 

229.7 

88.2 

7 

6.5 

2.5 

62.5 

24.0 

27      118.6  i  45.5 

87 

174.6 

67.0 

47 

230.6 

88.5 

8 

7.5 

2.9 

68 

63.5 

24.4 

28     119.'5  1  45.9 

88 

475.5 

67.4 

48 

231.5 

88.9 

9 

8.4 

3.2 

69 

64.4 

24.7 

29     120. 4     46. 2 

89 

176.4 

67.7 

49 

232.5 

89.2 

10 

9.3 

3.6 

70 

65.4 

25.1 

30  i  121.4  1  46.6 

90 

177.4 
178.  3 

68.1 
68.4 

50 
251 

233.4 
234.3 

89.6 
90.0 

11 

10.3 

3.9 

71 

66.3 

25.4 

131     122.3  1  46.9 

191 

12 

11.2 

4.3 

72 

67.2 

25.8 

32     123.2     47.3 

92 

179.2 

68.8 

52 

235.  3 

90.3 

13 

12.1 

4.7 

73 

68.2 

26.2 

33  1  124.2     47.7 

93 

180.2 

69.2 

53 

236.  2 

90.7 

14 

13.1 

5.0 

74 

69.1 

26.5 

34     125. 1  I  48.  0 

94 

181.1 

69.5 

54 

237.1 

91.0 

15 

14.0 

5.4 

75 

70.0 

26.9 

35     126.0     48.4 

95 

182.0 

69.9 

55 

238.1 

91.4 

16 

14.9 

5.  7 

76 

71.0 

27.2 

36     127.0     48.7 

96 

183.0 

70.2 

56 

239.0 

91.7 

17 

15.9 

6.1 

77 

71.9 

27.6 

37      127. 9     49. 1 

97 

183.9 

70.6 

57 

239.9 

92.1 

18 

16.8 

6.5 

78 

72.8 

28.0 

38  1  128.8     49.5 

98 

184.8 

71.0 

58 

240.9 

92.5 

19 

17.7 

6.8 

79 

73.8 

28.3 

39  1  129.8     49.8 

99 

185.8 

71.3 

59 

241.8 

92.8 

20 

18.7 

7.2 

80 

74.7 

28.7 

40     130.7     50.2 

200 

186.7 

71.7 

60 

242.7 
243.7 

93.2 
93.5 

21 

19.6 

7.5 

81 

75.6 

29.0 

141     131.6  1  50.5 

201 

187.6 

72.0 

261 

22 

20.5 

.   7.9 

82 

76.6 

29.4 

42     132.6  i  50.9 

02 

188.6 

72.4 

62 

244.6 

93.9 

23 

21.5 

8.2 

83 

77.5 

29.7 

43     133.5     51.2 

03 

189.5 

72.7 

63 

245.5 

94.3 

24 

22.4 

8.6 

84 

78.4 

30.1 

44     134.4     51.6 

04 

190.  5 

73.1 

64 

246.5 

94.6 

25 

23.3 

9.0 

85 

79.4 

30.5 

45     135.4  1  52.0 

05 

191.4 

73.5 

65 

247.4 

95.0 

26 

24.3 

9.3 

86 

80.3 

30.8 

46     136.3  \  52.3 

06 

192.  3 

73.8 

66 

248.3 

95.3 

27 

25.2 

9.7 

87 

81.2 

31.2 

47     137.2  i  52.7 

07 

193.  3 

74.2 

67 

249.  3 

95.  7 

28 

26.1 

10.0 

88 

82.2 

31.5 

48  ,  138.2     53.0 

08 

194.2 

74.5 

68 

250.2 

96.0 

29 

27.1 

10.4 

89 

83.1 

31.9 

49     139.1     53.4 

09 

195.1 

74.9 

69 

251.1 

96.4 

30 

28.0 

10.8 

90 

84.0 
85.0 

32.3 
32.6 

50 
151 

140.0  !  53.8 

10 

196.1 
197.0 

75.3 
75.6 

70 

252.1 
253.0 

96.8 
97.1 

31 

28.9 

11.1 

91 

141.0     54.1 

211 

271 

32 

29.9 

11.5 

92 

85.9 

33.0 

52     141.9     54.5 

12 

197.9 

76.0 

72 

253.  9 

97.5 

33 

30.8 

11.8 

93 

86.8 

33.  3 

53     142.8     54.8 

13 

198.9 

76.3 

73 

254.9 

97.8 

34 

31.7 

12.2 

94 

87.8 

33.7 

54     143.8  .  55.2 

14 

199.8 

76.7 

74 

255.  8 

98.2 

35 

32.7 

12.5 

95 

88.7 

34.0 

55  !  144.7  i  55.5 

15 

200.7 

77.0 

75 

256.  7 

98.6 

36 

33.6 

12.9 

96 

89.6 

34.4 

56     145.6     55.9 

16 

201.7 

77.4 

76 

257.  7 

98.9 

37 

34.5 

13.3 

97 

90.6 

34.8 

57     146.6     56.3 

17 

202.6 

77.8 

77 

258.  6 

99.3 

38 

35.5 

13.6 

98 

91.5 

35.1 

58     147.5     56.6 

18 

203.  5 

78.1 

78 

259. 5 

99.6 

39 

36.4 

14.0 

99 

92.4 

35.5 

59  1  148.4     57.0 

19 

204.5 

78.5 

79 

260.5 

100.0 

40 

37.3 

14.3 

100 

93.4 

35.8 
36.2 

60     149.4     57.3 

20 
221 

205.4 

78.8 

80 
281 

261.4 
262.  3 

100.3 

41 

38.3 

14.7 

101 

94.3 

161     150.3     57.7 

206.3 

79.2 

100.7 

42 

39.2 

15.1 

02 

95.2 

36.6 

62  :  151.2     58.1 

22 

207.3 

79.6 

82 

263.  3 

101.1 

43 

40.1 

15.4 

03 

96.2 

86.9 

63     152.2     58.4 

23 

208.2 

79.9 

83 

264.2 

101.4 

44 

41.1 

15.8 

04 

97.1 

37.3 

64  I  153.1     58.8 

24 

209.1 

80.3 

84 

265. 1 

101.8 

45 

42.0 

16.1 

05 

98.0 

37.6 

65     154. 0     59. 1 

25 

210.1 

80.6 

85 

266. 1 

102.1 

46 

42.9 

16.5 

06 

99.0 

38.0 

66     155. 0     59. 5 

26 

211.0 

81.0 

86 

267.0 

102. 5 

47 

43.9 

16.8 

07 

99.9 

38.3 

67 

155.9     59.8 

27 

211.9 

81.3 

87 

267.9 

102.9 

48 

44.8 

17.2 

08 

100.8 

38.7 

68 

156.8     60.2 

28 

212.9 

81.7 

88 

268.  9 

103.  2 

■     49 

45.7 

17.6 

09 

101.8 

39.1 

69 

157.8     60.6 

29 

213.  8 

82.1 

89 

269.8 

103.6 

50 
51 

46.7 

17.9 
18.3 

10 
111 

102.7 
103.  6~ 

39.4 
39.8 

70 
171 

158.7     60.9 

30 
231 

214.7 
215.7 

82.4 

90 

270.7 

103.9 
104.  3 

47.6 

159.6     61.3 

82.8 

291 

271.7 

52 

48.5 

18.6 

12 

104.6 

40.1 

72  1  160.6     61.6 

32 

216.6 

83.1 

92 

272.6 

104.6 

53 

49.5 

19.0 

13 

105.5 

40.5 

73  ;  161.5,    62.0 

33 

217.5 

83.5 

93 

273. 5 

105.  0 

54 

50.4 

19.4 

14 

106.4 

40.9 

74  j  162.4     62.4 

34 

318.5 

83.9 

94 

274.  5 

105.  4 

55 

51.3 

19.7 

15 

107.4 

41.2 

75  '  163.4     62.7 

35 

219.4 

84.2 

95 

275.  4 

105.7 

56 

52.3 

20.1 

16 

108.3 

41.6 

76  ;  164.3     63.1 

36 

220.  3 

84.6 

96 

276.3 

106.1 

57 

53.2 

20.4 

17 

109.2 

41.9 

77     165. 2     63. 4 

37 

221.3 

84.9 

97 

277.3 

106.4 

58 

54.1 

20.8 

18 

110.2 

42.3 

78     166.2     63.8 

38 

222.2 

85.3 

98 

278.2 

106.8 

59 

55.1 

21.1 

19 

111.1 

42.6 

79  1  167. 1     64. 1 

39 

233.1 

85.6 

99 

279.1 

107.2 

60 

56.0 

21.5 

20 

112.0 

43.0 

80     168.0  j  64.5 

40 

224.1 

86.0 

300 

280.1 

107.5 

Dist. 

Dep. 

Lat. 

Di.st. 

Dep. 

Lat. 

Dist.  1     Dep.    j    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

69°  (111°,  249°.,  291°). 

TABLE  2. 

[Page  409 

Difference  of  Latitude  and  Departure  for 

21°  (159°,  201°,  339 

")■ 

Dist. 

Lat.     1    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

281.0     107.9 

361 

337.0 

129.4 

421      393.0 

150.  9 

481 

449.0 

172.4 

541 

505.  1 

193.9 

02 

281.9    108.2 

62 

337.  9 

129.7 

22     394.0 

151.2 

82 

450.0 

172.7 

42 

506.0 

194.2 

08 

282.  9    108.  6 

63 

338.9 

130.1 

23     394.9 

151.  6 

83 

450.  9 

173.1 

43 

507.0 

194.6 

04 

283.  8  1  108. 9 

64 

339.  8 

130.4 

24  1  395.8 

152.0 

84 

451.8 

173.5 

44 

507.  9 

195.0 

05 

284.  7     109.  3 

65 

340.7 

130.  8 

25  1  396.8 

152.3 

85 

452.  8 

173.8 

45 

508.8 

195.3 

06 

285. 7  !  109. 7 

66 

341.7 

131.2 

26  !  397.  7 

152.7 

86 

453.  7 

174.2 

46 

509.8 

195.7 

07 

286.6 

110.0 

67 

342.6 

131.5 

27 

398.  6 

153.  0 

87 

454.  6 

174.5 

47 

510.7 

196.0 

08 

287.5 

110. 4 

68 

343.  5 

131.9 

28 

399.  6 

153.  4 

88 

455.6 

174.9 

48 

511.6 

196.4 

09 

288.5 

110.7 

79 

344.5 

132.2 

29 

400.5 

153.7 

89 

456.  5 

175.2 

49 

512.6 

196.8 

10 

289.4 

111.1 

Til.  5 

70 
371 

345.4 
346.3 

132.6 

30 

401.4 

154.1 

90 

457.4 

175.6 
176.0 

50 
551 

513.5 
514.4 

197.1 
197.5 

311 

290.3 

133. 0 

431 

402.4 

154.5 

491 

458.  4 

12 

291.3 

111.8 

72 

347.3 

133.3 

32 

403.3 

154.8 

92 

459.  3 

176.3 

52 

515.4 

197.8 

13 

292.2 

112.2 

73 

348.2 

133.  7 

33 

404.2 

155.  2 

93 

460.2 

176.7 

53 

516.  3 

198.2 

14 

293.1  1112.5 

74 

349.1 

134.0 

34 

405.  2 

155.  5 

94 

461.2 

177.0 

54 

517.2 

198.6 

15 

294.1     112.9 

75 

350. 1 

134.4 

35 

406.1 

155.9 

95 

462. 1 

177.4 

55 

518.2 

198.9 

16 

295. 0    113. 2 

76 

351.0 

134.7 

36 

407.0 

156.  3 

96 

463.0 

177.8 

56 

519.1 

199.3 

17 

295. 9    113. 6 

77 

351.9 

135.1 

37 

408.  0 

156.6 

97 

464.0 

178.1 

57 

520.0 

199.6 

18 

296.9    114.0 

78 

352.9 

135.5 

38 

408.9 

157.  0 

98 

464.9 

178.5 

58 

521.0 

200.0 

19 

297.8     114.3 

79 

353.8 

135.8 

39 

409.8 

157.3 

99 

465.8 

178.8 

59 

521.9 

200.3 

20 

298.7 

114.7 
115.0 

80 

354.  7 

136.2 

40 

410.8 

157.  7 

158.  0 

500 

566.8 

179.2 

60 

522.  8 
523.8 

200.7 
201.  0 

321 

299.7 

381 

355.  7 

136.  5 

441 

411.7 

501 

467.7 

179.5 

561 

22 

300.  6    115. 4 

82 

356.  6 

136.9 

42 

412.6 

158.  4 

02 

468.6 

179.9 

62 

524.7 

201.4 

23 

301. 5  1 115. 8 

83 

357. 5 

137.3 

43 

413.6 

158.8 

03 

469.6 

180.3 

63 

525.  6 

201.8 

24 

302.5    116.1 

84 

358. 5 

137.6 

44 

414.5 

159.1 

04 

470.  5 

180.6 

64 

526.6 

202.1 

25 

303.4 

116.5 

85 

359.4 

138.0 

45 

415.4 

159.5 

05 

471.5 

181.0 

65 

527.  5 

202.5 

26 

304.  3 

116.8 

86 

360.  3 

138.  3 

46 

416.4 

159.  8 

06 

472.4 

181.3 

66 

528.  4 

202.8 

27 

305.  3    117.  2 

87 

361.  3 

138.7 

47 

417.3 

160.2 

07 

473.3 

181.7 

67 

529.4 

203.2 

28 

306.  2  1  117.  5 

88 

362.2 

139. 1 

48 

418.2 

160.  5 

08 

474.3 

182.0 

68 

530.  3 

203.5 

29 

307.1  '117.9 

89 

363.1 

139.4 

49 

419.2 

160.  9 

09 

475.2 

182.4 

69 

531.2 

203.9 

30 

308.1  1118.3 

90 

364.1 
365. 0 

139.  8 
140. 1 

50 

420.1 

161.3 

10 

476.1 
477.1 

182.8 

70 

532.2 
533.1 

204.3 
204.6 

331 

309.0    118.6 

391 

451 

421.0 

161.6 

511 

183.1 

571 

32 

309.9 

119.0 

92 

365.9 

140.5 

52 

422.0     162.0 

12 

478.0 

183.5 

72 

534.  0 

205.0 

33 

310.9 

119.3 

93 

366.9 

140.8 

53 

422.  9    162.  3 

13 

478.9 

183.  8 

73 

535.  0 

205.  4 

34 

311.8 

119.7 

94 

367.8 

141.2 

54- 

423.  8     162.  7 

14 

479.9 

184.2 

74 

535.  9 

205.  7 

35 

312.  7 

120.1 

95 

368.7 

141.6 

55 

424. 8     163. 1 

15 

480.8 

184.6 

to 

536.8 

206.1 

36 

313.7 

120.4 

96 

369.7 

141.9 

56 

425.  7     163.  4 

16 

481.7 

184.9 

76 

537.8 

206.4 

37 

314.6 

120.8 

•  97 

370.  6 

142.3 

57 

426. 6    163. 8 

17 

482.7 

185.3 

77 

538.7 

206.  8 

38 

315.5 

121.1 

98 

371.5 

142.6 

58 

427.6     164.1 

18 

483.6 

185.  6 

78 

539.  6 

207.1 

39 

316.5 

121.5 

99 

372.5 

143.0 

59 

428.5     164.5 

19 

484.5 

186.0 

79 

540.  6 

207.5 

40 
341 

317.4 

121.8 

400 

373. 4 

143.4 
143.  7 

60 

429.4    164.9 

20 

485.  5 
486.4 

186.4 
186.7 

80 
581 

541.5 
'542.  4 

207.9 

318.3 

122: 2 

401 

374.3 

461 

430.  4  ,  165. 2 

521 

208.2 

42 

319.3 

122.6 

02 

375.3 

144. 1 

62 

431. 3    165.  6 

22 

487.3 

187.1 

82 

•543.4 

208.6 

43 

320.2 

122.9 

03 

376.2 

144.4 

63 

432. 2    165. 9 

23 

488.  3 

187.4 

83 

544.  3 

208.9 

44 

321.1 

123.2 

04 

377.1 

144.8 

64 

433.  2  '  166.  3 

24 

489.2 

187.8 

U 

545.  2 

209.3 

45 

322.1 

123.6 

05 

378.1 

145.1 

65     434.1     166.6 

25 

490.1 

188.1 

85 

546.2 

209.6 

46 

323.0 

124.0 

06 

379.  0 

145.  5 

66 

435. 0    167.  0 

26 

491.1 

188.5 

86 

547. 1 

210.0 

47 

323.  9    124. 4 

07 

379.9 

145.9 

67 

436.  0  ;  167.  4 

27 

492.0 

188.9 

87 

548.  0 

210.4 

48 

324.  9    124.  7 

08 

380.  9 

146.2 

68     436. 9    167. 7 

28 

492.9 

189.2 

88 

549.0 

210.7 

49 

325. 8  i 125. 1 

09 

381.8 

146.6 

69     437. 8    168. 1 

29 

493.  9 

189.6 

89 

549.9 

211.1 

50 

326. 7  1 125. 4 

10 

382.  7 

146.9 

70     438. 8  1  168.  4 

30 

494.8 

189.9 

90 

550.8 
551.8 

211.4 

351 

327.7 

125.8 

411 

383.7 

147.3 

471 

439. 7  ! 168. 8 

531 

495.  7 

190.3 

591 

211.8 

52 

328.6 

126.1 

12 

384.6 

147.7 

72 

440. 6    169.  2 

32 

496.7 

190.7 

92 

552.  7 

212.2 

53 

329.5 

126.5 

13 

385.5 

148.0 

73 

441.6     169.5 

33 

497.6 

191.  0 

93 

553.6 

212.5 

54 

330.5 

126.9 

14 

386.  5 

148.4 

74 

442.  5     169.  9 

34 

498.5 

191.4 

94 

554.6 

212.  9 

55 

331.4    127.2 

15 

387.4 

148.7 

75 

443.4  1170.2 

35 

499.5 

191.7 

95 

555.  5 

213.2 

56 

332.  3    127. 6 

16 

388.4 

149.1 

76 

444.4 

170.6 

36 

500.4 

192.1 

96 

556.4 

213.  6 

57 

333.3    127.9 

17 

389.  3 

149.4 

77     445.3 

170.9 

37 

501.3 

192.4 

97 

557. 4 

213.9 

58 

334.2 

128.3 

18 

390.2 

149.8 

78     446.2 

171.3 

38 

502.  3 

192.8 

98 

558.  2 

214.  3 

59 

335.1 

128.7 

19 

391.2 

150.2 

79  1  447.2 

171.7 

39 

503.  2 

193.  2 

99 

559.  2 

214.7 

60 

336.1 

129.0 

20 

392.1 

150.5 

80     448. 1 

t 

172.0 

40 

504.1 

193.5 

600 

560.1 

215.  0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  j     Dep.     1    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

6 

)9°  (111°,  249°,  291° 

)• 

Page  410] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  22°  (158°,  202,  338°) 

. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
22.9 

Dist. 

Lat. 

Dep.      Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

56.6 

121 

112.2 

45. 3      181 

167.8 

67.8 

241 

223.5 

90.3 

2 

1.9 

0.7 

62 

57.  5 

23.2 

22 

113.1 

45.7 

82 

168.7 

68.2 

42 

224.4 

90.7 

3 

2.8 

1.1 

63 

58.4 

23.6 

23 

114.0 

46.1 

83 

169.7 

68.6 

43 

225.3 

91.0 

4 

3.7 

1.5 

64 

59.3 

24.0 

24 

115.0 

46.5 

84 

170.6 

68.9 

44 

226.2 

91.4 

5 

4.6 

1.9 

65 

60.3 

24.3 

25 

115.9 

46.8 

85 

171.5 

69.3 

45 

227.2 

91.8 

6 

5.6 

2.2 

66 

61.2 

24.7 

26 

116.8 

47.2 

86 

172.5 

69.7 

46 

228.1 

92.2 

/ 

6.5 

2.6 

•   67 

62.1 

25.1 

27 

117.8 

47.6 

87 

173.4 

70.1 

47 

229.0 

92.5 

8 

7.4 

3.0 

68 

63.0 

25.5 

28 

118.7 

47.9 

88 

174.3 

70.4 

48 

229.9 

92.9 

9 

8.3 

3.4 

69 

64.0 

25.8 

29 

119.6 

48.3 

89 

175.2 

70.8 

49 

230.9 

93.3 

10 

9.3 

3.7 

70 

64.9 

26.2 

30 

120.5 

48.7 

90 
191 

176.2 

71.2 

50 

231.8 
232.7 

93.7 

11 

10.2 

4.1 

71 

65.8 

26.6 

131 

121.5 

49.1 

177.1 

71.5 

251 

94.0 

12 

11.1 

4.5 

72 

66.8 

27.0 

32 

122.4 

49.4 

92 

178.0 

71.9 

52 

233.7 

94.4 

13 

12.1 

4.9 

73 

67.7 

27.3 

33 

123.3 

49.8 

93 

178.9 

72.3 

53 

234.  6 

94.8 

14 

13.0 

5.2 

74 

68.6 

27.7 

34 

124.2 

50.2 

94 

179.9 

72.7 

54 

235.5 

95.2 

15 

13.9 

5.6 

75 

69.5 

28.1 

35 

125.2 

50.6 

95 

180.8 

73.0 

55 

236.4 

95.5 

16 

14.8 

6.0 

76 

70.5 

28.5 

36 

126.1 

50.9 

96 

181.7 

73.4 

56 

237.4 

95.9 

17 

15.8 

6.4 

77 

71.4 

28.8 

37 

127.0 

51.3 

97 

182.7 

73.8 

57 

238.3 

96.3 

18 

16.7 

6.7 

78 

72.3 

29.2 

38 

128.0 

51.7 

98 

183.6 

74.2 

58 

239.2 

96.6 

19 

17.6 

7.1 

79 

73.2 

29.6 

39 

128.9 

52.1 

99 

184.  5 

74.5 

59 

240.1 

97.0 

20 

18.5 

7.5 

80 

74.2 

30.0 

40 

129.8 

52.4 

200 

185.4 

74.9 

60 

241.1 
242.0 

97.4 

21 

19.5 

7.9 

81 

75.1 

30.3 

141 

130.7 

52.8 

201 

186.  4 

75.3 

261 

97.8 

22 

20.4 

8.2 

82 

76.0 

30.7 

42 

131.  7 

53.2 

02 

187.3 

75.7 

62 

242.9 

98.1 

23 

21.3 

8.6 

83 

77.0 

31.1 

43 

132.6 

53.  6 

03 

188.2 

76.0 

63 

243.8 

98.5 

24 

22.3 

9.0 

84 

77.9 

31.5 

44 

133.5 

53.9 

04 

189.1 

76.4 

64 

244.8 

98.9 

25 

23.2 

9.4 

85 

78.8 

31.8 

45 

134.4 

54.3 

05 

190.1 

76.8 

65 

245.7 

99.3 

26 

24.1 

9.7 

86 

79.7 

32.2 

46 

135.4 

54.7 

06 

191.0 

77.2 

66 

246.6 

99.6 

27 

25.0 

10.1 

87 

80.7 

32.6 

47 

136.3 

55.1 

07 

191.9 

77.5 

67 

247.6 

100.0 

28 

26.0 

10.5 

88 

81.6 

33.0 

48 

137.2 

55.4 

08 

192.9 

77.9 

68 

248.5 

100.4 

29 

26.9 

10.9 

89 

82.5 

33.3 

49 

138. 2 

55.8 

09 

■  193.  8 

78.3 

69 

249.4 

100.8 

30 

27.8 

28.7 

11.2 

90 

83.4 
84.4 

33.7 
34.1 

50 
151 

139. 1  1  56.  2 

10 

194.7 

78.7 

70 

250.3 

101.1 

31 

11.6 

91 

140.  0 

56.6 

211 

195.6 

79.0 

271 

251.3 

101.5 

32 

29.7 

12.0 

92 

85.3 

34.5 

52 

140.9 

56.9 

12 

196.6 

79.4 

72 

252.2 

101.  9' 

33 

30.6 

12.4 

93 

86.2 

34.8 

53 

141.9 

57.3 

13 

197.5 

79.8 

73 

253.1 

102.3 

34 

31.5 

12.7 

94 

87.2 

35.2 

54 

142.  8 

57.7 

14 

198.4 

80.2 

74 

254.0 

102.6 

35 

32.5 

13.1 

95 

88.1 

35.6 

55 

143.7 

58.1 

15 

199.3 

80.5 

75 

255.0 

103.0 

36 

33.4 

13.5 

96 

89.0 

36.0 

56 

144.6 

58.4 

16 

200.3 

80.9 

76 

255.9 

103.4 

37 

34.3 

13.9 

97 

89.9 

36.3 

57 

145.6 

58.8 

17 

201.2 

81.3 

77 

256.  8 

103.8 

38 

35.2 

14.2 

98 

90.9 

36.7 

58 

146.5 

59.2 

18 

202.1 

81.7 

78 

257.8 

104.1 

39 

36.2 

14.6 

99 

91.8 

37.1 

59 

147.4 

59.6 

19 

203.1 

82.0 

79 

258.7 

104.5 

40 
41 

37.1 
38.0 

15.0 

100 

92.7 
93.6 

37.5 
37.8 

60 

148.3 

59.9 
60.3 

20 

204.0 

82.4 
82.8 

80 
281 

259.6 
260.5 

104.9 

15.4 

101 

161 

149.3 

221 

204.9 

105.3 

42 

38.9 

15.7 

02 

94.6 

38.2 

62 

150.2 

60.7 

22 

205.8 

83.2 

82 

261.5 

105. 6 

43 

39.9 

16.1 

03 

95.5 

38.6 

63 

151.1 

61.1 

23 

206.8 

83.5 

83 

262.4 

106.0 

44 

40.8 

16.5 

04 

96.4 

39.0 

64 

152.1 

61.4 

24 

2or.7 

83.9 

84 

263.3 

106.4 

45 

41.7 

16.9 

05 

97.4 

39.3 

65 

153.0 

61.8 

25 

208.6 

84.3 

85 

264.2 

106.8 

46 

42.7 

17.2 

06 

98.3 

39.7 

66 

153.9 

62.2 

26 

209.5 

84.7 

86 

265.2 

107.1 

47 

43.6 

17.6 

07 

99.2 

40.1 

67 

154.8 

62.6 

27 

210.5 

85.0 

87 

266.1 

107.5 

48 

44.5 

18.0 

08 

100.1 

40.5 

68 

155.8 

62.9 

28 

211.4 

85.4 

88 

267.0 

107.9 

49 

45.4 

18.4 

09 

101.1 

40.8 

69 

156.7 

63.3 

29 

212.3 

85.8 

89 

268.0 

108.3 

50 
51 

46.4 
47.3 

18.7 

10 

102.0 

41.2 

70 

157.6 

63.7 

30 

213.3 

86.2 

90 

268.9 

108.6 

19.1 

111 

102.9 

41.6 

271 

158.5 

64.1 

231 

214.2 

86.5 

291 

269.8 

109.0 

52 

48.2 

19.5 

12 

103.8 

42.0 

72 

159.5 

64.4 

32 

215.1 

86.9 

92 

270.7 

109.4 

53 

49.1 

19.9 

13 

104.8 

42.3 

73 

160.4 

64.8 

33 

216.0 

87.3 

93 

271.7 

109.8 

54 

50.1 

20.2 

14 

105.7 

42.7 

74 

161.3 

65.2 

34 

217.0 

87.7 

94 

272.6 

110.1 

55 

51.0 

20.6 

15 

106.6 

43.1 

75 

162.3 

65.6 

35 

217.9 

88.0 

95 

273.5 

110.5 

56 

51.9 

21.0 

16 

107.6 

43.5 

76  1  163.2 

65.9 

36 

218.8 

88.4 

96 

274.4 

110.9 

57 

52.8 

21.4 

17 

108.5 

43.8 

77 

164.1 

66.3 

37 

219.7 

88.8 

97 

275. 4 

111.3 

58 

53.8 

21.7 

18 

109.4 

44.2 

78 

165.0 

66.7 

38 

220.7 

89.2 

98 

276.3 

111.6 

59 

54.7 

22.1 

19 

110.3 

44.6 

79 

166.0 

67.1 

39 

221.6 

89.5 

99 

277.2 

112.0 

60 

55.6 

22.5 

20 

111.3 

45.0 

80 

166.9 

67.4 

40 

222.5 

89.9 

300 

278.2 

112,4 

Dist. 

Dep. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

68°  (112°,  248°,  292°). 

TABLE  2. 

[Page  411 

Difference  of  Latitude  and  Departure  for  22°  (158°,  202 

°,  338° 

). 

Dist. 

.  Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.        Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

279.1 

112.7 

361 

334.7 

135.2 

421 

390.3 

157.7 

481 

446.0 

180.2 

541 

501.6 

202.7 

02 

280.  0 

113.1 

62 

335.  6 

135.  6 

22 

391.3 

158.1 

82 

446.9 

180.6 

42 

502.5 

203.1 

03 

280.9 

113.5 

63 

336.6 

136.0 

23 

392.2 

158.4 

83 

447.8 

180.9 

43 

503.4 

203.5 

04 

281.9 

113.9 

64 

337.5 

136.  3 

24 

393.1 

158.8 

84 

448.8 

181.3 

44 

504.4 

203.8 

05 

282.8 

114.2 

65 

338. 4 

136.7 

25 

394.1 

159.  2 

85 

449.7 

181.7 

45 

505.3 

204.2 

06 

283.  7 

114.6 

66 

339.3 

1.37. 1 

26 

395.  0 

159.6 

86 

450.6 

182.1 

46 

506.  2 

204.6 

07 

284.6 

115.0 

67 

340.  3 

137.5 

27 

395.9 

159.  9 

87 

451.6 

182.4 

47 

507.2 

205.  0 

08 

285.6 

115.  4 

68 

341.2 

137.8 

28 

396.8 

160.3 

88 

452. 5 

182.8 

48 

508. 1 

205.3 

09 

286.  5 

115.7 

69 

342.1 

138.2 

29 

397.8 

160.7 

89  !  453.4 

183.  2 

49 

509.0 

205.  7 

10 

287.4 

116.1 

70 

343.1 

138.6 

30 

398.7 

161.1 

90     454.3 

183.6 

50 
551 

510.0 

206.1 
206.5 

311 

288.4 

116. 5 

371 

344.0 

139.0 

431 

399.6 

161.4 

491  \  455.3 

184.  0' 

510.9 

12 

289.3 

116.8 

72 

344.9 

139.3 

32 

400.5 

161.8 

92 

456.2 

184.3 

52 

511.8 

206.8 

13 

290.2 

117.2 

73 

345.8 

139.7 

33 

401.5 

162.2 

93 

457.1 

184.7 

53 

512.7 

207.2 

14 

291.1 

117.6 

74 

346.8 

140.1 

34 

402.4 

162.6 

94 

458.0 

185.1 

54 

513.6 

207.6 

15 

292.1 

118.0 

75 

347.7 

140.5 

35 

403.  3 

162.9 

95 

459.0 

185.4 

55 

514.6 

208.0 

16 

293.0 

118.3 

76 

348.6 

140.8 

36 

404.3 

163.  3 

96 

459.9 

185.8 

56 

515.5 

208.3 

17 

293.9 

118.7 

77 

349.5 

141.2 

37 

405.2 

163.7 

97 

460.8 

186.2 

57 

516.4 

208.7 

18 

294.8 

119.1 

78 

350.5 

141.6 

38 

406.1 

164.1 

98 

461.8 

186.6 

58 

517.4 

209.1 

19 

295.  8 

119.5 

79 

351. 4 

141.9 

39 

407.0 

164.4 

99 

462.7 

186.9 

59 

518.3 

209.4 

20 

296.7 

119.8 

80 

352.  3 

142.3 

40 

408.0 

164.8 

500 

463.6 

187.3 

60 

519.2 

209.8 

321 

297.6 

120.2 

381 

353.3 

142.7 

441 

408.9 

165.2 

501 

464.5 

187.7 

561 

520.1 

210.2 

22 

298.6 

120.6 

82 

354.2 

143.1 

42 

409.8 

165.5 

02 

4a5.4 

188.0 

62 

521.0 

210.5 

23 

299.5 

121.0 

83 

355. 1 

143.4 

43 

410.7 

165.9 

03 

466.4 

188.4 

63 

522.0 

210.9 

24 

300.4 

121.3 

84 

356.0 

143.8 

44 

411.7 

166.  3 

04 

467.3 

188.8 

64 

522.9 

211.3 

25 

301.3 

121.7 

85 

357.0 

144.2 

45 

412.6 

166.7 

05 

468.2 

189.2 

65 

523.8 

211.7 

26 

302.3 

122.1 

86 

357.  9 

144.6 

46 

413.6 

167.0 

06 

469.2 

189.  5 

66 

524.8 

212.0 

27 

303.2 

122.5 

87 

358.8 

144.9 

47 

414.  5 

167.4 

07 

470.1 

189.9 

67 

525.7 

212.4 

28 

304.1 

122.8 

88 

359.7 

145.3 

48 

415. 4 

167.8 

08 

471.0 

190.  3 

68 

526.6 

212.8 

29 

305. 0 

123.2 

89 

360.7 

145.  7 

49 

■  416. 3 

168.2 

09 

471.9 

190.7 

69 

527.5 

213.2 

30 

306.  0 

123.  6 

90 

361.6 

146.1 

50 

417.2 

418.2 

168.5 

10 

472.9 

191.1 
191.  4 

70 
571 

528.5 

213.5 

331 

306.9 

124.0 

391 

362.5 

146.4 

451 

168.9 

511 

473.8 

529.4 

213.9 

32 

307.8 

124.3 

92 

363.5 

146.8 

52 

419.1 

169.3 

12 

474.7 

191.8 

72 

530.3 

214.3 

33 

308.8 

124.7 

93 

364.4 

147.2 

53 

420.0 

169.7 

.  13 

475.6 

192.2 

73 

531.2 

214.7 

34 

309.7 

125. 1 

94 

365.  3 

147.6 

54 

420.9 

170.0 

14 

476.6 

192.5 

74 

532.2 

215.  0 

35 

310.6 

125.5 

95 

366.2 

147.9 

55 

421.9 

170.4 

15 

477.5 

192.9 

75 

533.1 

215.  4 

36 

311.5 

125.8 

96 

367.2 

148.3 

56 

422.8 

170.8 

16 

478.4 

193.  3 

76 

534.0 

215.8 

37 

312. 5 

126.2 

97 

368.1 

148.7 

57 

423.7 

171.2 

17 

479.3 

193.  7 

77 

534.  9 

216.2 

38 

313.4 

126.6 

98 

369.0 

149.1 

58 

424.6 

171.5 

18 

480.3 

194.0 

78 

535. 9 

216.  5 

39 

314.3 

127.0 

99 

369.9 

149.4 

59 

425.  6 

171.9 

19 

481.2 

194.4 

79 

536.  8 

216.9 

40 
341 

315.  2 

127.3 

400 

370.9 

149.8 

60 

426.5 
427.4 

172.3 

20 

482.1 

194.8 
195.2 

80 
581 

537.  7 
538.6 

217.3 

316.2 

127.7 

401 

371.8 

150.2 

461 

172.7 

521 

483.0 

217.7 

42 

317.1 

128.1 

02 

372.  7 

150.  6 

62 

428.4 

173.0 

22 

484.0 

195.5 

82 

539.6 

218.0 

43 

318.0 

128.5 

03 

373.7 

150.9 

63 

429.3 

173.4 

23 

484.9 

195.9 

83 

540.5 

218.4 

44 

319.0 

128.8 

04 

374.6 

151.3 

64 

430.2 

173.8 

24 

485.8 

196.3 

84 

541.4 

218.8 

45 

319.9 

129.2 

05 

375.5 

151.7 

65 

431.1 

174.2 

25 

486.7 

196.7 

85 

542.4 

219.2 

46 

320.  8 

129.6 

06 

376. 4 

152.1 

66- 

432.1 

174.  5 

26 

487.7 

197.0 

86 

543.3 

219.  5 

47 

321.  7 

130.0 

07 

377.4 

152. 4 

67 

433.0 

174.9 

27 

488.6 

197.4 

87 

544.  2 

219.9 

48 

322.7 

130.3 

08 

378.  3 

152.8 

68 

433.  9 

175.  3 

28 

489.5 

197.8 

88 

545.1 

220.  3 

49 

323.6 

130.7 

09 

379.2 

153.2 

69 

434.8 

175.7 

29 

490.4 

198.2 

89 

546.1 

220.7 

50 

324.5 

131. 1 

10 

380.1 
381.  i 

153.6 
153.9 

70 
471 

435.8 
436.7 

176.0 
176.  4 

30 
531 

491.4 
492.3 

198.5 

90 

547.0 

221.0 

351 

325.  4 

131.5 

411 

198.9 

591 

547.9 

221.4 

52 

326.4 

131.8 

12 

382.0 

154.3 

72 

437.6 

176.8 

32 

493.2 

199.3 

92 

548.  9 

221.8 

53 

327.3 

132.2 

13 

382.9 

154.7 

73 

438.6 

177.2 

33 

494.2 

199.7 

93 

549.8 

222.2 

54 

328.2 

132.6 

14 

383.  9 

155. 1 

74 

439.5 

177.5 

34 

495.1 

200.0 

94 

550.7 

222.  5 

55 

329.2 

133.0 

15 

384.8 

155.4 

75 

440.4 

177.9 

35 

496.0 

200.4 

95 

551.  7 

222.9 

56 

330.1 

133.3 

16 

385.7 

155.8 

76 

441.3 

178.3 

36 

496.9 

200.8 

96 

552.6 

223.3 

57 

331.0 

133.7 

17 

386.6 

156.2 

77 

442.3 

178.7 

37 

497.9 

201.2 

97 

553.5 

223.7 

58 

332.0 

134.1 

18 

387.  6 

156.6 

78 

443.2 

179. 0 

38 

498.8 

201.5 

98 

554.4 

224.0 

59 

332.9 

134.5 

19 

388.5 

156.9 

79 

444.1 

179.4 

39 

499.7 

201.9 

99 

555. 4 

224.4 

60 

333.8 

134.8 

20 

389.4 

157.3 

80 

445.0 

179.8 

40 

500.7 

202.  3 

600 

556.3 

224.8 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

€ 

8°  (112°,  248°,  292° 

). 

Page  412] 

TABLE  L>. 

Difference  of  I-atitude  and  Departure  for  23°  (157°,  203°,  337°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

56.2 

2S.8 

121 

111.4 

47.3 

181 

166.6 

70.7 

241 

221.8 

94.2 

2 

1.8 

0.8 

62 

57.1 

24.2 

22 

112.3 

47.7 

82 

167. 5 

71.1 

42 

222.8 

94.6 

3 

2.8 

1.2 

63 

58.0     24.6 

23 

113.  2 

48.1 

83 

168.5 

71.5 

43 

223.7 

94.9 

4 

3.7 

1.6 

64 

58.9     25.0 

24 

114.1 

48.5 

84 

169.4 

71.9 

44 

224.6 

95.3 

5 

4.6 

2.0 

65 

59.  8     25. 4 

25 

115.1 

48.8 

85 

170.3 

72.3 

45 

225.5 

95.7 

6 

5.5 

2.3 

1? 

60.  8     25.  8 

26 

116.0 

49.2 

86 

171.2 

72.7 

46 

226.4 

96.1 

7 

6.4 

2.7 

61.  7     26.  2 

27 

116.9 

49.6 

•87 

172.1 

73.1 

47 

227.4 

96.5 

8 

7.4 

3.1 

68 

62.6  :  26.6 

28  !  117.8 

50.0 

88 

173.1 

73.5 

48 

228.3 

96.9 

9 

8.3 

3.5 

69 

63.5 

27.0 

29     118. 7 

50.4 

89 

174.0 

73.8 

49 

229.2 

97.3 

10 
11 

9.2 

3.9 

70 

64.4 
65.4 

27.4 
27.7 

30     119. 7 

50.8 
51.2 

90 
191 

174.9 
175.8 

74.2 

50 
251 

230.1 
231.0 

97.7 
98.1 

10.1 

4.3 

71 

131     120.6 

74.6 

12 

11.0 

4.7 

72 

66. 3  i  28. 1 

32  ,  121.5 

51.6 

92 

176.7 

75.0 

52 

232.0 

98.5 

13 

12.0 

5.1 

73 

67.2  1  28.5 

33 

122.4 

52.0 

93 

177.7 

75.4 

53 

232.  9 

98.9 

14 

12.9 

5.5 

74 

68.1 

28.9 

34 

123.3  !  52.4 

94 

178.6 

75.8 

54 

233.  8 

99.2 

15 

13.8 

5.9 

75 

69.0 

29.3 

35 

124.  3  i  52.  7 

95 

179,5 

76.2 

55 

234.7 

99.6 

16 

14.7 

6.3 

76 

70.0 

29.7 

36 

125.  2     53. 1 

96 

180.4 

76.6 

56 

235.6 

100.0 

17 

15.6 

6.6 

77 

70.9 

30.1 

37 

126. 1  i  53.  5 

97 

181.3 

77.0 

57 

236.6 

100.4 

18 

16.6 

7.0 

78 

71.8 

30.5 

38 

127.0 

53.9 

98 

182.3 

77.4 

58 

237.5 

100.8 

19 

17.5 

7.4 

79 

72.7     30.9 

39 

128.0 

54.3 

99 

183.2  1  77.8 

59 

238.4 

101.2 

20 
21 

18.4 

7.8 

80 
81 

73.6 

31.3 
31.6 

40 
141 

128.9 
129.8 

54.7 
55.1 

200 
201 

184.1 

78.1 

60 

239.3 
240.3 

101.6 

19.3 

8.2 

74.6 

185.0 

78.5 

261 

102.0 

22 

20.3 

8.6 

■  82 

75.5  1  32.0 

42 

130.7 

55.5 

02 

185.9 

78.9 

62 

241.2 

102.4 

23 

21.2 

9.0 

83 

76.4  \  32.4 

43 

131.6 

55.9 

03 

186.9 

79.3 

63 

242.1 

102.8 

24 

22.1 

9.4 

84 

77.3  1  32.8 

44 

132.6 

56.3 

04 

187.  8  1  79.7 

64 

243.0 

103.  2 

25 

23.0 

9.8 

85 

78.2  1  33.2 

45 

133.5 

56.7 

05 

188.7 

80.1 

65 

243.9 

103.5 

26 

23.9 

10.2 

86 

79.2     33.6 

46 

134.  4 

57.0 

06 

189.6 

80.5 

66 

244.9 

103.9 

27 

24.9 

10.5 

87 

80. 1     34. 0 

47 

135.3 

57.4 

07 

190.5 

80.9 

67 

245.  8 

104.3 

28 

25.8 

10.9 

88 

81.0  i  34.4 

48 

136.2 

57.8 

08 

191.5 

81.3 

68 

246.7 

104.7 

29 

26.7 

11.3 

89 

81.9  ;  34.8 

49 

137.  2 

58.2 

09 

192.4 

81.7 

69 

247.6 

105. 1 

30 
31 

27.6 
28.5 

11.7 

90 

82.8  1  35.2 

50 

138.1 
139.0 

58.6 
59.0 

10 
211 

193.3 
194.2 

82.1 
82.4 

70 
271 

248.0 
249. 5 

105.  5 
f05.  9 

12.1 

91 

83.8  '  35.6 

151 

32 

29.5 

12.5 

92 

84.  7  1  35. 9 

52     139. 9 

59.4 

12 

195.1 

82.8 

72 

250.4 

106.3 

33 

30.4 

12.9 

93 

85.6  i  36.3 

53 

140.8 

59.8 

13 

196.1 

83.2 

73 

251.3 

106.7 

34 

31.3 

13.3 

94 

86.  5  1  36.  7 

54 

141.8 

60.2 

14 

197.0 

83.6 

74 

252.2 

107.1 

35 

32.2 

13.7 

95 

87. 4  j  37. 1 

55 

142.7 

60.6 

15 

197.9 

84.0 

75 

253. 1 

107.5 

36 

33.1 

14.1 

96 

88.4  1  37.5 

56 

143.6 

61.0 

16 

198.8 

84.4 

76 

254.1 

107.8 

37 

34.1 

14.5 

97 

89.3     37.9 

57 

144.5 

61.3 

17 

199.7 

84.8 

77 

255. 0 

108.2 

38 

35.0 

14.8 

98 

90.  2     38.  3 

58 

145.4 

61.7 

18 

200.7 

85.2 

78 

255.9 

108.6 

39 

35.9 

15.2 

99 

91. 1     38.  7 

59 

146.4 

62.1 

19 

201.6 

85.6 

79 

256.  8 

109.0 

40 

36.8 

15.6 

100 

92. 1     39. 1 
93.0     39.5 

60 

147.3 

62.5 

20 
221 

202.5 

86.0 

80 

257.7 

258.7 

109.4 

41 

37.7 

16.0 

101 

161  j  148.2     62.9 

203.4 

86.4 

281 

109.8 

42 

38.7 

16.4 

02 

93.9  1  39.9 

62     149. 1  :  63.  3 

22 

204.4 

86.7 

82 

259.  6 

110.2 

43 

39.6 

16.8 

03 

94.8  ;  40.2 

63     150.0     63.7 

23 

205.3 

87.1 

83 

260.  5 

110.6 

44 

40.5 

17.2 

04 

95.  7  !  40.  6 

64     151.0  '  64.1 

24 

206.2 

87.5 

84 

261.4 

111.0 

45 

41.4 

17.6 

05 

96.  7  :  41. 0 

65     151.9     64.5 

25 

207.1 

87.9 

85 

262.  3 

111.4 

46 

42.3 

18.0 

06 

97.6     41.4 

66 

152.8     &4.9 

26 

208.0 

88.3 

86 

263.  3 

111.7 

47 

43.3 

18.4 

07 

98. 5     41.  8 

67 

153.7     65.3 

27 

209.0 

.88.7 

87 

264.2 

112.1 

48 

44.2 

18.8 

08 

99.  4     42.  2 

68 

154.6 

65.6 

28 

209.9 

89.1 

88 

2a5. 1 

112.5 

49 

45.1 

19.1 

09 

100.  3     42. 6 

69 

155.  6 

66.0 

29 

210.  8 

89.5 

89 

266.0 

112.9 

50 
51 

46.0  I 
46.9  1 

19.5 
19.9 

10 
111 

101. 3     43.  0 

70 

156.5 

66.4 

30 

211.7 
212.6 

89.9 
90.3 

90 
291 

266.  9 

267.  9 

113.3 
113.  7 

102.2 

43.4 

171 

157. 4 

66.8 

231 

52 

47.9  1 

:20.3 

12 

103.1 

43.8 

72 

158.3 

67.2 

32 

213.6 

90.6 

92 

268.8 

114.1 

53 

48.8 

20.7 

13 

104.0 

44.2 

73 

159.2 

67.6 

33 

214.5 

91.0 

93 

269.7 

114.5 

54 

49.7 

21.1 

14 

104.9 

44.5 

74 

160.2 

68.0 

34 

215.4 

91.4 

94 

270.6 

114.9 

55 

50.6 

21.5 

15 

105. 9 

44.9 

75 

161.1 

68.4 

35 

216.3 

91.8 

95 

271.  5 

115.3 

56 

51.5 

21.9 

16 

106.8 

4o.3 

76     162.0 

68.8 

36 

217.2 

92.2 

96 

272.  5 

115.7 

57 

52.5 

22.3 

17 

107.7 

45.7 

77  1  162.9 

69.2 

37 

218.2 

92.6 

97 

273.4 

116.0 

58 

53.4 

22.7 

18 

108.6 

46.1 

78  i  163.8 

69.6 

38 

219.1 

93.0 

98 

274.  3 

116.4 

59 

54.3 

23.1 

19 

109. 5 

46.5 

79 

164.8 

69.9 

39 

220.0 

93.4 

99 

275.  2 

116.8 

60 

55.2 

23.4 

20 

110.5 

46.9 

80 

165.7 

70.3 

40 

220.9 

93.8 

300 

276.2 

117.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.      Dist. 

Dep. 

Lat. 

67°  (113°,  247^,  293°). 

TABLE  2. 

[Page  413 

Difference  of  Latitude  and  Departure  for  23°  (157°,  203°,  337' 

')• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

277.1 

117.6 

361 

332.3 

141.1 

421 

387.5 

164.5 

481 

442.7 

188.0 

541 

498.0 

211.4 

02 

278.0 

118.0 

62 

333.2 

141.5 

22 

388.5 

164.9 

82 

443.7 

188.4 

42 

498.9 

211.  8 

03 

278.9 

118.4 

63 

334.1 

141.8 

23 

389.4 

165.  3 

83 

444.6 

188.8 

43 

499.8 

212.2 

04 

279.8 

118.8 

64 

335. 1 

142.2 

24 

390.3 

165.7 

84 

445.  5 

189.2 

44 

500.7 

212.6 

05 

280.8 

119.2 

65 

336.0 

142.6 

25 

391.2 

166.1 

85 

446.4 

189.5 

45 

501.7 

213.0 

06 

281.7 

119.  6 

66 

336.  9 

143.0 

26 

392.1 

166.5 

86 

447.3 

189.9 

46 

502.  6 

213.  4 

07 

282.6 

120.0 

67 

337.8 

143.4 

27 

393.1 

166.8 

87 

448.  3 

190.2 

47 

503. 5 

213.  8 

08 

283. 5 

120.4 

68 

338.7 

143.8 

28 

394.0 

167.2 

88 

449.  2  :  190. 6 

48 

504.4 

214.2 

09 

284.4 

120.8 

69 

339.  7 

144.2 

29 

.394.  9 

167.6 

89 

450. 1     191. 0 

49 

505.  3 

214.6 

10 
311 

285.  4 

121.2 

70 
371 

340.6 
341.  5 

144.6 
14.5.  0 

30 
431 

395.8 
396.7 

168.0 

90 

451.0 

191.4 
191.8 

50 

506.3 
507.2 

215.0 
215.3 

286.3 

121.6 

168.4 

491 

451.  9 

551 

12 

287.2 

121.9 

72 

342.4 

145.  4 

32 

397.7 

168.8 

92 

452.  9    192.  2 

52 

508.1 

215.6 

13 

288.1 

122.3 

73 

343.  4 

145.  7 

33 

398.6 

169.2 

93 

453.  8    192.  6 

53 

509.0 

216.  0 

14 

289.0 

122.7 

74 

344.  3 

146.1 

34 

399.5 

169.6 

94 

454.7     193.0 

54 

509.9 

216.4 

15 

290.0 

123.1 

75 

345.2 

146.5 

35 

400.4 

170.0 

95 

455.  6 

193.4 

55 

510.  9 

216.  S 

16 

290.9 

123.5 

76 

346.1 

146.9 

36 

401.3 

170.4 

96 

456.  6 

193.  8 

56 

511.  8 

217.2 

17 

291.8 

123.9 

77 

347.  0 

147.3 

37 

402.3 

170.8 

■   97 

457.  5 

194.2 

Oi 

512.  7 

217.6 

18 

292.7 

124.3 

78 

348.0 

147.7 

38 

403.  2 

171.1 

98 

458.4 

194.6 

58 

513.  6 

218.0 

19 

293.6 

124.6 

79 

348.  9 

148.1 

39 

404.1 

171.  5 

99 

459.  3 

195.  0 

59 

514.  5 

218.4 

20 

294.6 
295.5 

125.  0 

80 

349.  8 

148.  5 

40 

405.  0 

171.9 

500 

460.2 
461.2 

195.4 

60 

515. 5 
516.4 

218.  8 
219.2" 

321 

125.4 

381 

350.7 

148.9 

441 

405.9 

172.3 

501 

195.8 

561 

22 

296.4 

125.8 

82 

351.6 

149.3 

42 

406.9 

172.7 

02 

462.1 

196.2 

62 

517.3 

219.6 

23 

297.3 

126.2 

83 

352.6 

149.7 

43 

407.8 

173.1 

03 

463.0 

196.6 

63 

518.  2 

220.0 

24 

298.2 

126.6 

84 

353.5 

150.0 

44 

408.7 

173.5 

04 

463.9 

197.0 

64 

519.2 

220.4 

25 

299.2 

127.0 

85 

354. 4 

150.  4 

45 

409.6 

173.9 

05 

464.9 

197.4 

65 

520.1 

220.8 

26 

300.1 

127.4 

86 

355.  3 

150.8 

46 

410.5 

174.3 

06 

465.  8 

197.8 

66 

521.0 

221.2 

27 

301.0 

127.8 

87  1  356.2 

151.2 

47 

411.5 

174.7 

07 

466.7 

198.1 

67 

521.9 

221.6 

28 

301.9 

128.2 

88  1  357.2 

151.6 

48 

412.4 

175.1 

08 

467.6 

198.5 

68 

522.8 

222.0 

29 

302.8 

128.6 

89     358.1 

152.0 

49 

413.3 

175.4 

09 

468.  5 

198.8 

69 

523.  8 

222.3 

30 

303.  8 

128.9 

90     359.0 

1.52.  4 

50 

414.2 
415.2 

175.8 

10 

469.5 

199.3 

70 

524.  7 

222.7 
223.  1 

331 

304.7 

129.3 

391     359. 9 

152.8 

451 

176.2 

511  1  470.4 

199.7 

571 

525.  6 

32 

305.6 

129.7 

92     360. 8 

153.2 

52 

416.1 

176.6 

12     471.3 

200.0 

72 

526.5 

223.  4 

33 

306.  5 

130.1 

93     361. 8 

153. 6 

53 

417.0 

177.0 

13  !  472.2 

200.4 

73 

527.4 

223.  8 

34 

307.5 

130.5 

94     362.7 

154.0 

54 

417.9 

177.4 

14  ;  473. 1 

200.8 

74 

528.  4 

224.2 

35 

308.4 

130.9 

95     363. 6 

154.3 

55 

418.8 

177.8 

15  !  474.0 

201.2 

75 

529.  3 

224.  6 

36 

309.3 

131.3 

96 

364. 5 

154.7 

56 

419.8 

178.2 

16  \  475.0 

201.6 

76 

530.  2 

225.  0 

37 

310.2 

131.7 

97 

365.4 

155. 1 

57 

420.7 

178.6 

17  i  475.9 

202. 0 

77 

531.1 

225.  4 

38 

311.1 

132.1 

98 

366.4 

155.  5 

58 

421.6 

179.0 

18     476.8 

202.4 

78 

532.0 

225.  8 

39 

312.1 

132.5 

99 

367.3 

155.  9 

59 

422.  5 

179.4 

19     477. 7 

202.8 

79 

533. 0 

226.2 

40 
341 

313.0 

132.9 

400  j  368.2 

156.  3 

60 

423.4 
424.4 

179.7 

20  '  478.6 
521  ,  479.6 

203.2 
203.6 

80 

533.9 

226.6 

313.9 

133.2 

401 

369.1 

156.  7 

461 

180.1 

581 

534.8 

227.0 

42 

314.8 

133.6 

02 

370.0 

157. 1 

62 

425.  3 

180.5 

22  1  480.  5 

204.0 

82 

535.  7 

227.4 

43 

315.  7 

134.0 

03 

371.0 

157.5 

63 

426.2 

180.9 

23  i  481.4 

204.4 

83 

536.6 

227.8 

44 

316.7 

134.4 

04 

371.9 

157.9 

64 

427.1 

181.3 

24  1  482.3 

204.8 

84 

537.6 

228.2 

45 

317.6 

134.8 

05 

372.8 

158.  3 

65 

428.0 

181.7 

25  1  483.2 

205.  2 

85 

538. 5 

228.6 

46 

318.5 

135.2 

06 

373.7 

158.  6 

66 

429.0 

182.1 

26  '  484.  2 

205.  5 

86 

539. 4 

229.0 

47 

319.4 

135.  6 

07 

374.6 

159.  0 

67 

429.  9 

182.5 

27  i  485. 1 

205.  9 

87 

540.3 

229.4 

48 

320.3 

136.0 

08 

375.  6 

159.  4 

68 

430.8 

182.9 

28  !  486.0 

206.  3 

88 

.541.  2 

229.8 

49 

321.3 

136.4 

09 

376.5 

159.  8 

69 

431.7 

183.3 

29 

486.9 

206.7 

89 

542.  2 

230.  2 

50 

322.2 

136.8 
137.2 

10 

377.4 
378.3 

160.  2 
160.6 

70 
471 

432.6 
433.  6 

183.7 
184.0 

30 
531 

487.8 
488.8 

207.1 
207.  4 

90 
591 

543. 1 
.544.  0 

230.  6 
231.0 

351 

323.1 

411 

52 

324.0 

137.5 

12 

379.  3 

161.0 

72 

434.  5 

184.4 

32 

489.7 

207.8 

92 

544.  9 

231.3 

53 

324.9 

137.9 

13 

380.2 

161.4 

73 

435.  4 

184.8 

33 

490.6 

208.  2 

93 

545.  8 

231.7 

54 

325. 9 

138.3 

14 

381.1 

161.  8 

74 

436.  3 

185.  2 

34 

491.5 

208.6 

94 

.546.  8 

232.  0 

55 

326.8 

138.7 

15 

382.0 

162.2 

75 

437.2 

185.  6 

35 

492.  5 

209.0 

95 

547.  7 

232.4 

56 

327.7 

139.1 

16 

382.9 

162.5 

76 

438.2 

186.0 

36 

493.  4 

209.  4 

96 

548.6 

232.8 

57 

328.6 

139.5 

17 

383.9 

162.  9 

77 

4.39. 1 

186.4 

37 

494.3 

209.8 

97 

549.  5 

233.2 

58 

329.5 

139.9 

18 

384.8 

163.  3 

78 

440.0 

186.8 

38 

495.  2 

210.2 

98 

550.  4 

233.  6 

59 

330.5 

140.3 

19 

385.7 

163.  7 

79 

440.  9 

187.2 

39 

496.1 

210.6 

99 

.551.3 

234.  0 

60 

331.4 

140.7 

20 

386.6 

164.1 

80 

441.8 

187.6 

40 

497.1 

211.0 

600 

552.3 

234.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

)7°(11 

3°,  247°,  293°). 

Page  414] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  24' 

(156 

=,204°,  336°). 

Dlst. 

1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
49.2 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

0.9 

0.4 

61 

55.7 

24.8 

121 

110.5 

181 

165.4 

73.6 

241 

220.2 

98.0 

2 

1.8 

0.8 

62 

56.6 

25.2 

22 

111.5 

49.6 

82 

166. 3 

74.0 

42 

221. 1 

98.4 

3 

2.7 

1.2 

63 

57.6 

25.6 

23 

112.4 

50.0 

83 

167.2 

74.4 

43 

222.0 

98.8 

4 

3.7 

1.6 

64 

58.5 

26.0 

24 

113.3 

50.4 

84 

168.1 

74.8 

44 

222.9 

99.2 

5 

4.6 

2.0 

65 

59.4 

26.4 

25 

114.2 

50.8 

85 

169.0 

76.2 

45 

223.8 

99.7 

6 

5.5 

2.4 

i6 

60.3 

26.8 

26 

115.1 

51.2 

86 

169.9 

76.7 

46 

224.7 

100.1 

7 

6.4 

2.8 

67 

61.2 

27.3 

27 

116.0 

51.7 

87 

170.8 

76.1 

47 

226.  6 

100.5 

8 

7.3 

3.3 

68 

62.1 

27.7 

28 

116.9 

52.1 

88 

171.7 

76.6 

48 

226.  6 

1(X).9 

9 

8.2 

3.7 

69 

63.0 

28.1 

29 

117.8 

52.5 

89 

172.7 

76.9 

49 

227.  6 

101.3 

10 
11 

9.1 

4.1 

4.5' 

70 
71 

63.9 
64.9 

28.5 
28.  9 

30 
131 

118.8 
119.7 

52.9 
53.3 

90 

173.6 
174.5 

77.3 

"77.7 

60 

228.4 

101.7 
102.1 

10.0 

191 

251 

229.  3 

12 

11.0 

4.9 

72 

65.8 

29.3 

32 

120.6 

53.7 

92 

175.4 

78.1 

62 

230.2 

102.6 

13 

11.9 

5.3 

73 

66.7 

29.7 

33 

121.5 

54.1 

93 

176.3 

78.5 

63 

231.1 

102.9 

14 

12.8 

5.7 

74 

67.6 

30.1 

34 

122.4 

54.5 

94 

177.2 

78.9 

64 

232.0 

103.  3 

15 

13.7 

6.1 

75 

68.5 

30.5 

35 

123.3 

54.9 

95 

178.1 

79.3 

56 

233.  0 

103.  7 

16 

14.6 

6.5 

76 

69.4 

30.9 

36 

124.2 

55.3 

96 

179.1 

79.7 

66 

233.9 

104.1 

17 

15.5 

6.9 

77 

70.3 

31.3 

37 

125.2 

55.  7 

97 

180.0 

80.1 

67 

234.8 

104.5 

.  18 

16.4 

7.3 

78 

71.3 

31.7 

38 

126.1 

56.1 

98 

180.9 

80.5 

68 

235.  7 

104.  9 

19 

17.4 

7.7 

79 

72.2 

32.1 

39 

127.0 

56.5 

99 

181.8 

80.9 

69 

236.  6 

105.  3 

20 
21 

18.3 
19.2 

8.1 

8.5' 

80 
81 

73.1 
74.0 

32.5 
32.9 

40 
141 

127.9 

56.9 
57.3 

200 
201 

182.7 
183.6 

81.3 

60 
261 

237.6 

105.8 
106.  2 

128.8 

81.8 

238.4 

22 

20.1 

8.9 

82 

74.9 

33.4 

42 

129.7 

57.8 

02 

184.5 

82.2 

62 

239.3 

106.6 

23 

21.0 

9.4 

83 

75.8 

33.8 

43 

130.6 

58.2 

03 

185.4 

82.6 

63 

240.3 

107.0 

24 

21.9 

9.8 

84 

76.7 

34.2 

44 

131.6 

58.6 

04 

186.4 

83.0 

64 

241.2 

107.4 

25 

22.8 

10.2 

85 

77.7 

34.6 

45 

132.5 

69.0 

05 

187.3 

83.4 

66 

212.1 

107.8 

26 

23.8 

10.6 

86 

78.6 

35.0 

46 

133.4 

59.4 

06 

188.2 

83.8 

66 

243.0 

108.2 

27 

24.7 

11.0 

87 

79.5 

35.4 

47 

134.3 

59.8 

07 

189.1 

84.2 

67 

243.9 

108.  6 

28 

25.6 

11.4 

88 

80.4 

35.8 

48 

135.  2 

60.2 

08 

190.0 

84.6 

68 

244.8 

109.0 

29 

26.5 

11.8 

89 

81.3 

36.2 

49 

136.1 

60.6 

09 

190. 9 

85.0 

69 

246.7 

109.4 

30 

27.4 
28.3 

12.2 
12.6 

90 

82.2 

36.6 
37.0 

50 

137.0 

61.0 

10 

191.8 
192.8 

86.4 

85.8 

70 

246.7 

109.8 
110.2 

31 

91 

83.1 

151 

137.9 

61.4 

211 

271 

247.6 

32 

29.2 

13.0 

92 

84.0 

37.4 

52 

138.9  1  61.8 

12 

193.7 

86.2 

72 

248.5 

110.6 

33 

30.1 

13.4 

93 

85.0 

37.8 

53 

139.8  !  62.2 

13 

194.6 

86.6 

73 

249.4 

111.0 

34 

31.1 

13.8 

94 

85.9 

38.2 

54 

140.7  i  62.6 

14 

195.6 

87.0 

74 

260.3 

111.4 

35 

32.0 

14.2 

95 

86.8 

38.6 

55 

141.6  ,  63.0 

15 

196.4 

87.4 

76 

261.2 

111.9 

36 

32.9 

14.6 

96 

87.7 

39.0 

56 

142.5  '  63.5 

16 

197.3 

87.9 

76 

252.1 

112.3 

37 

33.8 

15.0 

97 

88.6 

39.5 

57 

143.4 

63.9 

17 

198.2 

88.3 

77 

253.1 

112.7 

38 

34.7 

15.5 

98 

89.5 

39.9 

58 

144.3 

64.3 

18 

199.2 

88.7 

78 

264.0 

113.1 

39 

35.6 

15.9 

99 

90.4 

40.3 

59 

145. 3  I  64.  7 

19 

200.1 

89.1 

79 

254.9 

113.6 

40 

36.5 
37.5 

16.3 

100 

91.4 
92.3 

40.7 

60 

146.2 
147.1 

65.1 

20 

201.0 
201.9 

89.5 

80 
281 

265.8 
256.7 

113.9 
"114. 3 

41 

16.7 

101 

41.1 

161 

65.5 

221 

89.9 

42 

38.4 

17.1 

02 

93.2 

41.5 

62 

148.0  !  65.9 

22 

202.8 

90.3 

82 

267.6 

114.7 

43 

39.3 

17.5 

03 

94.1 

41.9 

63 

148.9 

66.3 

23 

203.7 

90.7 

83 

258.5 

115.1 

44 

40.2 

17.9 

04 

95.0 

42.3 

64 

149.8 

66.7 

24 

204.6 

91.1 

84 

259.4 

115.5 

45 

41.1 

18.3 

05 

95.9 

42.7 

65 

150.7 

67.1 

25 

206.5 

91.5 

85 

260.4 

116.9 

46 

42.0 

18.7 

06 

96.8 

43.1 

66 

151.6 

67.5 

26 

206.5 

91.9 

86 

261.3 

116.  3 

47 

42.9 

19.1 

07 

97.7 

43.5 

67 

152.6 

67.9 

27 

207.4 

92.3 

87 

262.2 

116.7 

48 

43.9 

19.5 

08 

98.7 

43.9 

68 

153.5 

68.3 

28 

208.3 

92.7 

88 

263.1 

117.1 

49 

44.8 

19.9 

09 

99.6 

44.3 

69 

154.4 

68.7 

29 

209.2 

93.1 

89 

264.0 

117.5 

50 

45.7 

20.3 

10 
111 

100. 5 
101.4 

44.7 
45. 1' 

70 

155.3 

69.1 
69.  6 

30 

210.1 
211.0 

93.6 

90 
291 

264.9 

118.0 

51 

46.6 

20.7 

171 

156.2 

231 

94.0 

265.8 

118.4 

52 

47.5 

21.2 

12 

102.3 

45.6 

72 

157.1 

70.0 

32 

211.9 

94.4 

92 

266.8 

118.8 

53 

48.4 

21.6 

13 

103.2 

46.0 

73 

158.0 

70.4 

33 

212.9 

94.8 

93 

267.7 

119.2 

64 

49.3 

22.0 

14 

104.1 

46.4 

74 

159.0 

70.8 

34 

213.8 

96.2 

94 

268.6 

119.6 

55 

50.2 

22.4 

15 

105. 1 

46.8 

75 

159.9 

71.2 

35 

214.7 

95.6 

96 

269.6 

120.0 

56 

51.2 

22.8 

16 

106.0 

47.2 

76 

160.8 

71.6 

36 

215.6 

96.0 

96 

270.  4 

120.4 

57 

52.1 

23.2 

17 

106.9 

47.6 

77 

161.7 

72.0 

37 

216.6 

96.4 

97 

271.3 

120.8 

58 

53.0 

23.6 

18 

107.8 

48.0 

78 

162.6 

72.4 

38 

217.4 

96.8 

98 

272.2 

121.2 

59 

53.9 

24.0 

19 

108.7 

48.4 

79 

163.5 

72.8 

38 

218.3 

97.2 

99 

273.2 

121.6 

60 

54.8 

24.4 

20 

109.6 

48.8 

80 

164.4 

73.2 

40 

219.3 

97.6 

300 

274.1 

122.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

)6°  (1 

14°,  246°,  294° 

)• 

TABLE  2. 

[Page  415    | 

Difference  of  Latitude  and  Departure  for  24°  (156°,  204 

°,  336° 

)• 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.        Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

275.0 

122.4 

361 

329.8 

146.8 

421 

384.  6 

171.2 

481 

439.4 

195.6 

541 

494.2 

220.0 

02 

275.9 

122.8 

62 

330. 7  I  147. 2 

22 

385.5 

171.6 

82 

440.3 

196.0 

42 

495.1 

220.4 

03 

276.8 

123.2 

63 

331.6     147.6 

23 

386.4 

172.1 

83 

441.2 

196.5 

43 

496.0 

220.9 

04 

277.7 

123.7 

64 

332.5 

148.1 

24 

387.3 

172.5 

84 

442.1 

196.9 

44 

496.9 

.  221.3 

05 

278.6 

124.1 

65 

333.4 

148.5 

25 

388.2 

172.9 

85 

443.0 

197.3 

45 

497.8 

221.7 

06 

279.5 

124.5 

66 

334.3 

148.9 

26 

389.  2 

173.3 

86 

444.0 

197.7 

46 

498.8 

222.1 

07 

280.4 

124.9 

67 

335.  3 

149.3 

27 

390.1 

173.7 

87 

444.9 

198.1 

47 

499.7 

222.5 

08 

281.4 

125.3 

68 

336.2 

149.7 

28 

391.0 

174.1 

88 

445.8 

198.5 

48 

500.6 

222.9 

09 

282.3 

125.7 

69 

337.1 

150.1 

29 

391.9 

174.5 

89 

446.7 

198.9 

49 

501.5 

223.3 

10 

283.2 

126.1 

70 

338.0 

150.5 

30 

392.8 

174.9 

90 

447.6 

199.3 

50 

502.4 

223.7 

311 

284.1 

126.5 

371 

338.9 

m).9 

431 

393.7 

175.3 

491 

448.6 

199.7 

551 

503.  4 

224.1 

12 

285.0 

126.9 

72 

339.8 

32 

394.6 

175.7 

92 

449.5 

200.1 

52 

504.  3 

224.5 

13 

285.9 

127.3 

73 

340.  7, 

151.7 

33 

395.6 

176.1 

93 

450.4 

200.5 

53 

505.  2 

224.9 

14 

286.8 

127.7 

74 

341.  7^ 

152.1 

34 

396.5 

176.5 

94 

451.3 

200.9 

54 

506.1 

225.  3 

15 

287.8 

128.1 

75 

342.6 

152.5 

35 

397.4 

176.9 

95 

452.2 

201.3 

55 

507.0 

225.7 

16 

288.7 

128.5 

76 

343.5 

152.9 

36 

398.3 

177.3 

96 

453.1 

201.7 

56 

507.9 

226.1 

17 

289.6 

128.9 

77 

344.4 

153.3 

37 

399.2 

177.7 

97 

454.0 

202.2 

57 

508.8 

226.6 

18 

290.5 

129.3 

78 

345.  3 

153.7 

38 

400.1 

178.2 

98 

454.  9 

202.6 

58 

509.  7 

227.0 

19 

291.4 

129.8 

79 

346.2 

154.2 

39 

401.0 

178.6 

99 

455.  8 

203.  0 

59 

510.6 

227.4 

20 

292.3 
293.2 

130.2 
130.6 

80 
381 

347.1 
348.  i 

154.6 
155.0 

40 
441 

402.0 

179.0 

500 

456.8 

203.4 

60 

511.6 
512. 5 

227.8 

321 

402.9 

179.4 

501 

457.7 

203.8 

561 

228.2 

22 

294.2 

131.0 

82 

349.0 

155.4 

42 

403.8 

179.8 

02 

458.6 

204.2 

62 

513.4 

228.6 

23 

295.1 

131.4 

83 

349.  9 

155.8 

43 

404.7 

180.2 

03 

459.5 

204.6 

63 

514.3 

229.0 

24 

296.0 

131.8 

84 

350.  8 

156.  2 

44     405.6 

180.6 

04 

460.4 

205.0 

64 

515.2 

229.4 

25 

296.9 

132.  2 

85 

351.7 

156:6 

45     406.5 

181.0 

05 

461.3 

205.4 

65 

516.1 

229.8 

26 

297.8 

132.6 

86 

352.6 

157.0 

46 

407.4 

181.4 

06 

462.2 

205.  8 

66 

517.0 

230.2 

27 

298.7 

133.0 

87 

353.5 

157. 4 

47 

408.3 

181.8 

07 

463.2 

206.2 

67 

518.  0 

230.6 

28 

299.6 

133.4 

88 

354.4 

157.8 

48 

409.3 

182.2 

08 

464.1 

206.6 

.68 

518.9 

231.0 

29 

300.5 

133.8 

89 

355.4 

158.2 

49 

410.2 

182.6 

09 

465.0 

207.0 

69 

519.8 

231.4 

30 

301.5 
302.4 

134.2 

90     356. 3 

158.6 

50 

411.1 

183.0 

10 

465.9 

207.4 

70 
"571 

520.7 
521.6 

231.8 
232.2 

331 

134.6 

391     357.2 

159.0 

451 

412.0 

183. 4 

511 

466.8 

207.8 

32 

303.3 

135.0 

92     358.1 

159.4 

52 

412.9 

183.8 

12 

467.7 

208.2 

72 

522.5 

232.7 

33 

304.2 

135.4 

93 

359.0 

159.8 

53 

413.8 

184.3 

13 

468.6 

208.7 

73 

523.4 

233. 1 

34 

305.1 

135.9 

94 

359.9 

160.3 

54 

414.7 

184.7 

14 

469.5 

209.1 

74 

524.3 

233.5 

35 

306.0 

136.3 

95 

360.8 

160.7 

55 

415.7 

185.1 

15 

470.  5 

209.5 

75 

525.3 

233.9 

36 

306.  9 

136.7 

96 

361.8 

161.1 

56 

416.6 

185.5 

16 

471.4 

209.9 

76 

526.2 

234.  3 

37 

307.9 

137.1 

97 

362.7 

161.5 

57 

417.5 

185.9 

17 

472.3 

210.3 

77 

527.1 

234.  7 

38 

308.8 

137.5 

98 

363.6 

161.9 

58 

418.4 

186.3 

18 

473.2 

210.7 

78 

528. 0 

235. 1 

39 

309.7 

137.9 

99 

364.5 

162.3 

59 

419.  3 

186.7 

19 

474.1 

211.1 

79 

528. 9 

235.  5 

40 
341 

310.6 

138.3 

400 

365.4 
366.3 

162.7 

60 

420.2 

187.1 

20 

475.0 
475.9 

211.5 

80 

529.8 

235.9 
236.3 

311.5 

138.7 

401 

163.1 

461 

421.1 

187.5 

521 

211.9 

581 

530.8 

42 

312.4 

139.1 

02 

367.2 

163.5 

62 

422.0 

187.9 

22 

476.8 

212.3 

82 

531.7 

236.7 

43 

313.3 

139.5 

03  i  368.2 

163.9 

63 

423.0 

188.3 

23 

477.8 

212.7 

83 

532.  6 

237. 1 

44 

314.  3 

139.9 

04  1  369. 1 

164.3 

64 

423.9 

188.7 

24 

478.7 

213.1 

84 

533.  5 

237.5 

45 

315.2 

140.3 

05     370.0 

164.7 

65 

424.8 

189.1 

25 

479.6 

213.5 

85 

534.4 

237.9 

46 

316. 1 

140.7 

06     370.9 

165.1 

66 

425.7 

189.5 

26 

480.5 

213.9 

86 

535.  3 

238.3 

47 

317.0 

141.1 

07  i  371.8 

165.5 

67 

426.6 

189.9 

27 

481.4 

214.4 

87 

536. 2 

238.8 

48 

317.9 

141.5 

08  !  372.7 

165.9 

68 

427.5 

190.4 

28 

482.3 

214.8 

88 

537.1 

239.2 

49 

318.8 

142.0 

09  i  373.6 

166.4 

69 

428.4 

190.8 

29 

483.2 

215.  2 

89 

538.0 

239.6 

50 

319.7 

142.4 

10  !  374.  5 

166.8 
167.2 

70 

429.4 

191.2 

30 

484.2 
485. 1 

215.  6 

90 

539.0 
539. 9 

240.0 

351 

320.6 

142.8 

411  !  375.5 

471 

430.  3 

191.6 

531 

216.0 

591 

240.4 

52 

321.6 

143.  2 

12 

376.4 

167.6 

72 

431.2 

192.0 

32 

486.0 

216.4 

92 

540.8 

240.8 

53 

322.5 

143.6 

13 

377.3 

168.0 

73 

432.1 

192.4 

33 

486.9 

216.8 

93 

541.7 

241.2 

54 

323.4 

144.0 

14 

378.2 

168.4 

74 

433.0 

192.8 

34 

487.8 

217.2 

94 

542.6 

241.6 

55 

324.3 

144.4 

15 

379.1 

168.8 

75 

433.9 

193.2 

35 

488.7 

217.6 

95 

543.5 

242.0 

56 

325.2 

144.8 

16 

380. 0 

169.2 

76 

434.8 

193. 6 

36 

489.6 

218.0 

96 

544.4 

242.4 

57 

326.1 

145.2 

17 

380.9 

169.6 

77 

435.8 

194.0 

37 

490.6 

218.4 

97 

545.4 

242.8 

58 

327.0 

145.6 

18 

381.9 

170.0 

78 

436.7 

194.4 

38 

491.5 

218.8 

98 

546.3 

243.2 

59 

328.  0 

146.0 

19 

382.  8 

170.4 

79 

437.6 

194.8 

39 

492.4 

219.2 

99 

547.2 

243.6 

60 

328.9 

146.4 

20 

383.7 

170.8 

80 

438.5 

195.2 

40 

493.3 

219.6 

600 

548.1 

244.0 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

56°  (114°,  246 

°,  294° 

). 

Page  416] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  25°  (155°,  205 

°,  335° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

55.3 

25.8 

121 

109.7 

51.1 

181 

164.0 

76.5 

241 

218.4 

101.9 

2 

1.8 

0.8 

62 

56.2 

26.2 

22 

110.6 

51.6 

82 

164.9 

76.9 

42 

219.  3 

102.  3 

3 

2.7 

1.3 

63 

57.1 

26.6 

23 

111.5 

52.0 

83 

165.  9 

77.3 

43 

220.2 

102.7 

4 

3.6 

1.7 

64 

58.0 

27.0 

24 

112.4 

52.4 

84 

166.8 

77.8 

44 

221.1 

103. 1 

5 

4.5 

2.1 

65 

58.9 

27.5 

25 

113.3 

52.8 

85 

167.7 

78.2 

45 

222.0 

103.5 

6 

5.4 

2.5 

«6 

59.8 

27.9 

26 

114.2 

53.2 

86 

168.6 

78.6 

46 

223.  0 

104.0 

7 

6.3 

3.0 

67 

60.7 

28.3 

27 

115.1 

53.7 

87 

169.  5 

79.0 

47 

223.9 

104.4 

8 

7.3 

3.4 

68 

61.6 

28.7 

28 

116.0 

54.1 

88 

170.4 

79.5 

48 

224.8 

104.8 

9 

8.2 

3.8 

69 

62.5 

29.2 

29 

116.9 

54.5 

89 

171.3 

79.9 

49 

225.7 

105.2 

10 

9.1 
10.0 

4.2 

70 

63.4 

29.6 
30.0 

30 
131 

117.8 

54.9 

90 

172.2 

80.3 

50 

226.6 

105.7 
106.1 

11 

4.6 

71 

64.3 

118.7 

55.4 

191 

173.1 

80.7 

251 

227.5 

12 

10.9 

5.1 

72 

65.3 

30.4 

32 

119.6 

55.8 

92 

^74.0 

81.1 

52 

228.4 

106.5 

13 

11.8 

5.5 

73 

66.2 

30.9 

33 

120.5. 

56.2 

93 

174.9 

81.6 

53 

229.3 

106.9 

14 

12.7 

5.9 

74 

67.1 

31.3 

34 

121.4 

56.6 

94 

17^.8 

82.0 

54 

230.2 

107.  3 

15 

13.6 

6.3 

75 

68.0 

31.7 

35 

122.4 

57.1 

95 

176.7 

82.4 

55 

231.1 

107.8 

16 

14.5 

6.8 

76 

68.9 

32.1 

36 

123.3 

57.5 

96 

177.6 

82.8 

56 

232.0 

108.2 

17 

15.4 

7.2 

77 

69.8 

32.5 

37 

124.2 

57.9 

97 

178.5 

83.3 

57 

232.9 

108.6 

18 

16.3 

7.6 

78 

70.7 

33.0 

38 

125.1 

58.3 

98 

179.4 

83.7 

58 

233.8 

109.0 

19 

17.2 

8.0 

79 

71.6 

33.4 

39 

126.0 

58.7 

99 

180.4 

84.1 

59 

234.7 

109.5 

20 

18.1 
19.0 

8.5 

80 

72.5 
73.4 

33.8 
34.2 

40 

126.9 

59.2 
59.6 

200 
201 

181.3 
182.  2" 

84.5 
84.9 

60 
261 

235.6 
236.5 

109.9 
110.3 

21 

8.9 

81 

141 

127.8 

22 

19.9 

9.3 

82 

74.3 

34.7 

42 

128.7 

60.0 

02 

183.1 

85.4 

62 

237.5 

110.7 

23 

20.8 

9.7 

83 

75.2 

35.1 

43 

129.6 

60.4 

03 

184.0 

85.8 

63 

238.4 

111.1 

24 

21.8 

10.1 

84 

76.1 

35.5 

44 

130.5 

60.9 

04 

184.9 

86.2 

64 

239.3 

111.6 

25 

22.7 

10.6 

85 

77.0 

35.9 

45 

131.4 

61.3 

05 

185.8 

86.6 

65 

240.2 

112.0 

26- 

23.6 

11.0 

86 

77.9 

36.3 

46 

132.3 

61.7 

06 

186.7 

87.1 

66 

241.1 

112.4 

27 

24.5 

11.4 

87 

78.8 

36.8 

47 

133.2 

62.1 

07 

187.6 

87.5 

67 

242.0 

112.8 

28 

25.4 

11.8 

88 

79.8 

37.2 

48 

134.1 

62.5 

08 

188.5 

87.9 

68 

242.9 

113.  3 

29 

26.3 

12.3 

89 

80.7 

37.6 

49 

135.0 

63.0 

09 

189.4 

88.3 

69 

243.8 

113.7 

30 

27.2 

12.7 

90 

81.6 

38.0 
^38. 5 

50 

135.9 
136.9 

63.4 

10 

190.  3 

88.7 

70 
271 

244.7 

114.1 

31 

28.1 

13.1 

91 

82.5 

151 

63.8 

211 

191.2 

89.2 

245.6 

114.5 

32 

29.0 

13.5 

92 

83.4 

38.9 

52 

137.8 

64.2 

12 

192. 1 

89.6 

72 

246.5 

115.0 

33 

29.9 

13.9 

93 

84.3 

39.3 

53 

138.7 

64.7 

13 

193.0 

90.0 

73 

247.4 

115.  4 

34 

30.8 

14.4 

94 

85.2 

39.7 

54 

139.6 

65.1 

14 

193.9 

90.4 

74 

248.3 

115.8 

35 

31.7 

14.8 

95 

86.1 

40.1 

55 

140.5 

65.5 

15 

194.9 

90.9 

75 

249.2 

116.2 

36 

32.6 

15.2 

96 

87.0 

40.6 

56 

141.4 

65.9 

16 

195.8 

91.3 

76 

250.1 

116.6 

37 

33.5 

15.6 

97 

87.9 

41.0 

57 

142.  3 

66.4 

17 

196.7 

91.7 

77 

251.0 

117.1 

38 

34.4 

16.1 

98 

88.8 

41.4 

58 

143.2 

66.8 

18 

197.6 

92.1 

78 

252.0 

117.5 

39 

35.3 

16.5 

99 

89.7 

41.8 

59 

144.1 

67.2 

19 

198.5 

92.6 

79 

252.9 

117.9 

40 

36.3 

16.9 
17.3 

100 
101 

90.6 
91.5 

42.3 
42.7 

60 
161 

145.0 

67.6 

20 

221 

199.4 
200.3^ 

93.0 

80 

253.8 

118.3 
118.8 

41 

37.2 

145.9 

6870 

93.4 

281 

254.7 

42 

38.1 

17.7 

02 

92.4 

43.1 

62 

146.8 

68.5 

22 

201.2 

93.8 

82 

255.6 

119.2 

43 

39.0 

18.2 

03 

93.3 

43.5 

63 

147.7 

68.9 

23 

202.1 

94.2 

83 

256.  5 

119.6 

44 

39.9 

18.6 

04 

94.3 

44.0 

64 

148.6 

69.3 

24 

203.0 

94.7 

84 

257.4 

120.0 

45 

40.8 

19.0 

05 

95.2 

44.4 

65 

149.5 

69.7 

25 

203.  9 

95.1 

85 

258.3 

120.4 

46 

41.7 

19.4 

06 

96.1 

44.8 

66 

150.4 

70.2 

26  i  204.8 

95.5 

86 

259.2 

120.9 

47 

42.6 

19.9 

07 

97.0 

45.2 

67 

151.4 

70.6 

27  1  205.7 

95.9 

87 

260.1 

121.3 

48 

43.5 

20.3 

08 

97.9 

45.6 

68 

152.3 

71.0 

28  '•  206.6 

96.4 

88 

261.0 

121.7 

49 

44.4 

20.7 

09 

98.8 

46.1 

69 

153.2 

71.4 

29 

207. 5 

96.8 

89 

261.9 

122.1 

50 

45.3 

21.1 

10 
111 

99.7 
100.6 

46.5 
46.  9 

70 
171 

154.1 
155.0 

71.8 

30 

208.5 
209.4 

97.2 
97.6" 

90 

262.8 
263.7 

122.6 
123.0 

51 

46.2 

21.6 

72.3 

231 

291 

52 

47.1 

22.0 

12 

101.5 

47.3 

72 

155.9 

72.7 

32 

210.3 

98.0 

92 

264.  6 

123.4 

53 

48.0 

22.4 

13 

102.4 

47.8 

73 

156.  8 

73.1 

33 

211.2 

98.5 

93 

265.5 

123.  8 

54 

48.9 

22.8 

14 

103.3 

48.2 

74 

157.  7 

73.5 

34 

212.1 

98.9 

94 

266.5 

124.2 

55 

49.8 

23.2 

15 

104.2 

48.6 

75 

158.6 

74.0 

35 

213.0 

99.3 

95 

267.4 

124.7 

56 

50.8 

23.  7 

16 

105.1 

49.0 

76 

159.5 

74.4 

36 

213.9 

99.7 

96 

268.3 

125.1 

57 

51.7 

24.1 

17 

106.0 

49.4 

77 

160.4 

74.8 

37 

214.  8 

100.  2 

97 

269.2 

125.  5 

58 

52.6 

24.5 

18 

106.9 

49.9 

78 

161.3 

75.2 

38 

215.  7 

100.6 

98 

270.1 

125.  9 

59 

53.5 

24.9 

19 

107.9 

50.3 

79 

162.2 

75.6 

39 

216.6 

101.0 

99 

271.0 

126.4 

60 

54.4 

25.4 

20 

108.8 

50.7 

80 

163.1 

76.1 

40 

217.5 

101.4 

300 

271.9 

126.8 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

65°  (1 

15°,  245°,  295°). 

TABLE  2. 

[Page 

417 

Difference  of  Latitude  and  Departure  for  25°  (155°,  205 

^  335° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

272.8 

127.2 

361 

327. 1 

152.5 

421 

381.5 

177.9 

481 

435.9 

203.3 

541 

490.3 

228.6 

02 

273.7 

127.6 

62 

328.0 

153.  0 

22 

382.4 

178.3 

82 

436.8 

203.7 

42 

491.2 

229.0 

03 

274.6 

128.0 

63 

329.  0 

153.  4 

23 

383.  3 

178.7 

83 

437.7 

204.1 

43 

492.1 

229.4 

04 

275. 5 

128.4 

64 

329.  9 

153.  8 

24 

384.2 

179.2 

84 

438.6 

204.  5 

44 

493.0 

229.9 

05 

276.  4 

128.9 

65 

330.  8 

1.54.2 

25 

385. 1 

179.6 

85 

439.  5 

204.9 

45 

493.9 

230.3 

06 

277.3 

129.  3 

66 

331.  7 

154.6 

26 

386.0 

180.0 

86 

440.4 

205.  4 

46 

494.8 

230.  7 

07 

278.2 

129.  7 

67 

332.  6 

155. 1 

27 

387.0 

180.4 

87 

441.3 

205.  8 

47 

495.  7 

231. 1 

08 

279.1 

130. 1 

68 

333.  5 

155.5 

28 

387.9 

180.9 

88 

442.2 

206.2 

48 

496.6 

231.6 

09 

280.0 

130.  6 

69 

334.  4 

155.9 

29 

388.8 

181.3 

89 

443.1 

206.6 

49 

497.5 

232.0 

10 

280.9 

131.0 
131.4 

70 

335.  3 

156.3 

30 

389.7 

181.7 

90 
491 

444.0 

207.1 

50 
551 

498.4 

232.4 

311 

281.8 

371 

336.  2 

156.  8 

431 

390.6 

182.1 

444.9 

207.  5 

499.3 

232.8 

12 

282.7 

131.8 

72 

337. 1 

157.2 

32 

391.5 

182.5 

92 

445.9 

207.9 

52 

500.2 

233. 2 

13 

283.6 

132.  2 

73 

338.  0 

157.  6 

33 

392.4 

183.0 

93 

446.8 

208.3 

53 

501.1 

233.7 

14 

284.5 

132.7 

74 

338.  9 

158.0 

34 

393.  3 

183.4 

94 

447.7 

208.7 

54 

502.0 

234.1 

15 

285.4 

133. 1 

75 

339.8 

158.5 

35 

394.2 

183.8 

95 

448.6 

209.1 

55 

503.0 

234.5 

16 

286.4 

133.  5 

76 

340.  7 

158.9 

36 

395.1     184.2 

96 

449.5 

209.6 

56 

503. 9 

235.0 

17 

287.3 

133.9 

77 

341.  6 

159.  3 

37 

396.0 

184.7 

97 

450.4 

210.0 

57 

504.8 

235.4 

18 

288.2 

134.4 

78 

342.  5 

159.7 

38 

396.  9 

185. 1 

98 

451.3 

210.4 

58 

505.7 

235.8 

19 

289.1 

134.8 

79 

343. 5 

160. 1 

39 

397.  8 

185.5 

99 

452.2 

210.9 

59 

506.  6 

236.2 

20 

290.0 

135.2 

80 

344.  4 

160.6 

40 

398.  7  !  185.  9 

500 

453.1 

211.3 

60 

507.  5 

236.6 

321 

290.9 

135.  6 

381 

34573 

161.0 

441 

399.6    186.3 

501 

454.0 

211.7 

561 

508.4 

237.1 

22 

291.8 

136.1 

82 

346.  2 

161.4 

42 

400.6 

186.8 

02 

454.9 

212.1 

62 

509.3 

237. 5 

23 

292.7 

136.5 

83 

347.1 

161.8 

43 

401.5 

187.2 

03 

455.8 

212.5 

63 

510.2 

237.9 

24 

293.6 

136.9 

84 

348.  0 

162.  3 

44 

402.4 

187.6 

04 

456.7 

213.0 

64 

511.1 

238.3 

25 

294.5 

137.3 

85 

348.  9 

162.7 

45 

403.3 

188.0 

05 

457.7 

213.4 

65 

512.0 

238.7 

26 

295.4 

137.7 

86 

349.  8 

163. 1 

46 

404.  2  i 188. 5 

06 

458.6 

213.8 

66 

512.9 

239.2 

27 

296.3 

138.2 

87 

350.  7 

163.5 

47 

405.1  '188.9 

07 

459.5 

214.2 

67 

513.8 

239.6 

28 

297.2 

138.6 

88 

351.6 

163.9 

48 

406.  0  i 189. 3 

08 

460.4 

214.7 

68 

514.8 

240.1 

29 

298.1 

139.0 

89 

352. 5 

164.4 

49 

406.  9  i  189.  7 

09 

461.3 

215.1 

69 

515.  7 > 

240.5 

30 
331 

299.0 
300. 0 

139.4 
139.  9 

90 
391 

353.4 
354.  3 

164.8 

50 

407.8 

190.1 

10 

462.2 

215.5 
215.  9 

70 
571 

516.6 
517.5 

240.9 

165.2 

451^ 

408.7 

190.6 

511 

463.1 

241.3 

32 

300.9 

140.  3 

92 

355.  2 

165.  6 

52 

409.6 

191.0 

12 

464.0 

216.4 

72 

518.4 

241.7 

33 

301.8 

140.7 

93 

356.1 

166.1 

53 

410.5 

191.4 

13 

464.9 

216.8 

73 

519.3 

242.1 

34 

302.7 

141.1 

94 

357.  0 

166.5 

54 

411.4 

191.8 

14 

465.8 

217.2 

74 

520.  2 

242.6 

35 

303.6 

141.5 

95 

358.0 

166.9 

55 

412.3 

192.3 

15 

466.7 

217.7 

75 

521. 1 

243.0 

36 

304.5 

142.  0 

96 

358.9 

167.3 

56 

413.  2 

192.7 

16 

467.6 

218.1 

76 

522.0 

243.4 

37 

305.4 

142.4 

97 

359.  8 

167.7 

57 

414.1 

193.1 

17 

468.5 

218.5 

77 

522.  9 

243.  8 

38 

306.  3 

142.8 

98 

360.7 

168.2 

58 

415.1 

193.5 

18 

469.4 

218.9 

78 

523.  8 

244.3 

39 

307.  2 

143.2 

99 

361.6 

168.6 

59 

416.0 

194.0 

19 

470.3 

219.3 

79 

524.7 

244.7 

40 
341 

308.1 
309.0 

143.7 
144.  1 

400 

362.5 

169.0 
169.4 

60  I  416.9 

194.4 

20 

471.2 

219.8 
220.2 

80 
581 

525. 6 
526.  5 

245.1 
245.  5 

401 

363.4 

461 

417.8 

194.8 

521 

472.2 

42 

309.9 

144.5 

02 

364.3 

169.9 

62 

418.7 

195.  2 

22 

473.1 

220.6 

82 

527.4 

246.0 

43 

310.8 

144.9 

03 

365.2 

170.3 

63 

419.6 

195.6 

23 

474.0 

221.0 

83 

528.  3 

246.4 

44 

311.7 

145.4 

04 

366.1 

170.7 

64 

420.5 

196.1 

24 

474.9 

221.4 

84 

529.  3 

246.8 

45 

312.6 

145.8 

05 

367. 0 

171.1 

65 

421.4 

196.5 

25 

475.  8 

221.9 

85 

530.  2 

247.2 

46 

313.5 

146.2 

06 

367.9 

171.6 

66 

422.  3 

196.9 

26 

476.7 

222.3 

86 

531.1 

247.7 

47 

314.5 

146.6 

07 

368.8 

172.0 

67 

423.2 

197.3 

27 

477.6 

222.7 

87 

532.0 

248.1 

48 

315.4 

147.0 

08 

369.7 

172.4 

68 

424. 1 

197.8 

28 

478.5 

223.2 

88 

532.  9 

248.5 

49 

316.3 

147.5 

09 

370.6 

172.8 

69 

425.0 

198.2 

29 

479.4 

223.6 

89 

5.33.  8 

248.9 

50 

317.2 
318.1 

147.9 
148.3 

10 
411 

371.5 
372.5 

173.2 
173.7 

70 
471 

425.9 

426.8 

198.6 
199.0 

30 
531 

480.3 
481.2 

224.0 
224.  4 

90 

534.7 

249.4 
249.8 

351 

591 

535.  6 

52 

319.0 

148.7 

12 

373. 4 

174.1 

72 

427.7 

199.4 

32 

482.1 

224.8 

92 

536.  5 

250.  2 

53 

319.9 

149.2 

13 

374.3 

174.5 

73 

428.6 

199.9 

33 

483.0 

225.  3 

93 

537. 4 

250.  6 

54 

320.8 

149.6 

14 

375.2 

174.9 

74 

429.6 

200. 3 

34 

483.9 

225.7 

94 

538.3 

251. 1 

55 

321.7 

150.0 

15 

376.1 

175.4 

75 

430.5 

200.7 

35 

484.8 

226.1 

95 

539.2 

251.  5 

56 

322.6 

150.4 

16 

.377.  0 

175.8 

76 

431.4 

201.1 

36 

485.7 

226.5 

96 

540.1 

251.  9 

57 

323.5 

150.8 

17 

377.9 

176.2 

77 

432.3 

201.6 

37 

486.7 

226.9 

97 

541.0 

252.3 

58 

324.4 

151.3 

18 

378.  8 

176.  6 

78 

433.2 

202.0 

38 

487.  6 

227.4 

98 

541.9 

252.7 

59  1  325.3 

151.  7 

19 

379.  7 

177.0 

79 

434.  1 

202.4 

39 

488.  5 

227.8 

99 

542.8 

253. 1 

60     326.2 

152.1 

20 

380.6 

177.5 

80 

435.0 

202.8 

40 

489.4 

228.2 

600 

543.8 

253.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

55°  (115°,  245°,  295° 

)• 

22489—03- 


-2V 


Page  418] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  26°  (154°,  206°,  334 

'). 

Dist. 

Lat. 

Dep. 

Di.st. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist. 
241 

Lat. 

Dep. 

1 

0.9 

0.4 

61 

54.8 

26.7 

121 

108.8 

53.0 

162.7 

79.3 

216.6 

105.6 

2 

1.8 

0.9 

62 

55.  7 

27.2 

22 

109.7 

53.5 

82 

163.6 

79.8 

42 

217.5 

106.1 

3 

2.7 

1.3 

63 

56.6 

27.6 

23 

110.6 

53.9 

83 

164.5 

80.2 

43 

218.4 

106.5 

4 

3.6 

1.8 

64 

57.5 

28.1 

24 

111.5 

54.4 

84 

165.4 

80.7 

44 

219.3 

107.0 

5 

4.5 

2.2 

%5 

58.4 

28.5 

25 

112.3 

54.8 

85 

166.3 

81.1 

45 

220.2 

107.4 

6 

5.4 

2.6 

66 

59.  3 

28.9 

26 

113.2 

55.2 

86 

167.2 

81.5 

46 

221.1 

107.8 

7 

6.3 

3.1 

67 

60.2 

29.4 

27 

114.1 

55.7 

87 

168.1 

82.0 

47 

222.0 

108.3 

8 

7.2 

3.5 

68 

61.1 

29.8 

28 

115.0 

56.1 

88 

169.0 

82.4 

48 

222.9 

108.7 

9 

8.1 

3.9 

69 

62.0 

30.2 

29 

115.9 

56. 5 

89 

169.9 

82.9 

49 

223.8 

109.2 

10 
11' 

9.0 

4.4 

70 

62.9 

30.7 

30 

116.8 

57.0 

90 

170.8 

83.3 

50 

224.7 

109.  6 

9.9 

4.8 

71 

63.8 

31.1 

131  ,  117.7 

57.4 

191 

171.7' 

83.7 

251 

225.  6 

110.0 

12 

10.8 

5.3 

72 

64.7 

31.6 

32 

118.6 

57.9 

92 

172.6 

84.2 

52 

226.5 

110.5 

13 

11.7 

5.  7 

73 

65.6 

32.0 

33 

119.5 

58.3 

93 

173.5 

84.6 

53 

227.4 

110.9 

14 

12.6 

6.1 

74 

66.5 

32.4 

34 

120.4 

58.7 

94 

174.4 

85.0 

54 

228.  3 

111.3 

15 

13.5 

6.6 

75 

67.4 

32.9 

35 

121.3 

59.2 

95 

175.3 

85.5 

55 

229.2 

111.8 

16 

14.4 

7.0 

76 

68.3 

33.3 

36 

122.2 

59.6 

96 

176.2 

85.9 

56 

230.1 

112.2 

17 

15.3 

7.5 

77 

69.2 

33.  8 

37 

123.1 

60.1 

97 

177.1 

86.4 

57 

231.0 

112.7 

18 

16.2 

7.9 

78 

70.1 

34.2 

38 

124.0 

60.5 

98 

178.0 

86.8 

58 

231.9 

113.1 

19 

17.1 

8.3 

79 

71.0 

34.6 

39 

124.9 

60.9 

99 

178.9 

87.2 

59 

232.8 

113.5 

20 
21 

18.0 
18.y~ 

8.8 
9.2 

_80 
81 

71.9 

35.1 

40 

125.8 
126.  7 

61.4 

200 

179.8 

87.7 

60 

233.7 

114.0 

72.8 

35.5 

141 

61.8 

201 

180.7 

88.1 

261 

234.6 

114.4 

22 

19.8 

9.6 

82 

73.7 

35.9 

42 

127.6 

62.2 

02 

181.6 

88.6 

62 

235.  5 

114.9 

23 

20.7 

10.1 

83 

74.6 

36.4 

43 

128.5 

62.7 

03 

182.  5 

89.0 

63 

236.4 

115.3 

24 

21.6 

10.5 

84 

75.5 

36.8 

44 

129.4 

63.1 

04 

183.4 

89.4 

64  i  237.3 

115.7 

25 

22.5 

11.0 

85 

76.4 

37.3 

45 

130.3 

63.6 

05 

184.3 

89.9 

65  i  238.2 

116.2 

26 

23.4 

11.4 

86 

77.3 

37.7 

46 

131.2 

64.0 

06 

185.2 

90.3 

66  I  239. 1 

116.6 

27 

24.3 

11.8 

87 

78.2 

38.1 

47 

132.1 

64.4 

07 

186.1 

90.7 

67     240.0 

117.0 

28 

2p.2 

12.3 

88 

79.1 

38.6 

48 

133.0 

64.9 

08     186. 9 

91.2 

68  i  240.9 

117.5 

29 

26.1 

12.7 

89 

80.0 

39.0 

49 

133.9 

65.3 

09  i  187.8 

91.6 

69 

241.8 

117.9 

30 

27.0 
27.9 

13.2 

90 

80.9 

39.5 

50 

134.8 

65.8 

10  1  188.7 

92.1 

70 

242.7 
243.6 

118.4 
118.8 

31 

13.6 

91 

81.8 

39.9 

151 

135.7 

66.2 

211 

189.6 

92.5 

271 

32 

28.8 

14.0 

92 

82.7 

40.3 

52 

136.6 

66.6 

12 

190.5 

92.9 

72 

244.5 

119.2 

33 

29.7 

14.5 

93 

83.6 

40.8 

53 

137.5 

67.1 

13 

191.4 

93.4 

73 

245.4 

119.7 

34 

30.6 

14.9 

94 

84.5 

41.2 

54 

138.4 

67.5 

14 

192.3 

93.8 

74 

246.3 

120. 1 

35 

31.5 

15.3 

95 

85.4 

41.6 

55 

139.3 

67.9 

15 

193.2 

94.2 

75 

247.2 

120.6 

36 

32.4 

15.8 

96 

86.3 

42.1 

56 

140.2 

68.4 

16 

194.1 

94.7 

76 

248.1 

121.0 

37 

33.3 

16.2 

97 

87.2 

42.5 

57 

141.1 

68.8 

17 

195.0 

95.1 

77 

249.0 

121.4 

38 

34.2 

16.7 

98 

88.1 

43.0 

58 

142.0 

69.3 

18 

195.9 

95.6 

78 

249.9 

121.9 

39 

35.1 

17.1 

99 

89.0 

43.4 

59 

142.9 

69.7 

19 

196.8 

96.0 

79 

250.8 

122.3 

40 
41 

36.0 
36.9 

17.5 

100 
101 

89.9 
90.8^ 

43.8 

60 

143.8 
144.  7 

70.1 

20 

197.7 

96.4 

80 

251.7 
252.  6 

122.7 
123.2 

18.0 

44.3 

161 

70.6 

221 

198.6 

96.9 

281 

42 

37.7 

18.4 

02 

91.7 

44.7 

62 

145.6 

71.0 

22 

199. 5 

97.3 

82 

253.  5 

123.6 

43 

38.6 

18.8 

03 

92.6 

45.2 

63 

146.5 

71.5 

23 

200.4 

97.8 

83 

254.  4 

124.1 

44 

39.5 

19.3 

04 

93.5 

45.6 

64 

147.4 

71.9 

24 

201.3 

98.2 

84 

255.  3 

124.5 

45 

40.4 

19.7 

05 

94.4 

46.0 

65 

148.3 

72.3 

25 

202.2 

98.6 

85 

256.2 

124.9 

46 

41.3 

20.2 

06 

95.3 

46.5 

66 

149.2 

72.8 

26 

203.1 

99.1 

86 

257.1 

125.4 

47 

42.2 

20.6 

07 

96.2 

46.9 

67 

150.1 

73.2 

27     204. 0 

99.5 

87 

258.0 

125.  8 

48 

43. 1 

21.0 

08 

97.1 

47.3 

68 

151.0 

73.6 

28     204. 9 

99.9 

88 

258.9 

126.3 

49 

44.0 

21.5 

09 

98.0 

47.8 

69 

151.9 

74.1 

29     205. 8 

100.4 

89 

259.8 

126.7 

50 
51 

44.9 
45.8 

21.9 
22.4' 

10 

98.9 

48.2 

70 

152.8 

74.5 

30     206. 7 

100.8 

90 

260.7 

127.1 

111 

99.8 

48.7 

171 

153.7 

75.0 

231     207.6 

101.3 

291 

261.5 

127.6 

52 

46.7 

22.8 

12 

100.7 

49.1 

72 

154.  6 

75.4 

32     208.5 

101.7 

92 

262.4 

128.0 

53 

47.6 

23.2 

13 

101.6 

49.5 

73 

155.5 

75.8 

33  !  209.4 

102.1 

93 

263.3      128.4  1 

54 

48.5 

23.7 

14 

102.5 

50.0 

74 

156.4 

76.3 

34     210. 3 

102.6 

94 

264.2 

128.9 

55 

49.4 

24.1 

15 

103.4 

50.4 

75     157. 3 

76.7 

35 

211.2 

103.0 

95 

265.1 

129.3 

56 

50.3 

24.5 

16 

104. 3 

50.  9 

76     158. 2 

77.2 

36 

212.1 

103.  5 

96 

266.0 

129.  8 

57 

51.2 

25.0 

17 

105.  2 

51.3 

77 

159.1 

77.6 

37 

213.0 

103.  9 

97 

266.  9     130.  2 

58 

52.1 

25.4 

18 

106.1 

51.7 

78 

160.0 

78.0 

38 

213. 9 

104.  3 

98 

267.  8     130. 6 

59 

53.0 

25.9 

19 

107.0 

52.2 

79 

160.9 

78.5 

39 

214.8 

104.8 

99 

268.7     131.1 

60 

53.9 

26.3 

20 

107.9 

52.6 

80 

161.8 

78.9 

40 

215.7 

105.2 

300 

269.6 

131.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

34°  (116°,  244°,  296° 

)• 

TABLE  ± 

[Page  419    | 

Difference  of  Latitude  and  Departure  for  26°  (154°,  206°,  334). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

270.5 

132.0 

361 

324.  5 

158.  3 

421 

378.4 

184.6 

481 

432.  3 

210.9 

541 

486.2 

237.2 

02 

271.4 

132.4 

62 

325.4 

158.  7 

22 

379.  3 

185.0 

■    82 

433.  2 

211.3 

42 

487.1 

237.  6 

03 

272.3 

132.  8 

63 

326.  3 

159. 1 

23 

380.2 

185.4 

83 

434.1 

211.7 

43 

488.  0 

238.  0 

04 

273.2 

133.  3 

64 

327.  2 

1.59.  6 

24 

381.1 

185.  9 

84 

435.  0 

212.2 

44 

488.9 

238.  5 

05 

274.1 

133.  7 

65 

328.  1 

160.0 

25 

382.0 

186.  3 

85 

435.  9 

2li!6 

45 

489.8 

238.  9 

^06 

275.  0 

1.34. 1 

66 

329.  0 

160.4 

26 

382.  9 

186.7 

86 

436.8 

213.  0 

46 

490.  7 

239.  3 

07 

275.9 

134.  6 

67 

329.  9 

160.9 

27 

383.8 

187.2 

87 

437.7 

213.5 

47 

491.6 

239.  8 

08 

276.8 

135.  0 

68 

330.8 

161.3 

28 

384.7 

187.6 

88 

438.  6 

213.  9 

48 

492.5 

240.2 

09 

277.7 

135.  5 

69 

331.  7 

161.8 

29 

385.6 

188. 1 

89 

4.39.  5 

214.4 

49 

493.4 

240.  7 

10 

278.6 

135.  9 

136.  3 

70 

-37r 

332.  6 

162.2 

30 
431 

386.  5 
387.4 

188.  5 
188.9 

90 
491 

440.4 
441.  3 

214.8 
215.2 

50 

494.3 

241.1 

311 

279.5 

333.5 

162.6 

551 

495.2 

241.  5 

12 

280.4 

136.8 

72 

334.4 

163.1 

32 

388.3 

189.4 

92 

442.2 

215.7 

52 

496.1 

242.0 

13 

281.  3 

137.2 

73 

335.3 

163.5 

33 

389.2 

189.8 

93 

443. 1 

216.1 

53 

497. 0 

242.4 

14 

282.2 

137.  7 

74 

336.2 

164.0 

34 

390.1 

190.3 

94 

444.0 

216.6 

54 

497.9 

242.9 

15 

283.1 

138.1 

75 

337.1 

164.4 

35 

391.0 

190.7 

95 

444.9 

217.0 

55 

498.  8 

243.  3 

16 

284.0 

138.5 

76 

338.0 

164.8 

36 

391.9 

191.1 

96 

445.8 

217.4 

56 

499.7 

243.  7 

17 

284.9 

139.0 

77 

338. 9 

165.3 

37 

392.  8 

191.6 

97 

446.7 

217.9 

57 

500.6 

244.2 

18 

285.8 

139.4 

78 

339.8 

165.7 

38 

393.7 

192.0 

98 

447.6 

218.3 

58 

501.5 

244.6 

19 

286.7 

139.8 

79 

340.7 

166.2 

39 

394,6 

192.4 

99 

448.5 

218.7 

59 

502.4 

245.0 

20 
321 

287.6 
288.  5 

140.3 

80 

341.5 

166.6 

40 
441 

395.5 
396.4 

192.9 

500 

449.4 

219.2 

60 

503.3 
504.2 

245.5 
245.9 

140.7 

381 

342.4 

167. 0 

193. 3 

501 

450.  3 

219.  6 

561 

22 

289.4 

141.2 

82 

343.3 

167.  5 

42 

397.3 

193.8 

02 

451.2 

220. 1 

62 

505.1 

246.  4 

23 

290.  3 

141.6 

83 

344.2 

167.9 

43 

398.2 

194.2 

03 

452.1 

220.5 

63 

506.0 

246.8 

24 

291.2 

142.0 

84 

345. 1 

168.3 

44 

399.1 

194.7 

04 

453.0 

221.0 

64 

506. 9 

247.3 

25 

292.1 

142.5 

85 

346.0 

168.8 

45 

400.0 

195.1 

05 

453.9 

221.4 

65 

507.  8 

247.7 

26 

293.0 

142.9 

86 

346.9 

169.2 

46 

400.9 

195.5 

06 

454.8 

221.8 

•  66 

508.  7 

248. 1 

27 

293.  9 

143.  4 

87 

347.8 

169.7 

47 

401.8 

196.0 

07 

455.7 

222.3 

67 

509.6 

248.6 

28 

294.8 

143.  8 

88 

348.7 

170.1 

48 

402.7 

196.4 

08 

456.6 

222.7 

68 

510.  5 

249.0 

29 

295.  7 

144.2 

89 

349.  6 

170. 5 

49 

403.6 

196.8 

09 

457.5 

223.1 

69 

511.4 

249.4 

30 
331 

296.6 

297.  5 

144.7 
145. 1 

90 
391 

350.  5 

171.0 

50 

451 

404.5 
405.4 

197.3 
197.7 

10 

458.4 

223.6 

70 

512.3 

249.9 

351.4 

171.4 

511 

459.3 

224.0 

571 

513.2 

250.3 

32 

298.4 

145.6 

92 

352.3 

171.8 

52 

406.3 

198.1 

12 

460.2 

224.4 

72 

514.1 

250.8 

33 

299.  3 

146.0 

93 

353.2 

172.3 

53 

407.2 

198.6 

13 

461.1 

224.9 

73 

515. 0 

251.2 

34 

300.,2 

146.4 

94 

354. 1 

172.7 

54 

408. 1 

199.0 

.  14 

462.0 

225.3 

74 

515.9 

251.6 

35 

301.1 

146.9 

95 

355.0 

173.2 

55 

409.0 

199.5 

15 

462.9 

225.8 

75 

516.8 

252.1 

36 

302.0 

147.3 

96 

355.9 

173.6 

56 

409.9 

199.9 

16 

463.8 

226.2 

76 

517.  7 

252.  5 

37 

302.9 

147.7 

97 

356.  8 

174.0 

57 

410.8 

200.3 

17 

464.7 

226.6 

77 

518.6 

252.9 

38 

303.8 

148.2 

98 

357.  7 

174.5 

58 

411.7 

200.8 

18 

465.6 

227.1 

78 

519.5 

253. 4 

39 

304,7 

148.6 

99 

358.6 

174.9 

59 

412.6 

201.2 

19 

466.5 

227.5 

79 

520.4 

253.8 

40 

305.6 
306.5 

149.0 
149.  5 

400 
401 

359.5 

175.4 

60 

413.5 

201.7 
202.1 

20 
521 

467.4 
468.3 

228.0 
228.4 

80 

521.3 

254. 3 

341 

360. 4 

175.8 

461 

414.4 

581 

522.2 

254.7 

42 

307.4 

149.9 

02 

361.3 

176.2 

62 

415.2 

202.5 

22 

469.2 

228.8 

82 

523.1 

255.1 

43 

308.3 

150.4 

03 

362.  2 

176.7 

63 

416.1 

203.0 

23 

470.1 

229.3 

83 

524.0 

255.6 

44 

309.2 

150.  8 

04 

363. 1 

177.1 

64 

417.0 

203.4 

24 

471.0 

229.7 

84 

524.9 

256. 0 

45 

310. 1 

151.  2 

05 

364.0 

177.5 

65 

417.9 

203.8 

25 

471.9 

230. 1 

85 

525.8 

256.  4 

46 

311.0 

151.7 

06 

364.9 

178.0 

66 

418.8 

204.3 

26 

472.8 

230.6 

86 

526.  7 

256.9 

47 

311.9 

152.1 

07 

365.8 

178.4 

67 

419.7 

204.7 

27 

473.7 

231.0 

87 

527. 6 

257.3 

48 

312.  8 

152.  6 

08 

366.7 

178.9 

68 

420.  6 

205.2 

28 

474.6 

231.5 

88 

528.5 

257.8 

49 

313.  7 

153.0 

09 

367.6 

179.  3 

69 

421.5 

205.6 

29 

475.5 

231.9 

89 

529.4 

258.2 

50 

314.6 
315.  5~ 

153.4 

10 

368.5 

179.7 

70 

422.4 

206.0 
206.5 

30 

476.4 

232.  3 

90 

530.3 

258.6 
259. 1 

351 

153.9 

411 

369.4 

180.2 

471 

423.3 

531 

477.3 

232.  8 

591 

531.2 

52 

316.4 

154.3 

12 

370.  3 

180.6 

72 

424.2 

206.9 

32 

478.2 

233.2 

92 

532.1 

259.  5 

53 

317.  3 

154.7 

13 

371.2 

181.1 

73 

425.1 

207.3 

33 

479.1 

233.  6 

93 

533.0 

259.9 

54 

318.2 

155.  2 

14 

372.1 

181.5 

74  I  426.0 

207.8 

34 

480.0 

234.1 

94 

533.9 

260.  4 

55 

319.1 

155.  6 

15 

373.0 

181.9 

75  1  426.9 

208.2 

35 

480.9 

234.5 

95 

534.8 

260.8 

56 

320.  0 

156.1 

16 

373.  9 

182.4 

76 

427.8 

208.7 

36 

481.8 

235.0 

96 

535.7 

261.  3 

57 

320.9 

156.5 

17 

374.  8 

182.8 

77 

428.7 

209.1 

37 

482.7 

235.4 

97 

536.  6 

261.7 

58 

321.8 

156.9 

18 

375.7 

183.2 

78. 

429.6 

209.5 

38 

483.6 

235.8 

98 

537.5 

262.1 

59 

322.  7 

157.4 

19 

376.  6 

183.7 

79 

430.5 

210.0 

39 

484.5 

236.3 

90 

538.4 

262.6 

60 

323.6 

157.8 

20 

377. 5 

184.1 

80 

431.4 

210.4 

40 

485.3 

236.7 

600 

539.3 

263.  0 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

64° 

(116°,  244°,  296°). 

Page  420 

TABLE 

2. 

Difference  of  Latitude  and  Departure. for  27°  (153°,  207 

°,  333° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

54.4 

27.7 

121 

107.8 

54.9 

181      161.3 

82.2 

241 

214.7 

109.4 

2 

1.8 

0.9 

62 

55.2 

28.1 

22     108. 7 

55.  4 

82      162.2 

82.6 

42 

215.6 

109.9 

3 

2.7 

1.4 

63 

56.1 

28.6 

•23 

109.6 

55.8 

83  i  163. 1 

83.1 

43 

216.5 

110.3 

4 

3.6 

1.8 

64 

57.0 

29.1 

24 

110.5 

56.3 

84      163.9 

83.5 

44 

217.4 

110.8 

5 

4.5 

2.3 

65 

57.9 

29.5 

25 

111.4 

56.7 

85      164. 8 

84.0 

45 

218.3 

111.2 

6 

5.3 

2.7 

%S 

58.8 

30.0 

26 

112.3 

57.2 

86     165. 7 

84.4 

46 

219.2 

111.7 

7 

6.2 

3.2 

67 

59.7 

30.4 

27 

113.2 

57.7 

87     166. 6 

84.9 

47 

220.1 

112.1 

8 

7.1 

3.6 

68 

60.6 

30.9 

28  '  114.0 

58.1 

88     167. 5 

85.4 

48 

221.0 

112.6 

9 

8.0 

4.1 

69 

61.5 

31.3 

29     114.9 

58.6 

89  {  168.4 

85.8 

49 

221.9 

113.0 

10 

8.9 

4.5 
5.0 

70 

62.4 

31.8 

30 

115.8 
116.  7 

59.0 
59.5 

90 

169.3 
170.  2 

86.3 

86.7 

50 
251 

222.8 
223.6 

113.5 

11 

9.8 

71 

63.3 

32.2 

131 

191 

114.0 

12 

10.7 

5.4 

72 

64.2 

32.7 

32 

117.6 

59.9 

92     171. 1 

87.2 

52 

224.5 

114.4 

13 

11.6 

5.9 

73 

65.0 

33.1 

33 

118.5 

60.4 

93     172. 0 

87.6 

53 

225.4 

114.9 

14 

12.5 

6.4 

74 

65.9 

33.6 

34 

119.4 

60.8 

94     172.-9 

88.1 

54 

226.3 

115.  3 

15 

13.4 

6.8 

75 

66.8 

34.0 

35 

120.3 

61.3 

95 

173.7 

88.5 

55 

227.2 

115.8 

16 

14.3 

7.3 

76 

67.7 

34.5 

36 

121.2 

61.7 

96 

174.6 

89.0 

56 

228.1 

116.2 

17 

15.1 

7.  7 

77 

68.6 

35.0 

37 

1^2.1 

62.2 

97 

175.5 

89.4 

57 

229.0 

116.7 

18 

16.0 

8.2 

78 

69.5 

35.4 

38 

123.0 

62.7 

98 

176.4 

89.9 

58 

229.9 

117.1 

19 

16.9 

8.6 

79 

70.4 

35.9 

39 

123.8 

63.1 

99 

177.3 

90.3 

59 

230.8 

117.6 

20 

17.8 

9.1 

80 

71.3 

36.3 

40 

124.7 

63.6 

.200     178. 2 

90.8 

60 

231.7 

118.0 

21 

18.7 

9.5 

81 

72.2 

36.8 

141 

1%.6 

64.0 

201     179.1 

91.3 

261 

232.6 

118.5 

22 

19.6 

10.0 

82 

73.1 

37.2 

42 

126.5 

64.5 

02     180.0 

91.7 

62 

233.  4 

118.9 

23 

20.5 

10.4 

83 

74.0 

37.7 

43 

127.4 

64.9 

03     180.9 

92.2 

63 

234.  3 

119.4 

24 

21.4 

10.9 

84 

74.8 

38.1 

44 

128.3 

65.4 

04  j  181.  8 

92.6 

64 

235.2 

119.9 

25 

22.3 

11.3 

85 

75.7 

38.6 

45 

129.2 

65.8 

05  i  182.  7 

93.1 

65 

236.1 

120.3 

26 

23.2 

11.8 

86 

76.6 

39.0 

46 

130.1 

66.3 

06  !  183.5 

93.5 

66 

237.0 

120.8 

27 

24.1 

12.3 

87 

77.5 

39.5 

47 

131.0 

66.7 

07  !  184.4 

94.0 

67 

237.9 

121.2 

28 

24.9 

12.7 

88 

78.4 

40.0 

48 

131.9 

67.2 

08 

1«5.3 

94.4 

68 

238.8 

121.7 

29 

25.8 

13.2 

89 

79.3 

40.4 

49 

132.8 

67.6 

09 

186.2 

94.9 

69 

239.7 

122.1 

30 

26.7 

13.6 

90 

80.2 

40.9 

50 

133.7 

68.1 

10 

187.1 
188.0 

95.3 

70 

240.6 
241. 5 

122.6 

31 

27.6 

14.1 

91 

81.1 

41.3 

151 

134.5 

68.6 

211 

95.8' 

271 

123.0 

32 

28.5 

14.5 

92 

82.0 

41.8 

52 

135.  4 

69.0 

12 

188.9 

96.2 

72 

242.4 

123.5 

33 

29.4 

15.0 

93 

82.9 

42.2 

53 

136.3 

69.5 

13 

189.8 

96.7 

73 

243.2 

123.9 

34 

30.3 

15.4 

94 

83.8 

42.7 

54 

137.2 

69.9 

14 

190.7 

97.2 

74 

244.1 

124.4 

35 

31.2 

15.9 

95 

84.6 

43.1 

55 

138.1 

70.4 

15 

191.6 

97.6 

75 

245.0 

124.8 

36 

32.1 

16.3 

96 

85.5 

43.6 

56 

139.0 

70.8 

16 

192.5 

98.1 

76 

245.'9 

125.3 

37 

33.0 

16.8 

97 

86.4 

44.0 

57 

139.9 

71.3 

17 

193.3 

98.5 

77 

246.8 

125.8 

38 

33.9 

17.3 

98 

87.3 

44.5 

58 

140.8 

71.7 

18 

194.2 

99.0 

78 

247.7 

126.2 

39 

34.7 

17.7 

99 

88.2 

44.9 

59 

141.7 

72.2 

19 

195. 1 

99.4 

79 

248.6 

126.7 

40 

35.6 

18.2 

100 

89.1 

45.4 

60 

142.6 
143.5 

72.6 

20 

196.0 
196.9 

99.9 

80 

249.5 
250.4 

127.1 
127.6 

41 

36.5 

18.6 

101 

90.0 

45.9 

161 

73. 1 

221 

100.3 

281 

42 

37.4 

19.1 

02 

90.9 

46.3 

62 

144.3 

73.5 

22 

197.8 

100.8 

82 

251.3 

128.0 

43 

38.3 

19.5 

03 

91.8 

46.8 

63 

145.2 

74.0 

23 

198.7 

101.2 

83 

252.2 

128.5 

44 

39.2 

20.0 

04 

92.7 

47.2 

64 

146.1 

74.5 

24 

199.6 

101.7 

84 

253.0 

128.9 

45 

40.1 

20.4 

05 

93.6 

47.7 

65 

147.0 

74.9 

25 

200.5 

102.1 

85 

253.9 

129.4 

46 

41.0 

20.9 

06 

94.4 

48.1 

66 

147.9 

75.4 

26 

201.4 

102.6 

86 

254.8 

129.8 

47 

41.9 

21.3 

07 

95.3 

48.6 

67 

148.8 

75.8 

27 

202.3 

103.1 

87 

255.7 

130.3 

48 

42.8 

21.8 

08 

96.2 

49.0 

68 

149.7 

76.3 

28 

203.1 

103.5 

88 

256.6 

130.7 

49 

43.7 

22.2 

09 

97.1 

49.5 

69 

150.6 

76.7 

29     204.0 

104.0 

89 

257.  5 

131.2 

50 

44.6 

22.7 

10 
111 

98.0 

49.9 

70 

151.5 
152. 4 

77.2 
77.6 

30     204.9 

104.4 

90 

258.4 

131.7 

51 

45.4 

23.2 

98.9 

50.4 

171 

231     205.8 

104.9 

291 

259.3 

132.1 

52 

46.3 

23.6 

12 

99.8 

50.8 

72 

153.  3 

78.1 

32     206.7 

105.3 

92 

260.2 

132.6 

53 

47.2 

24.1 

13 

100.7 

51.3 

73 

154.1 

78.5 

33     207.6 

105.8 

93 

261.1 

133.0 

54 

48.1 

24.5 

14 

101.6 

51.8 

74 

155. 0 

79.0 

34     208.5 

106.2 

94 

262.0 

133.5 

55 

49.0 

25.0 

15 

102.5 

52.2 

75 

155. 9 

79.4 

35     209.4 

106.7 

95 

262.8 

133.9 

56 

49.9 

25.4 

16 

103.4 

52.7 

76 

156.8 

79.9 

36     210.3 

107.1 

96 

263.7 

134.4 

57 

50.8 

25.9 

17 

104.2 

53.1 

77 

157.7 

80.4 

37     211.2 

107.6 

97 

264.6 

134.  8 

58 

51.7 

26.3 

18 

105.1 

53.6 

78 

158.6 

80.8 

38  i  212. 1 

108.0 

98 

265.5 

135.3 

59 

52.6 

26.8 

19 

106.0 

54.0 

79 

159.5 

81.3 

39 

213.0 

108.5 

99 

266.4 

135.7 

60 

53.5 

27.2 

20 

106.9 

54.5 

80 

160.4 

81.7 

40 

213.8 

109.0 

300 

267. 3 

136.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

63°  (117°,  243 

°,  297°). 

TABLE  2. 

[Page 

421 

Difference  of  Latitude  and  Departure  for  27°  (153°,  207°,  333°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

268.2 

136.7 

361 

321.7 

163.9 

421 

375. 1 

191.1 

481 

428.6 

218.3 

541 

482.0 

245.6 

02 

269.1 

137.1 

62 

322.5 

164.4 

22 

376.0 

191.6 

82 

429.4 

218.8 

42 

482.9 

246.1 

03 

270.0 

137.  6 

63 

323.4 

164.8 

23 

376.9 

192.0 

83 

430.3 

219.2 

43 

483.8 

246.5 

04 

270.9 

138.  0 

64 

324.3 

165.3 

24 

377.8 

192.5 

84 

431.2 

219.7 

44 

484.7 

247.0 

05 

271.8 

138.  5 

65 

325.2 

165.7 

25 

378.7 

193.0 

85 

432.1 

220.1 

45 

485.6 

247.4 

06 

272.7 

138.9 

66 

326.1 

166.2 

26 

379.6 

193.4 

86 

433.0 

220.6 

46 

486.4 

247.9 

07 

273.5 

139.4 

67 

327.0 

166.6 

27 

380.5 

193.9 

87 

433.9 

221.1 

47 

487.3 

248.4 

08 

274.4 

139.8 

68 

327.9 

167.1 

28 

381.4 

194.3 

88 

434.8 

221.5 

48 

488.2 

248.8 

09 

275.3 

140.3 

69 

328.8 

167.5 

29 

382.2 

194.8 

89 

435.7 

222.0 

49 

489.1 

249.2 

10 
311 

276.2 
277.  1 

140.7 
141.2 

70 

329.7 
330.6 

168.0 

30 
431 

383.1 
384.0 

195.2 

90 

436.6 

222.4 
222.  9 

50 
551 

490.0 

249.7 

371 

168.4 

195.7 

491 

437.5 

490.9 

250.1 

12 

278.0 

141.7 

72 

331.5 

168.9 

32 

384.9 

196.1 

92 

438.3 

223.3 

52 

491.8 

250.6 

13 

278.  9 

142. 1 

73 

332.  3 

169.3 

33 

385.8 

196.6 

93 

439.2 

223.8 

53 

492.7 

251.0 

14 

279.8 

142.6 

74 

333.  2 

169.8 

34 

386.7  j  197.0 

94 

440.1 

224.2 

54 

493.6 

251.5 

15 

280.7 

143.  0 

75 

334.1 

170.3 

35 

387.  6    197. 5 

95 

441.0 

224.7 

55 

494.5 

252.0 

16 

281.6 

143.  5 

76 

335.0 

170.7 

36 

388. 5  ' 197. 9 

96 

441.9 

225.2 

56 

495.4 

252.4 

17 

282.5 

143.9 

77 

335.9 

171.2 

37 

389. 4    198.  4 

97 

442.8 

225.6 

57 

496.3 

252.9 

18 

283.3 

144.4 

78 

336.  8 

171.6 

38 

390.3    198.9 

98 

443.7 

226.1 

58 

497.2 

253.3 

19 

284.2 

144.8 

79 

337.  7 

172.1 

39 

391.2    199.3 

99 

444.6 

226.5 

59 

498.1 

253.8 

20 
321 

285.1 
286.0 

145.3 

80 

338.6 

172.5 
173.0^ 

40 
441 

392.0    199.8 
392.9    200.2 

500 
501 

445.5 
446.  4 

227.0 
227.5 

60 
561 

499.0 
499.8 

254.2 

145.  7 

381 

339.  5 

254.7 

22 

286.9 

146.2 

82 

340.4 

173.4 

42 

393.8    200.7 

02 

447.3 

227.9 

62 

500.7 

255.1 

23 

287.8 

146.6 

83 

341.3 

173. 9 

43 

394.7 

201.1 

03 

448.2 

228.4 

63 

501.6 

255.6 

24 

288.7 

147.1 

84 

342.1 

174.3 

44 

395.6 

201.6 

04 

449.0 

228.8 

64 

502.5 

256.0 

25 

289.6 

147.6 

85 

343.0 

174.8 

45 

396.5 

202.0 

05 

449.9 

229.3 

65 

503.4 

256.5 

26 

290.5 

148.0 

86 

343.  9 

175.2 

46 

397.4 

202.5 

06 

450.  8 

229.8 

66 

504.  3 

257.0 

27 

291.4 

148.5 

87 

344.8 

175.  7 

47 

398.3 

202.9 

07 

451.7 

230.2 

67 

505.2 

257.4 

28 

292.3 

148.9 

88 

345.7 

176.2 

48 

399.2 

203.4 

08 

452.  6 

230.6 

68 

506.1 

257. 9 

29 

293.2 

149.4 

89 

346.6 

176.6 

49 

400.1 

203.8 

09 

453.5 

231.0 

69 

507.0 

258.3 

30 

294.0 
294.9 

149.8 
150.  3 

90 
391 

347. 5 
348.4 

177.1 
177.5 

50 
451 

401.0 
401.8 

204.3 
204.7 

10 
511 

454.4 
455.3 

231.5 

70 

507.9 

258.8 
259.2 

331 

231.9 

571 

508.7 

32 

295.  8 

150.7 

92 

349.  3 

178.0 

52 

402.7 

205.  2 

12 

456.2 

232.4 

72 

509.6 

259.7 

33 

296.7 

151.2 

93 

350.2 

178.4 

53 

403.6 

205.  7 

13 

457.1 

232.9 

73 

510.5 

260.1 

34 

297.6 

151.6 

94 

351.1 

178.9 

54 

404.5 

206.1 

14 

458.0 

233.3 

74 

511.4 

260.6 

35 

298.5 

152.1 

95 

352.  0 

179.3 

55 

405.4 

206.6 

15 

458.8 

233.8 

75 

512.3 

261.1 

36 

299.4 

152.  5 

96 

352.8 

179.8 

56 

406.3 

207.0 

16 

459.7 

234.2 

76 

513.2 

261.5 

37 

300.3 

153.0 

97 

353.  7 

180.2 

57 

407.2 

207.5 

17 

460.6 

234.7 

77 

514.1 

262.0 

38 

301.2 

153.5 

98 

354.6 

180.7 

58 

408. 1 

207.9 

18 

461.5 

235.  2 

78 

515.0 

262.4 

39 

302.1 

153.9 

99 

355.  5 

181.2 

59 

409.0 

208.4 

19 

462.4 

235.7 

79 

515.9 

262.9 

40 
341 

302.9 

154.4 

154.  8 

400 
401 

356.4 
357.3 

181.6 

182.1 

60 
461 

409.9 
410.8 

208.8 
209.3 

20 

521 

463.3 
464.2 

236.1 

80 
581 

516.8 
517.7 

263.4 

303.8 

236.6 

263.8 

42 

304.7 

155.3 

02 

358.2 

182.5 

62 

411.6 

209.  8 

22 

465.1 

237. 0 

82 

518.5 

264.3 

43 

305.6 

155.7 

03 

359.1    183.0 

63 

412.5 

210.2 

23 

466.0 

237.5 

83 

519. 4 

264.7 

44 

306.5 

156.  2 

04 

360.  0    183.  4 

64 

413.4 

210.7 

24 

466.9 

237.9 

84 

520.3 

265.2 

45 

307.4 

156.6 

05 

360.9    183.9 

65 

414.3 

211.1 

25 

467.8 

238. 4 

85 

521.  2 

265.6 

46 

308.3 

157.1 

06 

361.  8  '  184.  3 

66 

415.2 

211.6 

26 

468.7 

238.8 

86 

522.1 

266.0 

47 

309.2 

157. 5 

07 

362. 6  :  184.  8 

67 

416.1 

212.0 

27 

469.5 

239.3 

87 

523.0 

266.5 

48 

310.1 

158.0 

08 

363. 5    185. 2 

68 

417.0 

212.5 

28 

470.4 

239.  7 

88 

523.9 

267.0 

49 

311.0 

158.5 

09 

364.4    185.7 

69 

417.9 

212.9 

29 

471.3 

240.2 

89 

524.8 

267.4 

50 

311.9 

158.9 
159.4 

10 

365.  3  !  186. 1 

70 

418.8 

213.4 

30 
531 

472.2 
473.1 

240.6 

90 

525.7 

267.9 
268.3 

351 

312.7 

411 

366.  2  j  186.  6 

471 

419.7 

213.8 

241.1 

591 

526.6 

52 

313.6 

159.8 

12 

367.1  Il87. 1 

72 

420.6 

214.  3 

32 

474.0 

241.5 

92 

527.5 

268.8 

53 

314.5 

160.3 

13 

368. 0  i  187.  5 

73 

421.4 

214.7 

33 

474.9 

242.0 

93 

528.4 

269.2 

54 

315.4 

160.7 

14 

368.9    188.0 

74 

422.3 

215.2 

34 

475.8 

242.4 

94 

529.3 

269.7 

55 

316.3 

161.2 

15 

369.8     188.4 

75 

423.2 

215.  7 

35 

476.7 

242.9 

95 

530.1 

270.1 

56 

317.2 

161.6 

16 

370.7    188.9 

76 

424.1 

216.1 

36 

477.6 

243.4 

96 

531.0 

270.6 

57 

318.1 

162.1 

17 

371.6    189.3 

77 

425.0 

216.6 

37 

478.4 

243.8 

97 

531.9 

271.1 

58 

319.0 

162.5 

18 

372.4    189.8 

78 

425.9 

217.0 

38 

479.3 

244.3 

98 

532.  8 

271.5 

59 

319.9 

163.0 

19 

373.3    190.2 

79 

426.8 

217.5 

39 

480.2 

244.7 

99 

533.  7 

272.0 

60 

320.8 

163.4 

20 

374.2    190.7 

80 

427.7 

217.9 

40 

481.1 

245.2 

600 

534.6 

272.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     1    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

J3°  (1 

17°,  243°,  297°, 

. 

1    Page  422] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  28°  (152°,  208°,  332° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

i)ep. 

1 

0.9 

0.5 

61 

53.9 

28.6 

121      106.8 

56.8 

181 

159.8 

85.0 

241 

212.8 

113.1 

2 

1.8 

0.9 

62 

54.7 

29.1 

22      107. 7 

57.3 

82 

160.7 

85.4 

42 

213.7 

113.6 

3 

2.6 

1.4 

63 

55.6 

29.6 

23     108.6 

57.7 

83 

161.6 

85.9 

43 

214.6 

114.1 

4 

3.5 

1.9 

64 

56.5 

30.0 

24 

109.  5 

58.2 

84 

162.5 

86.4 

44 

215.  4 

114.6 

5 

4.4 

2.3 

65 

57.4 

30.5 

25 

110.4 

58.7 

85 

163.3 

86.9 

45 

216.3 

115.0 

6 

5.3 

2.8 

66 

58.3 

31.0 

26 

111.  3 

59.2 

m 

164.2 

87.3 

46 

217.2 

115.5 

7 

6.2 

3.3 

^67 

59.2 

31.5 

27 

112.1 

59.6 

87 

165.1 

87.8 

47 

218.1 

116.0 

8 

7.1 

3.8 

•68 

60.0 

31.9 

28 

113.  0 

60.1 

88 

166.0 

88.3 

48 

219.0 

116.4 

9 

7.9 

4.2 

69 

60.9 

32.4 

29 

113.9 

60.6 

89 

166.9 

88.7 

49 

219.9 

116.9 

10 

8.8 

4.7 

70 
71 

61.8 
62.7 

32.9 
33.3 

30 

114.8 

61.0 
61.5 

90 

167.8 

89.2 

50 

220.7 

117.4 
117.8 

11 

9.7 

5.2 

131 

115.7 

191 

168.6 

89.  7 

251 

221.6 

12 

10.6 

5.6 

72 

63.6 

33.8 

32 

116.5 

62.0 

92 

169.5 

90.1 

52 

222.5 

118.3 

13 

11.5 

6.1 

73 

64.5 

34.3 

33 

117.4 

62.4 

93 

170.4 

90.6 

53 

223.4 

118.8 

14 

12.4 

6.6 

74 

65.3 

34.7 

34 

118.  3 

62.9 

94 

171.3 

91.1 

54 

224.3 

119.2 

15 

13.2 

7.0 

75 

66.2 

35.2 

35 

119.2 

63.4 

95 

172.2 

91.5 

55 

225.2 

119.7 

16 

14.1 

7.5 

76 

67.1 

35.7 

36 

120.1 

63.8 

96 

173.1 

92.0 

56 

226.0 

120.2 

17 

15.0 

8.0 

77 

68.0 

36.1 

37 

121.0 

64.3 

97 

173.9 

92.5 

57 

226.9 

120.7 

18 

15.9 

8.5 

78 

68.9 

36.6 

38 

121.8 

64.8 

98 

174.8 

93.0 

58 

227.8 

121.1 

19 

16.8 

8.9 

79 

69.8 

37.1 

39 

122.7 

65.3 

99 

175.7 

93.4 

59 

228.7 

121.6 

20 

17.7 

9.4 

80 

70.6 

37.6 
38.0 

40 
141 

123.  6  - 
124.5 

65.7 

200 

176.6 

93.9 

60 

229.6 
230.4 

122.1 

21 

18.5 

9.9 

81 

71.5 

66.2 

201 

177.5 

94.4 

261 

122.5 

22 

19.4 

10.3 

82 

72.4 

38.5 

42 

125.  4 

66.7 

02 

178.4 

94.8 

62 

231.3 

123.0 

23 

20.3 

10.8 

83 

73.3 

39.0 

43 

126.3 

67.1 

03 

179.2 

95.3 

63 

232.2 

123.5 

24 

21.2 

11.3 

84 

74.2 

39.4 

44 

127.1 

67.6 

04 

180.1 

95.8 

64 

233.1 

123.9 

25 

22.1 

11.7 

85 

75.1 

39.9 

45 

128.0 

68.1 

05 

181.0 

96.2 

()5 

234.0 

124.4 

26 

23.0 

12.2 

86 

75.9 

40.4 

46 

128.9 

68.5 

06 

181.9 

96.7 

66 

234.9 

124.9 

27 

23.8 

12.7 

87 

76.8 

40.8 

47 

129.8 

69.0 

07 

182.8 

97.2 

67 

235.  7 

125.3 

28 

24.7 

13.1 

88 

77.7 

41.3 

48 

130.7 

69.5 

08 

183.7 

97.7 

68 

236.6 

125.8 

29 

25.6 

13.6 

89 

78.6 

41.8 

49 

131.6 

70.0 

09 

184.5 

98.1 

69 

237.5 

126.3 

30 

26.5 

14.1 
14.6 

90 

79.5 

42.3 
42.7 

50 
151 

132.4 

70.4 

10 

185.4 

98.6 
99.1 

70 
271 

238.4 
239.3 

126.8 
127.2 

31 

27.4 

91 

80.3 

133.3 

70.9 

211 

186.3 

32 

28.3 

15.0 

92 

81.2 

43.2 

52 

134.2 

71.4 

12 

187.2 

99.5 

72 

240.2 

127.7 

33 

29.1 

15.5 

93 

82.1 

43.7 

53 

135. 1 

71.8 

13 

188.1 

100.0 

73 

241.0 

128.2 

34 

30.0 

16.0 

94 

83.0 

44.1 

54 

136.0 

72.3 

14 

189.0 

100.5 

74 

241.9 

128.6 

35 

30.9 

16.4 

95 

83.9 

44.6 

55 

136.9 

72.8 

15 

189.8 

100.9 

75 

242.8 

129.1 

36 

31.8 

16.9 

96 

84.8 

4.5.1 

56 

137.7 

73.2 

16 

190.7 

101.4 

76 

243.7 

129.6 

37 

32.7 

17.4 

97 

85.6 

4.5.5 

57 

138.6 

73.7 

17 

191.6 

101.9 

77 

244.6 

130.0 

38 

33.6 

17.8 

98 

86.5 

46.0 

58 

139.5 

74.2 

18 

192.5 

102.3 

78 

245.5 

130.5 

39 

34.4 

18.3 

99 

87.4 

46.5 

59 

140.4 

74.6 

19 

193.4 

102.8 

79 

246.3 

131.0 

40 

35.3 
36. 2 

18.8 
19.  2 

100 

88.3 

46.9 

60 

141.3 
142.2 

75.1 
75.6 

20 

221 

194.2 
195.1 

103.3 
103.8 

80 
281 

247.2 
248.  i 

131.5 

41 

101 

89.2 

47.4 

161 

131.9 

42 

37.1 

19.7 

02 

90.1 

47.9 

62 

143.0 

76.1 

22 

196.0 

104.2 

82 

249.0 

132.4 

43 

38.0 

20.2 

03 

90.9 

48.4 

63 

143.9 

76.5 

23 

196.9 

104.7 

83 

249.9 

132.9 

44 

38.8 

20.7 

04 

91.8 

48.8 

64 

144.8 

77.0 

24 

197.8 

105.2 

84 

250.  8 

133.3 

45 

39.7 

21.1 

05 

92.7 

49.3 

65 

145.  7 

77.  5 

25 

198.7 

105.  6 

85 

251.6 

133.8 

46 

40.6 

21.6 

06 

93.6 

49.8 

66 

146.  6 

77.9 

26 

199.  5 

106. 1 

86 

252.  5 

134.3 

47 

41.5 

22.1 

07 

94.5 

50.2 

67 

147.5 

78.4 

27 

200.4 

106.6 

87 

253.4 

134.7 

48 

42.4 

22.5 

08 

95.4 

50.7 

68 

148.3 

78.9 

28 

201.3 

107.0 

88 

254.3 

135.2 

49 

43.3 

23.0 

09 

96.2 

51.2 

69 

149.2 

79.3 

29 

202.2 

107.  5 

89 

255.2 

135.7 

50 

44.1 

23.5 

10 

97.1 

51.6 

70 

150.1 
151.0 

79.8 
80.3 

30 
231 

203.1 
204.0 

108.0 
108.4 

90 

256.1 
256. 9" 

136. 1 

51 

45.0 

23.9 

111 

98.0 

52.1 

171 

291 

136.  6 

52 

45.9 

24.4 

12 

98.9 

52.6 

72 

151.9 

80.7 

32 

204.8 

108.9 

92 

257.8 

137.1 

53 

46.8 

24.9 

13 

99.8 

53.1 

73 

152.7 

81.2 

33 

205.7 

109.4 

93 

258.7 

137.6 

54 

47.7 

25.4 

14 

100.7 

53.5 

74 

153.  6 

81.7 

34 

206.6 

109.9 

94 

259.6 

138.  0 

55 

48.6 

25.8 

15 

101.5 

54.0 

75 

154.5 

82.2 

35 

207.5 

110.  3 

95 

260.  5 

138. 5 

56 

49.4 

26.3 

16 

102.4 

54.5 

76 

155.4 

82.6 

36 

208.4 

110.8 

9f) 

261.4 

139.  0 

57 

50.  3 

26.8 

17 

103.3 

54.9 

77 

156.  3 

83.1 

37 

209.3 

111.3 

97 

262.  2 

139.  4 

58 

51.  2 

27.2 

18 

104.2 

55.4 

78 

157.2 

83.6 

38 

210.1 

111.7 

98 

263.1 

139.9 

59 

52.1 

27.7 

19 

105.1 

55.9 

79 

158.0 

84.0 

39 

211.0 

112.2 

99 

264.0 

140.4 

60 

53.0 

28.2 

20 

106.0 

56.3 

80 

158.9 

84.5 

40 

211.9 

112.7 

300 

264.9 

140.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

l^t. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

62°  (118°,  242°,  298° 

)• 

TABLE  2. 

[Page  423  | 

Dist. 

Difference  of  Latitude  and  Departure  for  28°  (152°,  208°,  332= 

). 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  ;   Lat. 

Dep. 

Di.st. 

Lat. 

Dep. 

301 

265.7 

141.3 

361 

318.7 

169.5 

421 

371.7 

197.7 

481 

424.7 

225.8 

541 

477.  7 

254.0 

02 

266.6 

141.8 

62 

319.6 

170.0 

22 

372.6 

198.1 

82 

425.  6 

226.3 

42 

478.6 

254.5 

03 

267.5 

142.  3 

63 

320.  5 

170.4 

23 

373. 5 

198.6 

83 

426.5 

226.8 

43 

479.4 

255.  0 

04 

268.4 

142.7 

64 

321.4 

170.9 

24 

374.  3 

199.1 

84 

427.4 

227.3 

44 

480.3 

255.  5 

05 

269.3 

143.  2 

65 

322.2 

171.4 

25 

375.2 

199.5 

85 

428.3 

227.7 

45 

481.1 

255.  9 

06 

270.2 

143.7 

66 

323.1 

171.8 

26 

376.1 

200.0 

86 

429.2 

228.2 

46 

482.0 

256.  4 

07 

271.0 

144.1 

67 

324.0 

172.3 

27 

377.0 

200.  5 

87 

430.1 

228.6 

47 

482.9 

256.9 

08 

271.9 

144.6 

68 

324.9 

172.8 

28 

377.9 

200.9 

88 

430.9 

229.1 

48 

483.8 

257.3 

09 

272.8 

145.1 

69 

325.8 

173.2 

29 

378.8 

201.4 

89 

431.8 

229.6 

49 

484.7 

257.  8 

10 

273.7 
274.6 

145.5 

70 

326.7 

173.7 

30 

379.6 

201.9 

90 

432.6 

230.0 
230.5 

50 

551 

485.6 

258.2 
258.  7 

311 

146.0 

371 

327.5 

174.2 

431 

380.  5 

202.3 

491 

433.5 

486.5 

12 

275.  5 

146.5 

72 

328.4 

174.6 

32 

381.4 

202.8 

92 

434.4 

231.0 

52 

487.4 

259.1 

13 

276.3 

146.9 

73 

329.3 

175.1 

33 

382.3 

203.3 

93 

435.3 

231.4 

53 

488.3 

259.6 

14 

277.2 

147.4 

74  !  330.2 

175.6 

34 

383.2 

203.8 

94 

436.2 

231.9 

54 

489.2 

260.1 

15 

278.1 

147.9 

75 

331. 1 

176.1 

35 

384.1 

204.2 

95 

437.1 

232.4 

55 

490.1 

260.6 

16 

279.0 

148.4 

76 

332.0 

176.5 

36 

384.9 

204.7 

96 

437.9 

232.9 

56 

490.9 

261.0 

17 

279.9 

148.8 

77 

332.8 

177.0 

37 

385.8 

205.2 

97 

438.8 

233.4 

57 

491.8 

261.5 

18 

280.7 

149.3 

78 

333.7 

177.5 

38 

386.7 

205.6 

.  98 

439.7 

233.8 

58 

492.7 

262.0 

19 

281.6 

149.8 

79 

334.6 

177.9 

39 

387.6 

206.1 

99 

440.6 

234.3 

59 

493.5 

262.5 

20 
321 

282.5 

150.2 

80 

335. 5 
336.4 

178.4 

40 

388.5 

206.6 

500 

441.5 

234.7 
235. 2 

60 

494.4 

262.9 

283.4 

150.  7 

381 

178.9 

441 

389.4 

207.  0 

501 

442.3 

561 

495.3 

263.4 

22 

284.3 

151.2 

82 

337.3 

179.3 

42 

390.2 

207.5 

02 

443.2 

235.6 

62 

496.2 

263.8 

23 

285.2 

151.6 

83 

338.1 

179.8 

43 

391.1 

208.0 

03 

444.1 

236.1 

63 

497.1 

264.3 

24 

286.0 

152. 1 

84 

339. 0 

180.3 

44 

392.0 

208.4 

04 

445.0 

236.6 

64 

498.0 

264.7 

25 

286.9 

152.6 

85 

339.9 

180.8 

45 

392.9 

208.9 

05 

445.9 

237.1 

65 

498.9 

265.2 

26 

287.8 

153. 1 

86 

340.8 

181.2 

46 

393.8 

209.4 

06 

446.8 

237.  5 

66 

499.8 

265.7 

27 

288.7 

153.  5 

87 

341.  7 

181.7 

47 

394.6 

209.9 

07 

447.6 

238.0 

67 

500.7 

266.2 

28 

289.6 

154.0 

88 

342.6 

182.2 

48 

395.5 

210.3 

08 

448.5 

238.5 

68 

501.6 

266.6 

29 

290.5 

154.5 

89 

343.4 

182.6 

49 

396.4 

210.8 

09 

449.4 

239.0 

69 

502.4 

267.1 

30 

291.3 

154.9 
155.4 

90 
391 

344.3 

183.1 

50 

397.3 
398.  2" 

211.3 

10 

450.3 

239.4 
239.  9 

70 
571 

503.3 

267.6 
268.0 

331 

292.2 

345.2 

183.6 

451 

211.  7 

511 

451.2 

504.2 

32 

293.1 

155.9 

92 

346.1 

184.0 

52 

399.1 

212.2 

12 

452.1 

240.4 

72 

505.1 

268.5 

33 

294.0 

156.3 

93 

347.0 

184.5 

53 

399.9 

212.7 

13 

452.9 

240.8 

73 

505.9 

269.0 

34 

294.9 

156.8 

94 

347.9 

185.0 

54 

400.8 

213.1 

14 

453.8 

241.3 

74 

506.8 

269.4 

35 

295.8 

157.3 

95 

348.  7 

185.4 

55 

401.7 

213.6 

15 

454.7 

241.8 

75 

507.7 

269.9 

36 

296.6 

157.7 

96 

349.6 

185.9 

56 

402.6 

214.1 

16 

455.6 

242.2 

76 

508.6 

270.4 

37 

297.5 

158.2 

97 

350.5 

186.4 

57 

403.5 

214.6 

17 

456.4 

242.7 

77 

509.4 

270.9 

38 

298.4 

158.7 

98 

351.4 

186.9 

58 

404.4 

215.0 

18 

457.  3 

243.2 

78 

510.3 

271.3 

39 

299.3 

159.  2 

99 

352.3 

187.3 

59 

405.2 

215.5 

19 

458.2 

243.7 

79 

511.2 

271.8 

40 
341 

300.2 
301.0 

159.6 

400 
401 

353. 1 

187.8 

60 

406. 1 
407.0 

216.0 

20 
521 

459.1 
460.0 

244.1 

80 

512.1 
513.0 

272.3 
272.  7 

160.1 

354 . 0 

188.3 

461 

216.4 

244.6 

581 

42 

301.9 

160.6 

02 

354.9 

188.7 

62 

407.9 

216.9 

22 

460.9 

245.  0 

82 

513. 9 

273.2 

43 

302.8 

161.0 

03 

355.8 

189.2 

63 

408.8 

217.4 

23 

461.8 

245.5 

83 

514.8 

273.7 

44 

303.7 

161.5 

04 

356.  7 

189.7 

64 

409.7 

217.8 

24 

462.7 

246.0 

84 

515.7 

274.2 

45 

304.6 

162.0 

05 

357.  6 

190.1 

65 

410.5 

218.3 

25 

463.5 

246.5 

85 

516.5 

274.7 

46 

305.5 

162.4 

06 

358.4 

190.  6 

66 

411.4 

218.8 

26 

464.4 

246.9 

86 

517.4 

275.1 

47 

306.4 

162.9 

07 

359.3 

191.1 

67 

412.3 

219.2 

27 

465.3 

247.4 

87 

518.3 

275.5 

48 

307.2 

163.4 

08 

360.2 

191.5 

68 

413.2 

219.7 

28 

466.2 

247.9 

88 

519.2 

276.0 

49 

308.1 

163.8 

09 

361. 1 

192.0 

69 

414.1 

220.2 

29 

467.1 

248.3 

89 

520.1 

276.5 

50 

309.0 

164.3 

10 
411 

362.0 
362.9 

192.5 
193.  0 

70 
471 

415.0 

415.8 

220.7 

30 
531 

468.0 

248.8 

90 

521. 0 
521.8 

277.0 

351 

309.9 

164.8 

221.1 

468.9 

249.3 

591 

277.4 

52 

310.8 

165.3 

12 

363.7 

193.4 

72 

416.7 

221.6 

32 

469.8 

249.8 

92 

522.6 

277.9 

53 

311.7 

165.7 

13 

364.  6 

193. 9 

73 

417.6 

222.1 

33 

470.7 

250.  2 

93 

523.5 

278.4 

54 

312.5 

166.2 

14 

365.  5 

194.4 

.74 

418.5 

222.5 

34 

471.5 

250.  7 

94 

524.4 

278.8 

55 

313. 4 

166.7 

15 

366.  4 

194.8 

75 

419.4 

223.0 

35 

472.4 

251.1 

95 

525.  3 

279.3 

56 

314.  3 

167.1 

16 

367.3 

195.  3 

76 

420.3 

223.5 

36 

473.3 

251.6 

96 

526.2 

279.8 

57 

315.2 

167.6 

17 

368.  2 

195.8 

77 

421. 1 

223.9 

37 

474.2 

252. 1 

97 

527.1 

280.3 

58 

316.1 

168.1 

18 

369.0 

196.2 

78 

422.0 

224.4 

38 

475.1 

252.6 

98 

528.0 

280.8 

59 

316.9 

168.5 

19 

369.9 

196.7 

79 

422.9 

224.9 

39 

476.0 

253.1 

99 

528.9 

281.3 

60 

317.8 

169.0 

20 

370.8 

197.2 

80 

423.8 

225.3 

40 

476.8 

253.6 

600 

529.8 

281.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

( 

52°  (118°,  242°,  298° 

). 

Page  424] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  29°  (151°,  209°,  331°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

53.4 

29.6 

121 

105.8 

58.7 

181 

158.3 

87.8 

241 

210.8 

116.8 

2 

1.7 

1.0 

62 

54.2 

30.1 

22 

106.7 

59.1 

82 

159.2 

88.2 

42 

211.7 

117.3 

3 

2.6 

1.5 

63 

55.1 

30.5 

23 

107.6 

59.6 

83 

160.1 

88.7 

43 

212.5 

117.8 

4 

3.5 

1.9 

64 

56.0 

31.0 

24 

108.5 

60.1 

84 

160.9 

89.2 

44 

213.4 

118.3 

5 

4.4 

2.4 

65 

56.9 

31.5 

25 

109.3 

60.6 

85 

161.8 

89.7 

45 

214.3 

118.8 

6 

5.2 

2.9 

66 

57.7 

32.0 

26 

110.2 

61.1 

86 

162.7 

90.2 

46 

215.2 

119.3 

7 

6.1 

3.4 

^7 

58.6 

32.5 

27 

111.1 

61.6 

87 

163.6 

90.7 

47 

216.0 

119.7 

8 

.    7.0 

3.9 

68 

59.5 

33.0 

28 

112.0 

62.1 

88 

164.4 

91.1 

48 

216.9 

120.2 

9 

7.9 

4.4 

69 

60.3 

33.5 

29 

112.8 

62.5 

89 

165.3 

91.6 

49 

217.8 

120.7 

10 

8.7 

4.8 

70 

61.2 

33.9 

30 

113.7 

63.0 

90 

166.2 

92.1 

50 

218.7 
"219. 5 

121.2 

11 

9.6 

5.3 

71 

62.1 

34.4 

131 

114.6 

63.5 

191 

167.1 

92.6 

251 

121.7 

12 

10.5 

5.8 

72 

63.0 

34.9 

32 

115.4 

64.0 

92 

167.9 

93.1 

52 

220.4 

122.2 

13 

11.4 

6.3 

73 

63.8 

35.4 

33 

116.3 

64.5 

93 

168.8 

93.6 

53 

221.3 

122.7 

14 

12.2 

6.8 

74 

64.7 

35.9 

34 

117.2 

65.0 

94 

169.7 

94.1 

54 

222.2 

123.1 

15 

.    13.1 

7.3 

75 

65.6 

36.4 

35 

118.1 

65.4 

95 

170.6 

94.5 

55 

223.0 

123.6 

16 

14.0 

7.8 

76 

66.5 

36.8 

36 

118.9 

65.9 

96 

171.4 

95.0 

56 

223.9 

124.1 

17 

14.9 

8.2 

77 

67.3 

37.3 

37 

119.8 

66.4 

97 

172.3 

95.5 

57 

224.8 

124.6 

18 

15.7 

8.7 

78 

68.2 

37.8 

38 

120.7 

66.9 

98 

173.2 

96.0 

58 

225.7 

125.1 

19 

16.6 

9.2 

79 

69.1 

38.3 

39 

121.6 

67.4 

99 

174.0 

96.5 

59 

226.5 

125.6 

20 

17.5 

9.7 

80 

70.0 

38.8 

40 

122.4 

67.9 

200 
201 

174.9 

97.0 

60 

227.4 

126. 1 
126.5 

21 

18.4 

10.2 

81 

70.8 

39.3 

141 

123.3 

68.4 

175.8 

97.4 

261 

228.3 

22 

19.2 

10.7 

82 

71.7 

39.8 

42 

124.2 

68.8 

02 

176.7 

97.9 

62 

229.2 

127.0 

23 

20.1 

11.2 

83 

72.6 

40.2 

43 

125.1 

69.3 

03 

177.5 

98.4 

63 

230.0 

127.5 

24 

21.0 

11.6 

84 

73.5 

40.7 

44 

125.9 

69.8 

04 

178.4 

98.9 

64 

230.9 

128.0 

25 

21.9 

12.1 

85 

74.3 

41.2 

45 

126.8 

70.3 

05 

179.3 

99.4 

65 

331.8 

128.5 

26 

22.7 

12.6 

86 

75.2 

41.7 

46 

127.7 

70.8 

06 

180.2 

99.9 

66 

232.6 

129.0 

27 

23.6 

13.1 

87 

76.1 

42.2 

47 

128.6 

71.3 

07 

181.0 

100.4 

67 

233.  5 

129.4 

28 

'24.5 

13.6 

88 

77.0 

42.7 

48 

129.4 

71.8 

08 

181.9 

100.8 

68 

234.4 

129.9 

29 

25.4 

14.1 

89 

77.8 

43.1 

49 

130.3 

72.2 

09 

182.8 

101.3 

69 

235.3 

130.4 

30 
31 

26.2 

14.5 

90 

78.7 

43.6 

50 

131.2 

72.7 

10 

183.7 

101.8 

70 

236.1 

130.9 

27.1 

15.0 

91 

79.6 

44.1 

151 

132.1 

73.2 

211 

184.5 

102.3 

271 

237.0 

131.4 

32 

28.0 

15.5 

92 

80.5 

44.6 

52 

132.9 

73.7 

12 

185.4 

102.8 

72 

237.9 

131.  9 

33 

28.9 

16.0 

93 

81.3 

45.1 

53 

133.8 

74.2 

13 

186.3 

103.3 

73 

238.8 

132.4 

34 

29.7 

16.5 

94 

82.2 

45.6 

54 

134.7 

74.7 

14 

187.2 

103.7 

74 

239.6 

132.8 

35 

30.6 

17.0 

95 

83.1 

46.1 

55 

135.6 

75.1 

15 

188.0 

104.2 

75 

240.5 

133.  3 

36 

31.5 

17.5 

96 

84.0 

46.5 

56 

136.4 

75.6 

16 

188.9 

104.7 

76 

241.4 

1.33.  8 

37 

32.4 

17.9 

97 

84.8 

47.0 

57 

137.3 

76.1 

17 

189.8 

105.2 

77 

242.3 

134.3 

38 

33.2 

18.4 

98 

85.7 

47.5 

58 

138.2 

76.6 

18 

190.7 

105.7 

78 

243.1 

134.8 

39 

34.1 

18.9 

99 

86.6 

48.0 

59 

139.1 

77.1 

19 

191.5 

106.2 

79 

244.0 

135.  3 

40 

'  35.0 

19.4 

100 

87.5 

48.5 

60 

139.9 
140.8 

77.6 

20 

192.4 

106.7 

80 

244.9 

245.8 

135.7 

41 

35.9 

19.9 

101 

88.3 

49.0 

161 

78.1 

221 

193.3 

107.1 

281 

136.2 

42 

36.7 

20.4 

02 

89.2 

49.5 

62 

141.7 

78.5 

22 

194.2 

107.6 

82 

246.6 

136.  7 

43 

37.6 

20.8 

03 

90.1 

49.9 

63 

142.6 

79.0 

23 

195. 0 

108.1 

83  '  247.5 

137.2 

44 

38.5 

21.3 

04 

91.0 

50.4 

64 

143.4 

79.5 

24 

195.9 

108.6 

84 

248.4 

137.7 

45 

39.4 

21.8 

05 

91.8 

50.9 

65 

144.3 

80.0 

25 

196.8 

109.1 

85 

249.3 

138.2 

46 

40.2 

22.3 

06 

92.7 

51.4 

66 

145.2 

80.5 

26 

197.7 

109.6 

86 

250. 1 

138.7 

47 

41.1 

22.8 

07 

93.6 

51.9 

67 

146.1 

81.0 

27 

198.5 

110.1 

87 

251.0 

139.1 

48 

42.0 

23.3 

08 

94.5 

52.4 

68 

146.9 

81.4 

28 

199.4 

110.5 

88 

251.9 

139.6 

49 

42.9 

23.8 

09 

95.3 

52.8 

69 

147.8 

81.9 

29 

200.3 

111.0 

89 

252.8 

140.1 

50 

43.7 

24.2 

10 

96.2 

53.3 

70 

148.7 

82.4 

30 

201.2 

111.5 

90 

253.6 

140.6 
141.1 

51 

44.6 

24.7 

111 

97.1 

53.8 

171 

149.6 

82.9 

231 

202.0 

112.0 

291 

254.5 

52 

45.5 

25.2 

12 

98.0 

54.3 

72 

150.4 

83.4 

32 

202.9 

112.5 

92 

255.4 

141.6 

53 

46.4 

25.7 

13 

98.8 

54.8 

73 

151.3 

83.9 

33 

203.8 

113.0 

93 

256.3 

142.0 

54 

47.2 

26.2 

14 

99.7 

55.3 

74 

152.2 

84.4 

34 

204.7 

113.4 

94 

257.1 

142.5 

55 

48.1 

26.7 

15 

100.6 

55.8 

75 

153. 1 

84.8 

35 

205. 5 

113.9 

95  1  258.0 

143.0 

56 

49.0 

27.1 

16 

101.5 

56.2 

76 

153.  9 

85.3 

36 

206.4 

114.4 

96  1  258.9 

143.5 

57 

49.9 

27.6 

17 

102.3 

56.7 

77 

154.8 

85.8 

37 

207.3 

114.9 

97 

259.8 

144.0 

58 

50.7 

28.1 

18 

103.2 

57.2 

78 

155.7 

86.3 

38 

208.2 

115.4 

98 

260.6 

144.5 

59 

51.6 

28.6 

19 

104.1 

57.7 

79 

156.6 

86.8 

39 

209.0 

115.9 

99 

261.5 

145.0 

60 

52.5 

29.1 

20 

105.0 

58.2 

80 

157.4 

87.3 

40 

209.9 

116.4 

300 

262.4 

145.  4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

61°  (1 

19°,  241 

°,  299= 

). 

TABLE  2. 

[Page  425 

Difference  of  Latitude  and  Departure  for  29°  (151°,  209°,  331° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

'     Lat. 

Dep. 

Dist. 
481 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

263.2 

145.9 

361 

315.  7 

175.0 

421 

368.2 

204.1 

420.7 

233.2 

541 

473.  2 

262.3 

02 

264.1 

146.4 

62 

316.6 

175.  5 

22 

369.1 

204.6 

82 

421.6 

233.7 

42 

474.0 

262.8 

03 

265.0 

146.9 

63 

317.5 

176.0 

23 

369.9 

205.1 

83 

422.4 

234.2 

43 

474.9 

263.2 

04 

265.9 

147.4 

64 

318.  3 

176.5 

24 

370.8 

205.  6 

84 

423.  3 

234.  6 

44 

475.8 

263.7 

05 

266.7 

147.9 

65 

319.2 

177.0 

25 

371.7 

206.0 

85 

424.2 

235.1 

45 

476.6 

264.2 

06 

267.  6 

148.4 

66 

320.1 

177.4 

26 

372.6 

206.5 

86 

425.0 

235.  6 

46 

477.5 

264.7 

07 

268.5 

148.8 

67 

321.0 

177.9 

27 

373.4 

207.0 

87 

425.9 

236. 1 

47 

478.4 

265.  2 

08 

269.4 

149.3 

68 

321.8 

178.4 

28 

374.3 

207.5 

88 

426.8 

236.6 

48 

479.3 

265.7 

09 

270.2 

149.8 

69 

322.7 

178.9 

29 

375.2 

208.0 

89 

427.  7 

237.1 

49 

480.1 

266.2 

10 
311 

271.1 

150.3 

150.8 

70 

323.6 
324.5 

179.4 

30 

376.1 
376.9 

208.5 

90 

428.5 
429.4 

237.6 

50 

481.0 

266.6 

272.0 

371 

179.9 

431 

209.0 

491 

238.0 

551 

481.9 

267.1 

12 

272.9 

151.3 

72 

325.3 

180.4 

32 

377.8 

209.4 

92 

430.3 

238.5 

52 

482.8 

267.6 

13 

273.7 

151.7 

73 

326.2 

180.8 

33 

378.7 

209.9 

93 

431.2 

2.39.  0 

53 

483.  6 

268.1 

14 

274.6 

152.2 

74 

327.1 

181.3 

34 

379.6 

210.4 

94 

432.0 

239.5 

54 

484.5 

268.6 

15 

275.5 

152.7 

75 

328.0 

181.8 

35     380.4 

210.9 

95 

432.9 

240.0 

55 

485.  4 

269.1 

16 

276.3 

153.  2 

76 

328.8 

182.3 

36     381.3 

211.4 

96 

433.8 

240.  5 

56 

486.3 

269.5 

17 

277.2 

153.  7 

77 

329.7 

182.8 

37 

382.2 

211.9 

97 

434.7 

240.9 

57 

487.1 

270.0 

18 

278.1 

154.2 

78 

230.6 

183.3 

38 

383.1 

212.3 

98 

435.5 

241.4 

58 

488.0 

270.5 

19 

279.0 

154.7 

79 

331.4 

183.7 

39 

383.9  j212.8 

99 

436.4 

241.9 

59 

488.9 

271.0 

20 
321 

279.8 
280.7 

155. 1 

80 

332.3 
333.  2 

184.2 

40 

384.8  1213.3 

500 

437.3 

242.4 

60 

489.8 

271.5 

155.  6 

381 

184.7 

441  1  385.7  1213.8 

501 

438.2 

242.9 

561 

490.6 

272.0 

22 

281.6 

156.1 

82 

334.1 

185.2 

42 

386.6  i214.3 

02 

439.0 

243.  4 

62 

491.5 

272. 5 

23 

282.5 

156. 6 

83 

334.9 

185.7 

43 

387.4    214.8 

03 

439.9 

243.9 

63 

492.4     272.9 

24 

283.  3 

157. 1 

84 

335.  8 

186.2 

44 

388.3    215.3 

04 

440.8 

244.3 

64 

493.2     273.4 

25 

284.2 

157.  6 

85 

336.  7 

186.7 

45 

389.2    215.7 

05 

441.6 

244.8 

65 

494.1  ,  273.9 

26 

285.1 

158.1 

86 

337.  6 

187.1 

46 

390.0    216.2 

06 

442. 5 

245.  3 

66 

495.0 

274.4 

27 

286.0 

158.  5 

87 

338.4 

187.6 

47     390.9    216.7 

07 

443.4 

245.  8 

67 

495.9 

274.9 

28 

286.8 

159.0 

88 

339.  3 

188.1 

48     391. 8 

217.2 

08 

444.3 

246.3 

68 

496.8     275.4 

29 

287.7 

159.  5 

89 

340.2 

188.6 

49     392. 7 

217.7 

09 

445.2 

246.8 

69 

497.7     275.9 

30 

288.6 

160.0 
160.5 

90 

341.1 
341.9 

189.1 

50     393. 5 

218.2 
218.7 

10 
511 

446.1 

247.3 

70 

498.5     276.3 

31 

289.5 

391 

189.6 

451 

394.4 

447.0 

247.8 

571 

499.4 

276.8 

32 

290.3 

161.0 

92 

.342.  8 

190.0 

52 

395.3 

219.1 

12 

447.8 

248.2 

72 

500.3 

277.3 

33 

291.2 

161.4 

93 

343.  7 

190. 5 

53 

396.2 

219.6 

13 

448.6 

248.7 

73 

501.1 

277.8 

34 

292.1 

161.9 

94 

344.  6 

191.0 

54 

397.0 

220.1 

14 

449.5 

249.2 

74 

502.0 

278.3 

35 

293.0 

162.4 

95 

345.  4 

191.5 

55 

397.9 

220.6 

15 

450.4 

249.7 

75 

502.9 

278.8 

36 

293.8 

162.9 

96 

346.  3 

192.0 

56 

398.8 

221.1 

16 

451.3 

250.2 

76 

503.7 

279.2 

37 

294.7 

163.4 

97 

347.2 

192.5 

57 

399.7 

221.6 

17 

452.2 

250.  6 

77 

504.6 

279.7 

38 

295.6 

163.9 

98 

348.1 

193. 0 

58 

400.5 

222.0 

18 

453.1 

251. 1 

78 

505.  5 

280.2 

39 

296.5 

164.4 

99 

348.  9 

193.4 

59 

401.4 

222.5 

19 

253.9 

251.6 

79 

506.4 

280.7 

40 

297.3 

298.2 

164.8 
165.3 

400 
401 

349.8 
350.  7 

193.9 
194.4 

60 
461 

402.3 
403.2 

223.0 

20 

454.8 

252. 1 

80 

507.2 

281.2 

341 

223.5 

521 

455.6 

252.6 

581 

508.1  !  281.7  1 

42 

299.1 

165.8 

02 

351.6 

194.9 

62 

404.0 

224.0 

22 

456.5 

253. 1 

82 

509. 0     282.  2  I 

43 

300.0 

166.3 

03 

352. 4 

195.4 

63 

404.9 

224.5 

23 

457.4 

253.6 

83 

509.9 

282.7 

44 

300.8 

166.8 

04 

353.3 

195.9 

64 

405.8 

225.  0 

24 

458.3  1254.0 

84 

510.7 

283.2 

45 

301.7 

167.3 

05 

354.2 

196.  3 

65 

406.7 

225.  4 

25 

459.1    254.5 

85 

511.6 

283.6 

46 

302.6 

167.7 

06 

355. 1 

196.  8 

66 

407.5 

225.  9 

26 

460.0    255.0 

86 

512.5 

284.1 

47 

303.5 

168.2 

07 

355.  9 

197.3 

67 

408.4 

226.4 

27 

460.9    255.5 

87 

513.4 

284.6 

48 

304.3 

168.7 

08 

356.8 

197.8 

68 

409.3 

226.9 

28 

461.8    256.0 

88 

514.3 

285.0 

49 

305.2 

169.2 

09 

357.7 

198.3 

69 

410.2 

227.4 

29 

462. 6    256. 5 

89 

515.1 

285.  5 

50 

306.1 

169.7 

10 

358.6 
359.4 

198.8 
199.  3 

70 
471 

411.0 
411.9 

227.9 
228.  3 

30 
531 

463.  5  i  256. 9 

90 

516.0 

286.0 

351 

307.0 

170.2 

411 

464.4 

257.4 

591 

516.9 

286.5 

52 

307.8 

170.7 

12 

360.  3 

199.7 

72 

412.8 

228.8 

32 

465.3 

257.9 

92 

517.7 

287.0 

53 

308.7 

171.1 

13 

361.2 

200.2 

73 

413.  7 

229.3 

33 

466.1 

258.4 

93 

518.6 

287.  5 

54 

309.6 

171.6 

14 

362.1 

200.7 

74 

414.  5 

229.8 

34 

467.0 

258.9 

94 

519.5 

288.0 

55 

310.5 

172.1 

15 

362.9  - 

201.2 

75 

415.4 

230.  3 

35 

467.9 

259.4 

95 

520.4 

288.5 

56 

311.  3 

172.6 

16 

363.8  ; 

201.7 

76 

416.3 

230.8 

36 

468.8 

259.9 

96 

521.2 

288.9 

57 

312.2 

173.1 

17 

364.7 

202.2 

77 

417.2 

231.  3 

37 

469.  6 

260.3 

97 

522.1 

289.4 

58 

313.1 

173.6 

18 

365.6 

202.7 

78 

418.0 

231.7 

38 

470.5 

260.8 

98 

523.0 

289.9 

59 

314.0 

174.0 

19 

366.4 

203. 1 

79 

418.9 

232.  2 

39 

471.4 

261.3 

99 

523. 9 

290.4 

60 

314.8 

174.5 

20 

367.3 

i 

203.6 

80 

419.8 

232.7 

40 

472.3 

261.8 

600 

524.8 

290.9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

6 

1°   (119°,  241°,  299°) 

Page  426 

TABLE  2. 

• 

Difference  of  Latitude  and  Departure  for  30°  (150°,  210 

°,  330° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Di.st. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

52.8 

30.5 

121 

104.8 

60.5 

181 

156.8 

90.5 

241 

208.7 

120.5 

2 

1.7 

1.0 

62 

53.  7 

31.0 

22 

105.  7 

61.0 

82 

157. 6 

91.0 

42 

209.6 

121.0 

3 

2.6 

1.5 

63 

54.6 

31.5 

23 

106.5 

61.5 

83 

158. 5 

91.5 

43 

210.4 

121.5 

4 

3.5 

2.0 

64 

55.4 

32.0 

24 

107.4 

62.0 

84 

159. 3 

92.0 

44 

211.3 

122.0 

5 

4.3 

2.5 

65 

56.3 

32.5 

25 

108.  3     62. 5 

85 

160.2 

92.5 

45 

212.2 

122.5 

6 

5.2 

3.0 

66 

57.2 

33.0 

26 

109.1  '.  63.0 

86 

161.1 

93.0 

46 

213.  0 

123.0 

7 

6.1 

3.5 

^7 

58.0 

33.5 

27 

110.0     63.5 

87 

161.9 

93.5 

47 

213.9 

123.5 

8 

6.9 

4.0 

B8 

58.9 

34.0 

28 

110.9  :  64.0 

88 

162. 8 

94.0 

48 

214.8 

124.0 

9 

7.8 

4.5 

69 

59. 8 

34.5 

29 

111.  7  !  64.  5 

89 

163.7 

94.5 

49 

215.  6 

124.5 

10 

8.7 

5.0 

70 

60.6 

35. 0 

30 

112.6     65.0 

90 

164.5 

95.0 

50 

216.  5 

125.0 
125.5 

11 

9.5 

5.5 

71 

61.5 

35.5 

131 

113. 4 

65.  5 

191 

165.4 

95.5 

251 

217.4 

12 

10.4 

6.0 

72 

62.4 

36.0 

32 

114.3 

66.0 

92 

166.3 

96.0 

52 

218.2 

126.0 

13 

11.3 

6.5 

73 

63.2 

36.5 

33 

115.2 

66.5 

93 

167. 1 

96.5 

53 

219.1 

126.5 

14 

12.1 

7.0 

74 

64.1 

37.0 

34  i 

116.0 

67.0 

94 

168.0 

97.0 

54 

220.0 

127.0 

15 

13.0 

7.  5 

75 

65.0 

37.5 

35 

116.9  i  67.5 

95 

168.9 

97.5 

55 

220.8 

127. 5 

16 

13.9 

8.0 

76 

65.8 

38.0 

36 

117.8  i  68.0 

96 

169.7 

98.0 

56 

221.7 

128.0 

17 

14.7 

8.5 

77 

66.7 

38.5 

37 

118.6  i  68.5 

97 

170.6 

98.5 

57 

222.6 

128.5 

18 

15.6 

9.0 

78 

67.5 

39.0 

38 

119.5  :  69.0 

98 

171.  5 

99.0 

58 

223.4 

129.0 

19 

16.5 

9.5 

79 

68.4 

39.5 

39 

120.4  1  69.5 

99 

172.  3 

99.5 

59 

224.3 

129.5 

20 

17.3 

10.0 
10.5 

80 

69.3 
70.1 

40.0 

40 

121.2  '  70.0 
122.1     70.5 

200 

201 

173.2 
174.1 

100.0 
100.  5" 

60 
261 

225.2 

130.0 

21 

18.2 

81 

40.5 

141 

226.0 

130.5 

22 

19.1 

11.0 

82 

71.0 

41.0 

42 

123.0     71.0 

02 

174.9 

101.0 

62 

226.9 

131.0 

23 

19.9 

11.5 

83 

71.9 

41.5 

43 

123.8     71.5 

03 

175.8 

101.5 

63 

227.8 

131.5 

24 

20.8 

12.0 

84 

72.7 

42.0 

44 

124.7 

72.0 

04 

176.7 

102.0 

64 

228.6 

132.0 

25 

21.7 

12.5 

85 

73.6 

42.5 

45 

125.  6 

72.5 

05 

177.5 

102.  5 

65 

229.5 

132.  5 

26 

22.5 

13.0 

86 

74.5 

43.0 

46 

126.4 

73.0 

06 

178.4 

103.0 

66 

230.4 

133.0 

27 

23.4 

13.5 

87 

75.3 

43.5 

47 

127.  3 

73.5 

07 

179.3 

103.5 

67 

231.2 

133.5 

28 

24.2 

14.0 

88 

76.2 

44.0 

48 

128.2 

74.0 

08 

180.1 

104.0 

68 

232. 1 

134.0 

29 

25.1 

14.5 

89 

77.1 

44.5 

49 

129.0 

74.5 

09 

181.0 

104.5 

69 

233.  0 

134.5 

30 

26.0 

15.0 
15.  5 

90 

77.9 

78.8 

45.0 

50 

129.9 
130.8 

75.0 

10 

181.9 

105.0 

70 
271 

233.  8 
234.7 

135.0 
135.5 

31 

26.8 

91 

45.5 

151 

75.  5 

211 

182.7 

105.5 

32 

27.7 

16.0 

92 

79.7 

46.0 

52 

131.6 

76.0 

12 

183.6 

106.0 

72 

233.  6 

136.0 

33 

28.6 

16.5 

93 

80.5 

46.5 

53 

132.5 

76.5 

13 

184.5 

106.  5 

73 

236.4 

136.  5 

34 

29.4 

17.0 

94 

81.4 

47.0 

54 

133.4 

77.0 

14 

185.3 

107.0 

74 

237.3 

137.0 

35 

30.3 

17.5 

95 

82.3 

47.5 

55 

134.2 

77.5 

15 

186.2 

107.5 

75 

238.2 

137.5 

36 

31.2 

18.0 

96 

83.1 

48.0 

56 

135.1 

78.0 

16 

187.1 

108.0 

76 

239.0 

138.0 

37 

32.0 

18.5 

97 

84.0 

48.5 

57 

136. 0 

78.5 

17 

187.9 

108.  5 

77 

239.9 

138.5 

38 

32.9 

19.0 

98 

84.9 

49.0 

58 

136.8 

79.0 

18 

188.8 

109.  0 

78 

240.8 

139.0 

39 

33.8 

19.5 

99 

85.7 

49.5 

59 

137.7 

79.5 

19 

189.7 

109.  5 

79 

241.6 

139.5 

40 
41 

34.6 
35.5 

20.0 
20.5 

100 
101 

86.6 

50.0 
50.5 

60 

138.6 
139.4 

80.0 
80.5 

20 

190.5 
191.4 

110.0 

80 

242.5 
243.4 

140.0 
140.5' 

87.5 

161 

221 

110.5 

281 

42 

36.4 

21.0 

02 

88.3 

51.0 

62 

140.3 

81.0 

22 

192.3 

111.0 

82 

244.2 

141.0 

43 

37.2 

21.5 

03 

89.2 

51.5 

63 

141.2 

81.5 

23 

193.1 

111.5 

83 

245.  1 

141.5 

44 

38.1 

22.0 

04 

90.1 

52.0 

64 

142.0 

82.0 

24 

194.0 

112.0 

84 

246.0 

142.0 

45 

39.0 

22.5 

05 

90.9 

52.5 

65 

142.9 

82.5 

25 

194.9 

112.  5 

85 

246.8 

142.  5 

46 

39.8 

23.0 

06 

91.8 

53.0 

66 

143.8 

83.0 

26 

195.  7 

113.0 

86 

247.7 

143.  0 

47 

40.7 

23.5 

07 

92.7 

53.5 

67 

144.6 

83.5 

27 

196.6 

113.5 

87 

248.  5 

143.5 

48 

41.6 

24.0 

08 

93.5 

54.0 

68 

145.  5 

84.0 

28 

197. 5 

114.0 

88 

249.4 

144.0 

49 

42.4 

24.5 

09 

94.4 

54.5 

69 

146.4  '  84.5 

29 

198.  3 

114.5 

89 

250.  3 

144.5 

50 

43.3 

25.0 

10 
111 

95.3 
96.1 

55. 0 

70 

147.2 

85.0 

30 

199.2 

115.0 
115.5 

90 
291 

251.1 
252.  0 

145.  0 

51 

44.2 

25.5 

55.  5 

171 

148.1 

85.5 

231 

200.1 

145.  5 

52 

45.0 

26.0 

12 

97.0 

56.0 

72 

149.0 

86.0 

32 

200.9 

116.0 

92 

252.9 

146.0 

53 

45.9 

26.5 

13 

97.9 

56.5 

73 

149.8 

86.5 

33 

201.8 

116.5 

93 

253.  7 

146.5 

54 

46.8 

27.0 

14 

98.7 

57.0 

74 

150.  7 

87.0 

34 

202.6 

117.0 

94 

254.  6 

147.0 

55 

47.6 

27.5 

15 

99.6 

57.5 

75 

151.6 

87.5 

35 

203.  5 

117.5 

95 

255.  5 

147.  5 

56 

48.5 

28.0 

10 

100.  5 

58.0 

76 

152.  4 

88.0 

36 

204.4 

118.  0 

96 

256.  3 

148.0 

57 

49.4 

28.5 

17 

101.3 

58.5 

77 

153.  3 

88.  5  •■ 

37 

•  205.  2 

118.-5 

97 

257.  2 

148.  5 

58 

50.2 

29.0 

18 

102.2 

59.0 

78 

154.  2 

89.0 

38 

206.1 

119.0 

98 

2.58.  1 

149.0 

59 

51.1 

29.5 

19 

103. 1 

59.5 

79 

155.  0 

89.5 

39 

207.0 

119.5 

99 

258.9 

149.5 

60 
Dist. 

52.0 

30.0 

20 

103.9 

60.0 

80 

155.  9 

90.0 

40 

207.8 

120.0 

300 

259.8 

150.0 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

80°  (120°,  240°,  300°). 

TABLE  2. 

[Page  427 

Difference  of  Latitude  and  Departure  for  30 

°  (150°,  210°.  .330°). 

Dist. 

Lat, 

Dep. 

Dist.  1     Lat.     1    Dep. 

Dist.        Lat. 

Dep. 

Dist.        Lilt.      :    Dep. 

Dist. 

Lat. 

Dep. 

301 

260.7 

150.5 

361      312. 6 

180.5 

421 

364.6 

210.5 

481     416. 6 

240.5 

541 

468.5 

270.5 

02 

261.5 

151.0 

62  i  313.5 

181.0 

22 

365.  5 

211.0 

82     417. 4 

241.0 

42 

469.4 

271.0 

03 

262.4 

151.5 

63     314.4 

181.5 

23  j  366.3 

211.5 

83     418. 3 

241.5 

43 

470.3 

271.5 

04 

263.  3 

152.0 

64     315. 2 

182.0 

24  j  367.2 

212.0 

84     419.2 

242.0 

44 

471.1 

272. 0 

05 

264. 1 

152.5 

65     316. 1 

182.5 

25  ,  368.  1 

212.5 

85     420. 0 

242.5 

45 

472.0 

272.5 

0() 

265.0 

153.0 

66     317.0 

183.  0 

26     368.9 

213.0 

86     420. 9 

243.  0 

46 

472.9 

273.0 

07 

2(i5. 9 

153. 5 

67     317.8 

183.  5 

27  .  369.  8  1 213. 5 

87     421.8 

243.  5 

47 

473.7 

273.  5 

08 

266.  7 

154.0 

68     318. 7 

184.0 

28  1  370.  7  1 214. 0 

88  :  422.6 

244.0 

48 

474.6 

274.0 

09 

267.6 

154.5 

6!)     319.6 

184.  5 

29     371.5  i214.5 

89  ;  423.5 

244.5 

49 

475.5 

274.  5 

10 

268.5 

155.0 

70     320. 4    185. 0 

30  !  372.4 

215.0 
215.  5 

90 
491 

424.4 

245.0 
245.  5 

50 
551 

476.3 

477.2 

275.0 

311 

269.3 

155.  5 

371      321.  3     185.  5 

431     373.3 

425.2 

275. 5 

12 

270.2 

156.0 

72     322.  2  i  186.  0 

32     374.1  ,216.0 

92 

426.1 

246.0 

52 

478.1 

276.0 

13 

271.1 

156.5 

73     323. 0 

186.5 

33     375.0 

216.  5 

93 

426.9 

246.5 

53 

478.9 

276.  5 

14 

271.9 

157.0 

74     32.3.9 

187.0 

34     375.9 

217.0 

94     427. 8 

247.0 

54 

479.8 

277.0 

15 

272.8 

157.5 

75     324.8 

187.5 

35  I  376.7 

217.5 

95     428. 7 

247.  5 

55 

480.7 

277.5 

16 

273.7 

158.0 

76     325.6 

188.0 

36     377.6 

218.0 

96     429. 6 

248.0 

56 

481.5 

278.0 

17 

274.5  ;  158.5 

77     326.5 

188.5 

37  i  378.5 

218.5 

97     430. 4 

248.  5 

57 

482. 4 

278.5 

18 

275. 4  ! 159. 0 

78     327. 4 

189.0 

38     379.3 

219.0 

98     431. 3 

249.0 

58 

483.3 

279.0 

19 

276. 3    159. 5 

79     328. 2 

189.5 

39  1  380.2 

219.5 

99     432.2 

249.5 

59 

484.1 

279.5 

20 
321 

277.1    160.0 

80     .329. 1 
381      330. 0 

190.0 

40     381. 1 

220.0 

500     433. 0  !  250. 0 

60 
561 

485.0 
485.9 

280.0 

278.  0  1 160. 5 

190. 5 

441     381.9 

220.5 

501     433. 9    250.  5 

280.5 

22 

278.9    161.0 

82     .330. 8 

191.0 

42     382. 8. 

221.  0 

02     434.8 

251.  0 

62 

486.7 

281.0 

23 

279.7     161.5 

83     331.7 

191.5 

43     383. 7 

221.5 

03     435.6 

251.5 

63 

487.6 

281.5 

24 

280.  6  1  162.  0 

84     332. 6 

192.0 

44     384.5  ,222.0 

04  1  436.5 

252.  0 

64 

488.5 

282.0 

25 

281.5  '162.5 

85     333. 4 

192.5 

45     385.4    222.5 

05 

437.4 

252.5 

65 

489.3 

282.5 

26 

282.3 

163.  0 

86     334.3 

193.0 

46     386.3    223.0 

06 

438.2 

253.  0 

66 

490.2 

283.0 

27 

283.2 

163.5 

87     335. 2 

193.5 

47     387.1    223.5 

07 

439.1 

253.5 

67 

491.1 

283.5 

28 

284.1 

164.0 

88     336.0 

194.0 

48     388.  0  1 224. 0 

08  \  440.0 

254.0 

68 

491.9 

284.0 

29 

284.9 

164.5 

89     336. 9 

194.5 

49     388.  9    2^4.  5 

09  '  440.8 

2.54.  5 

69 

492.8 

284.5 

30 
331 

285.8 
286.7 

165.0 

90     337. 8 

195.0 
195.  5 

50     389. 7 
451     390.6 

225.0 

10  i  441. 7 
511  1  442.6 

255.0 

70 
571 

493.6 
494.5 

285.0 
285.  5 

165.  5 

391     338.6 

225.5 

255.5 

32 

287.5 

166.0 

92     339. 5 

196.0 

52     391.5    226.0 

12  i  443.4 

256.0 

72 

495.4 

286.0 

33 

288.4 

166.5 

93     340.4 

196.5 

53     392.3    226.5 

13  ;  444.3 

256.  5 

73 

496.3 

286.5 

34 

289.3 

167.  0 

94     341.2  ;  197.0 

54     393.  2  ' 227.  0 

14     445.2 

257.  0 

74 

497.1 

287.0 

35 

290.1 

167.5 

95     342. 1 

197. 5 

55     394.0    227.5 

15  I  446.0 

257.  5 

75 

497.9 

287.5 

36 

291.0 

168.0 

96  ,  343.0 

198.0 

56     394.9  ,228.0 

.  16  [  446.9 

258.0 

76 

498.8 

288.0 

37 

291.9 

168.5 

97     34.3.8 

198.  5 

57     395.8  '228.5 

17  1  447.8 

258. 5 

77 

499.7 

288.  5 

38 

292.7 

169.0 

98     344.7 

199.0 

58     396.  6    229.  0 

18     448.6  i  2.59.0 

78 

500.5 

289.0 

39 

293.6 

169.5 

99     345.6 

199.  5 

59     397. 5  ;  229.  5 

19     449. 4    259. 5 

79 

501.3 

289.5 

40 
341 

294.5 
295.  3 

170.0 

400     .346. 4 

200.0 
200.5 

60 
461 

398.  4  1  230.  0 

20 
521 

450.  3  j  260. 0 

80 
581 

502.2 
503. 1 

290.0 
290.5 

170.5 

401      347.3 

399.2    230.5 

451. 2  1  260. 5 

42 

296.2 

171.0 

02     348.1    201.0 

62     400. 1  ;  231.  0 

22 

452.1  1261.0 

82 

504. 0 

291.0 

43 

297.1 

171.5 

03     .349.0 

201.  5 

63     401.0    231.5 

23  i  452.  9  1 261.  5 

83 

504.9 

291.5 

44 

297.9 

172.0 

04     349. 9 

202.0 

64     401.8  1232.0 

24 

453.8  1  262.0 

84 

505. 8 

292.0 

45 

298.8 

172.5 

05     350.7 

202.  5 

65  i  402.7    232.5 

25 

454.7  |262.5 

85 

506.6 

292.5 

46 

299.7 

173.0 

06     351. 6 

203.  0 

66     403.6    233.0 

26 

455.5    263.0 

86 

507.5 

293.0 

47 

300.  5 

173.5 

07     352.5 

203.  5 

67     404.4    2.33.5 

27 

456.4 

263.5 

87 

508.4 

293.  5 

48 

301.4 

174.0 

08     353.3  i  204.0 

68     405. 3    234. 0 

28 

457.3 

264.0 

88 

509.2 

294.0 

49 

302.3 

174.  5 

09     354.  2  !  204. 5 

69     406.2    234.5 

29 

458.1 

264.5 

89 

510.1 

294.5 

50 
351 

303.  1 
"304.  0 

175.0 

10     355. 1 

205.0 
205.  5 

70     407.0 
471     407. 9 

235.  0 

30  i  459.0 

265.0 

90 

591 

511.0 
511.8 

295.0 

175.  5 

411      355.9 

235.  5 

531  j  459.9 

265.5 

295.5 

52 

304.  8 

176.0 

12     356.8  1206.0 

72     408.8    236.01 

32  '  460.7    266.0 

92 

512.7 

296.0 

53 

305.7     176.51 

13     357.7  J206.5 

73     409.6 

236.5 

33     461.6    266.5 

93 

513.6 

296.5 

54 

306.  6 

177.0 

14     358.5    207.0 

74     410.5 

237. 0 

34 

462.5    267.0 

94 

514.4 

297.0 

55 

307.4 

177.5 

15     359.4    207.5 

75     411.4 

237.5 

35 

463.  3  ;  267.  5 

95 

515.3 

297.5 

5(3 

308.  3 

178.0 

16     360.3    208.0 

76     412.2 

238.0 

36 

464.  2  1  268. 0 

96 

516.2 

298.0 

57 

309.2 

178.5 

17     361.1  I-208.5 

77     413.1 

238.5 

37 

465.1  1268.5 

97 

517.0 

298.5 

58 

310.0 

179.0 

18     .362.0 

209.0 

78     414.0 

239.0 

38 

465.9 

269.0 

98 

517.9 

299.0 

59 

310.9 

179.5 

19  i  362.9 

209.5 

79  !  414.8 

239.5 

39 

466.8 

269.5 

99 

518.8 

299.5 

60 

311.  8 

180. 0' 

20  1  363.7 

i 

210.0 

80  j  415.  7 

240.0 

40 

467.7 

270.0 

600 

519.6 

300.0 

Dist. 

Dep. 

Lat. 

Dist.  j     Dep.         Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

6 

0°  (120°,  240°,  300° 

). 

Page  428 

TABLE  2. 

Difference  of  latitude  and  Departure  for  31°  (149°,  211°,  329° 

). 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.9 

0.5 

61 

52.3 

31.4 

121 

103.7 

62.3 

181 

155.1 

93.2 

241 

206.6 

124.1 

2 

1.7 

1.0 

62 

53.1 

31.9 

22 

104.6 

62.8 

82 

156.  0 

93.7 

42 

207.4 

124.6 

3 

2.6 

1.5 

63 

54  0 

32.4 

23 

105.4 

63.3 

83 

156.9 

94.3 

43 

208.3 

125.2 

4 

3.4 

2.1 

64 

54.9 

33.0 

21 

106.3 

63.9 

84 

157.  7 

94.8 

44 

209.1 

125.7 

5 

4.3 

2.6 

65 

55.7 

33.5 

25 

107.1 

64.4 

85 

158.6 

95.3 

45 

210.0 

126.2 

6 

5.1 

3.1 

^ 

56.6 

34.0 

26 

108.0 

64.9 

86 

159.4 

95.8 

46 

210.9 

126.7 

7 

6.0 

3.6 

57.4 

34.5 

27      108. 9 

65.4 

87 

160.3 

96.3 

47 

211.7 

127.2 

8 

6.9 

4.1 

68 

58.3 

35.0 

28     109.7 

65.9 

88 

161.1 

96.8 

48 

212.6 

127.7 

9 

7.7 

4.6 

69 

59.1 

35.5 

29 

110.6 

66.4 

89 

162.0 

97.3 

49 

213.4 

128.2 

10 

8.6 

5.2 

70 
71 

60.0 
60.9 

36.1 

30 

111.4 

112;  3 

67.0 

90 

162.9 

97.9 

50 

214.3 

128.8 
129.3 

11 

9.4 

5.  7 

36.6 

131 

67.5 

191 

163.7 

98.4 

251 

215.1 

12 

10.3 

6.2 

72 

61.7 

37.1 

32 

118:1 

68.0 

92 

164.6 

98.9 

52 

216.  0 

129.8 

13 

11.1 

6.7 

73 

62.6 

37.6 

33 

114.0 

68.5 

93 

165.4 

99.4 

53 

216.9 

130.  3 

14 

12.0 

7.2 

74 

63.4 

38.1 

34 

114.9 

69.0 

94 

166.3 

99.9 

54 

217.7 

130.8 

15 

12.9 

7.  7 

75 

64.3 

38.6 

35 

115.7 

69.5 

95 

167.1 

100.4 

55 

218.6 

131.3 

16 

13.7 

8.2 

76 

65.1 

39.1 

36 

116.6 

70.0 

96 

168.0 

100.9 

56 

219.4 

131.8 

17 

14.6 

8.8 

77 

66.0 

39.7 

37 

117.4 

70.6 

97 

168.9 

101.5 

57 

220.3 

132.4 

18 

15.4 

9.3 

78 

66.9 

40.2 

38 

118.3 

71.1 

98 

169.7 

102.0 

58 

221.1 

132.9 

19 

16.3 

9.8 

79 

67.7 

40.7 

39     119.1 

71.6 

99 

170.6 

102.5 

59 

222.0 

133.4 

20 

17.1 

10.3 
10.8 

80 
81 

68.6 
69.4 

41.2 

40 

120.0 
120.9 

72.1 

200 

171.4 

103.0 

60 
261 

222.9 
223.> 

133.  9 
134.4 

21 

18.0 

41.7 

141 

72.6 

201 

172.3     103.5 

22 

18.9 

11.3 

82 

70.3 

42.2 

42     121. 7 

73.1 

02 

173. 1     104.  0 

62 

224.6 

134.  9 

23 

19.7 

11.8 

83 

71.1 

42.7 

43     122. 6 

73.7 

03 

174. 0    104. 6 

63 

225.4 

135.5 

24 

20.6 

12.4 

84 

72.0 

43.3 

44      123.4 

74.2 

04 

174.9  !  105.1 

64 

22H.  3 

136.  0 

25 

21.4 

12.9 

85 

72.9 

43.8 

45 

124.3 

74.7 

05 

175.7 

105. 6 

65 

227.1 

136.5 

26 

22.3 

13.4 

86 

73.7 

44.3 

46 

125.1 

75.2 

06 

176.6 

-106. 1 

66 

228.0 

137.0 

27 

23.1 

13.9 

87 

74.6 

44.8 

47 

126.0 

75.7 

07 

177.4 

106.  6 

67 

228.9 

137.5 

28 

24.0 

14.4 

88 

75.4 

45.3 

48  I  126.9 

76.2 

08 

178.3     107.1 

68 

229.7 

138.0 

29 

24.9 

14.9 

89 

76.3 

45.8 

49     127.7 

76.7 

09 

179.1     107.6 

69 

230.6 

138.5 

30 

25.7 

15.5 
16.0 

90 

.    77.1 

46.4 
46.9 

50  '  128.6 
151  ;   129.4 

77.3 

10 

180.0  !l08.2 
180.'9     108.7 

70 
271 

231.4 

139.1 

31 

26.6 

91 

78.0 

77.8 

211 

232.3 

139.6 

32 

27.4 

16.5 

92 

78.9 

47.4 

52  1  130.3 

78.3 

12 

181.7 

lo;-^.  2 

72 

233. 1 

140.1 

33 

28.3 

17.0 

93 

79.7 

47.9 

53  :  131. 1 

78.8 

13 

182.6 

109.7 

73 

234. 0 

140.6 

34 

29.1 

17.5 

94 

80.6 

48.4 

54     132.0 

79.3 

14 

183.  4 

110.2 

74 

234.  9 

141.1 

35 

30.0 

18.0 

95 

81.4 

48.9 

55  i  132.9 

79.8 

15 

184.3 

110.7 

75 

235.7 

141.6 

36 

30.9 

18.5 

96 

82.3 

49.4 

56 

133.  7 

80.3 

16 

185.1 

111.2 

76 

236.6 

142.2 

37 

31.7 

19.1 

97 

83.1 

50.0 

57 

134.6 

80.9 

17 

186.0 

111.8 

77 

237.  4 

142.7 

38 

32.6 

19.  6 

98 

84.0 

50.  5 

58 

135.4 

81.4 

18 

186.9 

112.3 

78 

238.3 

143.2 

39 

33.4 

20.1 

99 

84.9 

51.0 

59 

136.3 

81.9 

19 

187.7' 

112.8 

79 

239.1 

143.  7 

40 

34.3 

20.6 
21.  i" 

100 
101 

85.7 

51.5 

60 

137.1 

82.4 
82. 9~ 

20 
221 

188.6 

113.  3 

80 

240.0 

144.2 

41 

35.1 

86.6 

52.0 

161 

138.0 

"189.  4 

113.  8 

281 

240.9 

144.7 

42 

36.0 

21.6 

02 

87.4 

52.5 

62 

138.9 

83.4 

22 

190.3 

114.3 

82 

241.7 

145.2 

43 

36.9 

22.1 

03 

88.3 

53.0 

63 

139.7 

84.0 

23 

191.1 

114.9 

83 

242.6 

145.8 

44 

37.7 

22.7 

04 

89.1 

53.6 

64 

140.6 

84.5 

24 

192.0 

115.4 

84 

243.4 

146.3 

45 

38.6 

23.2 

05 

90.0 

54.1 

65 

141.4 

85.0 

25 

192.9 

115.9 

85 

244.3 

146.8 

46 

39.4 

23.7 

06 

90.9 

54.6 

66 

142.3 

85.5 

26 

193.7 

116.4 

86 

245.1 

147.3 

47 

40.3 

24.2 

07 

91.7 

55.1 

67 

143.1 

86.0 

27 

194.6 

116.9 

87 

246.0 

147.8 

43 

41.1 

24.7 

08 

92.6 

55.6 

68 

144.0 

86.5 

28 

195.4 

117.4 

88- 

246.9 

148.3 

49 

42.0 

25.2 

09 

93.4 

56.1 

69 

144.9 

87.0 

29 

196.3 

117.9 

89 

247.7 

148.8 

50 

42.9 

25.8 

10 

94.3 

56.7 

70 

145.7 
146.6 

87.6 

30 

197.1 
198.0 

118.5 

90 
291 

248.6 

149.4 

51 

43.7 

26.3 

111 

95.1 

57.2 

171 

88.1 

231 

119.0 

249.4 

149.9 

52 

44.6 

26.8 

12 

96.0 

57.7 

72 

147.4 

88.6 

32 

198.9 

119.5 

92 

250.3 

150.  4 

53 

45.4 

27.3 

13 

96.9 

58.2 

73 

148.3 

89.1 

33 

199.7 

120.0 

93 

251.2 

150.9 

54 

46.3 

27.8 

14 

97.7 

58.7 

74 

149.1 

89.6 

34 

200.6 

120.5 

94 

252.0 

151.4 

55 

47.1 

28.3 

15 

98.6 

59.2 

75 

150.0 

90.1 

35 

201.4 

121.0 

95 

252. 9 

151.9 

56 

48.0 

28.8 

16 

99.4 

59.7 

76 

150. 9 

90.6 

36 

202.3 

121.5 

96 

253.7 

152.5 

57 

48.9 

29.4 

17 

100.3 

60.3 

77  '-151.7 

91.2 

37 

203. 1 

122.1 

97 

254.6 

153.0 

58 

49.7 

29.9 

18 

101.1 

60.8 

78      152.6 

91.7 

38 

204.0 

122.6 

98 

255.4 

153.5 

59 

50.6 

30.4 

19 

102.0 

61.3 

79     153. 4 

92.2 

39 

204.9 

123.1 

99 

256.3 

154.0 

60 

51.4 

30.9 

20 

102.9 

61.8 

80 

154.3 

92.7 

40 

205.7 

123.6 

300 

257. 1 

154.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

39°  (121°,  239 

°,.  301° 

). 

^■- 

TABLE  2. 

[Page  429 

Difference  of  Latitude  and  Departure  for  31°  (149°,  211°,  329' 

')• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.         Dep. 

Dist. 

Lat. 

Dep. 

301 

258.0 

155.0 

361 

309.4 

185.9 

421 

360.  9 

216.8 

481 

412.3    247.7 

541 

463.7 

278.6 

02 

258.9 

155.5 

62 

310.3 

186.4 

22 

361.7 

217.3 

82 

413.2    248.2 

42 

464.6 

279.1 

03 

259.  7 

156.1 

63 

311.2 

187.0 

23 

362.6 

217.  9 

83 

414.0  1248.8 

43 

465.4 

279.7 

04 

260.6 

156.6 

64 

312.0 

187  5 

24 

363.4 

218.4 

84 

414.9  1249.3 

44 

466.3 

280.2 

05 

261.4 

157.1 

65 

312.9 

188.0 

25 

364.3 

218.9 

85 

415.7    249.8 

45 

467.2 

280.7 

06 

262.3 

157.6 

66 

313.7 

188.5 

26 

365.2 

219.4 

86 

416.6 

250.  3 

46 

468.0 

281.2 

07 

263.2 

158.1 

67 

314.6 

189.0 

27 

366.0 

219.9 

87 

417.4 

250.  8 

47 

468.9 

281.7 

08 

264.0 

158.  6 

68 

315.4 

189.5 

28 

366.9 

220.4 

88 

418.3    251.3 

48 

469.7 

282.3 

09 

264.9 

159.2 

69 

316.  3 

190.1 

29 

367.7 

221.0 

89 

419.2  '251.9 

49 

470.6 

282.8 

10 
311 

265.  7 
266.6 

159.7 

70 

317.2 

190.6 

30 
431 

368.6 
369.4 

221.5 

90 

420.0  1252.4 
420.9  ,252.9 

50 
551 

471.4 
472.3 

2B3.3 

160.2 

371 

318.  0 

191.1 

222.0 

491 

283.8 

12 

267.4 

160.7 

72 

318.9 

191.6 

32 

370.  3 

222.5 

92 

421. 7  ! 253. 4 

52 

473.2 

284.3 

13 

268.  3 

161.2 

73 

319.7 

192.1 

33 

371.2 

223.0 

93 

422.  6  1  253. 9 

53 

474.0 

284.8 

14 

269.2 

161.7 

74 

320.6 

192.6 

34 

372.  0 

223.5 

94 

423.4 

254.  4 

54 

474.9 

285.  3 

15 

270.  0 

162.2 

75 

321.4 

193.1 

35 

372.9 

224.0 

95 

424.  3 

254.  9 

55 

475.7 

285.8 

16 

270.9 

162.8 

76 

322.3 

193.  7 

36 

373.  7 

224.6 

96 

425.  2 

255.  5 

56 

476.6 

286.4 

17 

271.7 

163.3 

77 

323.2 

194.2 

37 

374.6 

225.1 

97 

426.0 

256.  0 

57 

477.4 

286.9 

18 

272.6 

163.8 

78 

324.0 

194.7 

38 

375.  4 

225.6 

98 

426.9 

256.5 

58 

478.3 

287.4 

19 

273.4 

164.3 

79 

324.9 

195.2 

39 

376.  3 

226.1 

99 

427.7 

257.  0 

59 

479.2 

287.9 

20 
321 

274.3 
275.  2~ 

164.8 

80 

325.7 

195.7 

40 
441 

377.2 
378.  0 

226.6 

500 

428.6 

257.5 

60 

480.  0  i  288.  4  | 

165. 3 

381 

326.  6 

196.2 

227.1 

501 

429.4 

258.0 

561 

480.9 

288.9 

22 

276.0 

165.8 

82 

327.4 

196.7 

42 

378.9 

227.7 

02 

430.3 

258.6 

62 

481.7 

289.5 

23 

276.9 

166.4 

83 

328.3 

197.3 

43 

379.7 

228.2 

03 

431.2 

259.1 

63 

482.6 

290.0 

24 

277.7 

166.9 

84 

329.2 

197.8 

44 

380.6 

228.7 

04 

432.0 

259. 6 

64 

483.4 

290.5 

25 

278.6 

167.4 

85 

330.0 

198.3 

45 

381.4 

229.2 

05 

432.  9 

260.1 

65 

484.3  1  291.0 

26 

279.4 

167.9 

86 

3S0.9 

198.8 

46 

382.  3 

229.7 

06 

433.7 

260.6 

66 

485.2     291.5 

27 

280.  3 

168.4 

87 

331.7 

199.3 

47 

383.2 

230.2 

07 

434.6 

261.1 

67 

486.0  i  292.0 

28 

281.2 

168.9 

88 

332.  6 

199.8 

48 

384.0 

230.7 

08 

435.4 

261.6 

68 

486.9  i  292.5 

29 

282.0 

169.5 

89 

333.4 

200.4 

49 

384.  9 

231.3 

09 

436.  3 

262.2 

69 

487.7  (  293.1 

30 

282  9 

170.0 
"170.  5 

90 
391 

334.3 
335.2 

200.9 

50 

385.7 

231.8 

.10 

437.2 

262.7 

70 

488.6  '  293.6 

331 

283.7 

201.4 

451 

386.6 

232.3 

511 

438.0 

263.  2 

571 

489.4     294.1 

32 

284.6 

171.0 

92 

336.0 

201.9 

52 

387.4 

232.8 

12 

438.9 

263.7 

72 

490.3     294.6 

33 

285.4 

171.5 

93 

336.9 

202.4 

53 

388.3 

233.  3 

13 

439.7 

264.2 

73 

491. 2  1  295. 1 

34 

286.3 

172.0 

94 

337.7 

202.9 

54  1  389.2 

233.8 

14 

440.6 

264.7 

74 

492. 0     295. 6 

35 

287.2 

172.5 

95 

338.6 

203.4 

55  1  390.0 

234.3 

15 

441.4 

265.2 

75 

492.9 

296.1 

36 

288.0 

173.1 

96 

339. 4 

204.0 

56  1  390.9 

234.  9 

16 

442.3 

265.8 

76 

493.7 

296.7 

37 

288.9 

173.6 

97 

340.3 

204.5 

57     391. 7 

235.4 

17 

443.  2 

266.3 

77 

494.6 

297.2 

38 

289.7 

174.1 

98 

341.2 

205.0 

58     392. 6 

235. 9 

18 

444.0 

266.8 

78 

495.4 

297.7 

39 

290.6 

174.6 

99 

342.0 

205. 5 

59     393. 4 

236.4 

19 

444.9 

267.  3 

79 

496.3 

298.2 

40 

291.4 

175.1 

400 

342.9 

206.0 

60     394. 3 

236.9 
237. 4 

20 
521 

445.  7 

267.8 

80 

497.2 

298.7 
299.2 

341 

292.3 

175.6 

.401 

343.7 

206.5 

461     395. 2 

446.6 

268.3 

581 

498.0 

42 

293.2 

176.1 

02 

344. 6 

207.0 

62 

396.0 

238.0 

22 

447.4 

268.9 

82 

498.9 

299.8 

43 

294.0 

176.7 

03 

345.4 

207.6 

63 

396.9 

238.5 

23 

448.3 

269.4 

83 

499.7 

300.3 

44 

294.9 

177.2 

04 

346.  3 

208.1 

64 

397.7 

239.0 

24 

449.2 

269.9 

84 

500.6 

300.8 

45 

295.7 

177.7 

05 

347.2 

208.6 

65 

398.6 

239.  5 

25 

450.  0 

270. 4 

85 

501.4 

301.3 

46 

296.6 

178.2 

06 

348.0 

209.1 

66     399.4 

240.0 

26 

450.9    270.9 

86 

502.3 

301.8 

47 

297.4 

178.7 

07 

348.9 

209.6 

67     400.3 

240.5 

27 

451.7  1271.4 

87 

503. 2 

302.3 

48 

298.3 

179. 2 

08 

349.7 

210.1 

68  :  401.2 

241.0 

28 

452.6  i271.9 

88 

504.0 

302.8 

49 

299.2 

179.8 

09 

350.  6 

210.7 

69     402.0 

241.5 

29 

453.  4 

272.4 

89 

504.9 

303.3 

50 

300.0 

180.3 

10 

351. 4 
352.3 

211.2 
211.7 

70     402.9 
471     403!  7 

242.1 
242.  6 

30 
531 

454.3 

273.0 

90 
591 

505.7 

303.9 
304.  4 

351 

300.9 

180.8 

411 

455.  2 

273.5 

506.6 

52 

301.7 

181.3 

12 

353.2 

212.2 

72     404.6 

243.1 

32 

456.  0 

274.0 

92 

507.4 

304.9 

53 

302.6 

181.8 

13 

354.0 

212.7 

73  '  405.4 

243.6 

33 

456.9 

274.5 

93 

508.3 

305.  4 

54 

303.4 

182.3 

14 

354.9 

213.  2 

74  ,  406.3 

244.1 

34 

457.  7 

275. 0 

94 

509.2 

305.  9 

55 

304..3 

182.8 

15 

355.7 

213.7 

75 

407.2 

244.6 

35 

458.  6 

275.  5 

95 

510.0 

306.4 

56 

305.2 

183.4 

16 

356.6 

214.3 

76 

408.0 

245.2 

36 

459.  4 

276.1 

96 

510.9 

307.0 

57 

306.0 

183.  9 

17 

357.  4 

214.8 

77 

408.9 

245.7 

37 

460.  3 

276.6 

97 

511.7 

307. 5 

58 

306.9 

184.4 

18 

358.  3 

215.  3 

78     409. 7 

246.2 

38 

461.2 

277.1 

98 

512.6 

308.0 

59 

307.7 

184.9 

19 

359.2 

215.8 

79 

410.6 

246.7 

39  1 

462.0 

277.6 

99 

513. 4 

308.5 

60 

■ 

308.6 

185.4 

20 

360.0 

216.  3 

80 

411.4 

247.2 

40 

462.9 

278.1 

600 

514.3 

309.0 

Dist. 

Dep.     ! 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

K 

9°  (121°,  239°,  301° 

). 

Page  430 

TABLE  .2.    . 

Difference  of  Latitude  and 

Departure  for  32°  (148°,  212°,  328° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     !   Dep. 

Dist.  i 

Lat. 

Dep. 

1 

0.8 

0.5 

61 

51.7 

32.3 

121 

102.6 

64.1 

181 

153.5      95.9 

241 

204.4 

127.7 

2 

1.7 

1.1 

62 

52.6 

32.9 

22 

103.5 

64.7 

82 

154.3 

96.4 

42 

205.2 

128.2 

3 

2.5 

1.6 

63 

53. 4 

33.4 

23 

104.3 

65.2 

83 

155.2 

97.0 

43 

206. 1 

128.  8 

4 

3.4 

2.1 

64 

54.3 

33.9 

24 

105.2 

65.7 

84 

156.  0 

97.5 

44 

206.9 

129.3 

5 

4.2 

2.6 

^ 

55.1 

34.4 

25 

106.0 

66.2 

85 

156.9 

98.0 

45 

207.8 

129.8 

6 

5.1 

3.2 

66 

56.0 

35.0 

26 

106.  9 

66.8 

86 

157.  7 

98.6 

46 

208.6 

130.4 

7 

5.9 

3.7 

67 

56.8 

35.5 

27 

107.7 

67.3 

87 

158.6 

99.1 

47 

209.5 

130.9 

8 

6.8 

4.2 

68 

57.7 

36.0 

28 

108.6 

67.8 

88 

159.  4 

99.6 

48 

210.  3 

131.4 

9 

.     7.6 

4.8 

69 

58.5 

36.6 

29 

109.4 

68.4 

89 

160.  3 

100.2 

49 

211.2 

131.  9 

10 

8.5 

5.3 

70 

59.4 
60.2 

37.1 

30 

110.2 

68.9 

90 

161.1 
162.  0 

100.7 
101:2 

50 

212.0 
212.9 

132.5 

11 

9.3 

5.8 

71 

37.6 

131 

111.1 

69.4 

191 

251 

133.0 

12 

10.2 

6.4 

72 

61.1 

38.2 

32 

111.9 

69.9 

92 

162.8 

101.7 

52 

213.  7 

133.  5 

13 

11.0 

6.9 

73 

61.9 

38.7 

33 

112.8 

70.5 

93 

163.7 

102.3 

53 

214.  6 

134.  1 

14 

11.9 

7.4 

74 

62.8 

39.2 

34 

113.6 

71.0 

94 

164.5 

102.8 

54 

215.4 

134.  6 

15 

12.7 

7.9 

75 

63.6 

39.7 

35 

114.5 

71.5 

95 

165. 4 

103.  3 

55 

216.  3 

135. 1 

16 

13.6 

8.5 

76 

64.5 

40.3 

36 

115.3 

72.1 

96 

166.2 

103.  9 

56 

217. 1 

135.  7 

17 

14.4 

9.0 

77 

65.3 

40.8 

37 

116.2 

72.6 

97 

167. 1 

104.4 

57 

217.9 

136.  2 

18 

15.3 

9.5 

78 

66.1 

41.3 

.38 

117.0 

73.1 

98 

167.9 

104.9 

58 

218.8 

136.7 

19 

16.1 

10.1 

79 

67.0 

41.9 

39 

117.9 

73.7 

99 

168.8 

105.  5 

59 

219.  6 

137.2 

20 
21 

17.0 

10.6 

80 

67.8 

42.4 

40 

118.7 

74.2 

200 

169.6 

106.0 

60 

220.5 

137.  8 

17.8 

11.1 

81 

68.7 

42.9 

141 

119.6 

74.7 

201 

170.  5  1 106.  5 

261 

221.3 

138.3 

22 

18.7 

11.7 

82 

69.5 

43.5 

42 

120.4 

75.2 

02 

171.3    107.0 

62 

222.2 

138.8 

23 

19.5 

12.2 

83 

70.4 

44.0 

43 

121.3 

75.8 

03 

172.2    107.6 

63 

223.  0 

139. 4 

24 

20.4 

12.7 

84 

71.2 

44.5 

44 

122.1 

76.3 

04 

173.0 

108.1 

64 

223.9 

139.9 

25 

21.2 

13.2 

85 

72.1 

45.0 

45 

123.0 

76.8 

05 

173.8 

108.6 

65 

224.7 

140.4 

26 

22.0 

13.8 

86 

72.9 

45.6 

46 

123.8 

77.4 

06 

174.  7 

109.2 

66 

225.6 

141.0 

27 

22.9 

14.3 

87 

73.8 

46.1 

47 

124.7 

77.9 

07 

175.5 

109.7 

67 

226.4 

141.5 

28 

23.7 

14.8 

88 

74.6 

46.6 

48 

125.5 

78.4 

08 

176.4 

110.2 

68 

227.  3 

142.0 

29 

24.6 

15.4 

89 

75.5 

47.2 

49 

126.4 

79.0 

09 

177.2  |110.8 

69 

228.1 

142.5 

30 

25.4 

15.9 

90 

76.3 

47.7 

50 

127.2 

79.5 

10 

178.1  !lll.3 

70 

229.0 

143.1 

31 

26.3 

16.4 

91 

77.2 

48.2 

151 

128.1 

80.0 

211 

178.9 

111.8 

271 

229.8 

143.6 

32 

27.1 

17.0 

92 

78.0 

48.8 

52 

128.9 

80.5 

12 

179.8 

112.3 

72 

230.7 

144.1 

33 

28.0 

17.5 

93 

78.9 

49.3 

53 

129.8 

81.1 

13 

180.6 

112.9 

73 

231.5 

144.7 

34 

28.8 

18.0 

94 

79.7 

49.8 

54 

130.6 

81.6 

14 

181.5 

113.4 

74 

232.4 

145.2 

36 

29.7 

18.5 

95 

80.6 

50.3 

55 

131.4 

82.1 

15 

182.3 

113.9 

/o 

233.2 

145.  7 

36 

30.5 

19.1 

96 

81.4 

50.9 

56 

132.3 

82.7 

16 

183.2 

114.5 

76 

234.1 

146.3 

37 

31.4 

19.6 

97 

82.3 

51.4 

57 

133.1 

83.2 

17 

184.0 

115.0 

77 

234.9 

146.8 

38 

32.2 

20.1 

98 

83.1 

51.9 

58 

134. 0 

83.7 

18 

184.9 

115.5 

78 

235.  8 

147.3 

39 

33.1 

20.7 

99 

84.0 

52.5 

59 

134.8 

84.3 

19 

185.7 

116.1 

79 

236.6 

147.8 

40 

33.9 

21.2 
21.7 

100 

84.8 

53.0 

60 

135.7 
136.5 

84.8 
85.3 

20 
221 

186.6 
187. 4" 

116.6 

80 

237.5 
238.  3 

148.4 

41 

34.8 

101 

85.7 

53.5 

161 

117. 1 

281 

148.9 

42 

35.6 

22.3 

02 

86.5 

54.1 

62 

137.4 

85.8 

22 

188.  3 

117.6 

82 

239.1 

149.4 

43 

36.5 

22.8 

03 

87.3 

54.6 

63 

138.2 

86.4 

23 

189.1 

118.2 

83 

240.0 

150.  0 

44 

37.3 

23.  3 

04 

88.2 

55.1 

64 

139.1 

86.9 

24 

190.0 

118.7 

84 

240.8 

150.5 

45 

38.2 

23.8 

05 

89.0 

55.6 

65 

139.9 

87.4 

25 

190.8 

119.2 

85 

241.7 

151.0 

46 

39.0 

24.4 

06 

89.9 

56.2 

66 

140.8 

88.0 

26 

191.7 

119.8 

86 

242.  5 

151.6 

47 

39.9 

24.9 

07 

90.7 

56.7 

67 

141.6 

88.5 

27 

192.5 

120.3 

87 

243.4 

152.1 

48 

40.7 

25.4 

08 

91.6 

57.2 

68 

142.5 

89.0 

28 

193. 4 

120.8 

88 

244.2 

152.  6 

49 

41.6 

26.0 

09 

92.4 

57.8 

69 

143.3 

89.6 

29 

194.2 

121.4 

89 

245.  1 

153. 1 

50 

42.4 

26.5 
27.0 

10 

93.3 
94.1 

58.3 

70 

144.2 

90.1 

30 

195.1 
195.9 

121.9 

90 

245.  9 

153.7 
154.  2 

51 

43.3 

111 

58.8 

171 

145.0 

90.6 

231 

122.4 

291 

246.  8 

52 

44.1 

27.6 

12 

95.0 

59.4 

72 

145.  9 

91.1 

32 

196.7 

122.9 

92 

247.6 

154.7 

53 

44.9 

28.1 

13 

95.8 

59.9 

73 

146.7 

91.7 

33 

197.6 

123.5 

93 

248.  5 

155.  3 

54 

45.8 

28.6 

14 

96.7 

60.4 

74 

147.6 

92.2 

34 

198.4 

124.0 

94 

249.3 

155.8 

55 

46.6 

29.1 

15 

97.5 

60.9 

75 

148.4 

92.7 

35 

199.  3 

124.5 

95 

250.  2 

156.  3 

56 

47.5 

29.7 

16 

98.4 

61.5 

76 

149.  3 

93.3 

36 

200.1 

125. 1 

96 

251.0 

156.9 

57 

48.3 

30.2 

17 

99.2 

62.0 

77 

150.1 

93.8 

37 

201.0 

125.6 

97 

251.  9 

157.  4 

58 

49.2 

.30.7 

18 

100.1 

62.5 

78 

151.0 

94.3 

38 

201.8 

126.1 

98 

252.7 

157.9 

59 

50.0 

31.3 

19 

100.9 

63.1 

79 

151.  8 

94.9 

39 

202.  7 

126.7 

99 

253.  6 

158.  4 

60 

50.9 

31.8 

20 

101.8 

63.6 

80 

152.  6 

95.4 

40 

203.  5 

127.2 

300 

254.4 

159.0 
Lat. 

DIst. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

)8°    (1 

22°,  2.38 

°,  302° 

)• 

TABLE 

-  2. 

[Page 

(431 

Difference  of  Latitude  and 

Departure  for  32°  (148°,  212 

°,  328= 

)• 

IDist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

255.3 

159.5 

361 

.306.  2 

191.3 

421 

357.0 

223.1 

481 

407.  9 

254.9 

641 

458.8 

286.7 

02 

256.1 

160.0 

62 

307.  0 

191.8 

22 

357.9 

223.6 

82 

408.8 

255.  4 

42 

459.  6 

287.2 

03 

257.0 

160.5 

63 

307.9 

192.3 

23 

358.  7 

224.1 

83 

409.6 

255.9 

43 

460.5 

287.7 

04 

257.8 

161.1 

64 

308.7 

192.9 

24 

359.  6 

224.7 

84 

410.  5 

256.  5 

44 

461.3 

288.  3 

05 

258.7 

161.6 

65 

309.  5 

193.4 

25 

360.4 

225.2 

85 

411.3 

257.  0 

45 

462.  2 

288.8 

06 

259.5 

162.1 

66 

310.  4 

193.9 

26 

361.3 

225.  7 

86 

412.2 

257.  5 

46 

463.  0 

289.3 

07 

260.4 

162.7 

67 

311.  2 

194.5 

27 

362.1 

226.  3 

87 

413.  0 

258. 1 

47 

463.9 

289.9 

08 

261.2 

163.2 

68 

312. 1 

195.  0 

28 

363.0 

226.8 

88 

41,3.  9 

258.  6 

48 

464.7 

290.  4 

09 

262.1 

163.7 

69 

312.9 

195. 5 

29 

363.  8 

227.3 

89 

414.7 

259.1 

49 

465.  6 

290.9 

10 
311 

262.9 
263.  8 

164.3 
164.8 

70 
371 

313.  8 
314.6 

196.0 
196.  6" 

30 
431 

364.7 
365.  5 

227.8 
228.4 

90 

415.6 

259.6 

50 

466.4 
467.3 

291.5 

491 

416.4 

260.2 

551 

292.0 

12 

264.6 

165.3 

72 

315.5 

197.1 

32 

366.4 

228.9 

92 

417.3 

260.7 

52 

468.1 

292.5 

13 

265.  4 

165.8 

73 

316.3 

197.6 

33 

367.2 

229.4 

93 

418.1 

261.2 

53 

469.0 

293.0 

14 

266.3 

166.4 

74 

317.2 

198.2 

34 

368.1 

230.0 

94 

419.0 

261.8 

54 

469.8 

293.6 

15 

267.1 

166.9 

75 

318.0 

198.7 

35 

368.9 

230.5 

95 

419.8 

262.3 

55 

470.7 

294.1 

16 

268.0 

167.4 

76 

318.9 

199.2 

36 

369.8 

231.0 

96 

420.6 

262.8 

56 

471.5 

294.6 

17 

268.8 

168.0 

77 

319.7 

199.8 

37 

370.6 

231.6 

97 

421.  5 

263.  4 

57 

472.4 

295.  2 

18 

269.7 

168.5 

78 

320.6 

200.3 

38 

371.5 

232.1 

98 

422.3 

263.9 

58 

473.2 

295.7 

19 

270.5 

169.0 

79 

321.4 

200.8 

39 

372.3 

232.  6 

99 

423.  2 

264.4 

59 

474.1 

296.2 

20 
321 

271.4 
272.  2 

169.6 
170".  1 

80 
381 

322.3 

201.3 

40 

373.2 

233. 1 

500 

424.0 
424.9 

26.5.0 
"265.  5 

60 
561 

474.9 
475.  8 

296.7 
297.  3 

323.1 

201.9 

441 

374.0 

233.7 

501 

22 

273.1 

170.6 

82 

324.  0 

202.4 

42 

374.8 

234.2 

02 

425.  7 

266.0 

62 

476.6 

297.8 

23 

273.9 

171.1 

83 

324.  8 

202.9 

43 

375.7 

234.7 

03     426. 6 

266.  5 

63 

477.5 

298.3 

24 

274.8 

171.7 

84 

325.  7 

203.5 

44 

376.5 

235.3 

04     427. 4 

267.1 

64 

478.3 

298.9 

25 

275.6 

172.2 

85 

326.  5 

204.0 

45 

377.4 

235.  8 

05     428. 3 

267.6 

65 

479.2 

299.4 

26 

276.5 

172.7 

86 

327.4 

204.  5 

46 

378.2 

236.  3 

06  i  429.1 

268.1 

66 

480.0 

299.9 

27 

277.3 

173.3 

87 

328.2 

205. 1 

47 

379.1 

236.9 

07  !  430.0 

268.7 

67 

480.9 

300.5 

28 

278.2 

173.8 

88 

329. 1 

205.6 

48 

379.9 

237.  4 

08  !  430.8 

269.2 

68 

481.7 

301.0 

29 

279.0 

174.3 

89 

329.9 

206.1 

49 

380.8 

237.9 

09  t  431.7 

269.7 

69 

482.6 

301.5 

30 

279.9 

280.7 

*174. 9 

90 

330.8 
331.6 

206.6 

50 

381.6 
382.5 

238.4 

10 

432.5  1270.3 
433.4  1270.8 

70 

483.4 

.302. 1 

331 

175.4 

391 

207.2 

451 

239.0 

511 

571 

484.  3' 

302.6 

32 

281.6 

175.9 

92 

332.5 

207.7 

52 

383.3 

239.5 

12     434. 2 

271.4 

72 

485. 1 

303.2 

33 

282.4 

176.4 

93 

333.3 

208.2 

53 

384.2 

240.0 

13     435. 1 

271.9 

73 

486.0 

303.7 

34 

283.3 

177.0 

94 

334.  2 

208.8 

54 

385. 0 

240.6 

14     435. 9 

272.4 

74 

486.8 

304.2 

35 

284.1 

177.5 

95 

335.0 

209.3 

55 

385. 9 

241.1 

15     436. 8 

272.  9 

75 

487.7 

304.7 

36 

285.0. 

178.0 

96 

335.  8 

209.8 

56 

386.  7 

241.6 

16     437. 6 

273.5 

76 

488.5 

305.3 

37 

285.8 

178.6 

97 

336.  7 

210.4 

57 

387.6 

242.2 

17  i  438.5 

274.0 

77 

489.4 

305.8 

38 

286.7 

179.1 

98 

337.5 

210.9 

58 

388.4 

242.7 

18     439. 3 

274.5 

78 

490.2 

306.3 

39 

287.5 

179.6 

99 

338.4 

211.4 

59 

389.3 

243.2 

19 

440.2 

275. 0 

79 

491.1 

306.8 

40 
341 

288.3 

180.2 

400 

339.2 

211.9 

60 

390.1 
391.0 

243.8 

20 

441.0 

275.  6 

80 
581 

491.9 
492.8 

307.4 

289.2 

180.7 

401 

340.1 

212.5 

461 

244.3 

521 

441.9 

276.1 

307.9 

42 

290.0 

181.2 

02 

340.9 

213.0 

62 

391.8 

244.8 

22 

442.7 

276.6 

82 

493.6 

308.4 

43 

290.9 

181.7 

03 

341.8 

213. 5 

63 

.392.  7 

245.4 

23 

443.6 

277.2 

83 

494.5 

309.0 

44 

291.7 

182.3 

04 

342. 6 

214.1 

64 

393.5 

245.9 

24 

444.4 

277.7 

84 

495.3 

309.  5 

45 

292.6 

182.8 

05 

343.  5 

214.6 

65 

394.4 

246.4 

25 

445.  3 

278.2 

85 

496.2 

310.0 

46 

293.  4 

183.3 

06 

344.3 

215.1 

66 

395.2 

246.9 

26 

446.1 

278.7 

86 

497.0 

310.6 

47 

294.3 

183.9 

07 

345.2 

215.7 

67 

396. 0 

247.5 

27 

446.9 

279.3 

87 

497.8 

311.1 

48 

295. 1 

184.4 

08 

346.0 

216.2 

68 

396.9 

248.0 

28 

447.8 

279.8 

88 

498.7 

311.6 

49 

296.0 

184.  9 

09 

346.9 

216.7 

69 

397.7 

248.5 

29 

448.6 

280.3 

89 

499.5 

312. 1 

50 

296.8 

185.4 

10 

347.7 

217.2 

70 

398.6 

249.0 

30 

449.5 

280.9 

90 

500.3 

312.6 

361 

297.7 

186.0 

411 

348.6 

217.8 

471 

399.4 

249.6 

531 

450.  3 

281.4 

591 

501. 2 

313.2 

52 

298.5 

186.5 

12 

349.4 

218.3 

72 

400.3 

250.1 

32 

451.1 

281.9 

92 

502.0 

313.7 

53 

299.4 

187.0 

13 

350.3 

218.8 

73 

401.1 

250.6 

33 

452.0 

282.4 

93 

502.9 

314.2 

54 

300.2 

187.6 

14 

351.1 

219.4 

74 

402.0 

251.2 

34 

452.8 

283.0 

94 

503.  7 

314.8 

55 

301.1 

188.1 

15 

352.0 

219.9 

75 

402.8 

251.7 

35 

453.7 

283.  5 

95 

504.6 

315.  3 

56 

301.9 

188.6 

16 

:^2.8 

220.4 

76 

403.7 

252.2 

36 

454.  5 

284.0 

96 

505. 4 

315.8 

57 

302.  8 

189.2 

17 

353.  6 

221.0 

77 

404.5 

252.8 

37 

455.4 

284.6 

97 

506.2 

316.4 

58 

303.6 

189.7 

18 

354.  5 

221.5 

78 

405.4 

253.  3 

38 

456.2 

285.1 

98 

507.1 

316.9 

59 

304.5 

190.2 

19 

355.3 

222.0 

79 

406.2 

253.8 

39 

457.1 

285.6 

99 

508.0 

317.4 

60 

305.3 

190.8 

20 

356.2 

222.5 

80 

407.1 

254.3 

40 

467.9 

286.2 

600 

508.8 

318.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

•Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

5 

8°  (1 

22°,  238 

=  ,  302° 

). 

/ 

Page  432] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

33°  (147°,  213°,  327° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.5 

61 

51.2 

33.2 

121 

101.5 

65.9 

181 

151.  8 

98.6 

241 

202.1 

131. 3 

2 

1.7 

1.1 

62 

52.0 

33.8 

22 

102.3 

66.4 

82 

152.6 

99.1 

42 

203.0 

131.8 

3 

2.5 

1.6 

63 

52.8 

34.3 

23 

103.2 

67.0 

83 

153.5 

99.7 

43 

203.  8 

132. 3 

4 

3.4 

2.  2 

64 

53.7 

34.  9 

24 

104.0 

67.5 

84 

154.3     100.2 

44 

204.  6 

132.9 

5 

4.2 

2.7 

65 

54.5 

35.4 

25 

104.  8 

68.1 

85 

155.  2 

100.8 

45 

205.5 

133.4 

6 

5.0 

3.3 

m 

55.4 

35.9 

26 

105.7 

68.6 

86 

156.0 

101.3 

46 

206.3 

134.0 

7 

5.9 

3.8 

67 

56.2 

36.  5 

27 

106.5 

69.2 

87 

156.8 

101.8 

47 

207.2 

134.  5 

8 

6.7 

4.4 

68 

57.0 

37.0 

28 

107.3 

69.7 

88 

157.  7 

102.4 

48 

208.0 

135. 1 

9 

7.5 

4.9 

69 

57.9 

37.6 

29 

108.2 

70.3 

89 

158.5 

102.9 

49 

208.8 

135. 6 

10 

8.4 

5.4 

70 

58.7 

38.1 

30 

109.0 

70.8 

90 

159.3 

103.  5 

50 

209.7 
210. 5 

136.2 
136.7 

11 

9.2 

6.0 

71 

59.5 

38.7 

131 

109.9 

71.3 

191 

160.2 

104.0 

251 

12 

10.1 

6.5 

72 

60.4 

39.2 

32 

110.7 

71.9 

92 

.161.0 

104.6 

52 

211.3 

137.  2 

13 

10.9 

7.1 

73 

61.2 

39.8 

33 

111.5 

72.4 

93 

161.9 

105.1 

53 

212.2 

137.8 

14 

11.7 

7.6 

74 

62.1 

40.3 

34 

112.4 

73.  0 

94 

162.7 

105.7 

54 

213.0 

138.3 

15 

12.6 

8.2 

75 

62.9 

40.8 

35  i  113.2 

73.  5 

95 

163.  5 

106.2 

55 

213.9 

138.9 

16 

13.4 

8.7 

76 

63.7 

41.4 

36     114. 1 

74.1 

96 

164.4 

106.7 

56 

214.7 

139.4 

17 

14.3 

9.3 

/ 1 

64.6 

41.9 

37 

114.9 

74.6 

97 

165.  2 

107.3 

57 

215.  5 

140.0 

18 

15.1 

9.8 

78 

65.4 

42.5 

38 

115.  7 

75.2 

98 

166.1     107.8 

58 

216.4 

140.5 

19 

15.9 

10.3 

79 

66.3 

43.0 

39 

116.  6 

75.7 

99 

166.  9     108.  4 

59 

217.2 

141.1 

20 

16.8 

10.9 

80 

67.1 

43.6 

40 

117.4 
118.3 

76.2 

200 
201 

167.  7    108.  9 
168.6    109.5 

60 
261 

218.1 
218.9 

141.6 
142.2 

21 

17,6 

11.4 

81 

67.9 

44.1 

141 

76.8 

22 

18.5 

12.0 

82 

68.8 

44.7 

42     119. 1 

77.3 

02 

169.4  1110.0 

62 

219.  7 

142.7 

23 

19.3 

12.5 

83 

69.6 

45.2 

43     119.9 

77.9 

03 

170.3  1110.6 

63 

220.6 

143.2 

24 

20.1 

13.1 

84 

70.4 

45.7 

44      120.8 

78.4 

04 

171.1     111.1 

64 

221.4 

143.8 

25 

21.0 

13.6 

85 

71.3 

46.3 

45      121.6 

79.0 

05 

171.9    111.7 

65 

222.2 

144.3 

26 

21.8 

14.2 

86 

72.1 

46.8 

46  1  122.4 

79.5 

06 

172.2    112.2 

66 

223. 1 

144.9 

27 

22.6 

14.7 

87 

73.0 

47.4 

47      123.3 

80.1 

07 

173.6    112.7 

67 

223.  9 

145.  4 

28 

23.5 

15.2 

88 

73.8 

47.9 

48      124.  1 

80.6 

08 

174.4    113.3 

68 

224.8 

146.0 

29 

24.3 

15.8 

89 

74.6 

48.5 

49 

125.0 

81.2 

09 

175.  3  ,  113.  8 

69 

225.  6 

146.5 

30 
31 

25.2 
26.0 

16.3 
16.9 

90 

75.5 
76.3 

49.0 

50 

125.8 

81.7 
82.2 

10 
211 

176.1 
177.0 

114.4 

70 

226.4 

147.1 
147.6 

91 

49.6 

151 

126.6 

114.9 

271 

227.  3 

32 

26.8 

17.4 

92 

77.2 

50.1 

52  1  127.5 

82.8 

12 

177.8    115.5 

72 

228.1 

148.1 

33 

27.7 

18.0 

93 

78.0 

50.7 

53  !  128.3 

83.3 

13 

178.6 

116.0 

73 

229.0 

148.7 

34 

28.5 

18.5 

94 

78.8 

51.2 

54      129.2 

83.9 

14 

179.5 

116.6 

74 

229.8 

149.2 

35 

29.4 

19.1 

95 

79.7 

51.7 

55     130.0 

84.4 

15 

180.  3 

117.1 

75 

230.6 

149.8 

36 

30.2 

19.6 

96 

80.5 

52.3 

56  j  130.8 

85.0 

16 

181.2 

117.6 

76 

231.5 

150.  3 

37 

31.0 

20.2 

97 

81.4 

52.8 

57  !  131.7 

85.5 

17 

182.0 

118.2 

77 

232.3 

150.9 

38 

31.9 

20.7 

98 

82.2 

53.  4 

58, 

132.  5 

86.1 

18 

182.8 

118.7 

78 

233.  2 

151.4 

39 

32.7 

21.2 

99 

83.0 

53.9 

59 

133.  3 

86.6 

19 

183.7 

119.3 

79 

234. 0 

152.  0 

40 

33.5 

21.8 

100 

83.  9 

54.  5 

60 

134.2 
135.  0 

87.1 

20 

184.5 

119.8 

80 

234.8 
235.7 

152. 5 
153.0 

41 

34.4 

22.3 

101 

84.7 

55.0 

161 

87.7 

221 

185.3 

120.4 

281 

42 

35.2 

22.9 

02 

85.5 

55.6 

62 

135.9 

88.2 

22 

186.2 

120.9 

82 

236.  5 

153.6 

43 

36.1 

23.4 

03 

86.4 

56.1 

63     136.7 

88.8 

23 

187.0 

121.5 

83 

237.3 

154.1 

44 

36.9 

24.0 

04 

87.2 

56.6 

64  ;  137.5 

89.3 

24 

187.9 

122.0 

84 

238.  2 

154.7 

45 

37.7 

24.5 

05 

88.1 

57.2 

65      138. 4 

89.9 

25 

188.7 

122.5 

85 

239.  0 

155.2 

46 

38.6 

25.1 

06 

88.9 

57.7 

66     139. 2 

90.4 

26 

189.5 

123.1 

86 

239.9 

155.8 

47 

39.4 

25.6 

07 

89.7 

58.3 

67 

140.1 

91.0 

27 

190.4 

123.6 

87 

240.7 

156.3 

48 

40.3 

26.1 

08 

90.6 

58.8 

68 

140.9 

91.5 

28 

191.2 

124.2 

88 

241.5 

156.9 

49 

41.1 

26.7 

09 

91.4 

59.4 

69 

141.7 

92.0 

29 

192.1 

124.7 

89 

242.4 

157.4 

50 
51 

41.9 

27.2 

10 

92.3 
93.1" 

59.9 
60.  5 " 

70 

142.6 

92.6 

30 

192.9 
193.7 

125.  3 

90 
291' 

243.2 
244.1 

157.9 

42.8 

27.8 

111 

171 

143.  4 

93.1 

231 

125.  8 

158.5 

52 

43.6 

28.3 

12 

93.9 

61.0 

72 

144.3 

93.7 

32 

194.6 

126.4 

92 

244.9 

159.0 

53 

44.4 

28.9 

13 

94.8 

61.5 

73 

145. 1 

94.2 

33 

195.4 

126.9 

93 

245.7 

159.6 

54 

45.3 

29.4 

14 

95.6 

62.1 

74 

145.9 

94.8 

34 

196.2 

127.4 

94 

246.6 

160.1 

55 

46.1 

30.0 

15 

96.4 

62.6 

75 

146.8 

95.3 

35 

197.1 

128.0 

95 

247.4 

160.7 

56 

47.0 

•30.5 

16 

97.3 

63.2 

76 

147,6 

95.9 

36 

197.9 

128.5 

96 

248.2 

161.2 

57 

47.8 

31.0 

17 

98.1 

63.7 

77 

148.4 

96.4 

37 

198.8 

129.1 

97 

249.1 

161.8 

58 

48.6 

31.6 

18 

99.0 

64.3 

78 

149.  3 

96.^- 

'    38 

199.  6 

129.6 

98 

249.9 

162.3 

59 

49.5 

32.1 

19 

99.8 

64.8 

79 

150.1 

97.5 

39 

200.4 

130.2 

99 

250.  8 

162.8 

60 

50.3 

32.7 

20 

100.6 

65.4 

80 

151.0 

98.0 

40 

201.3 

130.7 

300 

251.6 

163.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

lAt. 

Dist. 

Dep. 

Lat. 

e. 

7°  (123°,  237°,  303° 

. 

TABLE  2. 

[Page  433    | 

Difference  of  Latitude  and  Departure  for  33°  (147°,  213°,  327' 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

252.4 

163.9 

361 

302.8 

196.6 

421 

353.1 

229.3 

481 

403.4 

262.0 

541 

453.7 

294.6 

02 

253.3 

164.4 

62 

303.6 

197.1 

22 

353.9 

229.8 

82 

404.2 

262.  5 

42 

454.6 

295.  2 

03 

254.1 

165.0 

63 

304.  4 

197.7 

23 

354.7 

230.  4 

83 

405. 1 

263.  1 

43 

455.  4 

295.7 

04 

255.  0 

165.  5 

64 

305.  3 

198.2 

24 

355.  6 

230.  9 

84 

405.  9 

263.  6 

44 

456.2 

296.2 

05 

255.  8 

166.1 

65 

306.1 

198.  8 

25 

356.4 

231.  4 

85 

406.7 

264.1 

45 

457.1 

296.8 

06 

256.6 

166.  6 

66 

307.  0 

199.3 

26 

357.3 

232.0 

86 

407.6 

264.7 

46 

457.9 

297.3 

07 

257.  5 

167.2 

67 

307.8 

199.8 

27 

358.1 

232.  5 

87 

408.4 

265.2 

47 

458.8 

297.  9 

08 

258.3 

167.7 

68 

308.6 

200.4 

28 

359.0 

233.1 

88 

409.3 

265.8 

48 

1  459.6 

298.4 

09 

259.2 

168.3 

69 

309.5 

200.9 

29 

359.8 

233.6 

89 

410.1 

266.3 

49 

460.4 

299.0 

10 
311 

260.0 
260.8 

168.8 
169.3 

70 
371 

310.  3 
311.2 

201.5 

30 

360.6 
361.5 

234.2 

90 

411.0 

266.8 

50 

461.3 

299.5 

202.0 

431 

234.7 

491 

411.8 

267.4 

551 

462.1 

300.  1 

12 

261.7 

169.9 

72 

312.  0 

202.6 

32 

362.3 

235.2 

92 

412.6 

267.9 

52 

463.0 

300.6 

13 

262.5 

170.4 

73 

312.  8 

203. 1 

33 

363.1 

235.8 

93 

413.  5 

268.  5 

53 

463.  8 

301.2 

14 

263.3 

171.0 

74 

313.  7 

203.7 

34 

364.0 

236.3 

94 

414.3 

269.0 

54 

464.  6 

301.7 

15 

264.2 

171.5 

75 

314.5 

204.2 

35 

364.8 

236.9 

95 

415. 1 

269.6 

55 

465.  5 

302.3 

16 

265.0  i  172.1 

76 

315.3 

204.7 

36 

365.7 

237.4 

96 

416.0 

270.1 

56 

466.  3 

302.  9 

17 

265.9    172.6 

77 

316.2 

205.3 

37 

366.  5 

238.0 

97 

416.8 

270.7 

57 

467.2 

303.4 

18 

266.7    173.2 

78 

317.  0 

205.8 

38 

367.3 

238.  5 

98 

417.6 

271.2 

58 

468.0 

303.  9 

19 

267.5    173.7 

79 

317.9 

206.4 

39 

368.2 

239.1 

99 

418.5 

271.8 

59 

468.8 

304.5 

20 
321 

268.4    174.2 
269.2    174.8 

80 
381 

318.7 

206.9 

40 

369.0 

239.6 

5C0 
501 

419.3 
420.2 

272.3 

60 
561 

469.7 
470.5 

305.  0 

319.5 

207.5 

441 

369.  9 

240.1 

272.8 

305.5 

22 

270.1    175.3 

82 

320.4 

208.0 

42 

370.7 

240.7 

02 

421.0 

273.4 

62 

471.3 

306.1 

23 

270. 9  1 175. 9 

83  [  321.2 

208.6 

43 

371.  5 

241.2 

03 

421.9 

273.9 

63 

472.2 

306.6 

24 

271.7 

176.4 

84 

322.1 

209.1 

44 

372.4 

241.8 

04 

422.7 

274.5 

64 

473.0 

307.  2 

25 

272.  d 

177.0 

85 

322.9 

209.6 

45 

373.  2 

242.3 

05 

423.  5 

275. 0 

65 

473.8 

307.7 

26 

273.4 

177.5 

86 

323.  7 

210.2 

46 

374. 1 

242.9 

06 

424.4 

275.  6 

66 

474.7 

308.  3 

27 

274.2 

178.1 

87 

324.6 

210.7 

47     374. 9 

243.4 

07 

425.  2 

276.1 

67 

475. 5 

308.8 

28 

275.1 

178.  6 

88 

325.4 

211.3 

48     375. 7 

244.0 

08 

426.0 

276.7 

68 

476.4 

309.4 

29 

275.9 

179.1 

89 

326.2 

211.8 

49     376.6 

244.5 

09 

426.9 

277.2 

69 

477.2 

309.9 

30 
331 

276.8 
277.6 

179.7 

90 

327.1 

212.4 
212.9 

50  1  377.4 

245.1 

10 

427.7 

277.8 

70 

478.0 

310.4 
311.0 

180.2 

391 

327.9 

451 

378.2 

245.  6 

511 

428.5 

278.3 

571 

478.9 

32 

278.4 

180.8 

92 

328.8 

213.5 

52 

379.1 

246.1 

12 

429.4 

278.8 

72 

479.7 

311.5 

33 

279.3 

181.3 

93 

329.6 

214.0 

53 

379.9 

246.7 

13 

430.2 

279.4 

73 

480.6 

312.0 

34 

280.1 

181.9 

94 

330.4 

214.6 

54 

380.8 

247.2 

14 

431.1 

279.9 

74 

481.4 

312.6 

35 

281,0 

182.4 

95 

331.3 

215.1 

55 

381.6 

247.8 

15 

431.9 

280.4 

75 

482.2 

313.1 

36 

281.8 

183.  0 

96 

332. 1 

215.6 

56 

382.4 

248.3 

16 

432.7 

281.0 

76 

483.1 

313.7 

37 

282.6 

183.5 

97 

333.0 

216.2 

57 

383.3 

248.9 

17 

433.6 

281.5 

77 

483.  9 

314.2 

38 

283.5 

184.1 

98 

333.8 

216.7 

58 

384.1 

249.4 

18 

434.4 

282.1 

78 

484.7 

314.  8 

39 

284.3 

184.6 

99 

334.6 

217.3 

59 

385.0 

250.  0 

19 

435.  3 

282.6 

79 

485.6 

315. 3 

40 

285.2 
286.0 

185.1 
185.  7 

400 
401 

335. 5 

217.8 

60 
461 

385.8 
386.6 

250.  5 

20 

436.1 
436.9 

283.  2 

80 

486.4 
487.  2 

315.  9 

341 

336. 3 

218.4 

251.0 

521 

283.7 

581 

316.4 

42 

286.8 

186.2 

02 

337.1 

218.9 

62     387. 5 

251.6 

22 

437.8 

284.3 

82 

488.1 

317.0 

43 

287.7 

186.8 

03 

338.0 

219.  5 

63 

388.3 

252. 1 

23 

438.6 

284.8 

83 

488.9 

317.5 

44 

288.5 

187.3 

04 

338.8 

220.0 

64 

389.1 

252.7 

24 

439.4 

285.4 

84 

489.8 

318.1 

45 

289.3 

187.9 

05 

339.7 

220.5 

65 

390.0 

253.2 

25 

440.3 

285.9 

85 

490.6 

318.6 

46 

290.2 

188.4 

06 

340.5 

221.1 

66 

390.8 

253.8 

26 

441.1 

286.5 

86 

491.5 

319.2 

47 

291.0 

189.0 

07 

341.3 

221.6 

67 

391.7 

254.3 

27 

442.0 

287.0 

87 

492.3 

319.  7 

48 

291.9 

189.5 

08 

342.2 

222.2 

68 

392.5 

254.9 

28 

442.8 

287.5 

88 

493.1 

320.2 

49 

292.  7 

190.0 

09 

343.0 

222.7 

69 

393.3 

255.  4 

29 

443.6 

288.1 

89 

494.0 

320.8 

50 

293.5 

190.6 

10 

343.  9 
344.7 

223.  3 
223.  8 

70 
471 

394.2 
395.0 

255.9 

30 

444.5 

288.6 
289.2 

90 

494.8 

321.3 

351 

294.4 

191.1 

411 

256.5 

531 

445.3 

591 

495.7 

321.9 

52 

295.2 

191.7 

12 

345. 5 

224.4 

72 

395.  8 

257.0 

32 

446.1 

289.7 

92 

496.  5 

322.4 

53 

296.1 

192.2 

13 

346.4 

224.9 

73 

396.7 

257.6 

33 

447.0 

290.3 

93 

497.  3 

322.  9 

54 

296.9 

192.8 

14 

347.2 

225.4 

74 

397.  5 

258.1 

34 

447.8 

290.8 

94 

498.1 

323.5 

55 

297.7 

193.3 

15 

348.1 

226.0 

75 

398.3 

258.7 

35 

448.7 

291.4 

95 

499.0 

324.1 

56 

298.6 

193.9 

16 

348.9 

226.5 

76     399.2 

259.2 

36 

449.5 

291.9 

96 

499.8 

324.6 

57 

299.4    194.4 

17 

349.7 

227.1 

77     400.0 

259.8 

37 

450.3 

292.  5 

97 

500.6 

325. 1 

58 

300.2     194.9 

18 

350.6 

227.6 

78     400. 9 

260.3 

38 

451.2 

293.  0 

98 

501.5 

325.  7 

59 

301.1     195.5 

19 

351.4 

228.2 

79     401. 7 

260.9 

39 

452.0 

293.6 

99 

502.3 

326.2 

60 

301.  9    196. 0 

20 

352.2 

228.7 

80 

402.6 

261.4 

40 

452.9 

294.1 

600 

503.2 

326.8 

Dist. 

Dep.     1    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

57°  (123°,  237' 

',  303°) 

. 

22489—03 28 


Page  434; 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  34°  (146°,  214°,  326° 

)■ 

DIst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  t     Lat. 

Dep. 

1 

0.8 

0.6 

61 

50.6 

34.1 

121  !  100.3 

67.7 

181 

150.1 

101.2 

241      199.8 

134.8 

2 

1.7 

1.1 

62 

51.4 

34.7 

22  1  101.1 

68.2 

82 

150.9    101.8 

42  '  200.6 

135.3 

3 

2.5 

1.7 

63 

52.2 

35.2 

23  1  102. 0  i  68.  8  1 

83 

151.7    102.3 

43  '<  201.5 

135.9 

4 

3.3 

2.2 

64 

53.1 

35.8 

24 

102.8      69.3 

84 

152.  5 

102.9 

44  !  202.3 

136.4 

5 

4.1 

2.8 

i 

53.9 

36.3 

25 

103.  6     69. 9 

85 

153.4 

103.  5 

45  1  203. 1 

137.0 

6 

5.0 

3.4 

54.7 

36.9 

26 

104. 5     70.  5 

86 

154.2 

104.0 

46     203. 9 

137.6 

7 

5.8 

3.9 

67 

55.5 

37.5 

27 

105.3  !  71.0 

87 

155. 0 

104.6 

47     204. 8 

138.1 

»   8 

6.6 

4.5 

68 

56.4 

38.0 

28 

106.1  i  71.6 

88 

155.9 

105.1 

48     205. 6 

138.7 

9 

7.5 

5.0 

69 

57.2 

38.6 

29 

106.9  1  72.1 

89 

156.7    105.71 

49     206. 4 

139.2 

10 

8.3 

5.6 

70 

58.0 
58.9 

39.1 

30 

107.8  1  72.7 

90 

157.5 
158.  3 

106.2 

50     207. 3 

139.8 

11 

9.1 

6.2 

71 

39.7 

131 

108.6  1  73.3 

191 

106.8 

251 

208.1 

140.4 

12 

9.9 

6.7 

72 

•    59.7 

40.3 

32     109.4  '  73.8 

92 

159.  2    107.  4 

52 

208.9 

140.9 

13 

10.8 

7.3 

73 

60.5 

40.8 

33     110.3  i  74.4 

93 

160. 0    107.  9 

53 

209.7 

141.  5 

14 

11.6 

7.8 

74 

61.3 

41.4 

34     111.1  '  74.9 

94 

160.  8    108.  5 

54     210. 6 

142.0 

15 

12.4 

8.4 

75 

62.2 

41.9 

35     111.  9  i  75.  5 

95 

161.7    109.0 

55  1  211.4 

142.6 

16 

13.3 

8.9 

76 

63.0 

42.5 

36     112.7     76.1 

96 

162.5 

109.6 

56     212.2 

143.2 

17 

14.1 

9.5 

77 

63.8 

43.1 

37     113.6     76.6 

97 

163.3 

110.2 

57     213. 1 

143.7 

18 

14.9 

10.1 

78 

64.7 

43.6 

38     114.4     77.2 

98 

164.1 

110.7 

58     213.9 

144.3 

19 

15.8 

10.6 

79 

65.5 

44.2 

39     115.  2  i  77.  7 

99 

165.  0 

111.3 

59  ;  214.  7 

144.8 

20 
21 

16.6 
17.4 

11.2 
11.7 

80 
81 

66.3 

44.7 

40     116. 1 

78.3 
78.'8 

200 

165.8    111.8 
166.6  ill2.4 

60     215.5 
261      216.4 

145.4 
145.  9 

67.2 

45.3 

141  1  116.9 

201 

22 

18.2 

12.3 

82 

68.0 

45.9 

42     117.7  1  79.4 

02 

167.5    113.0 

62     217.2 

146.5 

23 

19.1 

12.9 

83 

68.8 

46.4 

43     118. 6     80. 0 

03 

168.3    113.5 

63     218.0 

147.1 

24 

19.9 

13.4 

84 

69.6 

47.0 

44     119.4     80.5 

04 

169.1    114.1 

64     218.9 

147.6 

25 

20.7 

14.0 

85 

70.5 

47.5 

45     120.2     81.1 

05 

170.0  |114.6 

65     219.7 

148.2 

26 

21.6 

14.5 

86 

71.3 

48.1 

46     121.0     81.6 

06 

170.  8  1 115. 2 

66     220. 5 

148.7 

27 

22.4 

15.1 

87 

72.1 

48.6 

47     121.9     82.2 

07 

171.6    115.8 

67     221.4 

149.3 

28 

23.2 

15.7 

88 

73.0 

49.2 

48  1  122. 7  ;  82. 8 

08 

172.4    116.3 

68     222.2 

149.9 

29 

24.0 

16.2 

89 

73.8 

49.8 

49     123.5     83.3 

09 

173.3    116.9 

69  i  223.0 

150.4 

30 

24.9 

16.8 

90 

74.6 
75.4 

50.3 

50     124.4  1  83.9 

10 

174.1 
174.9 

117.4 

70  !  223.8 

151.0 

151.5 

31 

25.7 

17.3 

91 

50.9 

151      125.2  1  84.4 

211 

118.0 

271      224.7 

32 

26.5 

17.9 

92 

76.3 

51.4 

52  i  126.0  1  85.0 

12 

175.8    118.5 

72     225.5 

152. 1 

33 

27.4 

18.5 

93 

77.1 

52.0 

53  '  126.8     85.6 

13 

176.6    119.1 

73     226. 3 

152.7 

34 

28.2 

19.0 

94 

77.9 

52.6 

54     127.7  '  86.1 

14 

177.4  ill9.  7 

74 

227.2 

153.2 

35 

■    29.0 

19.6 

95 

78.8 

53.1 

55     128.5  ■  86.7 

15 

178.2 

120.2 

75 

228.0 

153.8 

36 

29.8 

20.1 

96 

79.6 

53.7 

56     129.3  :  87.2 

16 

179.1 

120.8 

76 

228.8 

154.  3 

37 

30.7 

20.7 

97 

80.4 

54.2 

57      130.2     87.8 

17 

179.9 

121.3 

77 

229.6 

154.  9 

38 

31.5 

21.  2 

98 

81.2 

54.8 

58  1  131.0  '  88.4 

18 

180.7 

121.9 

78 

230.  5 

155.  5 

39 

32.3 

21!  8 

99 

82.1 

55.  4 

59  1  131.8  1  88.9 

19 

181.6 

122.5 

79 

231.3 

156.0 

40 

33.2 

22.4 

100 

82.9 
83.7 

55.9 

60 
161 

132.6  1  89.5 

20 

182.4 

123.0 

80 

232.1 

156.6 
157.1 

41 

34.0 

22.9 

101 

56.5 

133.5  1  90.0 

221 

183.2 

123.6 

281 

233.0 

42 

34.8 

23.5 

02 

84.6 

57.0 

62     134.3  !  90.6 

22 

184.0 

124.1 

8S  '  233.8 

157.  7 

43 

35.6 

24.0 

03 

85.4 

57.6 

63     135.1     91.1 

23 

184.9 

124.7 

83  1  234.6 

158.  3 

44 

36.5 

24.6 

04 

86.2 

58.2 

64     136. 0     91. 7 

24 

185.  7 

125.  3 

84  1  235.4 

158.8 

45 

37.3 

25.2 

05 

87.0 

58.7 

65     136.8  t  92.3 

25 

186.5 

125.8 

85 

236.3 

159.4 

46 

38.1 

25.7 

06 

87.9 

59.3 

66     137.6 

92.8 

26 

187.4 

126.4 

86 

237.1 

159.9 

47 

39.0 

26.3 

07 

88.7 

59.8 

67 

138.4 

93.4 

27 

188.2 

126.9 

87 

237. 9 

160.5 

48 

39.8 

26.8 

08 

89.5 

60.4 

68 

139.3 

93.9 

28 

189.0 

127.5 

88 

238.  8 

161.0 

49 

40.6 

27.4 

09 

90.4 

61.0 

69 

140.1 

94.5 

29 

189.8 

128.1 

89 

239.6 

161.6 

50 

41.5 

28.0 

10 

91.2 
92.0 

61.5 

70 

140.9 

95.1 

30 

190.7 

128.6 

90 

240.4 

162.2 
162.7 

51 

42.3 

28.5 

111 

62.1 

171 

141.8 

95.6 

231 

191.5    129.2 

291 

241.2 

52 

43.1 

29.1 

12 

92.9 

62.6 

72  i  142.6 

96.2 

32 

192.3  fl29.7 

92 

242.1 

163. 3 

53 

43.9 

29.6 

13 

93.7 

63.2 

73     143. 4  ;  96.  7 

33 

193.2    130.3 

93  1  242.9 

163.8 

54 

44.8 

30.2 

14 

94.5 

63.7 

74     144.3  '  97.3 

34 

194.0    130.9 

94     243.7 

164.4 

55 

45.6 

30.8 

15 

95.3 

64.3 

75     145. 1  *  97. 9 

35 

194.  8  1 131. 4 

95     244.6 

165.0 

56 

46.4 

31.3 

16 

96.2 

64.9 

76  1  145.  9  1  98. 4 

36 

195.  7 

132.0 

96 

245.4 

165.  5 

57 

47.3 

31.9 

17 

97.0 

65.4 

77     146. 7     99. 0 

37 

196.5 

132.5 

97 

246.2 

166.1 

58 

48.1 

32.4 

18 

97.8 

66.0 

78     147.6     99.5 

38 

197.3 

133. 1 

98 

247.1 

166.6 

59 

48.9 

33.0 

19 

98.7 

66.5 

79     148.  4   100. 1 

39 

198.1 

133. 6 

99 

247.9 

167.2 

60 

49.7 

33.6 

20 

99.5 

67.1 

80  !  149. 2   100.  7 

40 

199.0 

134.2 

300 

248.7 

167.8 

Dist. 

Dep. 

■Lat. 

Dist. 

Dep. 

'    Lat. 

Dist.  1     Dep.        Lat. 

Dist. 

Dep.    '■    Lat. 

Dist. 

Dep. 

Lat. 

56°  (124°,  236",  304°). 

TABLE  2. 

[Page 

435 

Difference  of  Latitude  and  Departure  for  34°  (146°,  214 

=,  326° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.         Dep. 

Dist. 

Lat.     1 

Dep. 

Dist. 

Lat. 

Dep. 

301 

249.5 

168.3 

361 

299.3 

201.9 

421 

349.0 

235:4 

481 

398.8 

269.0 

541 

448.5 

302.5 

02 

250.4 

168.9 

62 

300.1 

202.4 

22 

349.9 

236.0 

82 

399.6  ! 

269.5 

42 

449.4 

303.1 

03 

251.2 

169.4 

63 

300.9 

203.0 

23     350.7 

236.  5 

83 

400.4 

270.1 

43 

450.2 

303.6 

04 

252.  0 

170.0 

64 

301.8 

203.5 

24     351. 5 

237.1 

84 

401.3  ; 

270.6 

44     451.0  1 

304.  2 

05 

252.  9 

170.6 

65 

302.6 

204.1 

25     352. 3 

237.7 

85 

402.1  ! 

271.2 

45 

451.8 

304.8 

06 

253.7 

171.1 

66 

303.4 

204.7 

26  1  353. 2 

238.2 

86     402.9 

271.8 

46 

452.6 

305.3 

07 

254.5 

171.7 

67 

304.3 

205.2 

27  1  354.0 

238.8 

87     403.8  i 

272.3 

47 

453.5 

305.  9 

08 

255.3 

172.2 

68 

305.1 

205.8 

28  ,  354.8 

239.3 

88     404.6  1 

272.8 

48  1  454.3 

306.4 

09 

256.  2 

172.8 

69 

305.  9 

206.3 

29  :  355.7 

239.9 

89     405.4  * 

273.4 

49 

455.2 

307.0 

10 

257.0    173.3 

70 

306.7 

206.9 

30     356.5    240.4 

90     406.2 

274.0 

50 

456.0 

307. 5 

311 

257.8     173.9 

371     307.6 

207.5 

431      357.3    241.0 

491     407.1 

274.6 

551 

456.8 

308.1 

^?. 

258.7    174.5 

72     308.4 

208.0 

32     358.1    241.6 

92     407.9  [ 

275.1 

52 

457.6 

308.7 

13 

259.5    175.0 

73  ;  309.2 

208.6 

33     359. 0    242. 1 

93 

408.7 ; 

275.7 

53 

458.4 

309.2 

14 

260.3 

175.6 

74  1  310. 1 

209.1 

■  34  ;  359.  8    242.  7 

94 

409.5  i 

276.2 

54 

459.  3 

309.8 

15 

261.2 

176.1 

75 

310.9 

209.7 

35  i  360.6    243.2 

95 

410.4  1 

276.8 

55 

460.1 

310.3 

16 

262.0 

176.7 

76 

311.7 

210.3 

36     361. 5    243. 8 

96     411. 2  1 

277.4 

56 

460.9 

310.9 

17 

262.8 

177.3 

77 

312.6 

210.8 

37     362.3  !244.4 

97     412.0  1 

277.9 

57     461. 7 

311.5 

18 

263.7 

177.8 

78 

313.4 

211.4 

38     363.1    244.9 

98 

412.8  1 

278.4 

58 

462.6 

312.0 

19 

264.5 

178.4 

79 

314.2 

211.9 

39     364.0    245.5 

99 

413.7 

279.0 

59 

463.4 

312.6 

20 

265.3 
266.1 

178.9 

80 

315.0 

212.5 
213.0 

40  \  364.8 
441     365. 6 

246.0 

500 
501 

414.5 
415.3 

279.6 
280.1 

60 

464.2 

313.1 
313.7 

321 

179.5 

381 

315.9 

246.6 

561      465. 1 

22 

267.0 

180.1 

82 

316.7 

213. 6 

42     366. 4 

247.2 

02 

416.2 

280.7 

62     465. 9 

314.3 

23 

267.8 

180.6 

83  1  317.5 

214.2 

43  :  367.3 

247.7 

03 

417.0 

281.3 

63     466. 8 

314.8 

24 

268.6 

181.2 

84     318. 4 

214.7 

44  j  368. 1 

248.3 

04 

417.8 

281.8 

64     467.6 

315.4 

25 

269.5 

181.7 

85 

319.2 

215.  3 

45     368.9  J  248.  8 

05 

418.  6 

282.4 

65  !  468.4 

315.9 

26 

270.3 

182.3 

86 

320.0 

215.8 

46     369.8  '249.4 

06     419. 4 

282.9 

66  i  469.2 

316.5 

27 

271.1 

182.9 

87 

320.8 

216.4 

47  ;  370.  6    250. 0 

07  !  420.3 

283.5 

67  !  470. 1 

317.1 

28 

271.9 

183.4 

88 

321.7 

217.0 

48     371.4    250.5 

08     421.  1 

284.1 

68  '  470.9 

317.6 

29 

272.8 

184.0 

89 

322.  5 

217.5 

49  1  372.2    251.1 

09 

421.9 

284.6 

69     471. 7 

318.2 

30 

273.6 
274.4 

184.5 

90 

323.3 
324.2 

218.1 
218.6 

50     373. 1    251. 6 
451  i  373. 9  1  252.  2 

10 

422.  8 

285.2 

70     472.6 
571     473.4 

318.7 
319.3 

331 

186.1 

391 

511 

423.6 

285.8 

32 

275.2 

185.6 

92 

325.0 

219.2 

52  '  374.  7    252.  8 

12 

424.4 

286.3 

72  ;  474.2 

319.9 

33 

276.1 

186.2 

93 

325.8 

219.8 

53     375.  6    253. 3 

13 

425.3 

286.9 

73 

475.0 

320.4 

34 

276.9 

186.8 

94 

326.6 

220.3 

54     376.4    253.9 

14 

426.1 

28r.4 

74 

475.9 

321.0 

35 

277.7 

187.3 

95 

327.5 

220.9 

55     377.2  i254.4 

15 

426.9 

288.0 

75 

476.7 

321.5 

36 

278.6 

187.9 

96  !  328.3 

221.4 

56  '  378.0    255.0 

16 

427.8 

288.5 

76 

477.5 

322.1 

37 

279.4 

188.4 

97 

329.1 

222.0 

57     378.9    255.5 

17  '  428.6 

289.1 

77 

478.3 

322.7 

38 

280.2 

189.0 

98 

330.0 

222.6 

58     379. 7    256. 1 

18  i  -429.4 

289.6 

78 

479.2 

323.2 

39 

281.0 

189.6 

99 

330.8 

223.1 

59     380.5    256.7 

19     430. 3 

290.2 

79  1  480.0 

323.8 

40 

281.9 

190.1 

400 

331.6 
332.4 

223.7 
224.2 

60 
461 

381.3    257.2 
382.2  '257.8 

20     431.1 

290.8 

80 

480.8 

324.3 
324.9 

341 

282.7 

190.7 

401 

521 

431.9 

291.3 

581 

481.6 

42 

283.5 

191.2 

02 

333.3 

224.8 

62 

383.0  1258.3 

22 

432.8 

291.9 

82 

482.5 

325.4 

43 

284.4 

191.8 

03 

334.1 

225.4 

63 

383.8    258.9 

23 

433.6 

292.5 

83 

483.3 

326.0 

44 

285.  2 

192.4 

04 

334.9 

225.9 

64 

384.7    259.5 

24 

434.4 

293.0 

84 

484.1 

326.6 

45 

286.0 

192.9 

05 

335.8 

226.  5 

65     385.5    260.0 

25 

435.3 

293.6 

85 

485.0 

327.2 

46 

286.9 

193.  5 

06 

336.6 

227.0 

66  \  386.3    260.6 

26 

436.1 

294.1 

86 

485.8 

327.7 

47 

287.  7  '  194.  0 

07 

337.4 

227.6 

67 

387.2  [261.1 

27 

436.9 

294.7 

87 

486.6 

328.2 

48 

288.  5  '  194.  6 

08 

338.3 

228.1 

68 

388. 0  i  261.  7 

28 

437.8 

295.  3 

88 

487.5 

328.8 

49 

289.3  !195.2 

09 

339. 1 

228.7 

69 

388. 8    262. 3 

29 

438.6 

295.8 

89 

488.3 

329.4 

50 

290.2 

195.  7 

10 

339. 9 

229.3 

70 

389.7    262.8 

30 

439.4 

296.4 

90 

489.2 

329.  9 

351 

291.0 

196.  3 

411 

340.7 

229.8 

471 

390.5 

263.4 

531 

440.3 

296. 9 

591 

490.0 

330.5 

52 

291.8 

196.8 

12 

341.6 

230.  4 

72 

391.3 

263.9 

32 

441.1 

297.4 

92 

490.8 

331.0 

53 

292.7 

197.4 

13 

342.4 

230.9 

73 

392.1 

264.5 

33  i  441.9 

298. 0 

93 

491.6 

331.6 

54 

293.5 

198.0 

14 

343.  2 

231. 5 

74 

393.0 

265.0 

34 

442.7 

298.6 

94 

492.5 

332.2 

55 

294.3 

198.5 

15 

344.1 

232.1 

75 

393.8 

265.6 

35 

443.6 

299.1 

95 

493.3 

332.7 

56 

295. 1 

199.1 

16 

344.9 

232.6 

76 

394.6 

266.2 

36 

444.4 

299.7 

96 

494.1 

333.3 

57 

296.0 

199.6 

17 

345.7 

233.2 

77 

395.5 

266.7 

37 

445.3 

300.2 

97 

494.9 

333.  8 

58 

296.8 

200.2 

18 

346. 5 

233.7 

78 

396.3 

267.3 

38 

446.1 

300.8 

98 

495.8 

334.4 

59 

297.6 

200.7 

19 

347.4 

234.  3 

79 

397.1 

267.9 

39 

446.9 

301.4 

99 

496.6 

334.  9 

60 

298.5 

201.3 

20 

348.2 

234.9 

80 

397.9 

268.4 

40 

447.7 

302.0 

600 

497.4 

335.  5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

56°  (124°,  236°,  304° 

)• 

Page  436] 

TABLE 

2. 

Difference  of  Latitude  and 

Departure  for 

35°  (145°,  215°,  325° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

50.0 

.35.0 

121 

99.1 

69.4 

181 

148.3 

103.8 

241 

197.4 

138.2 

2 

1.6 

1.1 

62 

50.8 

35.6 

22 

99.9 

70.0 

82 

149.1 

104.4 

42 

198.2 

138.8 

3 

2.5 

1.7 

63 

51.6 

36.1 

23 

100.8 

70.5 

83 

149.9 

105.0 

43 

199.1 

139.4 

4 

3.3 

2.3 

64 

52.4 

36.7 

24 

101.6 

71.1 

84 

150.7 

105.5 

44 

199.9 

140.0 

5 

4.1 

2.9 

65 

53.2 

37.3 

25 

102.4 

71.7 

85 

151.5 

106.1 

45 

200.7 

140.  5 

6 

4.9 

3.4 

«B 

54.1 

37.9 

26 

103.2 

72.3 

86 

152.4 

106.7 

46 

201.  5 

141.1 

7 

5.7 

4.0 

67 

54.9 

38.4 

27 

104.0 

72.8 

87 

153.  2  i  107.  3 

47 

202.3 

141.7 

8 

6.6 

4.6 

68 

55.7 

39.0 

28 

104.9 

73.4 

88 

154.  0  ;  107.  8 

48 

203.1 

142.2 

9 

7.4 

5.2 

69 

56.5 

39.6 

29 

105.7 

74.0 

89 

154.8    108.4 

49 

204.0 

142.8 

10 

8.2 

5.7 

70 
71 

57.3 
58.2 

40.2 

30 

106.5 

74.6 
75.1 

90 
191 

155.6 

109.0 

50 

204.8 
205.6 

143.4 
144.0 

11 

9.0 

6.3 

40.7 

131 

107.3 

156.5 

109.  H 

251 

12 

9.8 

6.9 

72 

59.0 

41.3 

32 

108.1 

75.7 

92 

157.3 

110.1 

52 

206.4 

144.5 

13 

10.6 

7.5 

73 

-  59.8 

41.9 

33 

108.9 

76.3 

93 

158. 1 

110.7 

53 

207.2 

145.1 

14 

11.5 

8.0 

74 

60.6 

42.4 

34 

109.8 

76.9 

94 

158.9 

111.3 

54 

208.1 

145.7 

15 

12.3 

8.6 

75 

61.4 

43.0 

35 

110.6 

77.4 

95 

159.7 

111.8 

55 

208.9 

146.3 

16 

13.1 

9.2 

76 

62.3 

43.6 

36 

111.4 

78.0 

96 

160.6 

112.4 

56 

209.7 

146.8 

17 

13.9 

9.8 

77 

63.1 

44.2 

37 

112.2 

78.6 

97 

161.4 

113.0 

57 

210.5 

147.4 

18 

14.7 

10.3 

78 

63.9 

44.7 

38 

113.0 

79.2 

98 

162.2 

113.6 

58 

211.3 

148.0 

19 

15.6 

10.9 

79 

64.7 

45.3 

39 

113.9 

79.7 

99 

163.0 

114.1 

59 

212.2 

148.6 

20 

16.4 

11.5 
12.0 

80 

65.5 

45.9 

40 

114.7 
115.5 

80.3 

200 
201 

163.8 
164:"6 

114.7 

60 

213.0 

149.1 
149.7 

21 

17.2 

81 

66.4 

46.5 

141 

80.9 

115.3 

261 

213.8 

22 

18.0 

12.6 

82 

67.2 

47.0 

42 

116.3 

81.4 

02 

165.  5 

115.9 

62 

214.6 

150.3 

23 

18.8 

13.2 

83 

68.0 

47.6 

43 

117.1 

82.0 

03 

166.3 

116.4 

63 

215.4 

150.9 

24 

19.7 

13.8 

84 

68.8 

48.2 

44 

118.0 

82.6 

04 

167.1 

117.0 

64 

216.3 

151.4 

25 

20.5 

14.3 

85 

69.6 

48.8 

45 

118.8 

83.2 

05 

167.9 

117.6 

65 

217.1 

152.0 

26 

21.3 

14.9 

86 

70.4 

49.3 

46 

119.6 

83.7 

06 

168.7 

118.2 

66 

217.9 

152.6 

27 

22.1 

15.5 

87 

71.3 

49.9 

47 

120.4 

84.3 

07 

169.6 

118.7 

67 

218.7 

153.1 

28 

22.9 

16.1 

88 

72.1 

50.5 

48 

121.2 

84.9 

08 

170.4 

119.3 

68 

219.5 

153.7 

29 

23.8 

16.6 

89 

72.9 

51.0 

49 

122.1 

85.5 

09 

171.2 

119.9 

69 

220.4 

154.  3 

30 

24.6 

17.2 

17.8 

90 
91 

73.7* 
74.5 

51.6 
52.2 

50 
151 

122.9 
123.7 

86.0 
86.6 

10 
211 

172.0 
172.  8 

120.5 

70 

221.2 
222.0 

154.9 
155.4 

31 

25.4 

121.0 

271 

32 

26.2 

18.4 

92 

75.4 

52.8 

52 

124.  5 

87.2 

12 

173.7 

121.6 

72 

222.8 

156.0 

33 

27.0 

18.9 

93 

76.2 

53.3 

53 

125.3 

87.8 

13 

174.5 

122.2 

73 

223.6 

156.  6 

34 

27.9 

19.5 

94 

77.0 

53.9 

54 

126.1 

88.3 

14 

175.3 

122.7 

74 

224.4 

157.2 

35 

28.7 

20.1 

95 

77.8 

54.5 

55 

127.0 

88.9 

15 

176. 1 

123.3 

75 

225.3 

157.7 

36 

29.5 

20.6 

96 

78.6 

55.1 

56 

127.8 

89.5 

16 

176.9 

123.9 

76 

226.1 

158.  3 

37 

30.3 

21.2 

97 

79.5 

55.  6 

57 

128.6 

90.1 

17 

177.8 

124.5 

77 

226.  9 

158.9 

38 

31.1 

21.8 

98 

80.3 

56.2 

58 

129.4 

90.6 

18 

178.6 

125.0 

78 

227.7 

159.5 

39 

31.9 

22.4 

99 

81.1 

56.8 

59 

130.2 

91.2 

19 

179.4 

125.  6 

79 

228.5 

160.0 

40 

32.8 

22.9 

100 

81.9 

57.4 

60 

131.1 

91.8 

20 

180.2 

126.2 

80 

229.4 

160.6 

41 

33.6 

23.5 

101 

82.7 

57.9 

161 

131.9 

92.3 

221 

181.0 

126.8 

281 

230.2 

161.2 

42 

34.4 

24.1 

02 

83.6 

58.5 

62 

132.7 

92.9 

22 

181.9 

127.3 

82 

231.0 

161.7 

43 

35.2 

24.7 

03 

84.4 

59.1 

63 

133.  5 

93.5 

23 

182.7  !127.9 

83 

231.8 

162.3 

44 

36.0 

25.2 

04 

85.2 

59.7 

64 

134.3 

94.1 

24 

183.  5 

128.5 

84 

232.6 

162.9 

45 

36.9 

25.8 

05 

86.0 

60.2 

65 

135.2 

94.6 

25 

184.3 

129.1 

85 

233.5 

163. 5 

46 

37.7 

26.4 

06 

86.8 

60.8 

66 

136.0 

95.2 

26 

185.1 

129.6 

86 

234.3 

164.0 

47 

38.5 

27.0 

07 

87.6 

61.4 

67 

136.8 

95.8 

27 

185.9 

130.2 

87 

235.1 

164.6 

48 

39.3 

27.5 

08 

88.5 

61.9 

68 

137.6 

96.4 

28 

186.8 

130.8 

88 

235.9 

165.2 

49 

40.1 

28.1 

09 

89.3 

62.5 

69 

138.4 

96.9 

29 

187.6 

131.3 

89 

236.  7 

165.8 

50 

41.0 

28.7 

10 

90.1 

63.1 

70 

139.3 

97.5 

30 

188. 4. 
189.2 

131.9 

90 

237.6 

166.3 

51 

41.8 

29.3 

111 

90.9 

63.7 

171 

140.1 

98.1 

231 

132.5 

291 

238.4 

166.9 

52 

42.6 

29.8 

12 

91.7 

64.2 

72 

140.9 

98.7 

32 

190.  0 

133.1 

92 

239.2 

167.5 

53 

43.4 

30.4 

13 

92.6 

64.8 

73 

141.7 

-  99.2 

33 

190.9 

133.6 

93 

240.0 

168.1 

54 

44.2 

31.0 

14 

93.4 

65.4 

74 

142.5 

99.8 

34 

191.7 

134.2 

94 

240.8 

168.6 

55 

45.1 

31.5 

15 

94.2 

66.0 

75 

143.4 

100.4 

35 

192.5 

1.34.  8 

95 

241.6 

169.2 

56 

45.9 

32.1 

16 

95.0 

66.5 

76 

144.2 

100.9 

36 

193.  3 

135.4 

96 

242.5 

169.8 

67 

46.7 

32.7 

17 

95.8 

67.1 

77 

145.0 

101.5 

37 

194.1 

135.  9 

97 

243.  3 

170.4 

58 

47.5 

33.  3 

18 

96.7 

67.7 

78 

145.8 

102.1 

38 

195.0 

136. 5 

98 

244.1 

170.9 

59 

48.3 

33.8 

19 

97.5 

68.3 

79 

146.6 

102.7 

39 

195.  8 

137.1 

99 

244.9 

171.5 

60 

49.1 

34.4 

20 

98.3 

68.8 

80 

147.4 

103.2 

40 

196.6 

137.7 

300 

245.7 

172.1 

DIst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

)5°  (1 

25°,  235 

°,  305° 

)■ 

TABLE  ± 

[Page  437 

Difference  of  Latitude  and  Departure  for  35°  (145°,  215°,  325° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.          Dep. 

JOl 

246.6 

172.6 

361 

295.7 

207.0 

421 

344.9 

241.5 

481 

394.0 

275.9 

541 

443.2 

310.3 

02 

247.4 

173.2 

62 

296.5 

207.6 

22 

345.  7 

242.0 

82 

394.8 

276.4 

42 

444.0 

310.9 

03 

248.2 

173.8 

63 

297.4 

208.2 

23 

346.5 

242.6 

83 

395.7 

277.0 

43 

444.8 

311.4 

04 

249.0 

174.3 

64 

298.2 

208.8 

24 

347. 3 

243.  2 

84 

396.5 

277.6 

44 

445.6 

312.0 

05 

249.  9 

174.9 

65 

299.0 

209.3 

25 

348.1 

243.8 

85 

397.3 

278.2 

45 

446.4 

312.6 

06 

250.7 

175.5 

66 

299.8 

209.9 

26 

349.0 

244.3 

86 

398.1 

278.7 

46 

447.3 

313.2 

07 

251.5 

176.1 

67 

300.  6 

210.  5 

27 

349.8 

244.9 

87 

398.9 

279.3 

47 

448.1 

313.  7 

08 

252.3 

176.6 

68 

301.5 

211.1 

28 

350.6 

245.  5 

88 

399.8 

279.9 

48 

448.9 

314.3 

09 

253. 1 

177.2 

69 

302.3 

211.6 

29 

351.4 

246.0 

89 

400.6 

280.5 

49 

449.7     314.9 

10 

253.9 

177.8 

70 

303.1 

212.2 

30 

352.2 
353. 1 

246.6 
247.2 

90 
491 

401.4 
402.2 

281.0 
281.6 

50 
551 

450.5  1  315.4 
451.4  1  316.0 

311 

254.8 

178.4 

371 

303.9 

212.8 

431 

12 

255.  6 

178.9 

72 

304.7 

213.4 

32  I  353.9 

247.8 

92 

403.0 

282.2 

52 

452.2  1  316.6 

13 

256.4 

179.5 

73 

305.6 

213.  9 

33  i  a54.  7 

248.3 

93 

403.9 

282.  8 

53 

453.0  i  317.2 

14 

257.2 

180.1 

74 

306.4 

214.5 

34 

355. 5 

248.9 

94 

404.7 

283.3 

54 

453.8  !  317.7 

15 

258.0 

180.7 

75 

307.2 

215. 1 

35 

356.3 

249.5 

95 

405.5 

283.9 

55 

454.6     318.3 

16 

258.9 

181.2 

76 

308.0 

215.  6 

36 

357.2 

250. 1 

96 

406.3 

284.5 

56 

455.5     318.9 

17 

259.  7 

181.8 

77 

308.8 

216.2 

37 

358.0 

250.6 

97 

407;  1  :285. 1 

57 

456.3     319.5 

18 

260.5 

182.4 

78 

309.  6 

216.8 

38 

358.8 

251.2 

98 

408.0  !285.6 

58 

457.1     320.0 

19 

261.3 

183.0 

79 

310.5 

217.4 

39 

359.  6 

251.8 

99 

408.8 

286.2 

59 

457.9     320.6 

20 
321 

262.1 
263. 0 

183.5 
184. 1 

80 

381 

311.3 
312.1 

217.9 

40 

360.4 
361.3 

252.4 
252.  9 

500 
501 

409.6 
410.4 

286.8 

60 

458.7     321.2 

218.5 

441 

287.4 

561 

459.6     321.8 

22 

263.  8 

184.7 

82 

312.9 

219.1 

42 

362.1 

253.  5 

02 

411.2 

287.9 

62 

460.4     322.3 

23 

264.6 

185.2 

83  :  313.7 

219.7 

43 

362.9 

254.1 

03 

412.1 

288.5 

63 

461. 2     322. 9 

24 

265.4 

185.8 

84  1  314.6 

220.2 

44 

363.7 

254.  7 

04 

412.9 

289.1 

64 

462.0     323.5 

25 

266.2 

186.4 

85     315.4 

220.8 

45 

364.  5 

255.  2 

05 

413.  7 

289.7 

65 

462.8     324.1 

26 

267.1 

187.0 

86     316.2 

221.4 

46 

365. 4 

255.  8 

06 

414.5 

290.2 

66 

463.7     324.6 

27 

267.9 

187.5 

87     317.0 

222.0 

47 

366.2 

256.  4 

07 

415.3 

290.8 

67 

464.5     325.2 

28 

268.7 

188.1 

88     317.8 

222.5 

48 

367.0 

256.9 

08 

416.1 

291.4 

68 

465. 3     325. 8 

29 

269.5 

188.7 

89  1  318.7 

223.1 

49 

367.8 

257.5 

09 

417. 0 

291.9 

69 

466.1     326.4 

30 
331 

270.3 

271.  r 

189.  3 
189.8 

90 
■391 

319.5 

223.7 

50 

368.6 
369.4 

258.1 
258.  7 

10 
511 

417.8 
418.6 

292.5 

70 

466.9 

326.  9  1 

320.3 

224.  3 

451 

293.1 

571 

467.8 

327.  5  1 

32 

272.0 

190.4 

92 

321.1 

224.8 

52 

370.3 

259.2 

12 

419.4 

293.7 

72 

468. 6     328. 1 

33 

272.8 

191.0 

93 

321.9 

225. 4 

53 

371.1 

259.8 

13 

420.2  (294.2 

73 

469.4     328.7 

34 

273. 6 

191.6 

94 

322.8 

226.0 

54 

371.9  !260.4 

14 

421.1  '294.8 

74 

470.2     329.2 

35 

274.4 

192.1 

95     323.6  1226.5 

55 

372.7 

261.0 

15 

421.9    295.4 

75 

471.0     329.8 

36 

275.2 

192.7 

96 

324.4  1227.1 

56 

373.5 

261.5 

16 

422.7    296.0 

76 

471.9     330.4 

37 

276.1 

193.3 

97 

325.2    227.7 

57 

374.4 

262.1 

17 

423.5    296.5 

77 

472.  7     331. 0 

38 

276.9 

193. 9 

98 

326.0    228.3 

58 

375.2 

262.7 

18 

424.3  1297.1 

78 

473. 5     331. 5 

39 

277.7 

194.4 

99 

326.9    228.8 

59 

376.0 

263.  3 

19 

425.2    297.7 

79 

474.3  ;  332.1 

40 
341 

278.5 
279.3 

195.0 

400 

327.7  |229.4 

60 
461 

376.8 
377.6 

263.8 

20 

426.0    298.3 

80 

475. 1  !  332.  7 
476.0     333.3 

195.6 

401 

328.5    230.0 

264.  4 

521 

426.8 

298.8 

581 

42 

280.2 

196.1 

02 

329.3    230.6 

62 

378.5 

265.0 

22 

427.6 

299.4 

82 

476.  8  i  333. 8 

43 

281.0 

196.7 

03 

330.1     231.1 

63 

379.3 

265.5 

23 

428.4 

300.0 

83 

477.6     334.4 

44 

281.8 

197.3 

04 

330.9  !231.7 

64 

380.1 

266.1 

24 

429.3 

300.5 

84 

478.4     335.0 

45 

282.6 

197.9 

05 

331.8  [232.3 

65  1  380.9 

266.7 

25 

430.1 

301.1 

85 

479.2     335.6 

46 

283.4 

198.4 

06 

332.  6 

232.  9 

66     381.7 

267.3 

26 

430.9    301.7 

86 

480. 1  j  336. 1 

47 

284.3 

199.0 

07     333.4 

233.4 

67  1  382.6 

267.8 

27 

431.7    302.3 

87 

480.  9  \  336.  7 

48 

285.1 

199.6 

08 

334.2 

234.  0 

68  1  383.4 

268.4 

28 

432.5 

302.8 

88 

481.  7     337. 3 

49 

285.9 

200.2 

09 

335.0 

234.6 

69  '  384.2 

269.0 

29 

433.4 

303.4 

89 

482. 5     337. 9 

50 
351 

286: 7 
287.5 

200.7 
201.3 

10 
411 

335.  9 
336.7 

235.1 
235.  7 

70  1  385.0 
471  ,  385.8 

269.6 
270. 1 

30 

434.2 

304.0 

90 

483.3  338.4 
484.2     339.0 

531 

435.0 

304.5 

591 

52 

288.3 

201.9 

12 

337.5 

236.3 

72     386. 6 

270.7 

32 

435.8 

305.1 

92 

485.0  !  339.6 

53 

289.2 

202.5 

13 

338.3 

236.  9 

73 

387.5 

271.3 

33 

436.6 

305.7 

93. 

485.8  !  340.2 

54 

290.0 

203.0 

14 

339. 1 

237.  4 

74 

388.3 

271.9 

34 

437.5 

306.3 

94 

486.6  {  340.7 

55 

290.8 

203. 6 

15 

340.0 

238.  0 

75 

389.1 

272.4 

35 

438. 3 

306.8 

95 

487.4  '  341.3 

56 

291.6 

204.2 

16 

340.  8 

238.6 

76 

389.9 

273.0 

36 

439.1 

307.4 

96 

488.3  \  341.9 

57 

292.4 

204.7 

17  '  341.6 

239.2 

77 

390.7 

273.6 

37 

439.9 

308.0 

97 

489.1      342.5 

58 

293.3 

205.  3 

18  !  342.4 

239.7 

78 

391.6 

274.2 

38 

440.7 

308.6 

98 

489.9     343.0 

59 

294.1 

205.9 

19  I  343.2 

240.3 

79 

392.4 

274.7 

39 

441.5 

309.1 

99 

490. 7     343. 6 

60 

294.9 

206.5 

20     344. 1 

240.9 

80 

393.2 

275.  3 

40 

442.3 

309.7 

600 

491.  5  ,  344. 1 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     j     Lat. 

, 

>5°  (125°,  235°,  305°). 

Page  438 

] 

TABLE  2. 

difference  of  Latitude  and 

Departure  for  36°  (144°,  216 

°,  324= 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.       Lat. 

Dep. 

1 

0.8 

0.6 

61 

49.4 

35.9 

121 

97.9 

71.1 

181 

146.  4 

106.  4 

241  '  195.0 

141.7 

2 

1.6 

1.2 

62 

50.2 

36.4 

22 

98.7  1    71.7 

82 

147.2 

107.0 

42  i  195.8 

142.2 

3 

2.4 

1.8 

63 

51.0 

37.0 

23 

99.5  !    72.3 

83 

148.1 

107.6 

43  i  196.6 

142.8 

4 

3.2 

2.4 

64 

51.8 

37.6 

24 

100.3  1    72.9 

84 

148.9 

108.2 

44  I  197.4 

143.4 

5 

4.0 

2.9 

65 

■   52.6 

38.2 

25 

101.1  1    73.5 

85 

149.7 

108.7 

45  1  198.2 

144.0 

6 

4.9 

3.5 

6» 

53.4 

.38.  8 

26 

101.9  1    74.1 

86 

150.5 

109.3 

46  ''  199.0 

144.6 

7 

5.7 

4.1 

67 

54.2     39.4 

27 

102.7  1    74.6 

87 

151.3 

109.9 

47      199. 8 

145.2 

8 

6.5 

4.7 

68 

,55;  0     40.  0 

28 

103.6  1    75.2 

88 

152. 1 

110.5 

48     200.6 

145.8 

9 

7.3 

5.3 

■   69 

55. 8  ■'  40.  (5 

29 

104.4      75.8 

89 

152.9 

111.1 

49     201.4 

146.  4 

10 

8.1 

5.9 

70 

56. 6  i  41. 1 

30 

105.2      76.4 

90 

153.  7 

111.7 
112.3 

50  i  202.3 
251      203.  i 

146.9 

11 

8.9 

6.5 

71 

57.4  i  41.7 

131  1  106.0      77.0 

191 

154. 5 

147.5 

12 

9.7 

7.1 

72 

58.2 

42.3 

32 

106.8      77.6 

92 

155.3 

112.9 

52     203.9 

148.1 

13 

10.5 

7.6 

73 

59.1 

42.9 

33 

107.6      78.2 

93 

156.1 

113.4 

53     204. 7 

148.7 

14 

11.3 

8.2 

74 

59.9 

43.5 

34 

108.4  '    78.8 

94 

156.  9 

114.0 

54     205.5 

149.3 

15 

12.1 

8.8 

75 

60.7 

44.1 

35 

109.2      79.4 

95 

157.  8 

114.6 

55     206.3 

149.9 

16 

12.9 

9.4 

76 

61. 5  1  44.  7 

36 

110.0      79.9 

96 

158. 6 

115.  2 

56     207. 1 

150.5 

17 

13.8 

10.0 

77 

62. 3  1  45.  3 

37 

110.8      80.5 

97 

159. 4 

115.  8 

57     207. 9 

151.1 

18 

14.6 

10.6 

78 

63. 1     45.  8 

38 

111.6      81.1 

98 

160.2 

116.4 

58     208. 7 

151.6 

19 

15.4 

n.2 

79 

63.9  1  46.4 

39 

112.5      81.7 

99 

161.0 

117.0 

59     209. 5 

152.2 

20 
21 

16.2 

11.8 
12.3 

80 
81 

64.7     47.0 

40 

113.3      82.3 

200 

161.8 
162.6 

117.6 
118.1 

60 
261 

210.  3 

152.8 

17.0 

65.5     47.6 

141 

114.1  '    82.9 

201 

211.2 

153.4 

22 

17.8 

12.9 

82 

66.  3  i  48.  2 

42 

114.9      83.5 

02 

163.4 

118.7 

62  '  212.0 

154.0 

23 

18.6 

13.5 

83 

67. 1     48.  8 

43 

115.  7      84. 1 

03 

164.2 

119.3 

63     212. 8 

154.6 

24 

19.4 

14.1 

84 

68. 0     49.  4 

44 

116. 5      84. 6 

04 

165.0 

119.9 

64     213. 6 

155.2 

25 

20.2 

14.7 

85 

68.  8     50.  0 

45 

117.3      85.2 

05 

165.8 

120.5 

G5     214.4 

155.8 

26 

21.0 

15.  3 

86 

69.  6     50. 5 

46 

118.1  !    85.8 

06 

166.7 

121.1 

66     215.2 

156.4 

27 

21.8 

15.9 

87 

70. 4     51. 1 

47 

118.9      86.4 

07 

167.5 

121.7 

67     216.0 

156.9 

28 

22.7 

16.5 

88 

71.2     51.7 

48 

119.7      87.0 

08 

16&.3 

122.3 

68     216. 8 

157.5 

29 

23.5 

17.0 

89 

72. 0     52.  3 

49 

120.5  ;    87.6 

09 

169.1 

122.8 

69     217. 6 

158.1 

30 
31 

24.3 

17.6 

90 

72. 8     52.  9 

50 

121.4 

88.2 
8'8.8 

10 
211 

169.9 
170.7 

123.4 

70 

218.4 
219.2 

158.7 
159.3 

25.1 

18.2 

91 

73.6  1  53.5 

151 

122.2 

124.0 

271 

32 

25.9 

18.8 

92 

74.4 

54.1 

52 

123.0      89.3 

12 

171.5 

124.6 

72     220. 1 

159.9 

33 

26.7 

19.4 

93 

75.2 

54.7 

53 

123.  8  i    89. 9 

13 

172.3 

125. 2 

73     220.9 

160.  5 

34 

27.5 

20.0 

94 

76.0  i  55.3 

54 

124.  6      90.  5 

14 

173.1 

125.8 

74     221.7 

161.1 

35 

28.3 

20.6 

95 

76.9 

55.8 

55 

125. 4      91. 1 

15 

173.9 

126.4 

75     222.5 

161.6 

36 

29.1 

21.  2 

96 

77.7 

56.4 

56 

126.2      91.7 

16 

174.7 

127.0 

76     223. 3 

162.2 

37 

29.9 

2L7 

97 

78.5 

57.0 

57 

127.0  i    92.3 

17 

175. 6 

127.  5 

77     224.1 

162.8 

38 

30.7 

22.3 

98 

79. 3  i  57. 6 

58 

127.8      92.9 

18 

176.4 

128.1 

78     224. 9 

163.4 

39 

31.6 

22.9 

99 

80. 1  1  58.  2 

59 

128.6      93.5 

19 

177.2 

128.7 

79     225.7 

164.0 

40 

32.4 
33.2 

23.5 

100 

80.  9  i  58.  8 

60 

129.4  j    94.0 

20 

178.0 
178.8 

129.3 
129."9 

80     226. 5 
281     227.3 

164.6 
165.2 

41 

24.1 

101 

81.7     59.4 

161 

130.3  i    94.6 

221 

42 

34.0 

24.7 

02 

82.5     60.0 

62 

131.1  1    95.2 

22 

179.6 

130.5 

82     228. 1 

165.  8 

43 

34.8 

25.3 

03 

83.  3     60. 5 

63 

131.9  j    95.8 

23 

180.4 

131.1 

83  :  229.0 

166.3 

44 

35.6 

25.9 

04 

84. 1     61. 1 

64 

132.7  1    96.4 

24 

181.2 

131.7 

84     229.8 

166.9 

45 

36:4 

26.5 

05 

84.9     61.7 

65 

133.5      97.0 

25 

182.0 

132. 3 

85     230. 6 

167.5 

46 

37.2 

27.0 

06 

85.8  j  62.3 

66 

134.3      97.6 

26 

182.8 

132.8 

86     231. 4 

168.1 

47 

38.0 

27.6 

07 

86.6  i  62.9 

67 

135. 1      98.  2 

27 

183.6 

133.4 

87      232.2 

168.7 

48 

38.8 

28.2 

08 

87.4  j  63.5 

68 

135. 9      98.  7 

28 

184.5 

134.0 

88     233. 0 

169.  3 

49 

39.6 

28.8 

09 

88. 2  1  64. 1 

69 

136.  7      99.  3 

29 

185.3 

134.6 

89     233.8 

169.9 

50 
5i 

40.5 
41.3 

29.4 

10 

89.0 

64.7 
65.2 

70 

137.5  1    99.9 

30 

186.1 

135.  2 

135.  8 

90     234.6 
291      235.4 

170.5 
171.0 

30.0 

111 

89.8 

171 

138.3 

100.  5 

231 

186.9 

52 

42.1 

30.6 

12 

90.6  ;  65.8 

72 

139.2 

101.1 

32 

187.7 

136.  4 

92     236.2 

171.6 

53 

42.9 

31.2 

13 

91.4  i  66.4 

73 

140.0 

101.7 

33 

188.5 

137.0 

93  '  237. 0 

172,2 

54 

43.7 

31.  7 

14 

92.2  1  67.0 

74 

140.8 

102.  3 

34 

189.3 

137. 5 

94 

237.  9 

172.8 

55 

44.5 

32.3 

15 

93.0 

67.6 

75 

141.6 

102.9 

35 

190.1 

138. 1 

95 

238.  7 

173.4 

56 

45.3 

32.  9 

16 

93.8 

68.2 

76 

142.4 

103.  5 

36 

190.9 

138.  7 

96 

239.  5 

174.0 

57 

46.1 

33.5 

17 

94.7 

68.8 

77 

143.2 

104.0 

37 

191.7 

139.3 

97 

240.3 

174.6 

58 

46.9 

34.1 

18 

95.5 

69.4 

78 

144.0 

104.6 

38 

192. 5 

139.9 

98 

241. 1 

175.  2 

59 

47.7 

34.7 

19 

96.3 

69.9 

79 

144.8 

105.2 

39 

193.  4 

140.5 

99 

241.9 

175.  7 

60 

48.5 

35.3 

20 

97.1     70.5 

80 

145.6 

105.8 

40 

194.2 

141.1 

300 

242.7 

176.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     j    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

i4°  (1 

26°,  234°,  306° 

)■ 

TABLE 

.  2. 

[Page  439 

Difference  of  Latitude  and  Departure  for  36°  (144°,  216°,  324° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

301 

243.5 

176.9 

361 

292.1 

212.2 

421 

340.6 

247.5 

481 

389.1 

282.7 

541 

437.7 

318.0 

02 

244.3 

177.5 

62 

292.9 

212.8 

22 

341.4 

248.1 

82 

390.0 

283.3 

42 

438.5 

318.6 

03 

245. 1 

178.1 

63 

293.7 

213.4 

23 

342.2 

248.6 

83 

390.8 

283.9 

43 

439.3 

319.1 

04 

246.0 

178.7 

64 

294.5 

214.0 

24 

343.0 

249.2 

84 

391.  6 

284.5 

44 

440.2 

319.7 

05 

246.8 

179.3 

65 

295.3 

214.6 

25 

343.8 

249.8 

85 

392.4 

285.1 

45 

441.0 

320.3 

06 

247.6 

179.9 

66 

296.1 

215.  1 

26 

344.7 

250.4 

86 

393.2 

285.6 

46 

441.8 

320.9 

07 

248.4 

180.5 

67 

296.9 

215.7 

27 

345.5 

251.0 

87 

394.0 

286.  2 

47 

442.6 

321.5 

08 

249.2 

181.1 

68 

297.7 

216.3 

28 

346.  3 

251.6 

88 

394.8  [286.8 

48 

443.4 

322. 1 

09 

250.0 

181.6 

69 

298.5 

216.9 

29 

347.1 

252.2 

89 

395.6  1287.4 

49 

444.2 

322.7 

10 

250.8 
251.6 

182.2 
182.  8 

70 

299.3 

217.5 

30 

347. 9 

252.8 

90 

396. 4    288.  0 

50 

445.0 

323.3 

311 

371 

300.2 

218.1 

431 

348.7 

253.3 

491 

397.3    288.6 

551 

445.8 

323.8 

12 

252.4 

183.4 

72 

301.0 

218.7 

32 

349.5 

253.9 

92 

398.1    289.2 

52 

446.6 

324.4 

13 

253.2 

184.0 

73 

301.8 

219.3 

33 

350.3 

254.5 

93 

398.9    289.8 

53 

447.4 

325.0 

14 

254.0 

184.6 

74 

302.6 

219.8 

34 

351. 1 

255.1 

94 

399.7  |290.3 

54 

448.2 

325.6 

15 

254.9 

185.  2 

75 

303.4 

220.4 

35 

351.9 

255.  7 

95 

400.5  ;290.9 

55 

449.0 

326.2 

16 

255.7 

185.8 

76 

304.2 

221.0 

36 

352.7 

256.3 

96 

401.3 

291.5 

56 

449.8 

326.8 

17 

256.5 

186.4 

77 

305.0 

221.6 

37 

353.6 

256.9 

97 

402.1 

292.1 

57 

450.7 

327.4 

18 

257.3 

186.9 

78 

305.8 

222.2 

38 

354.4 

257.5 

98 

402.9 

292.7 

58 

451.5 

328.0 

19 

258.1 

187.5 

79 

306.6 

222.8 

39 

355.2 

258.0 

99 

403.7 

293.3 

59 

452.3 

328.5 

20 
321 

258.9 

188.1 

80 

307.4 
308.2 

223.4 

40 

356.0 
356.8 

258.6 

500 

404.5 
405.3 

293.9 

60 

453.1 

329.1 

259.7 

188.7 

381 

224.0 

441 

259.2 

501 

294.5 

561 

453.9 

329.7 

22 

260.5 

189.3 

82 

309.1 

224.5 

42 

357.6 

259.8 

02 

406.1 

295.0 

62 

454.7 

330.3 

23 

261.  3 

189.9 

83 

309.9 

225. 1 

43 

358.4 

260.4 

03 

407.0    295.6 

63 

455.5 

330.9 

24 

262.1 

190.5 

84 

310.7 

225.  7 

44 

359.  2 

261.0 

04 

407.8    296.2 

64 

456.3 

331.5 

25 

262.9 

191.0 

85 

311.5 

226.3 

45 

360.0 

261.6 

05 

408.6 

296.  8 

65 

457.1 

332.1 

26 

263.7 

191.6 

86 

312.3 

226.9 

46 

360.8 

262.2 

06 

409.4 

297.4 

66 

457.9 

332.7 

27 

264.6 

192.2 

87 

313. 1 

227.5 

47 

361.6 

262.8 

07 

410.2 

298.0 

67 

458.7 

333.3 

28 

265.4 

192.8 

88 

313.9 

228.1 

48 

362.4 

263.  3 

08 

411.0 

298.6 

68 

459.5 

333.8 

29 

266.2 

193.4 

89 

314.7 

228.7 

49 

363.3 

263. 9 

09 

411.8 

299.2 

69 

460.3 

334.4 

30 

267.0 

194.0 

90 

315.5 

229.2 

50 

364.1 
364.9 

264.5 

10 

412.6 

299.8 

70 

461.1 

335.0 

331 

267.8 

194.6 

391 

316.3 

229.8 

451 

265.1 

511 

413.4 

300.3 

571 

462.0 

335.  6 

32 

268.6 

195.2 

92 

317.1 

230.4 

52 

365.7 

265.7 

12 

414.2 

300.9 

72 

462.8 

336.2 

33 

269.4 

195.  7 

93 

318.0 

231.0 

53 

366.5 

266.3 

13 

415.1 

301.  5 

73 

463.6 

336.8 

34 

270.2 

196.3 

94 

318.8 

231.6 

54 

367.  3 

266.9 

14 

415.9 

302.1 

74 

464.4 

337.4 

35 

271.0 

196.9 

95 

319.6 

232.2 

55 

368.1 

267.5 

15 

416.7 

302.7 

75 

4a5.2 

338.0 

36 

271.8 

197.5 

96 

320.4 

2.32. 8 

56 

368.9 

268.0 

16 

417.5 

303.3 

76 

466.0 

338.  5 

37 

272.6 

198.1 

97 

321.2 

233.4 

57 

369.7 

268.6 

17 

418.3 

303.9 

77 

466.8 

339.1 

38 

273.5 

198.7 

98 

322.0 

233.9 

58 

370.5 

269.2 

18 

419.1 

304.4 

78 

467.6 

339.7 

39 

274.3 

199. 3 

99 

322.8 

234.5 

59 

371.3 

269.  8 

19 

419.9 

305. 0 

79 

468.4 

340.3 

40 

275.1 

199.9 

400 

323.6 

235. 1 

60 

372.  2 

270.4 

20 

420.7 

305.6 

80 

469.3 

340.9 

341 

275. 9 

200.4 

401 

324.4 

235.  7 

461 

373.0 

271.0 

521 

421.5 

306.2 

581 

470.1 

341.5 

42 

276.7 

201.0 

02 

325.  2 

236.  3 

62 

373. 8 

271.6 

22 

422.3 

306.8 

82 

470.9 

342.1 

43 

277.  5 

201.6 

03 

326.0 

236.9 

63 

374.6 

272.2 

23 

423.1 

307.4 

83 

471.7 

342.7 

44 

278.3 

202.2 

04 

326.9 

237.5 

64 

375.4 

272.7 

24 

423.9 

308.0 

84 

472.5 

343.2 

45 

279;  1 

202.8 

05 

327.7 

238.1 

65 

376.2 

273.3 

25 

424.7 

308.6 

85 

473.3 

343.8 

46 

279.9 

203.4 

06 

328.  5 

238.  7 

66 

377.0 

273. 9 

26 

425. 5 

309.2 

86 

474.1 

344.4 

47 

280.7 

204.0 

07 

329.3 

239. 2 

67 

377.8 

274.5 

27 

426.4 

309.7 

87 

474.9 

345.0 

48 

281.5 

204.6 

08 

330. 1 

239.8 

68 

378. 6 

275.1 

28 

427.2 

310.3 

88 

475.7 

345.6 

49 

282.4 

205.1 

09 

330.9 

240.4 

69 

379.4 

275.7 

29 

428.0 

310.9 

89 

476.5 

346.2 

50 
351 

283.2 

205.7 

10 

331.7 

241.0 

70 

380.2 

276.3 

30 

428.8 

311.5 

90 

477.3 

346.8 

284.0 

206.3 

411 

332.5 

241.6 

471 

381.1 

276.9 

531 

429.6 

312.1 

591 

478.2 

347.4 

52 

284.8 

206.9 

12 

333.  3 

242.2 

72 

381.9 

277.4 

32 

430.4 

312.7 

92 

479.0 

347.9 

53 

285.  6 

207.5 

13 

334.1 

242.8 

73 

382.7 

278.0 

33 

431.  2 

313.  3 

93 

479.8 

348.5 

54 

286.4 

208.1 

14 

334.9 

243.4 

74 

383. 5 

278.6 

34 

432.0 

313.9 

94 

480.6 

349.1 

55 

287.2 

208.7 

15 

335.  8 

243.9 

75 

384.3 

279.  2 

35 

432.9 

314.4 

95 

481.4 

349.7 

56 

288.0 

209.3 

16 

336.6 

244.5 

76 

385.1 

279.8 

36 

433.7 

315. 0 

96 

482.2 

350.  3 

57 

288.8 

209.8 

17 

337.4 

245.1 

77 

385. 9 

280.4 

37 

434.5 

315. 6 

97 

483.0 

350.9 

58 

289.6 

210.4 

18 

338.  2 

245.  7 

78 

386.7 

281.0 

38 

435.3 

316.2 

98 

483.8 

351.5 

59 

290.4 

211.0 

19 

339.  0 

246.  3 

79 

387. 5  • 

281.6 

39 

436.1 

316.8 

99 

484.6 

352.1 

60 

291.3 

211.6 

20 

339.  8 

246.9 

80 

388.3 

282.1 

40 

436.9 

317.4 

600 

485.4 

352.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

DLst. 

Dep. 

Lat. 

Difct. 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

54°  (1 

26°,  234 

°,  306° 

)• 

Page  440] 

TABLE  ± 

Difference  of  Latitude  and  Departure  for  c 

!7°  (143°,  217°,  323° 

). 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

48.7 

36.7 

121 

96.6 

72.8 

181 

144.6 

108.9 

241 

192.5 

145.0 

2 

1.6 

1.2 

62 

49.5 

37.3 

22 

97.4 

73.4 

82 

145.  4 

109.5 

42 

193.3 

145.  6 

3 

2.4 

1.8 

63 

50.3 

37.9 

23 

98.2 

74.0 

83 

146.2 

110.1 

43 

194.1 

146.  2 

4 

3.2 

2.4 

64 

51.1 

38.5 

24 

99.0 

74.6 

84 

146.9 

110.7 

44 

194.9 

146.8 

5 

4.0 

3.0 

65 

51.9 

39.1 

25 

99.8 

75.2 

85 

147.7 

111.3 

45 

195.7 

147.4 

6 

4.8 

3.6 

m 

52.7 

39.7 

26 

100.6 

75.8 

86 

148.5 

111.9 

46 

196.5 

148.0 

7 

5.6 

4.2 

67 

53.5 

40.3 

27 

101.4 

76.4 

87 

149.3 

112.5 

47 

197.3 

148.6 

8 

6.4 

4.8 

68 

54.3 

40.9 

28 

102.2 

77.0 

88 

150.1 

113.1 

48 

198.1 

149.3 

9 

7.2 

5.4 

69 

55.1 

41.5 

29 

103.0 

77.6 

89 

150.9 

113.7 

49 

198.9 

149.9 

10 

8.0 

6.0 

70 

55.9 

42.1 

30 

103.8 

78.2 

90 

151.7 

114.3 

50 

199.7 
200.5 

150.5 
151.1 

11 

8.8 

6.6 

71 

56.7 

42.7 

131 

104.6 

78.8 

191 

152.5 

114.9 

251 

12 

9.6 

7.2 

72 

57.5 

43.3 

32 

105.4 

79.4 

92 

153.3 

115.5 

52 

201.3 

151.7 

13 

10.4 

7.8 

73 

58.3 

43.9 

33 

106.2 

80.0 

93 

154.1 

116.2 

53 

202.1 

152.3 

14 

11.2 

8.4 

74 

59.1 

44.5 

34 

107.0 

80.6 

94 

154.9 

116.8 

54 

202.9 

152.  9 

15 

12.0 

9.0 

75 

59.9 

45.1 

35 

107.8 

81.2 

95 

155.7 

117.4 

55 

203.7 

153.5 

16 

12.8 

9.6 

76 

60.7 

45.7 

36  !  108.6 

81.8 

96 

156.5 

118.0 

56 

204.5 

154.1 

17 

13.6 

10.2 

77 

61.5 

46.3 

37     109.4 

82.4 

97 

157.3 

118.6 

57 

205.2 

154.7 

18 

14.4 

10.8 

78 

62.3 

46.9 

38  !  110.2 

83.1 

98 

158.1 

119.2 

58 

206.0 

155.  3 

19 

15.2 

11.4 

79 

63.1 

47.5 

39  i  111.0 

83.7 

99 

158.9 

119.8 

59 

206.8 

155. 9 

20 

16.0 

12.0 

80 

63.9 

48.1 

40 

111.8 
112.  6 

84.3 
84.9 

200 
201 

159.7 

120.4 

60  !  207.6 

156.5 

21 

16.8 

12.6 

81 

64.7 

48.  7 

141 

160.5 

121.0 

261 

208.4 

157.1 

22 

17.6 

13.2 

82 

65.5 

49.3 

42 

113.4 

85.5 

02 

161.3 

121.6 

62 

209.2 

157.7 

23 

18.4 

13.8 

83 

66.3 

50.0 

43 

114.  2 

86.1 

03 

162.1 

122.2 

63 

210.0 

158.3 

24 

19.2 

14.4 

84 

67.1 

50.6 

44  '  115.0 

86.7 

04 

162.9 

122.8 

64 

210.8 

158.9 

25 

20.0 

15.0 

85 

67.9 

51.2 

45     115.8 

87.3 

05 

163.7 

123.4 

65 

211.6 

159.5 

26 

20.8 

15.6 

86 

68.7 

51.8 

46      116.6 

87.9 

06 

164.5 

124.0 

66 

212.4 

160.1 

27 

21.6 

16.2 

87 

69.5 

52.4 

47     117.4 

88.5 

07 

165.3 

124.6 

67 

213.  2 

160.7 

28 

22.4 

16.9 

88 

70.3 

53.0 

48 

118.2 

89.1 

08 

166.1 

125.2 

68 

214.0 

161.3 

29 

23.2 

17.5 

89 

71.1 

53.6 

49 

119.0 

89.7 

03 

166.9 

125.8 

69 

214.8 

161.9 

30 

24.0 

18.1 
18.7 

90 

71.9 

54.2 

50 

119.8 

90.3 

10- 

167.7 

126.4 
127.0 

70 

271 

215.  6 
216.4 

162.5 
163.1 

31 

24.8 

91 

72.7 

54.8 

151 

120.6 

90.9 

211 

168.5 

32 

25.6 

19.3 

92 

73.5 

55.4 

52 

121.4 

91.5 

12 

169.3 

127.6 

72 

217.2 

163.7 

33 

26.4 

19.9 

93 

74.3 

56.0 

53 

122.2 

92.1 

13 

170.1 

128.2 

73 

218.0 

164.3 

34 

27.2 

20.5 

94 

75.1 

56.6 

54 

123.0 

92.7 

14 

170.9 

128.8 

74 

218.8 

164.9 

35 

28.0 

21.1 

95 

75.9 

57.2 

55 

123.8 

93.3 

15 

171.7 

129.4 

75 

219.6 

165.5 

36 

28.8 

21.7 

96 

76.7 

57.8 

56 

124.6 

93.9 

16 

172.5 

130.0 

76 

220.4 

166.1 

37 

29.5 

22.3 

97 

77.5 

58.4 

57 

125.  4 

94.5 

17 

173.  3 

130.6 

77 

221.2 

166.7 

38 

30.3 

22.9 

98 

78.3 

59.0 

58 

126.2 

95.1 

18 

174.1 

131.  2 

78 

222.  0 

167.3 

39 

31.1 

23.5 

99 

79.1 

59.6 

59 

127.0 

95.7 

19 

174.9 

131.8 

79 

222.8 

167.9 

40 

31.9 
32.7 

24.1 

100 

79.9 

60.2 

60 

127.8 

96.3 

20 

175.7 

132.4 
133.0 

80 
281 

223.6 
224.4 

168.5 
169.  1 

41 

24.7 

101 

80.7 

60.8 

161 

128.6 

96.9 

221 

176.5 

42 

33.5 

25.3 

02 

81.5 

61.4 

62 

129.4 

97.5 

22 

177.  3 

133.6 

82 

225.  2 

169.7 

43 

34.3 

25.9 

03 

82.3 

62.0 

63 

130.2 

98.1 

23 

178.1 

134.2 

83 

226.0 

170.3 

44 

35.1 

26.5 

04 

83.1 

62.6 

64 

131.0 

98.7 

24 

178.9 

134.8 

84 

226.8 

170.9' 

45 

.35.9 

27.1 

05 

83.9 

63.2 

65 

131.8 

99.3 

25 

179.7 

135.4 

85 

227.6 

171.5 

46 

36.7 

27.7 

06 

84.7 

63.  8 

66 

132.6 

99.9 

26 

180. 5 

136.0 

86 

228.4 

172.1 

47 

37.5 

28.3 

07 

85.5 

64.4 

67 

133.4 

100.5 

27 

181.3 

136.  6 

87 

229.2 

172.7 

48 

38.3 

28.9 

08 

86.3 

65.0 

68 

134.  2 

101.1 

28 

182.1 

137.2 

88 

230.0 

173.3 

49 

39.1 

^.5 

09 

87.1 

65.6 

69 

135.  0 

101.7 

29 

182.9 

137.8 

89 

230.8 

173.9 

50 

39.9 

30.1 

10 

87.8 

66.2 

70 

135.8 
136.6 

102.3 

30 

183.  7 

138.4 

90 

231.6 

174.5 
175. 1 

51 

40.7 

30.7 

111 

88.6 

66.8 

171 

102.9 

231 

184.  5     139.  0 

291 

232.4 

52 

41.5 

31.3 

12 

89.4 

67.4 

72 

137.4 

103.5 

32 

185. 3  i 139. 6 

92 

233.2 

175.7 

53 

42.3 

31.9 

13 

90.2 

68.0 

73 

138.2 

104.1 

33 

186.  1     140.  2 

93 

234.0 

176.3 

54 

43.1 

32.5 

14 

91.0 

68.6 

74 

139.0 

104.7 

34 

186.9'  140.8 

94 

234.8 

176.9 

55 

43.9 

33.1 

15 

91.8 

69.2 

75 

139.8 

105.  3 

35 

187.7     141.4 

95 

235.  6 

177.5 

56 

44.7 

33.7 

16 

92.6 

69.8 

76 

140.6 

105. 9 

36 

188.  5     142.  0 

96 

236.4 

178.1 

57 

45.5 

34.3 

17 

93.4 

70.4 

77     141.4 

106.5 

37 

189.  3     142.  6 

97 

237.2 

178.7 

58 

46.3 

34.9 

18 

94.2 

71.0 

78 

142.2 

107.1 

38 

190. 1     143. 2 

98 

238.0 

179.3 

59 

47.1 

35.5 

19 

95.0 

71.6 

79 

143.0 

107.7 

39 

190.9 

143.8 

99 

238.  8 

179.9 

60 

47.9 

36.1 

20 

95.8 

72.2 

80 

143.8 

108.3 

40 

191.7 

144.4 

300 

239.6 

180.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep-. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

53°  (127°,  23S 

t°,  307= 

). 

TABLE  ± 

[Page  441 

Difference  of  Latitude  and  Departure  for  37°  (143°,  217°,  323 

'). 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

{   Dep. 

i 

Dist. 

Lat.         Dep. 

Dist.  i     Lat. 

Dep. 

301 

240.4 

181.1 

361 

288.  3 

217.3 

421 

336.2 

1 
253.  4 

481 

384.1     289.5 

541      432.0 

325.  6 

02 

241.2 

181.7 

62 

289.1 

217.9 

22     337.0 

254.  0 

82 

384.9    290.0 

42     432.8 

326.2 

03 

242.0 

182.4 

63 

289.9 

218.5 

23  1  337.8 

254.  6 

83 

385.7    290.6 

43     433.6 

326.8 

04 

242.7 

183.0 

64 

290.7 

219.1 

24     338.6 

255.  2 

84 

386.5  ,291.2 

44     434.4 

327.3 

05 

243.5 

183.  6 

65 

291.5 

219.7 

25  :  339.4 

255.  8 

85 

387.3    291.8 

45     435.2 

327.9 

06 

244.3 

184.2 

66 

292.3 

220.3 

26  i  340.2 

1 256. 4 

86 

388.1     292.4 

46     436.0 

328.  5 

07 

245.1 

184.8 

67 

293.1 

220.9 

27     341.0 

257.  0 

87 

388.9    293.0 

47     436.8 

329.1 

08 

245.9 

185.4 

68 

293.9 

221.5 

28  1  341.8 

257.  6 

88 

389.7    293.6 

48     437.6 

329.7 

09 

246.7 

186.0 

69 

294.7 

222.1 

29     342.6 

1 258. 2 

89 

390.5  .294.2 

49     438.4 

330.  3 

10 
311 

247.5 
248.3 

186.6 
18772 

70 

295.5 

222.7 

30 

343.4 
344.  2 

;  258.  8 
259.4 

90 
491 

391.3    294.8 

50     439.2 

330.9 

371 

296.3 

223.3 

431 

392.1    295.4 

551  1  440.0 

331.5 

12 

249.1 

187.8 

72 

297.1 

223.9 

32     345. 0 

260.  0 

92 

392.9    296.0 

52  :  440.  8 

332.1 

13 

249.9 

188.4 

73 

297.9 

224.5 

33     345. 8 

260.  6 

93 

393.7 

296.6 

53  '  441.6 

332.7 

14 

250.7 

189.0 

74 

298.7 

225.1 

34     346.6 

261.2 

94 

394.5 

297.  2 

54     442.4     333.3 

15 

251.5 

189.6 

75 

299.5 

225.7 

35     347.4 

261.8 

95 

395.3 

297.8 

55     443.2     333.9 

16 

252.  3 

190.2 

76 

300.3 

226.3 

36  1  348.2 

i  262. 4 

96 

396.1 

298.  5 

56     444.0     334.6 

17 

253.1 

190.8 

77 

301.1 

226.9 

37  i  349.0 

263.0 

97 

396.  9 

299. 1 

57     444.8     235.2 

18 

253.9 

191.4 

78 

301.8 

227.5 

38  !  349.8 

263.  6 

98 

397.7 

399.  7 

58     445.6     335.8 

19 

254.7 

192.0 

79 

302.6 

228.1 

39  i  350.6 

264.2 

99 

398.5 

300.3 

59     446.4     336.4 

20 
321 

255.5 
256.3 

192.6 

80 
381 

303.  4 
304.2 

228.7 

40 

351.4 
352.  2~ 

264.8 

500 

399.3 
400.1 

300.9 

60     447.2     337.0 

193.2 

229.  3 

441 

265.4 

501 

301.5 

561     448.0     337.6 

22 

257.1 

193.8 

82 

305.0 

229.9 

42     353.0 

266.0 

02 

400.9 

302. 1 

62     448. 8     338. 2 

23 

257.9 

194.4 

83 

305.8 

230.5 

43     353.8 

266.6 

03 

401.7 

302.  7 

63     449. 6     338. 8 

24 

258.7 

195. 0 

84 

306.  6 

231.1 

44     354.6 

267.2 

04 

402.5 

303.3 

64     450.4     339.4 

25 

259.5 

195.6 

85 

307.4 

231.7 

45  ,  355.4 

267.8 

05 

403.3 

303.9 

6.5     451. 2     340. 0 

26 

260.3 

196.2 

86 

308.  2 

232.3 

46     356.2 

268.4 

06 

404.1 

304. 5 

66     452.0     340.6 

27 

261.1 

196.8 

87 

309.0 

232.9 

47     357.0 

269.0 

07 

404.9 

305.1 

67  ;  452.8     341.2 

28 

I  261. 9 

197.4 

88 

309.8 

233.  5 

48  :  357.8 

269.6 

08 

405.7 

305.7 

68     453.6     341.8 

29 

262.  7 

198.0 

89 

310.6 

234.1 

49  '  358.6 

270.2 

09 

406.  5 

306.3 

69     454.4     342.4 

30 

263.5 
264.3 

198.6 

90 

311.4 
312.2 

234.7 
235.3 

50     359.4 
451      360.1 

270.8 
271.4 

10 
511 

407.  3 
408.1 

306.9 
307.5 

70  ,  455.2     343.0 
571     456.0     343.6 

331 

199.2 

391 

32 

265. 1 

199.8 

92 

313.0 

235.  9 

52  ■  360.9 

272.0 

12 

408.9 

308.2 

72     456.8     .344.3 

33 

265.9 

200.4 

93 

313.8 

236.  5 

53     361.7 

272.6 

13 

409.7 

308.8 

73     457.6     344.9 

34 

266.  7 

201.0 

94 

314.6 

237.1 

54     362.5 

273.2 

14 

410.5 

309. 4 

74     458.4     34.5.5 

35 

267.5 

201.6 

95 

315.4 

237.7 

55     363.3 

273.8 

15 

411.3 

310.0 

75     459. 2     346. 1 

36 

268.3 

202.2 

96 

316.2 

238.  3 

56     364. 1 

274.4 

16 

412.1 

310.6 

76     460. 0     346. 7 

37 

269.1 

202.8 

97 

317.0 

238.9 

57     364.9 

275.  0 

17 

412.9 

311.2 

77     460.8     347.3 

38 

269.9 

203.4 

98 

317.8 

239.  5 

58     365. 7 

^75.6 

18 

413.7 

311.8 

78     461.6     347.9 

39 

270.7 

204.0 

99 

318.6 

240.1 

59     366.5 

276.2 

19 

414.  5 

312.4 

79     462.4     348.5 

40 
341 

271.  5 
272.3 

204.6 

400 
401 

319.  4 
320.2 

240.7 
241.3 

60     367.3 
461      368.  1 

276.8 
277. 4 

20 
521 

415.3 
416.  1 

313.0 
313.6 

80     463. 2     349. 1 
581      464. 0     349. 7 

205.2 

42 

273.1 

205.8 

02 

321.0 

241.9 

62     368.9 

278.0 

22 

416.  9 

314.2 

82     464.8     3.50.3 

43 

273.9 

206.4 

03 

321.8 

242.5 

63     369.  7 

278.6 

23 

417.7 

314.8 

83     46.5.6     3,50.9 

44 

274.7 

.207. 0 

(4 

322.6 

243.1 

64     370.5 

279.2 

24 

418.5 

315. 4 

84     466.4     351.5 

45 

275.5 

207.6 

05 

323.  4 

243.7 

65     371.3 

279.8 

25 

419.3 

316.0 

85     467. 2     352.  1 

46 

276.3 

208.2 

06 

324.  2 

244.3 

66  1  372. 1 

280.4 

26 

420.1 

316.6 

86     468. 0     352. 7 

47 

277.1 

208.8 

07 

325.0 

244.9 

67  \  372.9 

281.0 

27 

420.9 

317.2 

87     468.8     353.3 

48 

277.9 

209.4 

08 

325.8 

245. 5 

68  j  373.  7 

281.6 

28 

421.7 

317.8 

88     469.6     3.53.9 

49 

278.7 

210.0 

09 

326.6 

246.1 

69     374.5 

282.3 

29 

422.  5 

318.4 

89     470.4     3.54.5 

50 
351 

279.5 
280.3 

210.6 

10 

327.4 
328.  2 

246.7 
247.  3 

70  1  375.3 

282.9 

30 

423.  3 
424.1 

319.0 
319.  6 

90     471. 2     355. 1 
.591      472. 0     3.55. 7 

211.2 

411 

471     376.  1     283.  5 

531 

52 

281.1 

211.8 

12 

329.0 

247.9 

72     376.  9  ' 284. 1 

32 

424.9 

320.2 

92  ,  472.8     3.56.3 

53 

281.9 

212.4 

13 

329.8 

248.5 

73     377.7    284.7 

33 

425.  7 

320.8 

93     473.6     356.9 

54 

282.7 

213.  0 

14 

330.6 

249.2 

74     378.5 

285.  3 

34     : 

426.  5 

321.4 

94     474.4     357.5 

55 

283.5 

213.6 

15 

331.4 

249.8 

75     379.3 

285.  9 

35 

427.  3 

322.0 

95     475. 2     358.  1 

56 

284.3 

214.2 

16 

332.  2 

250.4 

76     380. 1 

286.  5 

36 

428.1 

322.  6 

96     476. 0     358. 7 

57 

285.1 

214.8 

17 

333.  0 

251.  0 

77     380.9  '287.1 

37 

428.9 

323.2 

97  '  476.8     359.3 

58 

285.9 

215.4 

18 

333.8 

251.  6 

78  :  381.  7  i  287.  7 

38 

429.7 

323.8 

98     477.6     3.59.9 

59 

286.7 

216.1 

19 

334.6 

252.  2 

79     382.5    288.3 

39 

430.5 

324.4 

99  {  478.4  i  360.5 

60 

287.5 

216.7 

20 

335.4 

252.-8 

80  '  383.  3  1  288.  9 

40 

431.3 

325.0 
Lat. 

600  i  479.  2     361. 1 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist.       Dep.          Lat. 

Dist. 

Dep. 

Dist.  j    Dep.         Lat. 

5 

3°  (127°,  233°,  307° 

. 

Page  442] 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  38°  (142°,  218°,  322' 

)• 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

DLst. 

Lat. 

Dep. 

1 

i       0.8 

0.6 

61 

48.1 

37.6 

121 

95.3 

74.5 

181 

142.6 

111.4 

241 

189.9 

148.4 

2 

1.6 

1.2 

62 

48.9 

38.2 

22 

96.1 

75.1 

82 

143.4 

112.1 

42 

190.7 

149.0 

3 

2.4 

1.8 

63 

49.6 

38.8 

23- 

96.9 

75.7 

83 

144.2 

112.7 

43 

191.5 

149.6 

4 

3.2 

2.5 

64 

50.4 

39.4 

24 

97.7 

76.3 

84 

145.0 

113.3 

44 

192.3 

150.2 

5 

3.9 

3.1 

65 

51.2 

40.0 

25 

98.5 

77.0 

85 

145.8 

113.9 

45 

193.1 

150.8 

6 

4.7 

3.7 

«6 

52.0 

40.6 

26 

99.3 

77.6 

86 

146.6 

114.5 

46 

193.9 

151.5 

7 

5.5 

4.3 

67 

52.8 

41.2 

27 

100.1 

78.2 

87 

147.4 

115.1 

47 

194.6 

152.1 

8 

6.3 

4.9 

68 

53.6 

41.9 

28 

100.9 

78.8 

88 

148.1 

115.7 

48 

195.  4 

152.7 

9 

7.1 

5.5 

69 

54.4 

42.5 

29 

101.7 

79.4 

89 

148.9 

116.4 

49 

196.2 

153.  3 

10 

7.9 

6.2 

70 

55.2 

43.1 
43.7 

30 
131 

102.4 

80.0 

90 

149.7 
150.  5 

117.0 

50 
251^ 

197.0 
197.8 

153.9 

11 

8.7 

6.8 

71 

55.9 

103.2 

80.7 

191 

117.6 

154.5 

12 

9.5 

7.4 

72 

56.7 

44.3 

32 

104.0 

81.3 

92 

151.3 

118.2 

52 

198.  6 

155.1 

13 

10.2 

8.0 

73 

57.5 

44.9 

33 

104.8 

81.9 

93 

152.1 

118.8 

53 

199.4 

155.8 

14 

11.0 

8.6 

74 

58.3 

45.6 

34 

105.6 

82.5 

94 

152.  9 

119.4 

54 

200.2 

156.4 

15 

11.8 

9.2 

75 

59.1 

46.2 

35 

106.4 

83.1 

95 

153.7 

120.1 

55 

200.9 

157.0 

16 

12.6 

9.9 

76 

59.9 

46.8 

36 

107.2 

83.7 

96 

154.5 

120.7 

56 

201.7 

157.6 

17 

13.4 

10.5 

77 

60.7 

47.4 

37 

108.0 

84.3 

97 

155.  2 

121.  3 

57 

202.5 

158.2 

18 

14.2 

11.1 

78 

61.5 

48.0 

38 

108.7 

85.0 

98 

156.0 

121.9 

58 

203.3 

158.8 

19 

15.0 

11.7 

79 

62.3 

48.6 

39 

109.5 

85.6 

99 

156.8 

122.  5 

59 

204.1 

159.5 

20 

15.8 

12.3 
12.9 

80 

63.0 
63.8 

49.3 

40 

110.3 

86.2 

200 
201 

157.6 

123.1 

60 

204.9 
205.7 

160.1 

21 

16.5 

81 

49.9 

141 

111.1 

86.8 

158.4 

123.7 

261 

160.7 

22 

17.3 

13.5 

82 

64.6 

50.5 

42 

111.9 

87.4 

02 

159.2 

124.4 

62 

206.5 

161.3 

23 

18.1 

14.2 

83 

65.4 

51.1 

43 

112.7 

88.0 

03 

160.0 

125.0 

63 

207.2 

161.9 

24 

18.9 

14.8 

84 

66.2 

51.7 

44 

113.5 

88.7 

04 

160.8 

125.  6 

64 

208.0 

162.5 

25 

19.7 

15.4 

85 

67.0 

52.3 

45 

114.3 

89.3 

05 

161.5 

126.  2 

65 

208.8 

163.2 

26 

20.5 

16.0 

86 

67.8 

52.9 

46 

115.0 

89.9 

06 

162.  3 

126.8 

66 

209.6 

163.8 

27 

21.3 

16.6 

87 

68.6 

53.6 

47 

115.8 

90.5 

07 

163. 1 

127.4 

67 

210.  4 

164.4 

28 

22.1 

17.2 

88 

69.3 

54.2 

48 

116.6 

91.1 

08 

163.9 

128.1 

.  68 

211.2 

165.  0 

29 

22.9 

17.9 

89 

70.1 

54.8 

49 

117.4 

91.7 

09 

164.7 

128.7 

69 

212.0 

165.6 

30 

23.6 

18.5 
19.1 

90 

70.9 

55.4 

50 

118.2 
119.0 

92.3 

10 

165.5 
166.3 

129.3 

70 

212.8 

166.2 

31 

24.4 

91 

71.7 

56.0 

151 

93.0 

211 

129.9 

271 

213.6 

166.8 

32 

25.2 

19.7 

92 

72.5 

56.6 

52 

119.8 

93.6 

12 

167.1 

130.5 

72 

214.3 

167.5 

33 

26.0 

20.3 

93 

73.3 

57.3 

53 

120.6 

94.2 

13 

167.8 

131.1 

73 

215.1 

168.1 

34 

26.8 

20.9 

94 

74.1 

57.9 

54 

121.4 

94.8 

14 

168.6 

131.8 

74 

215.9 

168.7 

35 

27.6 

21.5 

95 

74.9 

58.5 

55 

122.1 

95.4 

15 

169.4 

132.4 

75 

216.7 

169.3 

36 

28.4 

22.2 

96 

75.6 

59.1 

56 

122.9 

96.0 

16 

170.2 

133.0 

76 

217.5 

169.9 

37 

29.2 

22.8 

97 

76.4 

59.7 

57 

123.  7 

96.7 

17 

171.0 

133.6 

77 

218.3 

170.5 

38 

29.9 

23.4 

98 

77.2 

60.3 

58 

124.5 

97.3 

18 

171.8 

134.  2 

78 

219.1 

171.2 

39 

30.7 

24.0 

99 

78.0 

61.0 

59 

125.  3 

97.9 

19 

172.6 

134.8 

79 

219.9 

171.8 

40 

31.5 

24.6 

100 

78.8 

61.6 

60 

126.1 

98.5 

20 

221 

173.4 

135.4 

80 

220.6 
221.4 

172.4 
173.0 

41 

32.3 

25.2 

101 

79.6 

62.2 

161 

126.9 

99.1 

174.2 

136.  1 

281 

42 

33.1 

25.9 

02 

80.4 

62.8 

62 

127.7 

99.7 

22 

174.9 

136.  7 

82 

222.2 

173.6 

43 

33.9 

26.5 

03 

81.2 

63.4 

63 

128.4 

100.4 

23 

175.7 

137.  3 

83 

223.0 

174.2 

44 

34.7 

27.1 

04 

82.0 

64.0 

64 

129.2 

101.0 

24 

176.5 

137.9 

84 

223.  8 

174.8 

45 

35.5 

27.7 

05 

82.7 

64.6 

65 

130.0 

101.6 

25 

177.  3 

138.5 

85 

224.6 

175.5 

46 

36.2 

28.3 

06 

83.5 

65.3 

66 

130.8 

102.2 

26 

178.1 

139. 1 

86 

225.4 

176.1 

47 

37.0 

28.9 

07 

84.3 

65.9 

67 

131.6 

102.8 

27 

178.9 

139.8 

87 

226.2 

176.7 

48 

37.8 

29.6 

08 

85.1 

66.5 

68 

132.4 

103.4 

28 

179.7 

140. 4 

88 

226.9 

177.3 

49 

38.6 

30.2 

09 

85.9 

67.1 

69 

133.2 

104.0 

29 

180.5 

141.0 

89 

227.7 

177.9 

50 
51 

39.4 
40.2 

30.8 

10 

86.7 
87.  5" 

67.7 

70 

134.0 

104.7 

30 

181.2 
182.0 

141.6 
142.2 

90 
29r 

228.5 
229.3 

178.5 
179.2 

31.4 

111 

68.3 

171 

134.  7 

105.3 

231 

52 

41.0 

32.0 

12 

88.3 

69.0 

72 

135.5 

105.  9 

32 

182.8 

142.8 

92 

230.1 

179.8 

53 

41.8 

32.6 

13 

89.0 

69.6 

73 

136.  3 

106.  5 

33 

183.6 

143.4 

93 

230.  9 

180.4 

54 

42.6 

33.2 

14 

89.8 

70.2 

74 

137.1 

107.1 

34 

184.4 

144. 1 

94 

231.7 

181.0 

55 

43.3 

.33.9 

15 

90.6 

70.8 

75 

137.  9 

107.7 

35 

185.  2 

144.7 

95 

232.  5 

181.6 

56 

44.1 

34.5 

16 

91.4 

71.4 

76 

138.7 

108.4 

36 

186.0 

145.3 

96 

233.  3 

182.2 

57 

44.9 

35.1 

17 

92.2 

72.0 

77 

139.  5 

109.0 

37 

186.8 

145.  9 

97 

234.  0 

182.9 

58 

45.7 

35.7 

18 

93.0 

72.6 

78 

140.3 

109.6 

38 

187.  5 

146.5 

98 

234.  8 

183. 5 

59 

46.5 

36.3 

19 

93.8 

73.3 

79 

141.1 

110.2 

39 

188.  3 

147.1 

99 

235. 6 

184.1 

60 

47.3 

36.9 

20 

94.6 

73.9 

80 

141.8 

110.8 

40 

189.1 

147.8 

300 

236.4 

184.7 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

52' 

(128 

°,  232°, 

308°). 

tablp:  2. 

[Page 

443    1 

Difference  of  Latitude  and  Departure  for  38°  (142°,  218 

°,  322° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.         Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

801 

237.2 

185.3 

361 

284.5 

222.3 

421 

331.8 

259.2 

481 

379.0 

296.2 

.541 

426.  3 

333. 1 

02 

238.0 

185.9 

62 

285.3  1222.9] 

22 

332.  5 

259.  8 

82 

379.8 

296.8 

42 

427.1 

333.  7 

03 

238.8 

186.6 

63 

286.0 

223.5 

23 

333.3 

260.4 

83 

380.6 

297.4 

43 

427.9 

334.3 

04 

239.6 

187.2 

64 

286.8 

224.1 

24 

334. 1 

261.0 

84 

381.4 

298.0 

44 

428.7 

335.  0 

05 

240.3 

187.8 

65 

287.6 

224.7 

25 

334.9 

261.7 

a5 

382.2 

298.6 

45 

429.  5 

335.6 

06 

241.1 

188.4 

66 

288.4 

225.  3 

26 

3.35.  7 

262.3 

86 

383.  0 

299.2 

46 

430.3 

336.2 

07 

241.9 

189.0 

67 

289.2 

226.0 

27 

336.  5 

262.9 

87 

383.8 

299.8 

47 

431.0 

336.8 

08 

242.7 

189.6 

68 

290.0 

226.6 

28 

337.3 

263.5 

88 

384.5 

300.4 

48 

431.8 

337.4 

09 

243.5 

190.2 

69 

290.8 

227.2 

29 

338. 1 

264.1 

89 

385.3 

301.1 

49 

432.6 

338.  0 

10 

244.3 

190.9 

70 

291.6 

227.8 
228.4 

30 

338.8 

264.7 

90 

386.1 

301.  7 
302.3 

50 

433.4 

338.6 

311 

245.1 

191.5 

371 

292.4 

431 

339.6 

265.4 

491 

386.9 

551 

434.2 

339.3 

12 

245.9 

192.1 

72 

293.1 

229.0 

32 

340.4 

266.0 

92 

387.7 

302.9 

52 

435.  0 

339.9 

13 

246.6 

192.7 

73 

293.9 

229.6 

33 

.341.  2 

266.6 

93 

388. 5 

.303.  5 

53 

435.  8 

340.  5 

14 

247.4 

193.3 

74 

294.7 

230.3 

34 

342.0 

267.2 

94 

389.3 

304.2 

54 

436.6 

341.1 

15 

248.2 

193.9 

75 

295.  5 

230.9 

35 

342.8 

267.  8 

95 

390.1 

304.8 

55 

437.4 

341.7 

16 

249.0 

194.6 

76 

296.3 

231.5 

36 

.343.6    268.4 

96 

390.9 

305.  4 

56 

438.1 

342.3 

17 

249.8 

195.  2 

77 

297.1 

232. 1 

37 

.344.  4  i  269. 1 

97 

391.6 

,306.  0 

57 

438.9 

343.0 

18 

250.6 

195.8 

78 

297.9 

232.7 

38 

345. 2  1  269. 7 

98 

392.4 

306.6 

58 

439.7 

343.  6 

19 

251.4 

196.4 

79 

298.7 

2,33.  3 

39 

345. 9  1  270. 3 

99 

393.2 

.307.  2 

59 

440.5 

344.2 

20 

252.2 

197.0 
197.6 

80 

299.4 

234.0 
234.  6 

40 

346.  7 

270.9 

500 

394.0 

307.  8 
308.4 

60 
561 

441.3 
442.1 

344.8 

321 

253.0 

381 

300.2 

441 

347.5 

271.5 

501 

394.8 

345.4 

22 

253.7 

198.2 

82 

301.0 

235.2 

42 

348.3 

272.1 

02 

395. 6 

309.1 

62 

442.9 

346.0 

23 

254.5 

198.9 

83 

301.8 

235.8 

43 

.349. 1 

272.7 

03 

396.4 

309.7 

63 

443.7 

346.6 

24 

255.3 

199.5 

84 

302.6 

236.4 

44 

349.9    273.4 

04 

397.2 

310.  3 

64 

444.4 

347.  2 

25 

256. 1 

200.1 

85 

303.4 

2.37.  0 

45 

350.7    274.0 

05 

397.9 

310.9 

65 

445.  2 

347.  8 

26 

256.9 

200.7 

86 

304.  2 

237.7 

46 

351.5    274.6 

06 

398.7 

311.6 

66 

446.0 

348.5 

27 

257.7 

201.3 

87 

305.0 

238.3 

47 

352. 2    275. 2 

07 

399.5 

312.2 

67 

446.8 

,349. 1 

28 

258.5 

201.9 

88 

305.7 

238.9 

48 

353.0 

275.8 

08 

400.3 

312.8 

68 

447.6 

349.7 

29 

259.3 

202.6 

89 

306.  5 

239.5 

49 

353.8 

276.4 

09 

401.1 

313.4 

69 

448.4 

3-50.  3 

30 

260.0 

203.2 

90 

307.3 

240.1 

50 
451 

354.6 
355.4 

277.1 

10 

401.9 

314.0 

70 

449.2 

350.9 
351.6 

331 

260.8 

203.8 

391 

308.1 

240.7 

277.7 

511 

402.7 

314.6 

571 

450.0 

32 

261.6 

204.4 

92 

308.9 

241.3 

52 

356.  2 

278.3 

12 

403.5 

315.  2 

72 

450.  7 

.352.  2 

33 

262.  4  1  205. 0 

93 

309.7 

242.0 

53 

.357.  0 

278.9 

13 

404.2 

315.8 

73 

451.5 

352.8 

34 

263.2 

205.  6 

94 

310.5 

242.6 

54 

357.8 

279.5 

14 

405. 0 

316.4 

74 

452.  3 

353. 4 

35 

264.0 

206.3 

95 

311.3 

243.2 

55 

358.  5 

280.1 

15 

405.8 

317.1 

75 

453.1 

354. 0 

36 

264.8 

206.9 

96 

312.1 

243.8 

56 

359.  3 

280.7 

16 

406.6 

,317.  7 

76 

453.  9 

354.  6 

37 

265.6 

207.5 

97 

312.8 

244.4 

57 

360.1  1281.4 

17 

407.4 

318. 3 

77 

454.7 

3.55.  2 

38 

266.3 

208.1 

98 

313.  6 

245.  0 

58 

360.  9  j  282.  0 

18 

408.2 

318.9 

78 

455. 5 

355.  8 

39 

267.1 

208.7 

99 

314.4 

245.7 

59 

361. 7    282. 6 

19 

409.0 

319.5 

79 

456.3 

356.  4 

40 

267.9 

209.3 

400 

.315.  2 

246.  3 

60 

362.5 
363.3 

283.2 

20 

409.8 

320.2 

80 

457.1 
457.8 

357.1 
357.7 

341 

268.7 

209.9 

401 

316.0 

246.9 

461 

283.8 

521 

410.6 

320.8 

581 

42 

269.5 

210.  6 

02 

316.8 

247.5 

62 

364.1 

284.4 

22 

411.3 

321.4 

82 

458.6 

358.3 

43 

270.3 

211.2 

03 

317.6 

248.1 

63 

364.9 

285. 1 

23 

412.1 

322.0 

83 

4.59. 4 

358. 9 

44 

271.1 

211.8 

04 

318.4 

248.7 

64 

365.6 

285.7 

24 

412.9 

322.6 

84 

460.2 

359.  5 

45 

271.9 

212.4 

05 

319.1 

249.3 

65 

366.4 

286.3 

25 

413.7 

323.2 

85 

461.0 

360.  2 

46 

272.7 

213.  0 

06 

319.9 

250.0 

66 

367.2 

286.  9 

26 

414.5 

,323.  8 

86 

461.8 

360.8 

47 

273.4 

213.6 

07 

320.7 

250.6 

67 

368.0 

287.5 

27 

415.3 

324.  5 

87 

462.6 

361.4 

48 

274. 2  I  214. 3 

08 

321.5 

251.2 

68 

368.8 

288.1 

28 

416.1 

.325. 1 

88 

463.  3 

362.0 

49 

275. 0    214. 9 

09 

322. 3 

251.8 

69 

369.6 

288.7 

29 

416.9 

325.  7 

89 

464.1 

362. 6 

50 
351 

275.8 
276.6 

215.5 

10 

323.1 

252.4 

70 

370.  4 

289.3 
290. 0 

30 
531 

417.6 

326.3 

90 

464.9 

363.2 

216.1 

411 

323.9 

253.0 

471 

371.2 

418.4 

326.9 

591 

465.7 

363.8 

52 

277.4  ;216.7 

12 

324.7 

253.  7 

72 

371.9 

290.6 

32 

419.2 

327.5 

92 

466.5 

364.4 

53 

278.2    217.3 

13 

325.5 

254.3 

73 

372.  7 

291.2 

33 

420.0 

328.2 

93 

467.3 

,365.  1 

54 

279.0    218.0 

14 

326.  2 

254.9 

74 

373.5 

291.8 

.34 

420.8 

328.  8 

94 

468.1 

365.7 

55 

279.7    218.6 

15 

327.0 

255. 5 

75 

374.3 

292.4 

35 

421.6 

329.4 

95 

468.9 

366.3 

56 

280.5 

219.2 

16 

327.8 

256.1 

76 

375. 1 

293.1 

36 

422.  4 

330.  0 

96 

469.7 

366.9 

57 

281.3 

219.8 

17 

328.6 

256.7 

77 

375.9 

293.7 

37 

423.  2 

330.6 

97 

470.5 

367. 5 

58 

282.1 

220.4 

18 

329. 4 

257.4 

78 

376.7 

294.3 

38 

424.0 

,331.  2 

98 

471.2 

368.1 

59 

282.9 

221.0 

19 

330.2 

258.0 

79 

.377. 5 

294.9 

39 

424.7 

331.8 

99 

472.0 

368.7 

60 
Dist. 

283.7 

221.6 

20 

331.0 

258.6 

80 

378.2 

295.5 

40 

425.5 

332.5 

600 

472.8 

369.4 

Dep.        Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

52°  (128°,  232°,  308° 

). 

Page  444J 

TABLE 

/    '2. 

Difference  of  Latit  d 

and  Departure  for  39°  (141°,  219°,  321° 

)• 

Dist. 

Lat. 

Dep. 
0.6 

Dist. 

Lat. 

Dep. 
38.4 

Dist.  j     Lat. 

Dep. 

Dist. 

Lat.        Dep. 
140.7     113.9 

Dist. 
241 

Lat. 

Dep. 

1 

0.8 

61 

47.4 

121       94. 0 

76.1 

181 

187.3 

151.7 

2 

1.6 

1.3 

62 

48.  2     39.  0  1 

22 

94.8 

76.8 

82 

141.4    114.5 

42 

188.1 

152.3 

3 

2.3 

1.9 

63 

49.0 

39.6 

23 

95.6 

77.4 

83 

142.2  ill5.2 

43 

188.8 

152.  9 

4 

3.1 

2.5 

64 

49.7 

40.3 

24 

96.4 

78.0 

84 

143.0    115.8 

44 

189.6 

153.6 

5 

3.9 

3.1 

65 

50.5 

40.9 

25 

97.1 

78.7 

85 

143.8    116.4 

45 

190.4 

154.  2 

6 

4.7 

3.8 

»  66 

51.3 

41.5 

26 

97.9 

79.3 

86 

144.5  1117.1 

46 

191.2 

154.  8 

7 

5.4 

4.4 

67 

52. 1  !  42.  2 

27 

98.7 

79.9 

87 

145.3  ill7.  7 

47 

192.0 

155.4 

8 

6.2 

5.0 

68 

52.8  I  42.8 

28 

99.5 

80.6 

88 

146.1  ;il8.3 

48 

192.7 

156.1 

9 

7.0 

5.7 

69 

53. 6     43. 4 

29 

100.3 

81.2 

89 

146.9 

118.9 

49 

193.5 

156.7 

10 

7.8 

6.3 

70 
71 

54. 4     44. 1 
55.  2     44.  7 

30 
131 

101. 0 

81.8 

90 

147.7 

119.6 

50 

194.3 

157.3 

11 

8.5 

6.9 

101.8 

82.4 

191 

148.4 

120.2 

251 

195.1 

158.0 

12 

9.3 

7.6 

72 

56.  0     45.  3 

32 

102.6 

83.1 

92 

149.2 

120.8 

52 

195.8 

158.6 

13 

10.1 

8.2 

73 

56.  7     45. 9 

33 

103.4 

83.7 

93 

150.0 

121.5 

53 

196.6 

159.2 

14 

10.9 

8.8 

74 

57.5 

46.6 

34 

104.1 

84.3 

94 

150.8 

122.1 

54 

197.4 

159.8 

15 

11.7 

9.4 

75 

58.3 

47.2 

35 

104.9 

85.0 

95 

151.5 

122.7 

55 

198.2 

160.5 

16 

12.4 

10.1 

76 

59.1 

47.8 

36 

105.7 

85.6 

96 

152.3 

123.3 

56 

198.9 

161.1 

17 

13.2 

10.7 

( 1 

59.8 

48.5 

37 

106.5 

86.2 

97 

153.1 

124.0 

57 

199.7 

161.7 

18 

14.0 

11.3 

78 

60.6 

49.1 

38 

107.2 

86.8 

98 

153.9 

124.6 

58 

200.5 

162.4 

19 

14.8 

12.0 

79 

61.4 

49.7 

39 

108.0 

87.5 

99 

154.7 

125.2 

59 

201.3 

163.0 

20 

15.5 
16.3 

12.6 
13.  2" 

80 

62.2 

50.3 
51.0 

40 

108.8 

88.1 

200 

155.4    125.9 

60 
261 

202.1 

202.8 

163.6 

21 

81 

62.9 

141 

109.6 

88.7 

201 

156.2 

126.5 

164.3 

22 

17.1 

13.8 

82 

63.7 

51.6 

42 

110.4 

89.4 

02 

157.0 

127.1 

62 

203.6 

164.9 

23 

17.9 

14.5 

83 

64.5 

52.2 

43 

111.1 

90.0 

03 

157.8 

127.8 

63 

204.4 

165.5 

24 

18.7 

15.1 

84 

65.3 

52.9 

44 

111.9 

90.6 

04 

158. 5 

128.4 

64 

205.2 

166.1 

25 

19.4 

15.7 

85 

66.1 

53.5 

45 

112.7 

91.3 

05 

159.3 

129.0 

65 

205.9 

166.8 

26 

20.2 

16.4 

86 

66.8 

54.1 

46 

113.5 

91.9 

06 

160.1 

129.6 

66 

206.7 

167.4 

27 

21.0 

17.0 

87 

67.6 

54.8 

47 

114.2 

92.5 

07 

160.9    130.3 

67 

207.5 

168.0 

28 

21.8 

17.6 

88 

68.4 

55.4 

48 

115.0 

93.1 

08 

■  161.  6 

130.9 

68 

208.  3 

168.  7 

29 

22.5 

18.3 

89 

69.2 

56.0 

49 

115.8 

93.8 

09 

162.4 

131.5 

69 

209.1 

169.3 

30 

23.3 

18.9 

90 

69.9 

56.6 

50 

116.6 

94.4 

10 

163.2 
164.0 

132.2 

70 

209.8 

169.9 
170.5 

31 

24.1 

19.5 

91 

70.  7     57.  3 

151 

117.3 

95.0 

211 

132.  8 

271 

210.6 

32 

24.9 

20.1 

92 

71.5     57.9 

52 

118.1 

95.7 

12 

164.8 

133.4 

72 

211.4 

171.2 

33 

25.6 

20.8 

93 

72. 3     58.  5 

53 

118.9 

96.3 

13 

165.5 

134.0 

73 

212.2 

171.8 

34 

26.4 

21.4 

94 

73.1 

59.2 

54 

119.7 

96.9 

14 

166.3 

134.  7 

74 

212.9 

172.4 

36 

27.2 

22.0 

95 

73.8 

59.8 

55 

120.5 

97.5 

15 

167. 1 

135.  3 

75 

213.7 

173.1 

36 

28.0 

22.7 

96 

74.6 

60.4 

56 

121.2 

98.2 

16 

167.9 

135.  9 

76 

214.5 

173.7 

37 

28.8 

23.3 

97 

75.4  i  61.0 

57     122. 0 

98.8 

17 

168.6 

136.6 

77 

215.3 

174.3 

38 

29.5 

23.9 

98 

76.  2     61.  7 

58     122. 8 

99.4 

18 

169.4 

137.2 

78 

216.0 

175.0 

39 

30.3 

24.5 

99 

76.  9     62.  3 

59     123. 6 

100.1 

19 

170.2 

137.  8 

79 

216.8 

175.  6 

40 
41 

31.1 

25.2 

100 

77.  7     62. 9 

60 

124. 3 

100.7 

20 

171.0 

138.  5 

80 

217.6 
218.4 

176.2 

31.9 

25.8 

101 

78.5 

63.6 

161 

125.1 

101.3 

221 

171.7 

139.1 

281 

176.8 

42 

32.6 

26.4 

02 

79.3 

64.2 

62 

125.9 

101.9 

22 

172. 5 

139.7 

82 

219.2 

177.5 

43 

33.4 

27.1 

03 

80.0 

64.8 

63 

126.7 

102.6 

23 

173.  3 

140.  3 

83 

219.9 

178.1 

44 

34.2 

27.7 

04 

80.8 

65.4 

64 

127.  5 

103.2 

24 

174.1 

141.0 

84 

220.7 

178.7 

45 

35.0 

28.3 

05 

81.6 

66.1 

65 

128.  2 

103.8 

25 

174.9 

141,6 

85 

221.5 

179.4 

46 

35.7 

28.9 

06 

82.4 

66.7 

66 

129.0 

104.5 

26 

175.6 

142.2 

86 

222.3 

180.0 

47 

36.5 

29.6 

07 

83.2 

67.3 

67 

129.8 

105.1 

27 

176.4 

142.9 

87 

223.  0 

180.6 

48 

37.3 

30.2 

08 

83.9 

68.0 

68 

130.  6 

105.7 

28 

177.2 

143.5 

88 

223.8 

181.2 

49 

38.1 

30.8 

09 

84.7 

68.6 

69 

131.3 

106.4 

29 

178.0 

144.1 

89 

224.6 

181.9 

50 

38.9 

31.5 

10 

85.5 

69.2 

70 

132.1 

107.0 
107.6 

30 
231 

178.7 
179.5 

144.7 

90 

225.4 

182.5 

51 

39.6 

32.1 

111 

86.3 

69.9 

171 

132.9 

145. 4 

291 

226.1 

183. 1 

52 

40.4 

32.7 

12 

87.0 

70.5 

72 

133.7 

108.2 

32 

180.3 

146.0 

92 

226.9 

183.  8 

53 

41.2 

33.4 

13 

87.8 

71.1 

73 

134.4 

108.9 

33 

181.1 

146.6 

93 

227.7 

184.4 

54 

42.0 

34.0 

14 

88.6 

71.7 

74 

135.2 

109.5 

34 

181.9 

147.3 

94 

228.5 

185.  0 

55 

42.7 

34.6 

15 

89.4 

72.4 

75 

136.0 

110.1 

35 

182.6 

147.9 

95 

229.3 

185.  6 

56 

43.  5 

35.2 

16 

90.1 

73.0 

76 

136.8 

110.8 

36 

183.4 

148.5 

96 

230.0 

186.  3 

57 

44.3 

35.9 

17 

90.9 

73.6 

77 

137.6 

111.4 

37 

184.2 

149.1 

97 

230.8 

186.9 

58 

45.1 

36.5 

18 

91.7 

74.3 

78 

138.3 

112.0 

38 

185.0 

149.8 

98 

231.6 

187.5 

59 

45.9 

37.1 

19 

92.5 

74.9 

79 

139.1 

112.6 

39 

18.5.7 

150.  4 

99 

232.  4 

188.2 

60 

46.6 

37.8 

20 

93.3 

75.5 

80 

139.9 

113.3 

40 

186.5 

151.0 
Lat. 

300 
Dist. 

233. 1 
Dep. 

188.8 

Dist. 

I)ep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

51°   (129°,  23 

1°,  309' 

'). 

TABLE  2.                                              [Page  445 

Difference  of  Latitude  and  Departure  for  39°  (141°,  219°,  321°).                                   1 

Dlst. 

'     Lat. 

1    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     !    Dep. 

1 

Dist. 

Lat. 

Dep.    1 

301 

233.9 

189.4 

361 

280.6 

227.1 

421 

327.  2 

264.9 

481 

373.8    .302.6 

541 

420.4  i  340.4 

02 

234.7 

190.0 

62. 

281.3 

227.8 

22 

328.0 

265.  5 

82 

374.6    303.3 

42 

421.2  !  341.0 

03 

235.  5 

190.6 

63 

282.1 

228.4 

23 

328.7 

266.2 

83 

375.4  1303.9 

43 

422.0  1  341.7 

04 

236.3 

191.3 

64 

282.9 

229.0 

24 

329.5 

266.8 

84 

376.  1    304.  5 

44 

422.7     342.3 

05 

:  237.0 

191.9 

65 

283.7 

229.7 

25 

'  330.3 

267.4 

85 

376.  9    305.  2 

45 

423.5  :  342.9 

0(3 

237.8 

192.5 

66 

1  284.4 

230.3 

26 

331.1 

268.0 

86 

377.7  1305.8 

46 

424.3     343.6 

07 

238.6 

193.2 

67 

285.2 

230.  9 

27 

331.9 

268.7 

87 

378. 5    306. 4 

47 

425.1      344.2 

08 

239.4 

193.8 

68 

286.0 

231.5 

28 

332.6 

269.  3 

88 

379.3  [307.1 

48 

425.9     344.8 

09 

i  240. 1 

194.4 

69 

286.8 

232.2 

29 

333. 4 

269.9 

89 

380.  0  ;  307.  7 

49 

426.6  I  345.5 

10 
311 

240.9 
i  241.7 

195.0 

70 

287.6 
288.3 

232.8 
233.4 

30 
431 

334.2  1270.6 
335.  0  :  271. 2 

90 
491 

380.8 
381.6 

308.3 
308.  9' 

50 
551 

427.  4  1  346. 1 

428.  2  1  346.  7 

195.7 

371 

12 

i  242.5 

196.3 

72 

289.  1 

234.1 

32 

335.7  |271.8 

92 

382.  4 

309.6 

52 

429.0     347.4 

13 

243.3 

196.9 

73 

289.9 

234.7 

33 

336.5    272.5 

93 

383. 1 

310.2 

53 

429.7     348.0 

14 

244.0 

197.6 

74 

290.7 

235.3 

34 

337.3  i273. 1 

94 

383.  9 

310.8 

54 

430.5  1  348.6 

15 

244.8 

198.2 

75 

291.4 

236.0 

35 

338.1     273.7 

95 

-384.  7 

311.5 

55 

431.3  '  349.2 

16 

245.6 

198.  8 

76 

292.2 

236.6 

36 

338.8    274.3 

96 

385.5 

312.1 

56 

432.  1      349.  9 

17 

246.4 

199.5 

77 

293.0 

237.2 

37 

339.  6    275.  0 

97 

386.2 

312.  7 

57 

432.8     350.5 

18 

247.1 

200.1 

78 

293.8 

237.  8 

38 

340.4    275.6 

98 

387.  0    313.  3 

58 

433.6     351.1 

19 

247.9 

200.7 

79 

294.5 

238.5 

39 

341.2    276.2 

99 

387.  8    314.  0 

59 

434.4     351.7 

20 
321 

248.7 
249.  5 

201.  3 

80 

295.3 
296.1 

239.1 

40 

342.0    276.9 
342.7    277.5 

500 
501 

388.6 
389.4 

314.  7 

60 
561 

4.35.2  i  352.4 
435.9     353.0 

202.0 

381 

239.7 

441 

315.  3 

22 

250.3 

202.6 

82 

296.9 

240.4 

42 

343.5    278.1 

02 

390.1  ;315.9 

62 

436.  7     353.  6 

23 

251.0 

203.2 

83 

297.7 

241.0 

43 

344.3    278.7 

03 

390.9    316.5 

63 

437.5     354.3 

24 

251.8 

203.9 

84 

298.4 

241.6 

44 

345.1   |279.4 

04 

391.7    317.1 

64 

438. 3     354. 9 

25 

252.6 

204.5 

85 

299.2 

242.2 

45 

345.8    280.0 

05 

392.5    317.8 

65 

439.  1      355. 5 

26 

253.  4 

205.1 

86 

300.  0 

242.9 

46 

346.6  [280.6 

06 

393.2    318.4 

66 

439.8     356.2 

27 

254.1 

205.7 

87 

300.  8 

243.5 

47 

347.  4 

281.3 

07 

394.0  1319.0 

67 

440.  6     356.  8 

28 

254.9 

206.4 

88 

301.5 

244.1 

48 

348.2 

281.9 

08 

394.8  1319.6 

68 

441.4  !  357.4 

29 

255.7 

207.0 

89 

302.  3 

244.8 

49 

349.0 

282.5 

09 

395.6 

320.3 

69 

442.  2  i  358.  1 

30 

256.5 
257.2 

207.6 

90 

303.1   ,245.4 

50 

349.7 

283.2 
283.  8" 

10 
511 

396.3 
397.1 

320.9 

70 

443. 0  I  358.  7 
443.  7     359.  3 

331 

208.3 

391 

303.9 

246.0 

451 

350.  5 

321.  6 

571 

32 

258.0 

208.9 

92 

304.7 

246.7 

52 

351.3 

284.4 

12 

397.9  i322.2 

72 

444.  5     359.  9 

33 

258.8 

209.  5 

93 

305.4 

247.3 

53 

352.1  1285.0 

13 

398.7    322.8 

73 

445.3  :  360.6 

34 

259.6 

210.2 

94 

306.2 

247.9 

54 

352.  8 

285.7 

14 

399.4    323.4 

74 

446.1  i  361.2 

35 

260.4 

210.8 

95 

307.0 

248.5 

55 

353.  6 

286.3 

15 

400.2    324.1 

75 

446.9  1  361.8 

36 

261.1 

211.4 

96 

307.8 

249.2 

56 

354.  4 

286.9 

16 

401.0    324.7 

76 

447.6     362.4 

37 

261.9 

212.0 

97 

308.  5 

249.8 

57 

355. 2 

287.6 

17 

401.  8  i  325.  3 

77 

448.4 

363.1 

38 

262.7 

212.7 

98 

309. 3 

250.4 

58 

355.  9 

288.2 

18 

402.5    325.9 

78 

449.2 

363.  7 

39 

263.5 

213.3 

99 

310.1 

251.1 

59 

356.  7 

288.8 

19 

403.3    326.6 

79 

450.0 

364.  3 

40 
341 

264.2 

213.9 

400 

310.  9 

251.7 

60 

357.  5 

289.4 

20 

404.1  i327.2 

80 

450.7 

365.  0 

265.0 

214.6 

401 

311.6 

252.  3 

461 

35873 

'290.  1 

521 

404.9 

327.8 

581 

451.5 

365.  6 

42 

265.8 

215.2 

02 

312.4 

252.9 

62 

359.1 

290.7 

22 

405.7 

328.5 

82 

452.  3 

366.2 

43 

266.  6 

215.8 

03 

313.2 

253.6 

63 

359.  8 

291.3 

23 

406.4 

329. 1 

83 

453.1 

366.9 

44 

267.3 

216.4 

04 

314.0 

254.2 

64 

360.6 

292.0 

24 

407.2 

329.7 

84 

453.9 

367. 5 

45 

268.1 

217.  1 

05 

314.8 

254.8 

65 

361.4 

292.  6 

25 

408.0 

330.  4 

85 

454.  6 

368. 1 

46 

268.9 

217.7 

06 

315.  5 

255.5 

66 

362.2 

293.  2 

26 

408.8 

331.0 

86 

455.  4 

368.8 

47 

269.7 

218.3 

07 

316.3 

256. 1 

67 

362.9 

293.8 

27 

409.  5 

331.  6 

87 

456.2 

369.4 

48 

270.  5 

219.0 

08 

317.1 

256.7 

68 

363.7 

294.5 

28 

410.3 

332.3 

88 

457.  0 

370.0 

49 

271.2 

219.6 

09 

317.9 

257.3 

69 

364.5 

295. 1 

29 

411.1 

332.  9 

89 

457.  8 

370.6 

50 
351 

272.0 
272.  8 

220.2 
220.  8 

10 
411 

318.6  I 

258.0 

70 

365.3 

295.  7 

30 

411.  9  !  333. 5 

90  i  458.5 

371.3 

319.4 

258.6 

471 

366.0 

296.4 

531 

412.6  j334.  1 

591      459.3 

371.9 

52 

273.6 

221.5 

12 

320.2 

259.2 

72 

366.8 

297.0 

32 

413.  4  1  334. 8 

92     460. 1 

372.5 

53 

274.3 

222.1 

13 

321.0 

259.9 

7.i 

367.6 

297.6 

33 

414. 2  1  335.  4 

93 

460.9 

373.2 

54 

275. 1 

222.7 

14 

321.8 

260.5 

74 

368.4 

298.3 

34 

415.  0    336.  1 

94 

461.6 

373.8 

55 

275.9 

223.4 

15 

322.  5 

261.1 

75 

369.2 

298.9 

35 

415.8    336.7 

95 

462.4 

374.4 

56 

276.7 

224.0 

16 

323.  3 

261.8 

76 

369.9 

299.  5 

36 

416.  5    337.  3 

96 

463.2 

375.1 

57 

277.5  ! 

224.6 

17 

324. 1 

262.4 

77 

370.7 

300.1 

37 

417.3    337.9 

97 

464.0 

375.  7 

58 

278.2 

225.3 

18 

324.9    263.0 

78 

371.5 

300.8 

38 

418.1    338.5 

98 

464.8  1 

376.  3 

59 

279.0 

225.9 

19 

325.6    263.6 

79 

372.3 

301.4 

39 

418. «    339.1 

99     465.5  ' 

376.  9 

60 

279.8 

226.5 

20 

326.  4  '  264.  3 

80 

373.0 

302.0 

40 

419.  6  '•  339.  8    600     466.  3  | 

i 

377.  6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     I    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.     '    Lat.      Di.st.  j     Dep.     j 

Lat. 

e 
c 

►1°   (11 

29°,  231°,  309°). 

Page  446J 

TABLE  2. 

■ 

Difference  of  Latitude  and  Departure  for  40°  (140°,  220°,  320°). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.6 

61 

46.7 

39.2 

121 

92.7 

77.8 

181 

138.7 

116.3 

241 

184.6 

154.9 

2 

1.5  i     1.3 

62 

47.5 

39.9 

22 

93.5 

78.4 

82 

139.4 

117.0 

42 

1&5.4 

155.6 

3 

2.3  i     1.9 

63 

48.3 

40.5 

23 

94.2 

79.1 

83 

140.2 

117.6 

43 

186.1 

156.2 

4 

3.1  i     2.6 

64 

49.0 

41.1 

24 

95.0 

79.7 

84 

141.0 

118.  3 

-  44 

186.9 

156.8 

5 

3.8  ;     3.2 

65 

49.8 

41.8 

25 

95.8 

80.3 

85 

141.7 

118.9 

45 

187.7 

157.5 

6 

4.6  1    3.9 

♦  66 

50.6 

42.4 

26 

96.5 

81.0 

86 

142.5 

119.6 

46 

188.4 

158.1 

7 

5.4 

4.5 

67 

51.3 

43.1 

27 

97.3 

81.6 

87 

143.3 

120.2 

47 

189.2 

158.  8 

8 

6.1 

5.1 

68 

52.1 

43.7 

28  !     98.1 

82.3 

88 

144.0 

120.8 

48 

190.0 

159.  4 

9 

6.9 

5.8 

69 

52.9 

44.4 

29 

98.8 

82.9 

89 

144.8 

121.5 

49 

190.  7 

160.1 

10 

7.7 

6.4 

70 

53.6 
54.4 

45.0 

30 

99.6 
100.4 

83.6 
84.2 

90 

145.5 

122.1 

50 
251 

191.5 

160.7 

11 

8.4 

7.1 

71 

45.6 

131 

191 

146.3 

122.8 

192.3 

161.3 

12 

9.2 

/.  1 

72 

55.2 

46.3 

32 

101.1 

84.8 

92 

147.1 

123.4 

52 

193.0 

162.0 

13 

10.0 

8.4 

73 

55.9 

46.9 

33 

101.9 

85.5 

93 

147.8 

124.1 

53 

193.8 

162.6 

14 

10.7  !     9.0 

74 

56.7 

47.6 

34 

102.6 

86.1 

94 

148.6 

124.7 

54 

194.6 

163.3 

15 

11.5       9.6 

75 

57.5 

48.2 

35 

103.4 

86.8 

95 

149.4 

125.3 

55 

195.3 

163.  9 

16 

12.  3     10.  3 

76 

58.2 

48.9 

36 

104.2 

87.4 

96 

150.1 

126.0 

56 

196.1 

164.6 

17 

13.0 

10.9 

77 

59.0 

49.5 

37 

104.9 

88.1 

97 

150.9 

126.6 

57 

196.9 

165.2 

18 

13.8 

11.6 

78 

59.8 

50.1 

38 

105.7 

88.7 

98 

151.7 

127.3 

58 

197.6 

165.8 

19 

14.6 

12.2 

79 

60.5 

50.8 

39 

106.5 

89.3 

99 

152.4 

127.9 

59 

198.4 

166.  5 

20 

15.3 

12.9 

80 

61.3 

51.4 

40 

107.2 

90.0 

200 
"201 

153.2 

128.6 

60 

199.2 
199.9 

167.1 
167.  8 

21 

16.1 

13.5 

81 

62.0 

52.1 

141 

108.0 

90.6 

154.0 

129.2 

261 

22 

16.9 

14.1 

82 

62.8 

52.7 

42 

108.8 

91.3 

02 

154.7 

129.8 

62 

200.7 

168.4 

23 

17.6 

14.8 

83 

63.6 

53.4 

43 

109.5 

91.9 

03 

155.5 

130.5 

63 

201.5 

169.1 

24 

18.4 

15.4 

84 

64.3 

54.0 

44 

110. 3 

92.6 

04 

156.3 

131.1 

64 

202.2 

169.7 

25 

19.2 

16.1 

85 

65.1 

54.6 

45 

111.1 

93.2 

05 

157.0 

131.8 

65 

203.0 

170.3 

26 

19.9 

16.7 

86 

65.9 

55.3 

46 

111.8 

93.8 

06 

157.8 

132.4 

66 

203.8 

171.0 

27 

20.7 

17.4 

87 

66.6 

55.9 

47 

112.6 

94.5 

07 

158.6 

133.1 

67 

204.5 

171.6 

28 

21.4 

18.0 

88 

67.4 

56.6 

48 

113.4 

95.1 

08 

•159.  3 

133.7 

68 

205.  3 

172.3 

29 

22.2 

18.6 

89 

68.2 

57.2 

49 

114.1 

95.8 

09 

160.1 

134.3 

69 

206. 1 

172.9 

30 

23.0 

19.3 

90 
91 

68.9 
69.7 

57.9 

50 

114.9 

96.4 

10 

160.9 

135.0 

70 

206.8 
207.6 

173.6 
174.2 

31 

23.7 

19.9 

58.5 

151 

115.  7  1    97. 1 

211 

161.6 

135.6 

271 

32 

24.5 

20.6 

92 

70.5 

59.1 

52 

116.4 

97.7 

12 

162.  4 

136.3 

72 

208.4 

174.8 

33 

25.3 

21.2 

93 

71.2 

59.8 

53 

117.2 

98.3 

13 

163.  2 

136.9 

73 

209.1 

175.  5 

34 

26.0 

21.9 

94 

72.0 

60.4 

54 

118.0 

99.0 

14 

163.9 

137.6 

74 

209.9 

176. 1 

35 

26.8 

22.5 

95 

72.8 

61.1 

55 

118.7 

99.6 

15 

164.7 

138.2 

75 

210.7 

176.8 

36 

27.6 

23.1 

96 

73.  5 

61.7 

56 

119. 5     100.  3 

16 

165.  5 

138.  8 

76 

211.4 

177.4 

37 

28.3 

23.8 

97 

74.3 

62.4 

57 

120.  3  1  100.  9 

17 

166.2 

139.5 

77 

212.2 

178. 1 

38 

29.1 

24.4 

98 

75.1 

6.3.0 

58 

121.0 

101.6 

18 

167.0 

140.1 

78 

213.0 

178.7 

39 

29.9 

25.1 

99 

75.8 

63.6 

59 

121.8 

102.2 

19 

167.8 

140.8 

79 

213.7 

179.3 

40 
41 

30.  6 
31.4 

25.7 
26.4 

100 

76.6 

64.3 

60 
161 

122.6 

102.8 

20 

168.5 

141.4 

80 

214.  5 

180.0 
180.  6 

101 

77.4 

64.9 

123.3 

103.5 

221 

169.3 

142.1 

281 

215.3 

42 

32.2 

27.0 

02 

78.1 

65.6 

62 

124.1 

104.1 

22 

170.1 

142.7 

82 

216.0 

181.3 

43 

32.9 

27.6 

03 

78.9 

66.2 

63 

124.9 

104.8 

23 

170.8 

143.  3 

83 

216.8 

181.9 

44 

33.7 

28.3 

04 

79.7 

66.8 

64 

125.6 

105.4 

24 

171.6 

144.0 

.   84 

217.6 

182.6 

45 

34.5 

28.9 

05 

80.4 

67. 5 

65 

126.4 

106.1 

25 

172.4 

144.6 

85 

218.3 

183.2 

46 

35.2 

29.6 

06 

81.2 

68.1 

66 

127.2 

106.7 

26 

173. 1 

145.3 

86 

219.1 

183.8 

47 

36.0 

30.2 

07 

82.0 

68.8 

67 

127.9 

107.3 

27 

173.  9 

145.9 

87 

219.9 

184.5 

48 

36.8 

30.9 

08 

82.7 

69.4 

68 

128.7 

108.0 

28 

174.7 

146.6 

88 

220.6 

185.1 

49 

.37.5 

31.5 

09 

83.5 

70.1 

69 

129. 5 

108.6 

29 

175.4 

147.2 

89 

221.4 

185.8 

50 

38.3  ' 
39.1 

32.1 

10 

84.3 
85.0 

70.7 

70 

130.2 
131.0 

109.3 

30 

176.2 

147.8 

90 

222.2 
222. 9 

186.4 

51 

32.8 

111 

71.3 

171 

109.9 

231 

177.0 

148.5 

291 

187.1 

52 

39.8 

33.4 

12 

85.8 

72.0 

72 

131.8 

110.6 

32 

177.7 

149.1 

92 

223.7 

187.7 

53 

40.6  i 

34.1 

13 

86.6 

72.6 

73 

132.5 

111.2 

33 

178.5 

149.8 

93 

224.5 

188.3 

54 

41.4    ; 

34.7 

14 

87.3 

73. 3 

74 

133.3 

111.8 

34 

179.3 

150.4 

94 

225.2 

189.  0 

55 

42.1  i 

35. 4 

15 

88.1 

73.9 

75 

134. 1 

112.5 

35 

180.0 

151.1 

95 

226.0 

189.  6 

56 

42.9  j 

36.0 

16 

88.9 

74.6 

76 

134.8 

113.1 

36 

180.8 

151.  7 

96 

226.7 

190.  3 

57 

43.7 

36.6 

17 

89.6 

75.2 

77 

135.6 

113.8 

37 

181.6 

152.3 

97 

227.5 

190.9 

58 

44.4 

37.3 

18 

90.4 

75.8 

78 

136.4 

114.4 

38 

182.3 

153.  0 

98 

228.3 

191.6 

59 

45.2 

37.9 

19 

91.2 

76.5 

79     137. 1 

115.1 

39 

183.  1 

153.  6 

99 

229.0 

192.  2 

60 

46.0 

38.6 

20 

91.9 

77.1 

80     137. 9 

115.7 

40 

183.  9 

154.3 

300 

229.8 

192.8 

Dist. 

Dep.     1 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

' 

>0°  (130°,  230°,  310° 

. 

- 

TABLE 

2. 

[Page  447 

Difference  of  Latitude  and  Departure  for 

40°  (140°,  220 

°,  320° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.         Dep. 

301 

230.6 

193.5 

361 

276.  5 

232.1 

421 

322.5 

270.6 

481 

368.5 

309.2 

541 

414.4 

347.7 

02 

231.3 

194.1 

62 

277.3 

232.7 

22 

323.  3 

271.3 

82 

369.  2 

309.8 

42 

415.2 

348.4 

03 

232.1 

194.8 

63 

278.1 

233.3 

23 

324.  0 

271.9 

83  I  370.0 

310.  5 

43 

416.0 

349.0 

04 

232.9 

195.4 

64 

278.8 

234.0 

24 

324.8 

272.6 

84 

370.  8 

311.1 

44 

416.  7     349.  7  | 

05 

233.6 

196.1 

65 

279.6 

234.6 

25 

325.  6 

273.  2 

85 

371.5 

311.7 

45 

417.5 

350.  3 

06 

234.4 

196.7 

66 

280.4 

235.  3 

26 

326.3 

273.8 

86 

372.3 

312.4 

46 

418.3 

351.0 

07 

235.2 

197.3 

67 

281.1 

235.9 

27 

327.1 

274.  5 

87 

373.1 

313.0 

47 

419.0     351.6 

08 

235.9 

198.0 

68 

281.9 

236.6 

28 

327.9 

275. 1 

88 

373.8 

313.6 

48 

419.8  1  352.2 

09 

236.7 

198.  6 

69 

282.7 

237.2 

29 

328.6 

275.  8 

89 

374.6 

314.3 

49 

420.6     352.9 

10 

237.5 

199.3 

70 

283.4 

237.8 

30 

329.4 

276.4 

90 

375.4 

314.9 

50 

421.3 

353.5 

311 

238.2 

199.9 

371 

284.2 

238.5 

431 

330.2 

277.1 

491 

376.1 

315.6 

551 

422.1 

354.2 

12 

239.0 

200.6 

72 

285.0 

239.1 

32 

330.9 

277.7 

92 

376. 9 

316.2 

52 

422.9 

354.8 

13 

239.8 

201.2 

73 

285.7 

239.7 

33 

331.7 

278.3 

93 

37?.  7 

316.9 

53 

423.6 

355.5 

14 

240.5 

201.8 

74 

286.5 

240.4 

34 

332.5 

279.0 

94 

378.4 

317.5 

54 

424.4 

356.1 

15 

241.3 

202.  5 

75 

287.3 

241.0 

35 

333.  2 

279.6 

95 

379.2 

318.2 

55 

425.2  i  356.8 

16 

242.1 

203.1 

76 

288.0 

241.7 

36 

334.  0 

280.3 

96 

380.0 

318.8 

56 

425.9     357.4 

17 

242.8 

203.8 

77 

288.8 

242.3 

37 

334.  8 

280.9 

97 

380.  7 

319.5 

57 

426.7  ,  358.0 

18 

243.6 

204.4 

78 

289.6 

243.  0. 

38 

335.  5 

281.6 

98 

381.5 

320.1 

58 

427.  5     358.  7 

19 

244.4 

205.1 

79 

290.3 

243.6 

39 

336.3 

282.2 

99 

382.3 

320.  8 

59 

428.2     359.3 

20 

245.1 

205.7 

80 

291.1 
291. '9 

244.3 

40 

337.1 

282.8 

500 

383.  0 

321.4 

60 

429.0  i  360.0 

321 

245.9 

206.3 

381 

244.9 

441 

337.8 

283.  5 

501 

383.  8 

322.  0 

561 

429.8  1  360.6 

22 

246.7 

207.0 

82 

292.6 

245.6 

42 

338.  6 

284.1 

02 

384.6 

322.  7 

62 

430.5  ,  361.2 

23 

247.4 

207.6 

83 

293.4 

246.2 

43 

339.4 

284.8 

03 

385.3 

323.  3 

63 

431.3  :  361.9 

24 

248.2 

208.3 

84 

294.2 

246.8 

44 

340.1 

285.4 

04 

386.1 

324.0 

64 

432. 1     362.  5 

25 

249.0 

208.9 

85 

294.  9 

247.5 

45 

340.9 

286.0 

05 

386.8 

324.6 

65 

432.8     363.2 

26 

249.7 

209.6 

86 

295.7 

248.1 

46 

341.7 

286.7 

06 

387.6 

325.  2 

66 

433.6     363.8 

27 

250.5 

210.2 

87 

296.5 

248.8 

47 

342.4 

287.3 

07  '  388.4 

325.  9 

67 

434.3     364.5 

28 

251.3 

210.8 

88 

297.2 

249.4 

48 

343.2 

288.0 

08  i  389.2 

326.5 

68 

435.1      365.1 

29 

252.0 

211.5 

89 

298.0 

250.1 

49 

344.0 

288.  6 

09     389.9 

327. 1 

69 

435.9     365.8 

30 

252.8 

212.1 

90 

298.8 

250.  7 

50 

344.7 
345.5 

289.3 

10 

390.  7 

391.  5 

327.8 

70 
571 

436.6     366.4 
437.4     367.0 

331 

253.6 

212.8 

391 

299.5 

251.3 

451 

289.9 

511 

328.4 

32 

254.3 

213.4 

92 

300.  3 

252.0 

52 

346.3 

290.5 

12     392. 2 

329. 1 

72 

438.2     367.7 

33 

255.1 

214.1 

93 

301.1 

252.6 

53 

.347.  0 

291.2 

13     393. 0 

329.  7 

73 

438.9     368.3 

34 

255.9 

214.7 

94 

301.8 

253.3 

54 

347.8 

291.8 

14     393. 8 

330.4 

74 

439. 7     369. 0 

35 

256.6 

215.3 

95 

302.6 

253.9 

55 

348.6 

292.5 

15     394. 5 

331.  0 

75 

440.5  '  369.6 

36 

257.4 

216.0 

96 

303.4 

254.6 

56 

349.3 

293.1 

16  :  395.3 

331.  6 

76 

441. 2     370. 2 

37 

258.2 

216.6 

97 

304.1 

255.2 

57 

350.1 

293.8 

17  i  396. 1 

332.  3 

77 

442.0     370.9 

38 

258. 9 

217.3 

98 

304.9 

255.8 

58 

350.8 

294.4 

18  i  396.8 

332.  9 

78 

442.8  (  371.5 

39 

259.7 

217.9 

99 

305.7 

256.5 

59 

351.6 

295.0 

19  1  397.6 

333.  6 

79 

443.5     372.2 

40 
341 

260.5 

218.6 

400 

306.4 

257.1 

60 

352.  4 

295.7 

20  i  398.3 
521  i  399.  1 

334.  2 
334.  9 

80 
581 

444.3     372.8 
445. 1     373.  5 

261.2 

219.  2 

401 

307.2 

257.8 

461 

353.1 

296.3 

42 

262.0 

219.8 

02 

308.0 

258.4 

62 

353.9 

297.0 

22     399.9 

335.  5 

82 

445.8  1  374.1 

43 

262.8 

220.5 

03 

308.7 

259. 1 

63 

354.7 

297.6 

23  1  400.6 

336. 1 

83 

446. 6     374.  8 

44 

263.  5 

221.1 

04 

309.  5 

259.7 

64 

355.  4 

298.3 

24     401.4 

336.8 

84 

447.  4     375. 4 

45 

264.  3 

221.8 

05 

310.2 

260.3 

65 

356.2 

298.9 

25     402. 2 

337.  4 

85 

448.1 

376.0 

46 

265.1 

222.4 

06 

311.0 

261.0 

66 

357.0 

299.5 

26     402. 9 

338.1 

86 

448.9 

376.7 

47 

265.8 

223.1 

07 

311.8 

261.6 

67 

357.7 

300.  2 

27     403. 7 

338.7 

87 

449.7 

377.3 

48 

266.6 

223.7 

08 

312.5 

262.3 

68 

358.5 

300.8 

28     404.5 

339.  4 

88 

450.4 

378.0 

49 

267.4 

224.3 

09 

313.  3 

262.9 

69 

359.  3 

301.  5 

29  1  405.2 

340,0 

89 

451.  2 

378.  6 

50 

268.1 

225.0 
225.6 

10 
411 

314.1 
314.8 

263.6 
264.2 

70 
471 

360.0 
360.8 

302. 1 
302.8 

30     406.0 

531  i  406.8 

340.  6 
"341.3 

90 

452.0 

379.2 

351 

268.9 

591 

452.  7 

379.9 

52 

■269.6 

226.3 

12 

315.6 

264.8 

72 

361.6 

303.  4 

32     407.5 

341.9 

92 

453.5  1  380.5 

53 

270.4 

226.9 

13 

316.4 

265.5 

73 

362.3 

304.  0 

33     408. 3 

342.  6 

93 

454.3     381.2 

54 

271.2 

227.6 

14 

317.1 

266.1 

74 

363. 1 

304.  7 

34  1  409. 1 

343.  2 

94 

455.0  1  381.8 

55 

271.9 

228.2 

15 

317.9 

266.8 

75 

363.  9 

305.  3 

35  !  409.8 

343.  9 

95 

455.8  :  382.4 

56 

272.7 

228.8 

16 

318.7 

267. 4 

76 

364.  6 

306.0 

36     410.6 

344.5 

96 

456.6 

383.1 

57 

273.  5 

229.5 

17 

319.  4 

268.1 

77 

365.  4 

306.  6 

37     411.4 

345.2 

97 

457.3 

383.  7 

58 

274.2 

230. 1 

18 

320.2 

268.7 

78 

366.2 

307.  3 

38     412. 1 

345.  8 

98 

458. 1 

384.4 

59 

275.0 

230.8 

19 

321.0 

269.3 

7^ 

366.9 

307.9 

39  !  412.9 

346.4 

99 

458.  9 

385. 0 

60 

275.8 

231.4 

20 

321.7 

270.0 

80 

367.7 

308.5 

40  '  413.  7 

347.1 

600 

459.6 

385.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep. 

Lat. 

Dist. 

Dep.         Lat. 

50°  (1 

30°,  230 

°,  310° 

)• 

Page  448] 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  41°  (139°,  221°,  319° 

). 

Dirt. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.8 

0.7 

61 

46.0 

40.0 

121 

91.3 

79.4 

181 

136.6 

118.7 

241 

181.9 

158. 1 

2 

1.5 

1.3 

62 

46.8 

40.7 

22 

92.1 

80.0 

82 

137.4 

119.4 

42 

182.6 

158.8 

3 

2.3 

2.0 

63 

47.5 

41.3 

23 

92.8 

80.7 

83 

138.1 

120.1 

43 

183.4 

159.  4 

4 

3.0 

2.6 

64 

48.3 

42.0 

24 

93.6 

81.4 

84 

138.9 

120.7 

44 

184.1 

160.1 

5 

3.8 

3.3 

65 

49.1 

42.6 

25 

94.3 

82.0 

85 

139.6 

121.4 

45 

184.9 

160.7 

6 

4.5 

3.9 

»  66 

49.8 

43.3 

26 

95.1 

82.7 

86 

140.4 

122.0 

46 

185.7 

161.4 

7 

5.3 

4.6 

67 

50.6 

44.0 

27 

95.8 

83.3 

87 

141.1 

122.7 

47 

186.4 

162.0 

8 

6.0 

5.2 

68 

51.3 

44.6 

28 

96.6 

84.0 

88 

141.9 

123.  3 

48 

187.2 

162.7 

9 

6.8 

5.9 

69 

52.1 

45.3 

29 

97.4 

84.6 

89 

142.6 

124.0 

49 

187.9 

163.4 

10 

7.5 

6.6 

70 

52.8 

45.9 

30 

98.1 
98.9 

85.3 

90 

143.4 

124.7 

50 

188.7 

164.0 

11 

8.3 

7.2 

71 

53.6 

46.6 

131 

85.9 

191 

144.1 

125.  3 

251 

189.4 

164.7 

12 

9.1 

7.9 

72 

54.3 

47.2 

32 

99.6 

86.6 

92 

144.9 

126.0 

52 

190.2 

165.3 

13 

9.8 

8.5 

73 

55.1 

47.9 

33 

100.4 

87.3 

93 

145.7 

126.6 

53 

190.9 

166.0 

14 

10.6 

9.2 

74 

55.8 

48.5 

34- 

101.1 

87.9 

94 

146.4 

127.3 

54 

191.7 

166.6 

15 

11.3 

9.8 

75 

56.6 

49.2 

35 

101.9 

88.6 

95 

147.2 

127.9 

55 

192.5 

167.3 

16 

12.1 

10.5 

76 

57.4 

49.9 

36 

102.6 

89.2 

96 

147.9 

128.6 

56 

193.2 

168.0 

17 

12.8 

11.2 

77 

58.1 

50.5 

37 

103.4 

89.9 

97 

148.7 

129.2 

57 

194.0 

168.6 

18 

13.6 

11.8 

78 

58.9 

51.2 

38 

104. 1 

90.5 

.98 

149.4 

129.9 

58 

194.7 

169.3 

19 

14.3 

12.5 

79 

59.6 

51.8 

39 

104.9 

91.2 

99 

150.2 

130.6 

59 

195.5 

169.9 

20 

15.1 

13.1 

80 

60.4 

52.5 

40 

105.7 

91.8 

200 
'201 

150.9 
151.7 

131.2 

60 

196.2 

170.6 
171.2 

21 

15.8 

13.8 

81 

61.1 

53.1 

141 

106.4 

92.5 

131.9 

261 

197.0 

22 

16.6 

14.4 

82 

61.9 

53.8 

42 

107.2 

93.2 

02 

152.  5 

132.5 

62 

197.7 

171.9 

23 

17.4 

15. 1 

83 

62.6 

54.5 

43 

107.9 

93.8 

03 

153.2 

133.  2 

63 

198.5 

172.5 

24  ' 

18.1 

15.7 

84 

63.4 

55.1 

44 

108.7 

94.5 

04 

154.0 

133.8 

64 

199.2 

173.2 

25 

18.9 

16.4 

85 

64.2 

55.8 

45 

109.4 

95.1 

05 

154.7 

134.5 

65 

200.0 

173.9 

26 

19.6 

17.1 

86 

64.9 

56.4 

46 

110.2 

95.8 

06 

155.5 

135.1 

66 

200.8 

174.5 

27 

20.4 

17.7 

87 

65.7 

57.1 

47 

110.9 

96.4 

07 

156.2 

135.  8 

67 

201.5 

175.2 

28 

21.1 

18.4 

88 

66.4 

57.7 

48 

111.7 

97.1 

08 

•  157.  0 

136. 5 

68 

202.3 

175.8 

29 

21.9 

19.0 

89 

67.2 

58.4 

49 

112.5 

97.8 

09 

157.  7 

137. 1 

69 

203.0 

176.5 

30 

22.6 

19.7 

90 

67.9 
68.7 

59.0 

50 

113.2 
114.0 

98.4 

10 

158.5 

137.8 
138.4 

70 
271' 

203.8 
204.5 

177.1 
177.8 

31 

23.4 

20.3 

91 

59.7 

151 

99.1 

211 

159.2 

32 

24.2 

21.0 

92 

69.4 

60.4 

52 

114.  7 

99.7 

12 

160.0 

1.39. 1 

72 

205.3 

178.4 

33 

24.9 

21.6 

93 

70.2 

61.0 

53 

115.5 

100.4 

13 

160.  8 

139.7 

73 

206.0 

179.1 

34 

25.7 

22.3 

94 

70.9 

61.7 

54 

116.2 

101.0 

14 

161.5 

140.4 

74 

206.8 

179.8 

35 

26.4 

23.0 

95 

71.7 

62.3 

55 

117.0 

101.7 

15 

162.3 

141.1 

75 

207.5 

180.4 

36 

27.2 

23.6 

96 

72.5 

63.0 

56 

117.7 

102.3 

16 

1^3.0 

141.7 

76 

208.3 

181.1 

37 

27.9 

24.3 

97 

73.2 

63.6 

57 

118.5 

103.0 

17 

163.8 

142.4 

77 

209.1 

181.7 

38 

28.7 

24.9 

98 

74.0 

64.3 

58 

119.2 

103.7 

18 

164.5 

143.  0 

78 

209.8 

182.4 

39 

29.4 

25.6 

99 

74.7 

64.9 

59 

120.0 

104.3 

19 

165.3 

143.7 

79 

210.6 

183.0 

40 

30.2 

26.2 

100 

75.5 

65.6 

60 

120.8 
121.5 

105.0 
105.6 

20 
221 

166.0 
166.8 

144.3 
145.  0~ 

80 
281 

211.3 
212.1 

183.7 

41 

30.9 

26.9 

101 

76.2 

66.3 

161 

184.4 

42 

31.7 

27.6 

02 

77.0 

66.9 

62 

122.3 

106.  3 

22 

167.5 

145.6 

82 

212.8 

185.0 

43 

32.5 

28.2 

03 

77.7 

67.6 

63 

123.  0 

106.9 

23 

168.3 

146.3 

83 

213.6 

185.  7 

44 

33.2 

28.9 

04 

78.5 

68.2 

64 

123.  8 

107.6 

24 

169.1 

147.0 

84 

214.3 

186.  3 

45 

34.0 

29.5 

05 

79.2 

68.9 

65 

124.5 

108.2 

25 

169.8 

147.6 

'  85 

215.1 

187.0 

46 

34.7 

30.2 

06 

80.0 

69.5 

66 

125.3 

108.9 

26 

170.6 

148.3 

86 

215.8 

187.6 

47 

35.5 

30.8 

07 

80.8 

70.2 

67 

126.0 

109.6 

27 

171.3 

148.9 

87 

216.6 

188.3 

48 

.36.2 

31.5 

08 

81.5 

70.9 

68 

126.8 

110.2 

28 

172.1 

149.6 

88 

217.4 

188.9 

49 

37.0 

32.1 

09 

82.3 

71.5 

69 

127.5 

110.9 

29 

172.8' 

150. 2 

89 

218.1 

.  189.  6 

50 

37.7 

32.8 

10 

83.0 

72.2 

70 

128.3 

111.5 
112.  2 

30 
231 

173.6 
174.3 

150.9 

90 

218.9 
219.6 

190.3 
190.  9" 

51 

38.5 

33.5 

111 

83.8 

72.8 

171 

129.1 

151.5 

291 

52 

39.2 

34.1 

12 

84.5 

73.5 

72 

129.8 

112.8 

32 

175.1 

152.  2 

92 

220.4 

191.6 

53 

40.0 

34.8 

13 

85.3 

74.1 

73 

130.6 

113.5 

33 

175.8 

152.  9 

93 

221.1 

192.2 

54 

40.8 

35.4 

14 

86.0 

74.8 

74 

131.3 

114.2 

34 

176.6 

153.  5 

94 

221.9 

192.9 

55 

41.5 

36.1 

15 

86.8 

75.4 

75 

132.1 

114.8 

35 

177.4 

154.2 

95 

222.6 

193.  5 

56 

42.3 

36.7 

16 

87.5 

76.1 

76 

132.8 

115.5 

36 

178.1 

154.8 

96 

223.4 

194.2 

57 

43.0 

37.4 

17 

88.3 

76.8 

77 

133.6 

116.1 

37 

178.9 

155.5 

97 

224.1 

194.8 

58 

43.8 

.38.1 

18 

89.1 

77.4 

78 

134.3 

116.8 

38 

179.6 

156. 1 

98 

224.9 

195.  5 

59 

44.5 

38.7 

19 

89.8 

78.1 

79 

135.1 

117.4 

39 

180.4 

156.8 

99 

225.7 

196.2 

60 

45.3 

39.4 

20 

90.6 

78.7 

80 

135.8 

118.1 

40 

181.1 

157.5 

300 

226.4 

196.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

49°  (1 

31°,  229 

°,  311° 

). 

TABLE  2. 

[Page  449    | 

Difference  of  Latitude  and  Departure  for  41°  (139°,  221 

°,  319° 

)• 

Dist. 
301 

Lat. 

Dcp. 

Dist. 
361 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

227.2 

197.5 

272.5 

236.9 

421 

317.7 

276.2 

481 

363.0 

315.  6 

541 

408.3 

354.  9 

02 

227.9 

198.1 

62 

273.2 

237.5 

22 

318.  5 

276.9 

82 

363.8 

316.2 

42 

409.0 

355.6 

03 

228.7 

198.8 

63 

274.0 

238.2 

23 

319.  2 

277.5 

83 

364.5 

316.9 

43 

409.8 

356.2 

04 

229.4 

199.4 

64 

274.7 

238.8 

24 

320.0 

278.2 

84 

365.  3 

317.  5 

44 

410.6 

356.9 

05 

230.2 

200.1 

65 

275.5 

239.5 

25 

320.  8 

278.8 

85 

366.0 

318.2 

45 

411.3 

357.5 

08 

230.9 

200.8 

66 

276.2 

240.1 

26 

321.5 

279.5 

86 

366.8 

318.8 

46 

412.1 

358.2 

07 

231.7 

201.4 

67 

277.0 

240.8 

27 

322.  3 

280.1 

87 

367.5 

319.5 

47 

412.8 

358.8 

08 

232.5 

202.1 

68 

277.7 

241.4 

28 

323.0 

280.8 

88 

368.3 

320.1 

48 

413.6 

359.5 

09 

233.2 

202.7 

69 

278. 5 

242.1 

29 

323.8 

281.5 

89 

369.0 

320.8 

49 

414.3 

360.2 

10 

234.0 
234.7 

203.4 

70 

279.2 

242.7 

30 
431 

324.  5 

282.1 

90 

369.8 
370.6 

321.5 
322.1 

50 
551 

415.1 

360.8 

811 

204.0 

371 

280.0 

243.4 

325.3 

282.8 

491 

415.8 

361.5 

12 

235.5 

204.7 

72 

280.8 

244.1 

32 

326.  0 

283.4 

92 

371.3 

322.8 

52 

416.6 

362.1 

13 

236.2 

205.4 

73 

281.5 

244.7 

33 

326.8 

284.1 

93 

372.1 

323.4 

53 

417.  3 

362.8 

14 

237.0 

206.0 

74 

282.3 

245.4 

34 

327.  5 

284.7 

94 

372.8 

324.1 

54 

418.1 

363.4 

15 

237.7 

206.7 

75 

283.0 

246.0 

35 

328.3 

285.4 

95 

373.6 

324.7 

55 

418.9 

364.1 

16 

238.5 

207.3 

76 

283.8 

246.7 

36 

329.1 

286.0 

96 

374.3 

325.4 

56 

419.6 

364.8 

17 

239.2 

208.0 

77 

284.5 

247.3 

37 

329.8 

286.7 

97 

375.1 

326.0 

57 

420.4 

365.4 

18 

240.0 

208.6 

78 

285.3 

248.0 

38 

330.6 

287.4 

98 

3^5. 8 

326.7 

58 

421.1 

366.1 

19 

240.8 

209.3 

79 

286.0 

248.7 

39 

331.3 

288.0 

99 

376.6 

327.4 

59 

421.9 

366.7 

20 

241.5 

209.9 

80 

286.8 
287.5 

249.3 

40 

332.1 

288.7 

500 
501 

377.  3 
378.1 

328.0 

60 

422.6 

367.4 

321 

242.3 

210.6 

381 

250.0 

441 

332.  8  i  289. 3 

328.7 

561 

423.4 

368.0 

22 

243.0 

211.3 

82 

288.3 

250.  6 

42 

333.6    290.0 

02 

378.9 

329.3 

62 

424.1 

368.7 

23 

243.8 

211.9 

83 

289.1 

251.3 

43 

334.  3 

290.6 

03 

379.6 

330.0 

63 

424.9 

369.4 

24 

244.5 

212.6 

84 

289.8 

251.  9 

44 

335. 1 

291.3 

04 

380.4 

330.6 

64 

425.7 

370.0 

25 

245.  3 

213.2 

85 

290.6 

252.6 

45 

335.8 

292.0 

05 

381.1 

331.3 

6.5 

426.4 

370.7 

26 

246.0 

213.9 

86 

291.3 

253.  2 

46 

336.  6 

292.6 

06 

381.9 

332.0 

66 

427.2 

371.3 

27 

246.8 

214.5 

87 

292.1 

253.9 

47 

337.4 

293.3 

07 

382.6 

332.6 

67 

427.9 

372.0 

28 

247.5 

215.2 

88 

292.8 

254.6 

48 

338.1 

293.9 

08 

383.4 

333.  3 

68 

428.7 

372.6 

29 

248.3 

215.9 

89 

293.6 

255.  2 

49 

338.  9 

294.6 

09 

384.1 

333.9 

69 

429.4 

373.3 

30 
331 

249.1 

216.5 

90 

294.3 

255.9 
256.  5 

50 

339.6 

295.2 

10 

384.9 
385.7 

334.6 
335.2 

70 
571 

430.  2 

374.0 

249.8 

217.2 

391 

295.1 

451 

340.4 

295.9 

511 

430.9 

374.6 

32 

250.6 

217.8 

92 

295.8 

257.2 

52 

341. 1 

296.5 

■  12 

386.4 

335.9 

72 

431.7 

375.  3 

33 

251.3 

218,5 

93 

296.6 

257.8 

53 

341.  9 

297.2 

13 

387.2 

336.5 

73 

432.4 

375.  9 

34 

252.1 

219.1 

94 

297.4 

258. 5 

54 

342.6 

297.9 

14 

387.9 

337.2 

74 

433.2 

376.6 

35 

252.8 

219.8 

95 

298.1 

259.  2 

55 

343.4 

298.5 

15 

388.7 

337.9 

75 

434.  0 

377.2 

36 

253.6 

220.4 

96 

298.9 

259.8 

56 

344. 1 

299.2 

16 

389.4 

338.5 

76 

434.7 

377.9 

37 

254.  3 

221.1 

97 

299.6 

260.5 

o/ 

344.9 

299.8 

17 

390.2 

339.2 

1 1 

435.5 

378. 5 

38 

255.1 

221.8 

98 

300.4 

261. 1 

58 

345.  7 

300.5 

18 

390.9 

339.  8 

78 

436.2 

379.2 

39 

255.8 

222.4 

99 

301.1 

261.8 

59 

346.4 

301.1 

19 

391.7 

340.5 

79 

437.0 

379.8 

40 

256.  6 
257.4 

223.1 

400 

301.9 

262.4 

60 
461 

347.2 
347.9 

301.8 
302.5 

20 

392.4 
393.  2 

341.1 

80 

437.7 

380.5 

341 

223.7 

401 

302.6 

263.1 

521 

341.  8 

581 

438.5 

381.2 

42 

258.1 

224.4 

02 

303.4 

263.7 

62 

348.7 

303. 1 

22 

394.0 

342.5 

82 

439.2 

381.8 

43 

258.9 

225.0 

03 

304.2 

264.4 

63 

349.4 

303.8 

23 

394.7 

343.1 

83 

440.0 

382.5 

44 

259.6 

225.7 

04 

304.9 

265.1 

64 

350.  2 

304.4 

24 

395.  5 

343.8 

84 

440.7 

383.2 

45 

260.4 

226.3 

05 

305.7 

265.  7 

65 

350.9 

305. 1 

25 

396.2 

344.4 

85 

441.5 

383.8 

46 

261.1 

227.0 

06 

306.  4 

266.4 

66 

351.  7 

305.  7 

26 

397.0 

345.1 

86 

442.3 

384.5 

47 

261.9 

227.7 

07 

307.2 

267.0 

67 

352. 5 

306.4 

27 

397.7 

345.  7 

87 

443.0 

385. 1 

48 

262.6 

228.  3 

08 

307.9 

267.7 

68 

353.  2 

307.0 

28 

398.5 

346.4 

88 

443.8 

385.8 

49 

263.4 

229.0 

09 

308.7 

268.3 

69 

354.0 

307.7 

29 

399.2 

347.0 

89 

444.5 

386.4 

50 

264.2 
264.  9 

229.6 

10 

309.4 

269.0 
269.6 

70 
471 

354.7 
355:5 

308.4 

30 
531 

400.0 
400.7 

347.7 

90 

445.3 

387.1 

351 

230.3 

411 

310.2 

309.0 

348.4 

591 

446.0 

387.7 

52 

265.7 

230.9 

12 

310.9 

270.3 

72 

356.  2 

309.  7 

32 

401.5 

349. 0 

92 

446.8 

388.4 

53 

266.4 

231.6 

13 

311.7 

271.0 

73 

357.  0 

310.  3 

33 

402.2 

349.  7 

93 

447.5 

389.1 

54 

267.2 

232.3 

14 

312.  5 

271.6 

74 

357.7 

311.0 

34 

403.  0 

350.  3 

94 

448.3 

389.7 

55 

267.9 

232.9 

15 

313.2 

272.3 

75 

358.  5 

311.6 

35 

403.8 

351.  0 

95 

449.1 

390.4 

56 

268.7 

233.6 

16 

314. 0  ,  272. 9 

76 

359.2 

312.  3 

36 

404.5 

351.6 

96 

449.8 

391.0 

57 

269.4 

234.2 

17 

314.7 

273.6 

77 

360.0 

312.9 

37 

405.3 

352.  3 

97 

450.6 

391.  7 

58 

270.2 

234.9 

18 

315.5 

274.2 

78 

360.8 

313.6 

38 

406.0 

352.  9 

98 

451.  3 

392.  3 

59 

270.9 

235. 5 

19 

316.  2 

274.9 

79 

361.5  1314.3 

39 

406.8 

353.  6 

•  99 

452.1 

393.0 

60 

271.7 

236.2 

20 

317.0 

275.6 

80 

362.3    314.9 

40 

407.5 

354.3 

600 

452.8 

393.6 

Dist. 

Dep. 

Lat. 

Diet. 

Dep. 

Lat. 

Dist. 

Dep.     1    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

49°  (1 

31°,  229°,  311° 

)• 

22489—03- 


-29 


Page  450 

1 

TABLE  '2. 

Difference  of  Latitude  and  Departure  for  42°  (138°,  222°,  318° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  1    Lat. 

Dep. 

Dist. 

Lat.    !    Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

45.3 

40.8 

121 

89.9 

81.0 

181 

134.5 

121.1 

241 

179.1 

161.3 

2 

1.5 

1.3 

62 

46.1 

41.5 

22 

90.7 

81.6 

82 

135.3 

121.8 

42 

179.8 

161.9 

3 

2.2 

2.0 

63 

46.8 

42.2 

23 

91.4 

82.3 

83 

136.0 

122.5 

43 

180.6 

162.6 

4 

3.0 

2.7 

64 

47.6 

42.8 

24  i    92. 1 

83.0 

84 

136.  7 

123.1 

44 

181.3 

163.3 

5 

3.7 

3.3 

65 

48.3 

43.5 

25 

92.9 

83.6 

85 

137.5 

123.8 

45 

182.1 

163.  9 

6 

4.5 

4.0 

•66 

49.0 

44.2 

26 

93.6 

84.3 

86 

138.2    124.5 

46 

182.8 

164.6 

7 

5.2 

4.7 

67 

49.8 

44.8 

27 

94.4 

85.0 

87 

139.  0  !  125. 1 

47 

183.6 

165.  3 

8 

5.9 

5.4 

68 

50.5 

45.5 

28 

95.1 

85.6 

88 

139.7 

125.8 

48 

184.3 

165.  9 

9 

6.7 

6.0 

69 

51.3 

46.2 

29 

95.9 

86.3 

89 

140.5 

126.5 

49 

185.0 

166.6 

10 

7.4 

6.7 

7.4 

70 
71" 

52.0 

46.8 

30 

96.6 
97.4 

87.0 

90 

141.2 
141.9 

127.1 

50 
251 

185.8 
186.5 

167.3 

11 

8.2 

52.8 

47.5 

131 

87.7 

191 

127.8 

168.0 

12 

8.9 

8.0 

72 

53.5 

48.2 

32 

98.1 

88.3 

92 

142.7 

128.5 

52 

187.3 

168.6 

13 

9.7 

8.7 

73 

54.2 

48.8 

33 

98.8 

89.0 

93 

143.4 

129.1 

53 

188.0 

169.3 

14 

10.4 

9.4 

74 

55.0 

49.5 

34 

99.6 

89.7 

94 

144.2  1129.8 

54 

188.8 

170.0 

15 

11.1 

10.0 

75 

55.7 

50.2 

35 

100.3 

90.3 

95 

144.9 

130.5 

55 

189.5 

170.6 

16 

11.9 

10.7 

76 

56.5 

50.9 

36 

101.1 

91.0 

96 

145.7 

131.1 

56 

190.2 

171.3 

17 

12.6 

11.4 

77 

57.2 

51.5 

37 

101.8 

91.7 

97 

146.4 

131.8 

57 

191.0 

172.0 

18 

13.4 

12.0 

78 

58.0 

52.2 

38 

102.6 

92.3 

98 

147.1 

132. 5 

58 

191.7 

172.6 

19 

14.1 

12.7 

79 

58.7 

52.9 

39 

103.3 

93.0 

99 

147.  9  \  133.  2 

59 

192.5 

173.3 

20 

14.9 

13.4 

80 

59.5 

53.5 

40 

104.0 

93.7 

200 

148.6 
149.4 

133.8 
134.5 

60 
261 

193.2 
194.0 

174.0 

21 

15.6 

14.1 

81 

60.2 

54.2 

141 

104.8 

94.3 

201 

174.6 

22 

16.3 

14.7 

82 

60.9 

54.9 

42 

105.5 

95.0 

02 

150.1 

135.  2 

■62 

194.7 

175.3 

23 

17.1 

15.4 

83 

61.7 

55.5 

43 

106.3 

95.7 

03 

150. 9 

135.8 

63 

195.4 

176.0 

24 

17.8 

16.1 

84 

62.4 

56.2 

44 

107.0 

96.4 

04 

151.6 

136.5 

64 

196.2 

176.7 

25 

18.6 

16.7 

85 

63.2 

56.9 

45 

107.8 

97.0 

05 

152.  3 

137.2 

65 

196.9 

177.3 

26 

19.3 

17.4 

86 

63.9 

57.5 

46 

108.5 

97.7 

06 

153. 1 

137.8 

66 

197.7 

178.0 

27 

20.1 

18.1 

87 

64.7 

58.2 

47 

109.2 

98.4 

07 

153.8 

138.5 

67 

198.4 

178.  7 

28 

20.8 

18.7 

88 

65.4 

58.9 

48 

110.0 

99.0 

08 

154. 6 

139.2 

68 

199.2 

179.3 

29 

21.6 

19.4 

89 

66.1 

59.6 

49 

110.7 

99.7 

09 

155.3 

139.8 

69 

199.9 

180.0 

30 
31 

22.3 

20.1 

90 

66.9 
67.6 

60.2 

50 

111.5 
112.2 

100.4 

10 

156.1 
156.8 

140.5 

70 

200.6 

180.7 

23.0 

20.7 

91 

60.9 

151 

101.0 

211 

141.2 

271 

201.4 

181.3 

32 

23.8 

21.4 

92 

68.4 

61.6 

52 

113.0 

101.7 

12 

157.5 

141.9 

72 

202.1 

182.0 

33 

24.5 

22.1 

93 

69.1 

62.2 

53 

.113.7 

102.4 

13 

158.3 

142.5 

73 

202.9 

182.7 

34 

25.3 

22.8 

94 

69.9 

62.9 

54 

114.4 

103.0 

14 

159.0 

143.2 

74 

203.6 

183.3 

35 

26.0 

23.4 

95 

70.6 

63.6 

55  1  115.2 

103.7 

15 

159.8 

143.9 

75 

204.4 

184.0 

36 

26.8 

24.1 

96 

71.3 

64.2 

56 

115.9 

104.4 

16 

160.5 

144.5 

76 

205.1 

184.7 

37 

27.5 

24.8 

97 

72.1 

64.9 

57 

116.7 

105.1 

17 

161.3 

145.  2 

77 

205.9 

185.3 

38 

28.2 

25.4 

98 

72.8 

65.6 

58 

117.4 

105.7 

18 

162.0 

145.9 

78 

206.6 

186.0 

39 

29.0 

26.1 

99 

73.6 

66.2 

59 

118.2 

106.4 

19 

162.7 

146.5 

79 

207.3 

186.7 

40 
41 

29.7 

26.8 

100 
101 

74.3 

66.9 

60 

118.9 

107.1 

20 

163.  5 
164.2 

147.2 

80 
281 

208.1 
208.8 

187.4 
188.0 

30.5 

27.4 

75.1 

67.6 

161     119.6 

107.7 

221 

147.9 

42 

31.2 

28.1 

02 

75.8 

68.3 

62     120.4 

108.4 

22 

165.0 

148.5 

82 

209.6 

1"88.7 

43 

32.0 

28.8 

03 

76.5 

68.9 

63 

121.1 

109.1 

23 

165.7 

149.2 

83 

210.3 

189.4 

44 

32.7 

29.4 

04 

77.3 

69.6 

64 

121.9 

109.7 

24 

166.5 

149.9 

84 

211.1 

190.0 

45 

33.4 

30.1 

05 

78.0 

70.3 

65 

122.6 

110.4 

25 

167.2 

150.6 

85 

211.8 

190.7 

46 

34.2 

30.8 

06 

78.8 

70.9 

66 

123. 4 

111.1 

26 

168.0 

151.2 

86 

212.5 

191.4 

47 

34.9 

31.4 

07 

79.5 

71.6 

67 

124.1 

111.7 

27 

168.7 

151.9 

87 

213.3 

192.0 

48 

35.7 

32.1 

08 

80.3 

72.3 

68 

124.  8  '  112.  4 

28 

169.4 

152.6 

88 

214.0 

192.7 

49 

36.4 

32.8 

09 

81.0 

72.9 

69 

125. 6  i  113. 1 

29 

170.2 

153. 2 

89 

214.8 

193.4 

50 
51 

37.2 
37.9 

33.5 

10 

81.7 

73.6 

70 

126.3 
127.1 

113.8 

30 

170.9 
171.7 

153.9 

90 

215.5 

194.0 
194.7 

34.1 

111 

82.5 

74.3 

171 

114.4 

231 

154.6 

291 

216.3 

52 

38.6 

34.8 

12 

83.2 

74.9 

72 

127.8 

115.1 

32 

172.4 

155.2 

92 

217.0 

195.4 

53 

39.4 

35.5 

13 

84.0 

75.6 

73 

128.6 

115.8 

33 

173.2 

155.9 

93 

217.7 

196.1 

54 

40.1 

36.1 

14 

84.7 

76.3 

74 

129.3 

116.4 

34 

173.9 

156.6 

94 

218.5 

196.7 

55 

40.9 

36.8 

15 

85.5 

77.0 

75 

130.1 

117.1 

35 

174.6 

157.2 

95 

219.2 

197.4 

56 

41.6 

37.  5 

16 

86.2 

77.6 

76 

130.8 

117.8 

36 

175.4 

157.9 

96 

220.0 

198.1 

57 

42.4 

38.1 

17 

86.9 

78.3 

77 

131.5 

118.4 

37 

176.1     158.6 

97 

220.7 

198.7 

58 

43.1 

38.8 

18 

87.7 

79.0 

78 

132.3 

119.1 

38 

176.9 

159.3 

98 

221.5 

199.4 

59 

43.8 

39.5 

19 

88.4 

79.6 

79 

133.0    119.8 

39 

177.6 

159.9 

99 

222.2 

200.1 

60 

44.6 

40.1 

20 

89.2 

80.3 

80 

133.8    120.4 

40 

178.4 

160.6 

300 

222.9 

200.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.       Dep.    1    Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

48°  (132°, 228°,  312).                                                                           1 

TABLE  2. 

[Page  451     | 

Difference  of  Latitude  and  Departure  for  42°  (138°,  222°,  318° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     ;    Dep. 

Dist. 

Lat.         Dep. 

Dist. 

Lat. 

Dep. 

301 

223.7 

201.4 

361 

268.3 

241.6 

421 

312.9 

281.7 

481 

357.5  '321.9 

541 

402.1 

362.0 

02 

224.4 

202.1 

62 

269.0 

242.2 

22 

313.6 

282.4 

82 

358.2    322.5 

42 

402.8 

362.7 

03 

225.2 

202.8 

63 

269.8 

242.9 

23 

314.4 

283.  0 

83 

358.9 

323.  2 

43 

403.5 

363.3 

04 

225.9 

203.4 

64 

270.5 

243.6 

24 

315.1 

283.7 

84 

359.7 

323.9 

44 

404.3 

364.0 

05 

226.6 

204.1 

65 

271.2 

244.2 

25 

315.8 

284. 4 

85 

360.4 

324.6 

45 

405.0 

364.7 

i    06 

227.4 

204.8 

66 

272.0 

244.9 

26 

316.6 

285.1 

86 

361.2 

325.2 

46 

405.8 

365.4 

07 

228.1 

205.4 

67 

272.7 

245.6 

27 

317.3 

285.  7 

87 

361.9 

325.9 

47 

406.5 

366.0 

08 

228.9 

206.1 

68 

273.5 

246.2 

48 

318.1 

286.4 

88 

362.7 

326.6 

48 

407.2 

366.7 

09 

229.6 

206.8 

69 

274.2 

246.9 

29 

318.8 

287.1 

89 

363.  4 

327.2 

49 

408.0 

367.4 

10 
311 

230.4 
231.1 

207.4 
208.1 

70 

275.0 

247.6 

30 

319.6 

287.7 

90 

.364.1  :327.9 

50 

408.7 

368.  0 

371 

275.7 

248.  3 

431 

320.3 

288.4 

491 

364.9    328.6 

551 

409.5 

368.7 

12 

231.9 

208.8 

72 

276.5 

248.9 

32 

321.  0 

289.1 

92 

365. 6 

329.2 

52 

410.2 

369.4 

13 

232.6 

209.4 

73 

277.2 

249.6 

33 

321.8 

289.7 

93 

366.  4 

329.9 

53 

411.0 

370.0 

14 

233.  3 

210.1 

74 

277.9 

250.3 

34 

322.5 

290.4 

94 

367.1 

330.6 

54 

411.7 

370.7 

15 

234.1 

210.8 

75 

278.7 

250.9 

35 

323.3 

291.1 

95 

367.9 

331.3 

55 

412.4 

371.4 

16 

234.8 

211.5 

76 

279.4 

251.6 

36 

324.0 

291.7 

96 

368.6 

331.9 

56 

413.2 

372.0 

17 

235.6 

212.1 

77 

280.2 

252.3 

37 

324.8 

292.4 

97 

369.3 

332.6 

57 

413.  9 

372.7 

18 

236.  3 

212.8 

78 

280.9 

252.9 

38 

325.  5 

293.1 

98 

370.1 

333. 3 

58 

414.7 

373.4 

19 

237.1 

213.5 

79 

281.7 

253.6 

39 

326.2 

293.8 

99 

370.8 

333.9 

59 

415.4 

374.1 

20 
321 

237.8 

214.1 

80 

282.4 

254.3 

40 

327.0 

294.4 
295.1 

500 

371.6 

334.6 

60 

416.2 
416.9 

374.7 

238.6 

214.8 

381 

283.1 

254.9 

441 

327.7 

501 

372.3 

335.3 

561 

375. 4 

22 

239.3 

215.5 

82 

283. 9 

255.6 

42 

328.5 

295.8 

02 

373. 1 

335.9 

62 

417.6 

376.1 

23 

240.0 

216.1 

83 

284.6 

256.3 

43 

329.  2 

296.4 

03 

373.8 

336.6 

63 

418.4 

376.7 

24 

240.8 

216.8 

84 

285.4 

257.0 

44 

330.0 

297.1 

04 

374.5 

337.2 

64 

419.1 

377.4 

25 

241.5 

217.5 

85  i  286.1 

257.6 

45 

330.7 

297.8 

05 

375.  3 

337.9 

65 

419.9 

378.1 

26 

242.3 

•218. 1 

86     286.9 

258.3 

46 

331.4 

298.4 

06 

376.0 

338.6 

66 

420.6 

378.7 

27 

243.0 

218.8 

87 

287.6 

259.0 

47 

332.2 

299.1 

07 

376.8 

339.3 

67 

421.4 

379.4 

28 

243.8 

219.5 

88 

288.3 

259.6 

48 

332.9 

299.8 

08 

377.5 

339.9 

68 

422.1 

380.1 

29 

244.5 

220.1 

89 

289.1 

260.3 

49 

333.  7 

300.4 

09 

378.3 

340.6 

69 

422.8 

380.7 

30 

245.2 

220.8 

90 

289.8 

261.0 

50 
451" 

334.4 
335.2 

301.1 

10 

379.0 

341.3 

70 

423.6 
424.3 

381.4 

331 

246.0 

221.5 

391 

290.6 

261.6 

301.8 

511 

379.7 

341.9 

571 

382.1 

32 

246.7 

222.2 

92 

291.3 

262.  3 

52 

335.9 

302.5 

12 

380.5 

342.6 

72 

425.1 

382.8 

33 

247.5 

222.8 

93 

292.1 

263.0 

53 

336.6 

303.1 

13 

381.2 

343.3 

73 

425.8 

383.4 

34 

248.2 

223.5 

94 

292.8 

263.6 

54 

337.4  1303.8 

14 

382.0 

343.9 

74 

426.6 

384.1 

35 

249.0 

224.2 

95 

293.  5 

264.3 

55 

338.1 

304.5 

15 

382.7 

344.6 

75 

427.3 

384.8 

36 

249.7 

224.8 

96 

294.3 

265.0 

56 

338.9 

305.1 

16 

383.5 

345.3 

76 

428.0 

385.4 

37 

250.4 

225.5 

97  ;  295.0 

265.7 

57 

339.6 

305. 8 

17 

384.2 

346. 0 

77 

428.8 

386.1 

38 

251.2 

226.2 

98  i  295.8 

266.3 

58 

340.4 

306.5 

18 

384.9 

346.6 

78 

429.5 

386.8 

39 

251.9 

226.8 

99 

296.5 

267.0 

59 

341.1 

307.1 

19 

385.  7 

347.3 

79 

430.3 

387.4 

40 
341 

252.7 
253.4 

227.5 

400 

297.  3 

267.7 

60 

341.8 

307.8 

20 

386.4 

348.0 

80 

431.0 

388.1 

228.2 

401  i  298.0 

268.3 

461 

342.6 

308. 5 

521 

387.2 

348.6 

581 

431.8 

388.8 

42 

254.2 

228.8 

02  i  298.  7 

269.0 

62 

343.3 

309. 1 

22 

387.9 

349.3 

82 

432.5 

389.4 

43 

254.  9 

229.5 

03  1  299.5 

269.7 

63 

344.1 

309.8 

23 

388.7 

350.0 

83 

433.2 

390.1 

44 

255.6 

230.2 

04 

300.  2 

270.3 

64 

344.  8 

310.  5 

24 

■389.  4 

350.6 

84 

434.0 

390.8 

45 

256.4 

230.9 

05 

301.0 

271.0 

65 

345.6    311.2 

25 

390.1 

351.3 

85 

434.7 

391.4 

46 

257.1 

231.5 

06 

301.7 

271.7 

6(5 

346.3 

311.8 

26 

390.9  ;  352.0 

86 

435.5 

392. 1 

47 

257.9 

232.2 

07 

302.5 

272.3 

67 

347.0 

312. 5 

27 

391.  6 

352.6 

87 

436.2 

392.8 

48 

258.6 

232.9 

08 

303.  2 

273.  0 

()A 

347.8 

313.  2 

28 

392.4 

353.3 

88 

437.0 

393.4 

49 

259.4 

233.5 

09     303.9 

273.  7 

69 

348.5 

313.8 

29 

393.1 

354.0 

89 

437.7 

394.1 

50 

260.1 

234.2 

10 

304.  7 

274.3 

70 

349.3 
350.  0 

314.5 
315.2 

30 

393. 9  i  354.  6 

90 

438.4 

394.  8 

351 

260.8 

234.9 

411 

305.  4 

275.0 

471 

531 

394.6 

355.3 

591 

439.2 

395.4 

52 

261.6 

235.5 

12 

306.  2 

275.7 

72 

350.8 

315.8 

32 

395.  3 

356.0 

92 

440.0 

396. 1 

53 

262.3 

236.2 

13 

306.  9 

276.4 

73 

351.  5 

316.5 

33 

396.1 

356.6 

93 

440.7 

396.  8 

54 

263. 1 

236.9 

14 

307.  7 

277.0 

74 

352.3 

317.  2 

34 

396.8 

357.  3 

94 

441.4 

397.5 

55 

263.  8 

237.5 

15 

308.  4 

277.7 

75 

353.0 

317.8 

35 

397.6 

358.0 

95 

442.2 

398.1 

56 

264.6 

238.2 

16 

309. 1 

278.4 

76 

353.  7 

318.5 

36 

398.  3' 

358.6 

96 

442.9 

398.  8 

57 

265.3 

238.9 

17 

309.  9 

279.0 

77 

354.5 

319.2 

37 

399.1 

359.3 

97 

443.7 

399.5 

58 

266.0 

239.6 

18  i  310.6 

279.7 

78 

355.  2 

319.  9 

38 

399.8 

360.0 

98 

444.4 

400.1 

59 

266.8 

240.2 

19  i  311.4 

280.4 

79 

356.0 

320.  5 

39 

400.6 

360.6 

99 

445.2 

400.8 

60 

267.5 

240.9 

20 

312. 1 

281.0 

80 

356.7 

321.2 

40 

401.3 

361.3 

600 

445.9 

401.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

48°  (1 

32°,  228°,  312° 

). 

Page  452 

TABLE  2. 

Difference  of  Latitude  and  Departure  for  43°  (137°,  223 

°,  317° 

)• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  {     Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

44.6 

41.6 

121  '\     88.5 

82.5 

181 

132.4 

123.4 

241 

176.3 

164.4 

2 

1.5 

1.4 

62 

45.3 

42.3 

22  1     89.2 

83.2 

82 

133.1 

124.1 

42 

177.0 

165.0 

3 

2.2 

2.0 

63 

46.1 

43.0 

23  i     90.0 

83.9 

83 

133.8 

124.8 

43 

177.7 

165.7 

4 

2.9 

2.7 

64 

46.8 

43.6 

24  :     90.7 

84.6 

84 

134.6 

125.5 

44 

178.5 

166.4 

5 

3.7 

3.4 

65 

47.5 

44.3 

25  i     91.4 

85.2 

85 

135.  3 

126.2 

45 

179.2 

167.1 

6 

4.4 

4.1 

^6 

48.3 

45.0 

26       92.2 

85.9 

86 

136.0 

126.9 

46 

179.9 

167.8 

7 

5.1 

4.8 

67 

49.0 

45.7 

27       92.9 

86.6 

87 

136.  8 

127.5 

47 

180.6 

168.5 

8 

5.9 

5.5 

68 

49.7 

46.4 

28       93.6 

87.3 

88 

137.5 

128.2 

48 

181.4 

169.1 

9 

6.6 

6.1 

69 

50.5 

47.1 

29       94.3 

88.0 

89 

138.2 

128.9 

49 

182.1 

169.8 

10 

7.3 

6.8 

70 

51.2 

47.7 

30 

95.1 
95.8 

88.7 
89.3 

90 

139.0 

129.6 

50 

182.8 

170.5 

11 

8.0 

7.5 

71 

51.9 

48.4 

131 

191 

139.7 

130.3 

251 

183.6 

171.2 

12 

8.8 

8.2 

72 

52.7 

49.1 

32       96. 5 

90.0 

92 

140.4 

130.9 

52 

184.3 

171.9 

13 

9.5 

8.9 

73 

53.4 

49.8 

33  i     97.3 

90.7 

93 

141.2 

131.6 

53 

185.0 

172.5 

14 

10.2 

9.5 

74 

54.1 

50.5 

34 

98.0 

91.4 

94 

141.9 

132.3 

54 

185.8 

173.2 

15 

11.0 

10.2 

75 

54.9 

51.1 

35 

98.7 

92.1 

95 

142.6 

133.0 

55 

186.5 

173.9 

16 

11.7 

10.9 

76 

55.6 

51.8 

36 

99.5 

92.8 

96 

143.3 

133.7 

56 

187.2 

174.6 

17 

12.4 

11.6 

77 

56.3 

52.5 

37 

100.2 

93.4 

97 

144.1 

134.4 

57 

188.0 

175.3 

18 

13.2 

12.3 

78 

57.0 

53.2 

38 

100.9 

94.1 

98 

144.8 

135.0 

58 

188.7 

176.0 

19 

13.9 

13.0 

79 

57.8 

53.9 

39  i  101.7 

94.8 

99 

145.5 

135.7 

59 

189.4 

176.6 

20 

14.6 

13.6 

80 

58.5 

54.6 

40 

102.4 
103.1 

95.5 
96.2 

200 

146.3 

136.4 

60 

190.2 

177.3 

21 

15.4 

14.3 

81 

59.2 

55.2 

141 

201 

147.0 

137.1 

261 

190.9 

178.0 

22 

16.1 

15.0 

82 

60.0 

55.9 

42  1  103.9 

96.8 

02 

147.7 

137.8 

62 

191.6 

178.7 

23 

16.8 

15.7 

83 

60.7 

56.6 

43  {  104.6 

97.5 

03 

148.5 

138.4 

63 

192.3 

179.4 

24 

17.6 

16.4 

84 

61.4 

57.3 

44 

105.3 

.98.2 

04 

149.2 

139.1 

64  !  193.1 

180.0 

25 

18.3 

17.0 

85 

62.2 

58.0 

45 

106.0 

98.9 

05 

149.9 

139.8 

65     193.8 

180.7 

26 

19.0 

17.7 

86 

62.9 

58.7 

46 

106.8 

99.6 

06 

150.7 

140.5 

66  i  194.5 

181.4 

27 

19.7 

18.4 

87 

63.6 

59.3 

47  '  107.5 

100.3 

07 

151.4 

141.2 

67  1  195.3 

182.1 

28 

20.5 

19.1 

88 

64.4 

60.0 

48 

108.2 

100.9 

08 

152. 1 

141.9 

68 

196.0 

182.8 

29 

21.2 

19.8 

89 

65.1 

60.7 

49 

109.0 

101.6 

09 

152.9 

142.5 

69 

196.  7  i  183. 5  1 

30 

21.9 

20.5 

90 

65.8 

61.4 

50 

109.7 

102.3 

10 

153.6 

143.2 

70 

197.5 
198.2 

184.1 

31 

22.7 

21.1 

91 

66.6 

62.1 

151 

110.4 

103.0 

211 

154.3 

143.9 

271 

184.8 

32 

23.4 

21.8 

92 

67.3 

62.7 

52 

111.2 

103.7 

12 

155.0 

144.6 

72 

198.9 

185.5 

33 

24.1 

22.5 

93 

68.0 

63.4 

53 

111.9 

104.3 

13 

155.8 

145.3 

73 

199.7 

186.2 

34 

24.9 

23.2 

94 

68.7 

64.1 

54 

112.6 

105.0 

14 

156.5 

145.9 

74 

200.4 

186.9 

35 

25.6 

23.9 

95 

69.5 

64.8 

55 

113.4 

105.7 

15 

157.2 

146.6 

75 

201.1 

187.5 

36 

26.3 

24.6 

96 

70.2 

65.5 

56 

114.1 

106.4 

16 

158.0 

147.3 

76 

201.9 

188.2 

37 

27.1 

25.2 

97 

70.9 

66.2 

57 

114.8 

107.1 

17 

158.7 

148.0 

77 

202.6 

188.9 

38 

27.8 

25.9 

98 

71.7 

66.8 

58 

115.  6 

107.8 

18 

159.4 

148.7 

78 

203.3 

189.6 

39 

28.5 

26.6 

99 

72.4 

67.5 

59 

116.3 

108.4 

19 

160.2 

149.4 

79 

204.0 

190.3 

40 

29.3 

27.3 

100 

73.1 

68.2 

60 

117.0 
117.7 

109.1 

20 

160.9 

150.0 

80 
281 

204.8 

191.0 

41 

30.0 

28.0 

101 

73.9 

68.9 

161 

109.8 

221 

161.6 

150.7 

205.5 

191.6 

42 

30.7 

28.6 

02 

74.6 

69.6 

62 

118.5 

110.5 

22 

162.4 

151.4 

82 

206.2 

192.3 

43 

31.4 

29.3 

03 

75.3 

70.2 

63 

119.2 

111.2 

23 

163.1 

152.1 

83 

207.0 

193.0 

44 

32.2 

30.0 

04 

76.1 

70.9 

64 

119.9 

111.8 

24 

163.8 

152.8 

84 

207.7 

193.7 

45 

32.9 

30.7 

05 

76.8 

71.6 

65 

120.7 

112.5 

25 

164.6 

153.4 

85 

208.4 

194.4 

46 

33.6 

31.4 

06 

77.5 

72.3 

66 

121.4 

113.2 

26 

165.3 

154.1 

86 

209.2 

195.1 

47 

34.4 

32.1 

07 

78.3 

73.0 

67 

122.1 

113.9 

27 

166.0 

154.8 

87 

209.9 

195.7 

48 

35.1 

32.7 

08 

79.0 

73.7 

68 

122.9 

114.6 

28 

166.7 

155.5 

88 

210.6 

196.4 

49 

35.8 

33.4 

09 

79.7 

74.3 

69 

123.6 

115.3 

29 

167.5 

156.2 

89 

211.4 

197.1 

50 

36.6 

34.1 

10 

80.4 

75.0 

70 
171 

124.3 

115.9 

30 

168.2 

156.  9 
157.5 

90 

212.1 

197.8 

51 

37.3 

34.8 

111 

81.2 

75.7 

125.1 

116.6 

231 

168.9 

291 

212.8 

198.5 

52 

38.0 

35.5 

12 

81.9 

76.4 

72 

125.8 

117.3 

32 

169.7 

158.2 

92 

213.6 

199.1 

53 

38.8 

36.1 

13 

82.6 

77.1 

73 

126.5 

118.0 

33 

170.4 

158.9 

93 

214.3 

199.8 

54 

39.5 

36.8 

14 

83.4 

77.7 

74 

127.3 

118.7 

34 

171.1 

159.6 

94 

215.0 

200.5 

55 

40.2 

37.5 

15 

84.1 

78.4 

75 

128.0 

119.3 

35 

171.9 

160.3 

95 

215.7 

201.2 

56 

41.0 

38.2 

16 

84.8 

79.1 

76 

128.7 

120.0 

36 

172.6 

161.0 

96 

216.5 

201.9 

57 

41.7 

38.9 

17 

85.6 

79.8 

77 

129.4 

120.7 

37 

173.  3 

161.6 

97 

217.2 

202.6 

58 

42.4 

39.6 

18 

86.3 

80.5 

78 

130.2 

121.4 

38 

174.1 

162.3 

98 

217.9 

203.2 

59 

43.1 

40.2 

19 

87.0 

81.2 

79 

130.  9 

122.1 

39 

174.8 

163.0 

99 

218.7 

203.9 

60 

43.9 

40.9 

20 

87.8 

81.8 

80 

131.6 

122.8 

40 

175.5 

163.7 

300 

219.4 

204.6 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

t7°  (133°,  227 

°,  313° 

). 

TABLE  2. 

[Page  453 

Dist. 

Difference  of  Latitude  and  Departure  for  43°  (137°,  223°,  317° 

). 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.     1    Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.          Dep. 

301 

220.1 

205.3 

361 

264.0 

246.2 

421 

307.  9    287. 1 

481 

351.8 

328.1 

541 

395. 7     369. 0 

02 

220.9 

206.0 

62 

264.8  1246.9 

22 

308.  6  j  287.  8 

82 

352.5 

328.7 

42 

396.4 

369.7 

03 

221.6 

206.7 

63 

265.  5 

247.6 

23 

309.4    288.5 

83 

353.2 

329.4 

43 

397.1 

370.3 

04 

222.3 

207.3 

64 

266.2 

248.3 

24 

310.1  |289.2 

84 

354.0 

330.1 

44 

397.9 

371.0 

05 

223.1 

208.0 

65 

267.0 

248.9 

25 

310.8 

289. 9 

85 

354.7 

330.8 

45 

398.6 

371.7 

06 

223.  8 

208.7 

66 

267.7 

249.6 

26 

311.6 

290.5 

86 

355.4 

331.4 

46 

399.3 

372.4 

07 

224.5 

209.4 

67 

268.4 

250.3 

27 

312.3 

291.2 

87 

356.2 

332.1 

47 

400.1 

373.1 

08 

225.3 

210.1 

68 

269.1 

251.0 

28 

313. 0 

291.9 

88 

356.9 

332.8 

48 

400.8 

373.7 

09 

226.0 

210.7 

69 

269.9 

251.7 

29 

313.8 

292.6 

89 

357.7 

333.5 

49 

401.5 

374.4 

10 
311 

226.-7 
227.5 

211.4 

70 

270.6 

252.3 

30 
431" 

314.5 

293.3 

90 

358.4 

334.2 

50 

402.2 
403.0 

375.1 
375.8 

212.1 

371 

271.3 

253.0 

315.2 

293.9 

491 

359.1 

334.9 

551 

12 

228.2 

212.8 

72 

272.1 

253.7 

32 

316.0 

294.6 

92 

359.8 

335.  5 

52 

403.7 

376.5 

13 

228.9 

213.5 

73 

272.8 

254.4 

33 

316.  7 

295.3 

93 

360.6 

336.2 

53 

404.4 

377.1 

14 

229.7 

214.2 

74 

273.5 

255.1 

34 

317.4 

296.0 

94 

361.3 

336.9 

54 

405.2 

377.8 

15 

230.4 

214.8 

75 

274.3 

255.  8 

35 

318.1 

296.7 

95 

362.0 

337.6 

55 

405.9 

378.5 

16 

231.1 

215.5 

76 

275.0 

256.4 

36 

318.9 

297.4 

96 

362.8 

338.3 

56 

406.6 

379.2 

17 

231.8 

216.2 

77 

275.7 

257.1 

37 

319.6 

298.0 

97 

363.5 

338.9 

57 

407.4 

379.9 

18 

232.6 

216.9 

78 

276.5 

257.8 

38 

320.3 

298.7 

98 

364.2  1339.6 

58 

408.1 

380.6 

19 

233.3 

217.6 

79 

277.2 

258.5 

39 

321.1 

299.4 

99 

364.9  1340.3 

59 

408.8 

381.2 

20 
321 

234.0 

218.2 

80 
381 

277.9 

278.7 

259.2 
259.  8 

40 

321.8 

300.1 
300.8 

500 

365.7  i  341.0 

60 

409.6 

381.9 
382.6 

234.8 

218.9 

441  1  322.5 

501 

366.4 

341.7 

561 

410.3 

22 

235.5 

219.6 

82 

279.4 

260.5 

42 

323.3 

301.4 

02 

367. 1 

342.4 

62 

411.0 

383.  3 

23 

236.2 

220.3 

83 

280.1 

261.2 

43 

324.0 

302.1 

03 

367.8 

343.0 

63 

411.8 

384.0 

24 

237.0 

221.0 

84 

280.8 

261.9 

44 

324.7 

302.8 

04 

368.6 

343.7 

64 

412.5 

384.6 

25 

237.7 

221.7 

85 

281.6 

262.6 

45 

325.5 

303.5 

05 

369.3 

344.4 

65 

413.2 

385.  3 

26 

238.4 

222.3 

86 

282.3 

263.3 

46 

326.2 

304.2 

06 

370.0 

345.1 

66 

414.0 

386.0 

27 

239.2 

223.0 

87 

283.0 

263. 9 

47 

326.9 

304.9 

07 

370.8 

345.8 

67 

414.7 

386.7 

28 

239.9 

223.7 

88 

283.7 

264.6 

48 

327.7 

305.5 

08 

371.5 

346.5 

68 

415.4 

387.4 

29 

240.6 

224.4 

89 

284.5 

265.3 

49 

328.4 

306.2 

09 

372.3 

347.1 

69 

416.2 

388.1 

30 

241.4 

225.1 

90 

285.2 
286.0 

266.0 

50 
451 

329.1 

306.9 

10 

373.0 

347.8 

70 

416.9 

388.7 
389.4 

331 

242.1 

225.7 

391 

266.7 

329.9 

307.6 

511 

373.8    348.5 

571 

417.6 

32 

242.8 

226.4 

92 

286.7 

267.3 

52 

330.6 

308.3 

12 

374.5    349.2 

72 

418.3 

390.1 

33 

243. 5 

227.1 

93 

287.4 

268.0 

53 

331.3 

309.0 

13 

375.2  1349. 9 

73 

419.1 

390.8 

34 

244.3 

227.8 

94 

288.2 

268.7 

54 

332.1 

309.6 

14 

376. 0  {  350. 5 

74 

419.8 

391.5 

35 

245.0 

228.5 

95 

288.9 

269.4 

55 

332.8 

310.3 

15 

376.6  i351.2 

75 

420.5 

392.2 

36 

245.7 

229.2 

96 

289.6 

270.1 

56 

333.5 

311.  0 

16 

377.4 

351.9 

76 

421.3 

392.8 

37 

246.5 

229.8 

97 

290.4 

270.8 

57 

334.3 

311.7 

17 

378.2 

352.6 

77 

422.0 

393.5 

38 

247.2 

230.  5 

98 

291.1 

271.4 

58 

335.0 

312.4 

18 

378.9 

353.3 

78 

422.7 

394.2 

39 

247.9 

231.2 

99 

291.8 

272.1 

59 

335.7 

313.0 

19 

379.6 

354.0 

79 

423.5 

394.9 

40 

248.7 
249.4 

231.9 
232.6 

400 

292.6 

272.8 

60 

336.5 
337.2 

313.7 

20 

380.3 

354.6 

80 

424.2 

395.6 

341 

401 

293.3 

273.5 

461 

314.4 

521 

381.1 

355.3 

581 

424.9 

396.2 

42 

250.1 

233.2 

02 

294.0 

274.2 

62 

337.9 

315.1 

22 

381.8 

356.0 

82 

425.7 

396.9 

43 

250.9 

233.9 

03 

294.7 

274.9 

63 

338.7 

315.8 

23 

382.6 

356.7 

83 

426.4 

397.6 

44 

251.6 

234.6 

04 

295.5 

275.5 

64  !  339.4 

316.5 

24 

383.3 

357. 4 

84 

427.1 

398.3 

45 

252.  3 

235.3 

05 

296.2 

276.2 

65 

340.1 

317.1 

25 

384.0 

358.1 

85 

427.9 

399.0 

46 

253.1 

236.0 

06 

296.9 

276.9 

66 

340.8 

317.8 

26 

384.7 

358.7 

86 

428.6 

399.6 

47 

253.8 

236.7 

07 

297.7 

277.6 

67 

341.6 

318.5 

27 

385.5    359.4 

87 

429.3 

400.3 

48 

254.5 

237.3 

08 

298.4 

278.3 

68 

342.3 

319.2 

28 

386.2    360.1 

88 

430.1 

401.0 

49 

255.3 

238.0 

09 

299. 1 

278.9 

69 

343.0 

319.9 

29 

386. 9 

360.8 

89 

430.8 

401.7 

50 

256.0 

238.7 

10 

299.9 

279.6 

70 

343.7 

320.5 
321. 2 

30 

387.6 
388. 4 

361.5 

90 

431.5 

402.4 

351 

256.7 

239.4 

411 

300.6 

280.3 

471 

344.5 

531 

362.1 

591 

432.3 

403.1 

52 

257.4 

240.1 

12 

301.3 

281.0 

72 

345.2 

321.9 

32 

389.1 

362.8 

92 

433.0 

403.7 

53 

258.2 

240.8 

13 

302.1 

281.7 

73 

345.9 

322.6 

33 

389.9 

363.5 

93 

433.7 

404.4 

54 

258.9 

241.4 

14 

302.8 

282.4 

74 

346.7 

323.3 

34 

390.6 

364.2 

94 

434.5 

405.1 

55 

259.6 

242.1 

15 

303.5 

283.0 

75 

347.4 

324.0 

35 

391.3 

364.9 

95 

435.2 

405.  8 

56 

260.4 

242.8 

16 

304.3 

283.7 

76 

348.1 

324.6 

36 

392.0 

365.5 

96 

435.9 

406.5 

57 

361.1 

243.5 

17 

305.0 

284.4 

77 

348.9 

325.3 

37 

392.8 

366.2 

97 

436.7 

407.2 

58 

261.8 

244.2 

18 

305.7 

285.1 

78 

349.6 

326.0 

38 

393.5 

366.9 

98 

437.4 

407.8 

59 

262.6 

244.8 

19 

306.4 

285.8 

79 

350.3 

326.7 

39 

394.2 

367.6 

99 

438.1 

408.5 

60 

263.3 

245.5 

20 

307.2 

286.4 

80  !  351.1 

327.4 

40 

394.9 

368.3 

600 

438.8 

409.2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  j     Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.          Lat. 

4 

7°  (133°,  227°,  313° 

)• 

Page  454 

1 

TABLE  2. 

Difference  of  Latitude  and  Departure  for 

44°  (136°,  224°,  316° 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.        Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

43.9 

42.4 

121 

87.0 

84.1 

181 

130.  2    125.  7 

241 

173.4 

167.4 

2 

1.4 

1.4 

62 

44.6 

43.1 

22 

87.8 

84.7 

82 

130.9     126.4 

42 

174.1 

168.1 

3 

2.2 

2.1 

63 

45.3 

43.8 

23 

88.5 

85.4 

83  i  131. 6  1  127. 1 

43 

174.8 

168.8 

4 

2.9 

2.8 

64 

46.  0  1  44.  5  1 

24 

89.2 

86.1 

84 

132.  4    127.  8 

44 

175.5 

169.5 

6 

3.6 

3.5 

65 

46.8 

45.2 

25 

89.9 

86.8 

85 

133.1 

128.5 

45 

176.2 

170.2 

6 

4.3 

4.2 

•66 

47.5 

45.8 

26 

90.6 

87.5 

86 

13.3.8 

129.2 

46 

177.0 

170.9 

7 

5.0 

4.9 

67 

48.2 

46.5 

27 

91.4 

88.2 

87 

134.5    129.91 

47 

177.7 

171.6 

8 

5.8 

5.6 

68 

48.9 

47.2 

28       92. 1 

88.9 

88 

135.2 

130.6 

48 

178.4 

172.3 

9 

6.5 

6.3 

69 

49.6 

47.9 

29       92. 8 

89.6 

89 

136.0 

131.3 

49 

179.1 

173. 0 

10 

7.2 

6.9 

70 

50.4 

48.6 

30 

93.5 
94.2 

90.3 

90 

136.7 
137.4 

132.0 
132.7 

50 
251 

179.8 
180.6 

173.7 

11 

7.9 

7.6 

71 

51.1 

49.3 

131 

91.0 

191 

174.4 

12 

8.6 

8.3 

72 

51.8 

50.0 

32       95.0 

91.7 

92 

138.1 

133.4 

52 

181.3 

175.1 

13 

9.4 

9.0 

73 

52.5 

50.7 

33       95.7 

92.4 

93 

138.8 

134.1 

53 

182.0 

175.7 

14 

10.1 

9.7 

74 

53.2 

51.4 

34 

96.4 

93.1 

94 

139.6 

134.8 

54 

182.7 

176.4 

15 

10.8 

10.4 

75 

54.0 

52.1 

35 

97.1 

93.8 

95 

140.3 

135.5 

55 

183.4 

177.1 

16 

11.5 

11.1 

76 

54.7 

52.8 

36 

97.8 

94.5 

96 

141.0 

136.2 

56 

184.2 

177.8 

17 

12.2 

11.8 

77 

55.4 

53.5 

37 

98.5 

95.2 

97 

141.7 

136.8 

57 

184.9 

178.5 

18 

12.9 

12.5 

78 

56.1 

54.2 

38 

99.3 

95.9 

98 

142.4 

137.5 

58 

185.6 

179.2 

19 

13.7 

13.2 

79 

56.8 

54.9 

39 

100.0 

96.6 

99 

143.1 

138.2 

59 

186.3 

179.9 

20 

14.4 

13.9 

80 

57.5 

55.6 

40 

100.7 

97.3 

200 

143.9 
144.6 

138.9 

60 

187. 0 
187.7 

180.6 

21 

15.1 

14.6 

81 

58.3 

56.3 

141 

101.4 

97.9 

201 

139.6 

261 

181.3 

22 

15.8 

15.3 

82 

59.0 

57.0 

42 

102.1 

98.6 

02 

145.3 

140.3 

62 

188.5 

182.0 

23 

16.5 

16.0 

83 

59.7 

57.7 

43 

102.9 

99.3 

03 

146.0 

141.0 

63 

189.2 

182.7 

24 

17.3 

16.7 

84 

60.4 

58.4 

44 

103.6 

100.0 

04 

146.7 

141.7 

64 

189.9 

183.4 

25 

18.0 

17.4 

85 

61.1 

59.0 

45 

104.3 

100.7 

05 

147.  5 

142.4 

65 

190.6 

184.1 

26 

18.7 

18.1 

86 

61.9 

59.7 

46 

105.0 

101.4 

06 

148.2 

143.1 

66 

191.3 

184.8 

27 

19.4 

18.8 

87 

62.6 

60.4 

47  1  105.  7 

102.1 

07 

148.9 

143.8 

67 

192.1 

185.5 

28 

20.1 

19.5 

88 

63.3 

61.1 

48  !  106.5 

102.8 

08 

149.6 

144.5 

68 

192.8 

186.2 

29 

20.9 

20.1 

89 

64.0 

61.8 

49  j  107.2 

103.5 

09 

150.3 

145.2 

69 

193.5 

186.9 

30 

21.6 

20.8 
21.5 

90 

64.7 

62.5 

50  !  107.9 

104.2 

10 

151.1 

145. 9 
Y46.  6 

70 
271 

194.2 

187.6 

31 

22.3 

91 

65.5 

63.2 

151     108. 6 

104.9 

211 

151.8 

194.9 

188.3 

32 

23.0 

22.2 

92 

66.2 

63.9 

52     109. 3 

105.6 

12 

152.  5  i  147.  3 

72 

195.7 

188.9 

33 

23.7 

22.9 

93 

66.9 

64.6 

53 

110.1 

106.3 

13 

153.  2    148. 0 

73 

196.4 

189.6 

34 

24.5 

23.6 

94 

67.6 

65.3 

54 

110.8 

107.0 

14 

153. 9  1 148.  7 

74 

197.1 

190.3 

35 

25.2 

24.3 

95 

68.3 

66.0 

55 

111.5 

107.7 

15 

154.  7    149. 4 

75 

197.8 

191.0 

36 

25.9 

25.0 

96 

69.1 

66.7 

56 

112.2 

108.4 

16 

155. 4    150.  0 

76 

198.5 

191.7 

37 

26.6 

25.7 

97 

69.8 

67.4 

57 

112.9 

109.1 

17 

156.1    150.7 

77 

199.3 

192.4 

38 

27.3 

26.4 

98 

70.5 

68.1 

58 

113.  7 

109.8 

18 

156.8    151.4 

78 

200.0 

193.1 

39 

28.1 

27.1 

99 

71.2 

68.8 

59 

114.4 

110.5 

19 

157.  5    152. 1 

79 

200.7 

193.8 

40 

28.8 

27.8 
28.5 

100 
101 

71.9 

72.7 

69.5 

60 

115.1 
115.8' 

111.1 
111.8 

20 

158.3 

152.8 

80 

201.4 

194.5 

41 

29.5 

70.2 

161 

221 

159.0 

153. 5 

281 

202. 1 

195.2 

42 

30.2 

29.2 

02 

73.4 

70.9 

62 

116.5 

112.5 

22 

159.7 

154.2 

82 

202.9 

195.9 

43 

30.9 

29.9 

03 

74.1 

71.5 

63 

117.3 

113.2 

23 

160.4 

154.9 

83 

203.6 

196.6 

44 

31.7 

30.6 

04 

74.8 

72.2 

64 

118.0 

113.9 

24 

161.1 

155.6 

84 

204.3 

197.3 

45 

32.4 

31.3 

05 

75.5 

72.9 

65 

118.7 

114.6 

25 

161.9 

156.3 

85 

205.0 

198.0 

46 

33.1 

32.0 

06 

76.3 

73.6 

66 

119.4 

115.3 

26 

162.6 

157.0 

86 

205.7 

198.7 

47 

33.8 

32.6 

07 

77.0 

74.3 

67 

120.1 

116.0 

27 

163.3 

157.7 

87 

206.5 

199.4 

48 

34.5 

33.3 

08 

77.7 

75.0 

68 

120.  8 

116.7 

28 

164.0 

158.4 

88 

207.2 

200.1 

49 

35.2 

34.0 

09 

78.4 

75.7 

69 

121.  6 

117.4 

29 

164.7 

159.1 

89 

207.9 

200.8 

50 

36.0 
36.7 

34.7 

10 

79.1 
79.8 

76.4 

70 

122.3 

118.1 

30 

165.4 
166.2 

159.8 

90 

208.6 

201.5 

51 

35.4 

111 

77.1 

171 

123.0 

118.8. 

231 

160.5 

291 

209.3 

202.1 

52 

.37.4 

36.1 

12 

80.6 

77.8 

72  '  123.7 

119.  5 

32 

166.9 

161.2 

92 

210.0 

202.8 

53 

38.1 

36.8 

13 

81.3 

78.5 

73  1  124.4 

120.2 

33 

167.6  1161.9 

93 

210.8 

203.  5 

54 

38.8 

37.5 

14 

82.0 

79.2 

74  i  125.2 

120.9 

34 

168. 3    162. 6 

94 

311.5 

204.2 

55 

39.6 

38.2 

15 

82.7 

79.9 

75 

125.9 

121.6 

35 

169. 0    163.  2 

95 

212.2 

204.9 

56 

40.3 

38.9 

16 

83.4 

80.6 

76 

126.6 

122.3 

36 

169. 8    163.  9 

96 

212.9 

205.  6 

57 

41.0 

39.6 

17 

84.2 

81.3 

77 

127.  3 

123.0 

37 

170. 5  i  164.  6 

97 

213.6 

206.3 

58 

41.7 

40.3 

18 

84.9 

82.0 

78 

128.0 

123.6 

38 

171.2  |165.3 

98 

214.4 

207.0 

59 

42.4 

41.0 

19 

85.6 

82.7 

79 

128.8 

124.3 

39 

171.9 

166.0 

99 

215.1 

207.7 

60 

43.2 

41.7 

20 

86.3 

83.4 

80 

129.  5 

125.0 

40 

172.6 

166.7 

300 

215.8 

208.4 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

16°  (134°,  226 

°,  314° 

)• 

TABLE  2. 

[Page  455 

Dist. 

Difference  of  Latitude  and  Departure  for  44°  (136°,  224°,  316 

'). 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Di.st. 

Lat. 

Dep. 

Dist.        Lilt. 

Dep. 

Dist. 

1     Lat. 

Dep. 

801 

216.  5 

209.  1 

361 

259.7 

250.  8 

421 

302.  8 

292.5 

481 

346.0 

334. 1 

541 

1 

i  389.2 

375.8 

02 

217.2 

209.8 

()2 

260.4 

251.  5 

22 

303.6 

293.2 

82 

346.7 

334.  8 

42 

389.9 

376.5 

03 

218.0 

210.5 

(53 

261.1 

252.  2 

23 

304.3 

293.8 

83 

347.4 

335.  5 

43 

390.6 

377.2 

04 

218.7 

211.2 

64 

261.8 

252.  9 

24 

305.  0 

294.5 

84 

348.2 

336.2 

44 

391.3 

377.9 

05 

219.  4 

211.9 

65 

262.6 

253.  6 

25 

305.  7 

295.2 

85 

348.9 

336.  9 

45 

392.0 

378.6 

06 

220.1 

212.6 

66 

263.3 

254.  3 

26 

306.4 

295.9 

86 

349.  6 

337.  6 

46 

392.8 

379.3 

07 

220.8 

213.3 

67 

264.  "0 

254.  9 

27 

307.2 

296.6 

87  !  350.3 

338.3 

47 

393.5 

380.0 

08 

221.6 

214.0 

68 

264.7 

255.  6 

28 

307.9 

297.3 

88 

351.0 

339.0 

48 

394.2 

380.  7 

09 

222.  3- 

214.7 

69 

265.4 

256.  3 

29 

308.6 

298.0 

89 

351.7 

339.7 

49 

394.9 

381.4 

10 
311 

223.0 
223.7 

215.4 

70 

266.2 
266.9 

257.0 

30 
431 

309.3 
310.0 

298.7 
299.4 

90 
491 

352.5 
353.2 

340.4 
341.1 

50 
551 

395.6 
396.4 

382.1 

382.7 

216.0 

371 

257.7 

12 

224.4 

216.7 

72 

267.6 

258.4 

32 

310.  8 

300. 1 

92  ^  .353.9 

341.8 

52 

397.1 

383.  4 

13 

225.  2 

217.4 

73 

268.  3 

259.1 

33 

311.  5 

300.  8 

93     354.6 

342.5 

53 

397.8 

384.1 

14 

225.  9 

218.1 

74 

269.0 

259.8 

34 

312.  2 

301.5 

94     355.3 

343.2 

54 

398.5 

384.8 

15 

226.6 

218.8 

75 

269.8 

260.5 

35 

312.  9 

302.  2 

95  1  356. 1 

343.9 

55 

399.2 

385.5 

16 

227.  3 

219.5 

76 

270.5 

261.2 

36 

313.  6 

302.  9 

96  i  356.8 

344.6 

56 

400.0 

386.  2 

17 

228.0 

220.2 

77 

271.2 

261.9 

37 

314.  4 

303.6 

97  1  357.5 

345.2 

57 

400.7 

386.9 

18 

228.8 

220.9 

78 

271.9 

262.6 

38 

315.1 

304.3 

98 

358.2 

345.9 

58 

401.4 

387.6 

19 

229.5 

221.6 

79 

272.6 

263.3 

39 

315.8 

305.0 

99 

358.9 

346.  6 

59 

402.1 

388.3 

20 
321 

230.2 
230.9 

222.3 

80 

273.4 

264.0 
264.7 

40 
441 

316.  5 

305.7 

500 

359.7 
360.4 

347.3 
348.0 

60 
561 

402.8 
403.6 

389.0 
389.7 

223.0 

381 

274.1 

317.  2 

306.  4 

501 

22 

231.6 

223.7 

82 

274.8 

265.4 

42 

318.  0 

307.0 

02 

361.1 

348.7 

62 

404.3 

39D.4 

23 

232.3 

224.4 

83 

275.5 

266.1 

43 

318.  7 

307.7 

03 

361.8 

349.4 

63 

405.0 

391.1 

24 

233.1 

225.1 

84 

276.2 

266.8 

44 

319.4 

308.4 

04 

362.5 

350.1 

64 

405.  7 

391.8 

25 

233.8 

225.8 

85 

276.9 

267.5 

45 

320. 1 

309.1 

05 

363.3 

350.8 

65 

406.4 

392.5 

26 

234.5 

226.5 

86 

377.7 

268.1 

46 

320.8 

309.8 

06 

364.0 

351. 5 

66 

407.2 

393.2 

27 

235.2 

227.  2 

87 

278.4 

268.8 

47 

321.5 

310.5 

07 

364.7 

352.2 

67 

407.9 

393.9 

28 

235.9 

227.9 

88 

279.1 

269.5 

48 

322.  3 

311.2 

08 

365.4 

352.9 

68 

408.6 

394.6 

29 

236.7 

228.6 

89 

279.8 

270.2 

49 

323.  0 

311.9 

09 

366.1 

353.6 

69 

409.3 

395.3 

30 
331 

237.4 
238.1 

229.2 
229.9 

90 
391 

280. 5 

270.9 

50 

323.7 

312.6 

10 

366. 9 

354.3 

70 

410.0 
410.7 

396.0 
396.7 

281.3 

271.6 

451 

324.4 

313.3 

511 

367.6 

355.0 

571 

32 

238.8 

230.6 

92 

282.0 

272.3 

52 

325.2 

314.0 

12 

368.3 

355.  7 

72 

411.5 

397.3 

33 

239.5 

231.3 

93 

282.7 

273.0 

53 

325.9 

314.7 

13 

369.0 

356.  4 

73 

412.2 

398.0 

34 

240.3 

232.  0 

94 

283.4 

273.7 

54 

326.  6 

315.4 

14 

369.7 

357. 1 

74 

412.9 

398.7 

35 

241. 0 

232.  7 

95 

284.1 

274.4 

55 

327.  3 

316.1 

15     370.5 

357.  8 

75 

413.6 

399.4 

36 

241.7 

233. 4 

96 

284.9 

275. 1 

56 

328.  0 

316.8 

16 

371.2 

358.  4 

76 

414.3 

400.1 

37 

242.4 

234.1 

97 

285.6 

275.8 

57 

328.  7 

317.5 

17 

371.9 

359.1 

77 

415.1 

400.8 

38 

243.1 

234.8 

98 

286.3 

276. 5 

58 

329.5 

318.2 

18 

372.6 

359.8 

78 

415.8 

401.5 

39 

243.9 

335.5 

99 

287.0 

277.2 

59 

330.  2 

318.9 

19 

373.3 

360.5 

79 

416.5 

402.2 

40 

244.6 

2.36.  2 

400 

287.7 
288.5 

277.9 

60 

330.9 

319.6 

20 

374.1 

361.2 

80 

417.2 
417.9 

402.9 
403.6 

341 

245.3 

236.9 

401 

278.6 

461 

331.6 

320.2 

521     374. 8 

361.9 

581 

42 

246.0 

237. 6 

02 

289.2 

279.3 

62 

332.3 

320.9 

22     375. 5 

362.  6 

82 

418.7 

404.3 

43 

246.7 

238.3 

03 

289.9 

280.0 

63 

333. 1 

321.6 

23  !  376.2 

363.3 

83 

419.4 

405.0 

44 

247.5 

239. 0 

04 

290.6 

280.7 

64 

333.  8 

322.3 

24     376.9 

364.0 

84 

420.1 

405.7 

45 

248.2 

239.7 

05 

291.3 

281.3 

65 

334.5 

323.0 

25 

377.7 

364.7 

85 

420.8 

406.4 

46 

248.9 

240.4 

06 

292.1 

282.0 

66 

335.2 

323.7 

26 

378.4 

365.4 

86 

421.5 

407.1 

47 

249.6 

241.1 

07 

292.8 

282.7 

67 

335.9 

324.4 

27 

379.1 

366.1 

87 

422.3 

407.8 

48 

250.3 

241.7 

08 

293.5 

283.4 

68 

336.  7 

325.1 

28 

379.8 

366.8 

88 

423.  0 

408.5 

49 

251.1 

242.4 

09 

294.2 

284.1 

69 

337.4 

325.8 

29 

380.5 

367.5 

89 

423.  7 

409.1 

50 

251.8 

243.1 

10 

294.9 

284.8 

70 

338. 1 

326.5 

30 

381.2 

368.2 

90 

424.4 

409.9 

351 

252.5 

243.8 

411 

295.7 

285.5 

471 

338.8 

327.2 

531 

382.0 

368.9 

591 

425.1 

410.5 

62 

253.2 

244.5 

12 

296.4 

286.2 

72 

339.5 

327.9 

32 

382.7 

369.6 

92 

425.9 

411.2 

53 

253.9 

245.2 

13 

297.1 

286.9 

73 

340.3 

328.6 

33 

383.4 

370.  3 

93 

426.6 

411.9 

54 

254.6 

245.9 

14 

297.8 

287.6 

74 

341.0 

329.3 

34 

384. 1 

371.0 

94 

427.3 

412.6 

55 

255.4 

246.6 

15 

298.5 

288.3 

75 

341.7 

330.0 

35 

384.8 

371.  7 

95 

428.0 

413.3 

56 

256.1 

247.3 

16 

299.  2 

289.0 

76 

342.  4 

330.7 

36 

385.  6 

372.4 

96 

428.7 

414.0 

57 

256.8 

248.0 

17 

300.0 

289.7 

77 

343. 1 

331.4 

37 

386.3 

373.1 

97 

429.5 

414.7 

58 

257.5 

248.7 

18 

300.7 

290.4 

78 

343.  8 

332. 1 

38 

387.0 

373.7 

98 

430.2 

415.  4 

59 

258.2 

249.4 

19 

301.4 

291.1 

79 

344.6 

332.7 

39 

387.7 

374.4 

99 

430.9 

416.1 

60 

259.  0 

250.1 

20 

302.1 

291.8 

80 

345.3 

333.4 

40 

388.4 

375,1 

600 

431.6 

416.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.    j     Lat.     1 

46°  (134°,  226°,  314°). 

Page  456J 

TABLE  2. 

Difference  of  Latitude  and 

Departure  for  46°  (135",  225°,  315' 

). 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

0.7 

0.7 

61 

43.1 

43.1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

1.4 

1.4 

62 

43.8 

43.8 

22 

86.3 

86.3 

82 

128.  7 

128.7 

42 

171.1 

171.1 

3 

2.1 

2.1 

63 

44.5 

44.5 

23 

87.0 

87.0 

83 

129.4 

129.4 

43 

171.8 

171.8 

4 

2.8 

2.8 

64 

45.3 

45.3 

24 

87.7 

87.7 

84 

130.1 

130.1 

44 

172.5 

172.5 

5 

3.5 

3.5 

65 

46.0 

46.0 

25 

88.4 

88.4 

85 

130.8 

130.8 

45 

173.2 

173.2 

6 

4.2 

4.2 

•66 

46.7 

46.7 

26 

89.1 

89.1 

86 

131.5 

131.5 

46 

173.9 

173.9 

7 

4.9 

4.9 

67 

47.4 

47.4 

27 

89.8 

89.8 

87 

132.2 

132.2 

47 

174.7 

174.7 

8 

5.7 

5.7 

68 

48.1 

48.1 

28 

90.5 

90.5 

88 

132.9 

132.9 

48 

175.4 

175.4 

9 

6.4 

6.4 

69 

48.8 

48.8 

29 

91.2 

91.2 

89 

133.6 

133.6 

49 

176.1 

176. 1 

10 
11 

7.1 

7.1 

70 

49.5 

49.5 

30 

91.9 

91.9 

90 

134.4 

134.4 
135.1 

50 

251 

176.8 
177.6 

176.8 

7.8 

7.8 

71 

50.2 

50.2 

131 

92.6 

92.6 

191 

136.1 

177.5 

12 

8.5 

8.5 

72 

50.9 

50.9 

32 

93.3 

93.3 

92 

135.8 

135.8 

52 

178.2 

178.2 

13 

9.2 

9.2 

73 

51.6 

51.6 

33 

94.0 

94.0 

93 

136.5 

136.5 

53 

178.9 

178.9 

14 

9.9 

9.9 

74 

52.3 

52.3 

34 

94.8 

94.8 

94 

137.2 

137.2 

54 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

35 

95.5 

95.5 

95 

137.9 

137.9 

55 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

36 

96.2 

96.2 

96 

138.6 

138.6 

56 

181.0 

181.0 

17 

12.0  I  12.0 

77 

54.4 

54.4 

37 

96.9 

96.9 

97 

139.3 

139.3 

57 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

38 

97.6 

97.6 

98 

140.0 

140.0 

58 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.9 

55.9 

39 

98.3 

98.3 

99 

140.7 

140.7 

59 

183.1 

183.1 

20 

14.1 

14.1 

80 

56.6 

56.6 

40 

99.0 

99.0 

200 

141.4 

141.4 

60 

183.8 
184.6 

183.8 

21 

14.8 

14.8 

81 

57.3 

57.3 

141 

99.7 

99.7 

201 

142.1 

142.1 

261 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

43 

101.1 

101.1 

03 

143.5 

143.5 

63 

186.0 

186.0 

24 

17.0 

17.0 

84 

59.4 

59.4 

44 

101.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.1 

60.1 

45 

102.5 

102.5 

05 

145.  0 

145.0 

65 

187.4 

187.4 

26 

18.4 

18.4 

86 

60.8 

60.8 

46 

103.2 

103.2 

06 

145.7 

145.7 

66 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

47 

103.9 

103.9 

07 

146.4 

146.4 

67 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

48 

104.7 

104.7 

08 

147.1 

147.1 

68 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

49 

105.4 

105.4 

09 

147.8 

147.8 

69 

190.2 

190.2 

30 

21.2 

21.2 

90 

63.6 

63.6 

50 

106.1 

106.1 

10 

148.5 

148.5 

70 

190.9 

190.9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

106.8 

211 

149.  2  1 149.  2 

271 

191.6 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

52 

107.5 

107.5 

12 

149.9 

149.9 

72 

192.3 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

53 

108.2 

108.2 

13 

150.6 

150.6 

73 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

54 

108.9 

108.9 

14 

151.3 

151.3 

74 

193.  7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

55 

109.6 

109.6 

15 

152.0    152.0 

75 

194.5 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

56 

110.3 

110.3 

16 

152.7    152.7 

76 

195.2 

195.2 

37 

26.2 

26.2 

97 

68.6 

68.6 

57 

111.0 

111.0 

17 

153.4    153.4 

.77 

195.9 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

58 

111.7 

111.7 

18 

154. 1  1  154. 1 

78 

196.6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

59 

112. 4 

112.4 

19 

154.9 

154.9 

79 

197.3 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

60 

113.1 

113.1 

20 

155.6 
156.3 

155.6 

80 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

113.8 

221 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

02 

72.1 

72.1 

62 

114.6 

114.6 

22 

157.0 

157.0 

82 

199.4 

199.4 

43 

30.4 

30.4 

03 

72.8 

72.8 

63 

115.3 

115.3 

23 

157.7 

157.7 

83 

200.1 

200.1 

44 

31.1 

31.1 

04 

73.5 

73.5 

64 

116.0 

116.0 

24 

158.4 

158.4 

84 

200.8 

200.8 

45 

31.8 

31.8 

05 

74.2 

74.2 

65 

116.7 

116.7 

25 

159. 1 

159.1 

85 

201.5 

201.5 

46 

32.5 

32.5 

06 

75.0 

75.0 

66 

117.4 

117.4 

26  \ 

159.8 

159.8 

86 

202.2 

202.2 

47 

33.2 

33.2 

07 

75.7 

75.7 

67 

118.1 

118.1 

27 

160.5 

160.5 

87 

202.9 

202.9 

48 

33.9 

33.9 

08 

76.4 

76.4 

68 

118.8 

118.8 

28 

161.2 

161.2 

88 

203.6 

203.6 

49 

34.6 

34.6 

09 

77.1 

77.1 

69 

119.5 

119.5 

29 

161.9 

161.9 

89 

204.4 

204.4 

50 
51 

35.4 

35.4 

10 

77.8 

77.8 

70 

120.2 

120.2 

30 

162.6 
163.  3 

162.6 

90 

205.1 

205.1 

36.1 

36.1 

111 

78.5 

78.5 

171 

120.9 

120.9 

231 

163.3 

291 

205.8 

205.8 

52 

36.8 

36.8 

12 

79.2 

79.2 

72 

121.6 

121.6 

32 

164.0 

164.0 

92 

206.5 

206.5 

53 

37.5 

37.5 

13 

79.9 

79.9 

73 

122.3 

122.3 

33 

164.8 

164.8 

93 

207.2 

207.2 

54 

38.2 

38.2 

14 

80.6 

80.6 

74 

123.0 

123.0 

34 

165.5 

165.5 

94 

207.9 

207.9 

55 

38.9 

38.9 

15 

81.3 

81.3 

75 

123.7 

123.7 

35 

166.2 

166.2 

95 

208.6 

208.6 

56 

39.6 

39.6 

16 

82.0 

82.0 

76 

124.5 

124.5 

36 

166.9 

166.9 

96 

209.3 

209.3 

57 

40.3 

40.3 

17 

82.7 

82.7 

77 

125.2 

125.2 

37 

167.6 

167.6 

97 

210.0 

210.0 

58 

41.0 

41.0 

18 

83.4 

83.4 

78 

125. 9 

125.9 

38 

168.  3 

168.  3 

98 

210.7 

210.7 

59 

41.7 

41.7 

19 

84.1 

84.1 

79 

126.6 

126.6 

39 

169.0 

169.0 

99 

211.4 

211.4 

60 

42.4 

42.4 

20 

84.9 

84.9 

80 

127.3 

127.3 

40 

169.7 

169.7 

300 

212,1 

212.1 

Dist. 

Dep.        Lat.   | 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

4 

5°  (i; 

J5°,  225°,  315° 

. 

TABLE  2. 

[Page  457 

Difference  of  Latitude  and  Depart 

are  for  45°  (135°,  225°,  315 

=  )• 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.         Dep. 

Dist. 

Lat. 

Dep. 

301 

212.8 

212.8 

361 

255.3 

255.  3 

421 

297.7 

297.7 

481 

340.1   !340.  1 

541 

382.5 

382.5 

02 

213.5 

213.5 

62 

256.0 

256.0 

22 

298.4 

298.4 

82 

340. 8  '  340.  8 

42 

383.2 

383.2 

03 

214.3 

214.3 

63 

256.7 

256.  7 

23 

299.1 

299.1 

83 

.341.5     341.5 

43 

383.  9 

383.9 

04 

215.0 

215.0 

64 

257.  4 

257.  4 

24 

299.8 

299.8 

84 

342.2    342.2 

44 

384.7 

384.7 

05 

215.7 

215.7 

65 

258. 1 

258.1 

25 

300.5 

300.5 

85 

342.9    342.9 

45 

385.4 

385.4 

06 

216.4 

216.4 

66 

258.8 

258.8 

26 

301.2 

301.2 

86 

343.6    343.6 

46 

386.1 

386.1 

07 

217.1 

217.1 

67 

259.5 

259.  5 

27 

301.9 

301.9 

87 

344.3    344.3 

47 

386.  8 

386.8 

08 

217.8' 

217.8 

68 

260.2 

260.2 

28 

302.6 

302.6 

88 

345.1     34.5.1 

48 

387.5 

387.5 

09 

218.5 

218.5 

69 

260.9 

260.9 

29 

303.  4 

303.4 

89 

345.8    345.8 

49 

388.2 

388.2 

10 

219.2 

219.2 

70 
371 

261.6 
262.3 

261.6 

30 

304.1 

304.1 

90 

346.5 
347.2 

346.5 

50 

388.9 

388.9 

311 

219.9 

219.9 

262.3 

431 

304.8 

304.8 

491 

347.2 

551 

389.6 

389.6 

12 

220.6 

220.6 

72 

263.0 

263.0 

32 

305. 5 

305.5 

92 

347.9    347.9 

52 

390.3 

390.3 

13 

221.3 

221.3 

73 

263.8 

263.8 

33 

306.2 

306.2 

93 

348.6    348.6 

53 

391.0 

391.0 

14 

222.0 

222.0 

74 

264.5 

264.5 

34 

306.9 

306.9 

94 

349.3    349.3 

54 

391.7 

391.7 

15 

222.7 

222.7 

75 

265.2 

265.2 

35 

307.6 

307.6 

95 

350.0    350.0 

55 

392.4 

392.4 

16 

223.4 

223.4 

76 

265.9 

265.9 

36 

308.  3 

308.3 

96 

350.7    350.7 

56 

393.1 

393.1 

17 

224.2 

224.2 

77 

266.6 

266.6 

37 

309.0 

309.0 

97 

351.4    351.4 

57 

393.9 

393.9 

18 

224.9 

224.9 

78 

267.3 

267.3 

38 

309.7 

309.7 

98 

352.1    352.1 

58 

394.6 

394.6 

19 

225.6 

225.6 

79 

268.0 

268. 0 

39 

310.4 

310.4 

99 

352.8    352.8 

59 

395.3 

395.3 

20 

226.3 
227.0 

226.3 

80 

268.7 

268.7 
269.4 

40 

311.1 
31178 

311.1 
311.8 

500 
501 

353.5 

353.5 
354.3 

60 
561 

396. 0  !  396. 0  | 

321 

227.0 

381 

269.4 

441 

354.3 

396.7 

396.7 

22 

227.7 

227.7 

82 

270.1 

270.1 

42 

312.5 

312.5 

02 

355.0    355.0 

62 

397.4 

397.4 

23 

228.4 

228.4 

83 

270.8 

270.8 

43 

313.3 

313.3 

03 

355.7 

355.7 

63 

398.1 

398.1 

24 

229.1 

229.1 

84 

271.5 

271.5 

44 

314.0 

314.0 

04 

356.4 

356.4 

64 

398.8  1  398.8 

25 

229.8 

229.8 

85 

272.2 

272.2 

45 

314.7 

314.7 

05 

357.1 

357.1 

65 

399. 5     399. 5 

26 

230.5 

230.5 

86 

272.9 

272.9 

46 

315.  4 

315.4 

06 

357.8 

357.  8 

66 

400.  2     400.  2 

27 

231.2 

231.2 

87 

273.7 

273.7 

47 

316.1 

316.1 

07 

358.5 

358.5 

67 

400.9     400.9 

28 

231.9 

231.9 

88 

274.4 

274.4 

48 

316.8 

316.8 

08 

359.2 

359.2 

68 

401.6  *  401.6 

29 

232.6 

232.6 

89 

275.1 

275.1 

49 

317.5 

317.5 

09 

359.9 

359.9 

69 

402.3  ,  402.3 

30 

233.3 

233.3 

90 

275.8 
276.5 

275.8 

50 

318.2 

318.2 

10 
511 

360.6 

360.6 

70 

403.0 
403.8 

403.0 

331 

234.1 

234.1 

391 

276.5 

451 

318.9 

318.  9 

361.3 

361.3 

571 

403.8 

32 

234.8 

234.8 

92 

277.2 

277.2 

52 

319.6 

319.6 

12 

362.0 

362.0 

72 

404.5  i  404.5 

33 

235.  5 

235. 5 

93 

277.9 

277.9 

53 

320.3 

320.  3 

13 

362.7    362.7 

73 

405.2  ,  405.2 

34 

236.2 

236.2 

94 

278.6 

278.6 

54 

321.0 

321.0 

14 

363. 5    363.  5 

74 

405.9     405.9 

35 

236.9 

236. 9 

95 

279.3 

279.3 

55 

321.7 

321.7 

15 

364.  2    364.  2 

75 

406.6     406.6 

36 

237.6 

237.6 

96 

280.0 

280.0 

56 

322.4 

322.4 

16 

364.9    364.9 

76 

407.3     407.3 

37 

238.3 

238.3 

97 

280.7 

280.7 

57 

323.2 

323.2 

17 

365.6  !365.6 

77 

408.0     408.0 

38 

239.0 

239.0 

98 

281.4 

281.4 

58 

323.9 

323.  9 

18 

366.3    366.3 

78 

408.  7  '  408.  7 

39 

239.7 

239.7 

99 

282.1 

282.1 

59 

324.6 

324.6 

19 

367.0  1367.0 

79 

409.4     409.4 

40 

240.4 

240.4 

400 

282.8 
283.6 

282.8 

60 

325. 3 
326.0 

325.3 
326. 0 

20 
521 

367.7  1367:7 
368.4    368.4 

80 
581 

410.1 
410.8 

410.1 

341 

241.1 

241.1 

401 

283.6 

461 

410.8 

42 

241.8 

241.8 

02 

284.3 

284.3 

62 

326.7 

326.7 

22 

369.1  j  369.1 

82 

411.5     411.5 

43 

242.5 

242.5 

03 

285.0 

285.0 

63 

327.4 

327.4 

23 

369. 8    369.  8 

83 

412.  2     412.  2 

44 

243.2 

243.2 

04 

285.7 

285.7 

64 

328.1 

328.1 

24 

370.5  [370.5 

84 

412.  9     412.  9 

45 

244.0 

244.0 

05 

286.4 

286.4 

65 

328.8 

328.8 

25 

371.2  1371.2 

85 

413.  7     413.  7 

46 

244.7 

244.7 

06 

287.1 

287.1 

66 

329.5 

329.5 

26 

371.9    371.9 

86 

414.4     414.4 

47 

245.4 

245.4 

07 

287.8 

287.8 

67 

330.2 

330.2 

27 

372.  6  I  372.  6 

87 

415. 1     415. 1 

48 

246.1 

246.1 

08 

288.5 

288.5 

68 

330.9 

330.9 

28 

373.4    373.4 

88 

415.8  !  415.8 

49 

246.8 

246.8 

09 

289.2 

289.2 

69 

331.6 

331.6 

29 

374.1    374.1 

89 

416.5  '.  416.5 

50 

247.5 
248.2 

247.5 

10 

289.9 

289.9 
290.6 

70 

332.3 

332.  3 

30 

374.8    374.8 

90 
591 

417.2 
417.9 

417.2 
417.9 

351 

248.2 

411 

290.6 

471 

333. 1 

333.1 

531 

375.5 

375.5 

52 

248.9 

248.9 

12 

291.3 

291.3 

72 

333. 8 

333.8 

32 

376.2 

376.  2 

92 

418.6 

418.6 

53 

249.6 

249.6 

13 

292.0 

292.0 

73 

334. 5 

334.5 

33 

376.9 

376.9 

93 

419.3 

419.3 

54 

250.3 

250.3 

14 

292.7 

292.7 

74 

335.  2 

335.2 

34 

377.6 

377.6 

94 

420.0 

420.0 

55 

251.0 

251.0 

15 

293.5 

293.5 

75 

335. 9 

335.9 

35 

378.3 

378.3 

95 

420.7 

420.7 

56 

251.7 

251.7 

16 

294.2 

294.2 

76 

336.  6 

336. 6 

36 

379.0 

379.0 

96 

421.4 

421.4 

57 

252.4 

252.4 

17 

294.9 

294.9 

77 

337.  3 

337.3 

37 

379.7 

379.7 

97 

422.1 

422.1 

58 

253.1 

253.1 

18 

295.6 

295.6 

78 

338.0 

338.0 

38 

380.  4  !  380. 4 

98 

422.8 

422.8 

59 

253.  9 

253.9 

19 

296.3 

296.3 

79 

338.7 

338.7 

39 

381.1  1381.1 

99 

423.6 

423.6 

60 

254.6 

254.6 

20 

297.0 

297.0 

80 

339.4 

339.4 

40 

381.8 

381.8 

600 

424.3 

424.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

45°  (■ 

L35°,  22. 

)°,  315< 

'). 

1 

Page  458] 

TABLE  3. 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp 

1 

293.465 

M. 

0° 

1° 

20 

go 

4° 

5° 

6° 

JO 

8° 

90 

M. 

0 

0.0 

59.6 

119.2 

178.9 

238.6 

298.3 

358.2 

418.2 

478.3 

538.6 

0 

1 

1.0 

60.6 

20.2 

79.9 

39.6 

99.3 

59.2. 

19.2 

79.3 

39.6 

1 

2 

2.0 

61.J 

62;b 

21.2 

80.8 

40.6 

300.3 

60.2 

20.2 

80.3 

40.6 

2 

3 

3.0 

22.2 

81.8 

41.6 

01.3 

61.2 

21.2 

81.3 

41.6 

3 

4 

4.0 

63.6 

23.2 

82.8 

42.5 

02.3 

62.2 

22.2 

82.3 

42.6 

4 

5 

5.0 

64.6 

124.2 

183.8 

243.5 

303.3 

363.2 

423.2 

483.3 

543.6 

5 

6 

6.0 

65.6 

25.2 

84.8 

44.5 

04.3 

64.2 

24.2 

84.3 

44.6 

6 

7 

7.0 

66.5 

26.2 

85.8 

45.5 

05.3 

65.2 

25.2 

85.3 

45.6 

7 

8 

7.9 

67.5 

27.2 

86.8 

46.5 

06.3 

66.2 

26.2 

86.3 

46.6 

8 

9 

8.9 

68.5 

28.2 

87.8 

47.5 

07.3 

67.2 

27.2 

87.3 

47.6 

9 

10 

9.9 

69.5 

129.1 

188.8 

248.5 

308.3 

368.2 

428.2 

488.3 

548.6 

10 

11 

10.9 

70.5 

30.1 

89.8 

49.5 

09.3 

69.2 

29.2 

89.3 

49.6 

11 

12 

11.9 

71.5 

31.1 

90.8 

50.5 

10.3 

70.2 

30.2 

90.4 

50.6 

12 

13 

12.9 

72.5 

32.1 

91.8 

51.5 

11.3 

71.2 

31.2 

91.4 

51.7 

13 

14 

13.9 

73.5 

33.1 

92.8 

52.5 

12.3 

72.2 

32.2 

92.4 

52.7 

14 
15 

15 

14.9 

74.5 

134.1 

193.8 

253.5 

313.3 

373.2 

433.2 

493.4 

553.7 

16 

15.9 

75.5 

35.1 

94.8 

54.5 

14.3 

74.2 

34.2 

94.4 

54.7 

16 

17 

16.9 

76.5 

36.1 

95.8 

55.5 

15.3 

75.2 

35.2 

95.4 

55.7 

17 

18 

17.9 

77.5 

37.1 

96.8 

56.5 

16.3 

76.2 

36.2 

96.4 

56.7 

18 

19 

18.9 

78.5 

38.1 

97.8 

57.5 

17.3 

77.2 

37.2 

97.4 

57.7 

19 

20 

19.9 

79.5 

139.1 

198.8 

258.5 

318.3 

378.2 

438.2 

498.4 

558.7 

20 

21 

20.9 

80.5 

40.1 

99.7 

59.5 

19.3 

79.2 

39.2 

99.4 

59.7 

21 

22 

21.9 

81.5 

41.1 

200.7 

60.5 

20.3 

80.2 

40.2 

500.4 

60.7 

22 

23 

22.8 

82.4 

42.1 

01.7 

61.5 

21.3 

81.2 

41.2 

01.4 

61.7 

23 

24 

23.8 

83.4 

43.1 

02.7 

62.5 

22.3 

82.2 

42.2 

02.4 

62.7 

24 

25 

24.8 

84.4 

144.1 

203.  7 

263.5 

323.3 

383.2 

443.2 

503.4 

563.7 

25 

26 

25.8 

85.4 

45.1 

04.7 

64.5 

24.3 

84,2 

44.2 

04.4 

64.7 

26 

27 

26.8 

86.4 

46.0 

05.7 

65.5 

25.3 

85.2 

45.2 

05.4 

65.7 

27 

28 

27.8 

87.4 

47.0 

06.7 

66.5 

26.3 

86.2 

46.2 

06.4 

66.8 

28 

29 

28.8 

88.4 

48.0 

07.7 

67.4 

27.3 

87.2 

47.2 

07.4 

67.8 

29 

30 

29.8 

89.4 

149.0 

208.7 

268.4 

328.3 

388.2 

448.2 

508.4 

568.8 

30 

31 

30.8 

90.4 

50.0 

09.7 

69.4 

29.3 

89.2 

49.2 

09.4 

69.8 

31 

32 

31.8 

91.4 

51.0 

10.7 

70.4 

30.3 

90.2 

50.2 

10.4 

70.8 

32 

33 

32.8 

92.4 

52.0 

11.7 

71.4 

31.3. 

91.2 

51.2 

11.4 

71.8 

33 

34 

33.8 

93.4 

53.0 

12.7 

72.4 
273.4 

32.3 

92.2 

52.2 

12.4 

72.8 

34 

35 

34.8 

94.4 

154.0 

213.7 

333.3 

393.2 

453.2 

513.4 

573.8 

35 

36 

35.8 

95.4 

55.0 

14.7 

74.4 

34.3 

94.2 

54.3 

14.5 

74.8 

36 

37 

36.7 

96.4 

56.0 

15.7 

75.4 

35.3 

95.2 

55.3 

15.5 

75.8 

37 

38 

37.7 

97.3 

57.0 

16.7 

76.4 

36.2 

96.2 

56.3 

16.5 

76.8 

38 

39 

38.7 

98.3 

58.0 

17.7 

77.4 

37.2 

97.2 

57.3 

17.5 

77.8 

39 
40 

40 

39.7 

99.3 

159.0 

218.7 

278.4 

338.2 

398.2 

458.3 

518.5 

578.8 

41 

40.7 

100.3 

60.0 

19.7 

79.4 

39.2 

99.2 

59.3 

19.5 

79.9 

41 

42 

41.7 

01.3 

61.0 

20.6 

80.4 

40.2 

400.2 

60.3 

20.5 

80.9 

42 

43 

42.7 

02.3 

62.0 

21.6 

81.4 

41.2 

01.2 

61.3 

21.5 

81.9 

43 

44 

43.7 

03.3 

63.0 

22.6 

82.4 

42.2 

02.2 

62.3 

22.5 

82.9 

44 

45 

44.7 

104.3 

164.0 

223.6 

283.4 

343.2 

403.2 

463.3 

523. 5 

583.9 

45 

46 

45.7 

05.3 

65.0 

24.6 

84.4 

44.2 

04.2 

64.3 

24.5 

84.9 

46 

47 

46.7 

06.3 

66.0 

25.6 

85.4 

45.2 

05.2 

65.3 

25.5 

85.9 

47 

48 

47.7 

07.3 

67.0 

26.6 

86.4 

46.2 

06.2 

66.3 

26.5 

86.9 

48 

49 

48.7 

08.3 

68.0 

27.6 

87.4 

47.2 

07.2 

67.3 

27.5 

87.9 

49 

50 

49.7 

109.3 

168.9 

228.6 

288.4 

348.2 

408.2 

468.3 

528.5 

588.9 

50 

51 

50.7 

10.3 

69.9 

29.6 

89.4 

49.2 

09.2 

69.3 

29.5 

89.9 

51 

52 

51.6 

11.3 

70.9 

30.6 

90.4 

50.2 

10.2 

70.3 

30.5 

90.9 

52 

53 

52.6 

12.3 

71.9 

31.6 

91.4 

51.2 

11.2 

71.3 

31.5 

91.9 

53 

54 

53.6 

13.2 

72.9 

32.6 

92.4 

52.2 

12.2 

72.3 

32.5 

93.0 

54 

55 

54.6 

114.2 

173.9 

233.6 

293.4 

353.2 

413.2 

473.3 

533.5 

594.0 

55 

56 

55.6 

15.2 

74.9 

34.6 

94.4 

54.2 

14.2 

74.3 

34.6 

95.0 

56 

57 

56.6 

16.2 

75.9 

35.6 

95.4 

55.2 

15.2 

75.3 

35.6 

96.0 

57 

58 

57.6 

17.2 

76.9 

36.6 

96.3 

56.2 

16.2 

76.3 

36.6 

97.0 

58 

59 

58.6 

18.2 

77.9 

37.6 

97.3 

57.2 

17.2 

77.3 

37.6 

98.0 

59 

M. 

0° 

1° 

2° 

8° 

4° 

5° 

6° 

7° 

8° 

9° 

M. 

TABLE  3. 

[Page  459    | 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp 

1 

293.465 

M. 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

M. 

0 

599.0 

659.6 

720.5 

781.5 

842.8 

904.4 

966.3 

1028.  5 

1091.0 

1153. 9 

0 

1 

GOO.O 

60.6 

21.5 

82.5 

43.9 

05.4 

67.3 

29.5 

92.0 

54.9 

1 

2 

01.0 

61.7 

22.5 

83.6 

44.9 

06.5 

68.3 

30.5 

93.1 

56.0 

2 

3 

02.0 

62.7 

23.5 

84.6 

45.9 

07.5 

69.4 

31.6 

94.1 

57.0 

3 

4 

03.0 

63.7 

24.5 

85.6 

46.9 

08.5 

70.4 

32.6 

95.2 

58.1 

4 

5 

604.1 

664.7 

725.5 

786.6 

847.9 

909.6 

971.4 

1033.  7 

1096.  2 

1159. 1 

5 

6 

05.1 

65.7 

26.6 

87.6 

49.0 

10.6 

72.5 

34.7 

97.3 

60.2 

6 

7 

06.1 

66.7 

27.6 

88.7 

50.0 

11.6 

73.5 

35.7 

98.3 

61.2 

t 

8 

07.1 

67.7 

28.6 

89.7 

51.0 

12.6 

74.6 

36.8 

99.4 

62.3 

8 

9 

08.1 

68.7 

29.6 

90.7 

52.0 

13.7 

75.6 

37.8 

1100.4 

63.3 

9 

10 

609.1 

669.8 

730.6 

791.7 

853.1 

914.7 

976.6 

1038.  9 

1101.4 

1164. 4 

10 

11 

10.1 

70.8 

31.6 

92.7 

54.1 

15.7 

77.7 

39.9 

02.5 

65.4 

11 

12 

11.1 

71,8 

32.7 

93.8 

55.1 

16.8 

78.7 

40.9 

03.5 

66.5 

12 

13 

12.1 

72.8 

33.7 

94.8 

56.1 

17.8 

79.7 

42.0 

04.6 

67.5 

13 

14 

13.1 

73.8 

34.7 

95.8 

57.2 

18.8 

80.8 

43.0 

05.6 

68.6 

14 

15 

614.1 

674.8 

735.7 

796.8 

858.2 

919.8 

981.8 

1044. 1 

1106.  7 

1169. 7 

15 

16 

15.2 

75.8 

36.7 

97.8 

59.2 

20.9 

82.8 

45.1 

07.7 

70.7 

16 

17 

16.2 

76.8 

37.7 

98.9 

60.2 

21.9 

83.9 

46.1 

08.8 

71.8 

17 

18 

17.2 

77.9 

38.8 

99.9 

61.3 

22.9 

84.9 

47.2 

09.8 

72.8 

18 

19 

18.2 

78.9 

39.8 

800.9 

62.3 

24.0 
925.0 

85.9 
987.0 

48.2 

10.9 

73.9 

19 

20 

.  619.  2 

679.9 

740.8 

801.9 

863.3 

1049.  3 

1111.9 

1174. 9 

20 

21 

20.2 

80.9 

41.8 

02.9 

64.3 

26.0 

88.0 

50.3 

13.0 

76.0 

21 

22 

21.2 

81.9 

42.8 

04.0 

65.4 

27.1 

89.0 

51.3 

14.0 

77.0 

22 

23 

22.2 

82.9 

43.8 

05.0 

66.4 

28.1 

90.1 

52.4 

15.0 

78.1 

23 

24 

23.2 

83.9 

44.9 

06.0 

67.4 

29.1 

91.1 

53.4 

16.1 

79.1 

24 

25 

624.2 

684.9 

745.9 

807.0 

868.5 

930. 1 

992.1 

1054. 5 

1117. 1 

1180. 2 

25 

26 

25.3 

86.0 

46.9 

08.1 

69.5 

31.2 

93.2 

55.5 

18.2 

81.2 

26 

27 

26.3 

87.0 

47.9 

09.1 

70.5 

32.2 

94.2 

56.6 

19.2 

82.3 

27 

28 

27.3 

88.0 

48.9 

10.1 

71.5 

33.2 

95.3 

,57.6 

20.3 

83.3 

28 

29 

28.3 

89.0 

49.9 

11.1 

72.6 

34.3 

96.3 

58.6 

21.3 

84.4 

29 

30 

629.3 

690.0 

751.0 

812.1 

873.6 

935.3 

997.3 

1059.  7 

1122. 4 

1185.5 

30 

31 

30.3 

91.0 

52.0 

13.2 

74.6 

36.3 

98.4 

60.7 

23.4 

86.5 

31 

32 

31.3 

92.0 

53.0 

14.2 

75.6 

37.4 

99.4 

61. '8 

24.5 

87.6 

32 

33 

32.3 

93.1 

54.0 

15.2 

76.7 

38.4 

1000.4 

62.8 

25.5 

88.6 

33 

34 
35 

33.3 

94.1 

55.0 

16.2 

77.7 

39.4 

01.5 

63.9 
1064.  9" 

26.6 

89.7 
1190.  7 

34 
35 

634.3 

695.1 

756.0 

817.3 

878.7 

940.5 

1002.5 

1127.6 

36 

35.4 

96.1 

57.1 

18.3 

79.7 

41.5 

03.6 

65.9 

28.7 

91.8 

36 

37 

36.4 

97.1 

58.1 

19.3 

80.8 

42.5 

04.6 

67.0 

29.7 

92.8 

37 

38 

37.4 

98.1 

59.1 

20.3 

81.8 

43.6 

05.6 

68.0 

30.8 

93.9 

38 

39 

38.4 

99.1 

60.1 

21.3 

82.8 

44.6 

06.7 

69.1 

31.8 

95.0 

39 

40 

639.4 

700.2 

761.1 

822.4 

883.8 

945.6 

1007.  7 

1070. 1 

1132. 9 

1196,0 

40 

41 

40.4 

01.2 

62.2 

23.4 

84.9 

46.7 

08.7 

71.2 

33.9 

97.1 

41 

42 

41.4 

02.2 

63.2 

24.4 

85.9 

47.7 

09.8 

72.2 

35.0 

98.1 

42 

43 

42.4 

03.2 

64.2 

25.4 

86.9 

48.7 

10.8 

73.2 

36.0 

99.2 

43 

44 

43.4 

04.2 

65.2 

26.5 

88.0 

49.7 

11.8 

74.3 

37.1 

1200.2 

44 

45 

644.5 

705.2 

766.2 

827.5 

889.0 

950.8 

1012. 9 

1075. 3 

1138. 1 

1201. 3 

45 

46 

45.5 

06.2 

67.3 

28.5 

90.0 

51.8 

13.9 

76.4 

39.2 

02.3 

46 

47 

46.5 

07.3 

68.3 

29.5 

91.0 

52.8 

15.0 

77.4 

40.2 

03.4 

47 

48 

47.5 

08.3 

69.3 

30.5 

92.1 

53.9 

16.0 

78.5 

41.3 

04.5 

48 

49 

48.5 

09.3 

70.3 

31.6 

93.1 

54.9 

17.0 

79.5 

42.3 

05.5 

49 

50 

649.5 

710.  3 

771.3 

832.6 

894.1 

955.9 

1018. 1 

1080.  5 

1143.  .4 

1206. 6 

50 

51 

50.5 

11.3 

72.3 

33.6 

95.2 

57.0 

19.1 

81.6 

44.4 

07.6 

51 

52 

51.5 

12.3 

73.4 

34.6 

96.2 

58.0 

20.2 

82.6 

45.5 

08.7 

52 

53 

52.5 

13.4 

74.4 

35.7 

97.2 

59.0 

21.2 

83.7 

46.5 

09.7 

53 

54 

53.6 

14.4 

75.4 

36.7 

98.2 

60.1 

22.2 

84.7 

47.6 

10.8 

54 

55 

654.6 

715.4 

776.4 

837.7 

899.3 

961.1 

1023.  3 

1085. 8 

1148. 6 

1211.8 

55 

56 

55.6 

16.4 

77.4 

38.7 

900.3 

62.1 

24.3 

86.8 

49.7 

12.9 

56 

57 

56.6 

17.4 

78.5 

39.8 

01.3 

63.2 

25.3 

87.9 

50.7 

14.0 

57 

58 

57.6 

18.4 

79.5 

40.8 

02.3 

64.2 

26.4 

88.9 

51.8 

15.0. 

58 

59 

58.6 

19.4 

80.5 

41.8 

03.4 

65.2 

27.4 

89.9 

17° 

52.8 

16.1 

59 

M. 

10° 

11° 

12° 

13° 

14° 

15° 

lfi° 

1S° 

1J.° 

M. 

Page  460] 

TABLE  3. 

Meridional  Parts,  or  Increased  Latitudes. 

Comp.  293.466 

M. 

2©° 

210 

22° 

28° 

24° 

26° 

26° 

27° 

28° 

29° 

M. 

0 

1217. 1 

1280. 8 

1344. 9 

1409.5 

1474. 5 

1540.1 

1606. 2 

1672. 9 

1740. 2 

1808.1 

0 

1 

18.2 

81.9 

46.0 

10.6 

75.6 

41.2 

07.3 

74.0 

41.3 

09.2 

1 

% 

19.3 

82.^ 
84.^ 

47.1 

11.6 

76.7 

42.3 

08.4 

75.1 

42.4 

10.4 

2 

3 

20.3 

48.1 

12.7 

77.8 

43.4 

09.5 

76.2 

43.6 

11.5 

3 

4 

21.4 

85.1 

49.2 

13.8 

78.9 

44.5         10.6  1 

77.4 

44.7 

12.6 

4 

5 

1222. 4 

1286. 1 

1350. 3 

1414. 9 

1480. 0 

1545.6 

1611.7 

1678. 5 

1745.8 

1813. 8 

5 

6 

23.5 

87.2 

51.4 

16.0 

81.1 

46.7 

12.9 

79.6 

46.9 

14.9 

6 

7 

24.5 

88.3 

52.4 

17.1 

82.2 

47.8 

14.0 

80.7 

48.1 

16.1 

7 

8 

25.6 

89.3 

53.5 

18.1 

83.3 

48.9 

15.1 

81.8 

49.2 

17.2 

8 

9 

26.7 

90.4 

54.6 

19.2 

84.3 

50.0 

16.2 

82.9 

50.3 

18.3 

9 

10 

1227. 7 

1291.5 

1355.7 

1420.  3 

1485.4 

1551. 1 

1617.  3 

1684. 1 

1751.5 

1819. 5 

10 

11 

28.8 

92.5 

56.7 

21.4 

86.5 

52.2 

18.4 

85.2 

52.6 

20.6 

11 

12 

29.8 

93.6 

57.8 

22.5 

87.6 

53.3 

19.5 

86.3 

53.7 

21.8 

12 

13 

30.9 

94.7 

58.9 

23.5 

88.7 

54.4 

20.6 

87.4 

54.8 

22.9 

13 

14 

32.0 

95.7 

59.9 

24.6 

89.8 

55.5 

21.7 

88.5 

56.0 

24.0 

14 

15 

1233. 0 

1296.  8 

1361. 0 

1425.  7 

1490. 9 

1556. 6 

1622.  8 

1689.  7 

1757. 1 

1825. 2 

15 

16 

34.1 

97.9 

62.1 

26.8 

92.0 

57.  7         23. 9  1 

90.8 

58.2 

26.3 

16 

17 

35.1 

98.9 

63.2 

27.9 

93.1 

58.8 

25.0 

91.9 

59.4 

27.5 

17 

18 

36.2 

1300.0 

64.2 

29.0 

94.2 

59.9 

26.2 

93.0 

'60.5 

28.6 

18 

19 

37.3 

01.1 

65.3 

30.0 

95.2 

61.0 

27.3 

94.1 

61.6 

29.7 

19 
20 

20 

1238.  3 

1302. 1 

1366.4 

1431. 1 

1496. 3 

1562. 1 

1628.  4 

1695. 3 

1762.  7 

1830. 9 

21 

39.4 

03.2 

67.5 

32.2 

97.4 

63.2 

29.5 

96.4 

63.9 

32.0 

21 

22 

40.4 

04.3 

68.5 

33.3 

98.5 

64.3 

30.6 

97.5 

65.0 

33.2 

22 

23 

41.5 

05.3 

69.6 

34.4 

99.6 

65.4 

31.7 

98.6 

66.1 

34.3 

23 

24 

42.6 

06.4 

70.7 

36.4 

1500.7 

66.5 

32.8. 

99.7 

67.3 

35.4 

24 

25 

1243. 6 

1307.  5 

1371.8 

1436.  5 

1501.  8 

1567. 6 

1633. 9 

1700.9 

1768. 4 

1836. 6 

25 

26 

44.7 

08.5 

72.8 

37.6 

02.9 

68.7 

35.0 

02.0 

69.5 

37.7 

26 

27 

45.7 

09.6 

73.9 

38.7 

04.0 

69.8 

36.1 

03.1 

70.7 

38.9 

27 

28 

46.8 

10.7 

75.0 

39.8 

05.1 

70.9 

37.3 

04.2 

71.8 

40.0 

28 

29 

47.9 

11.7 

76.1 

40.9 

06.2 

72.0 

38.4 

05.3 

72.9 

41.2 

29 
30 

30 

1248. 9 

1312. 8 

1377. 1 

1442.0 

1507.  3 

1573. 1 

1639. 5 

1706.5 

1774. 1 

1842.3 

31 

50.0 

13.9 

78.2 

43.0 

08.4 

74.2 

40.6 

07.6 

75.2 

43.4 

31 

32 

51.0 

14.9 

79.3 

44.1 

09.4 

75.3 

41.7 

08.7 

76.3 

44.6 

32 

33 

52.1 

16.0 

80.4 

45.2 

10.5 

76.4 

42.8 

09.8 

77.4 

45.7 

33 

34 

53.2 

17.1 

81.5 

46.3 

11.6 

77.5 

43.9 

10.9 

78.6 

46.9 

34 

35 

1254. 2 

1318. 2 

1382. 5 

1447.4 

1512.  7 

1578. 6 

1645.0 

1712. 1 

1779.7 

1848. 0 

35 

36 

55.3 

19.2 

83.6 

48.5 

13.8 

79.7 

46.2 

13.2 

80.8 

49.2 

36 

37 

56.4 

20.3 

84.7 

49.5 

14.9 

80.8 

47.3 

14.3 

82.0 

50.3 

37 

38 

57.4 

21.4 

85.8 

50.6 

16.0 

81.9 

48.4 

15.4 

83.1 

51.4 

38 

39 

58.5 

22.4 

86.8 

51.7 

17.1 

83.0 

49.5 

16.6 

84.2 

52.6 

39 

40 

1259. 5 

1323. 5 

1387. 9 

1452.  8 

1518.  2 

1584. 1 

1650.  6 

1717.7 

1785.4 

1853.7 

40 

41 

60.6 

24.6 

89.0 

53.9 

19.3 

85.2 

51.7 

18.8 

86.5 

54.9 

41 

42 

61.7 

25.6 

90.1 

55.0 

20.4 

86.3 

52.8 

19.9 

87.6 

56.0 

42 

43 

62.7 

26.7 

91.1 

56.1 

21.5 

87.4 

53.9 

21.1 

88.8 

57.2 

43 

44 

63.8 

27.8 

92.2 

57.1 

22.6 

88.5 

55.1 

22.2 

89.9 

58.3 

44 

45 

1264.9 

1328. 9 

1393.  3 

1458.2 

1523.  7 

1589.  6 

1656.2 

1723. 3 

1791. 1 

1859.5 

45 

46 

65.9 

29.9 

94.4 

59.3 

24.8 

90.7 

57.3 

24.4 

92.2 

60.6 

46 

47 

67.0 

31.0 

95.5 

60.4 

25.9 

91.8 

58.4 

25.5 

93.3 

61.8 

47 

48 

68.0 

32.1 

96.5 

61.5 

27.0 

92.9 

59.5 

26.7 

94.5 

62.9 

48 

49 

69.1 

33.1 

97.6 

62.6 

28.0 

94.1 

60.6 

27.8 

95.6 

64.0 

49 

50 

1270.  2 

1334. 2 

1398.  7 

1463.  7 

1529.1 

1595.  2 

1661.  7 

1728. 9 

1796.  7 

1865.2 

50 

51 

71.2 

35.3 

99.8 

64.8 

30.2 

96.3 

62.9 

30.0 

97.9 

66.3 

51 

52 

72.3 

36.3 

1400.9 

65.8 

31.3 

97.4 

64.0 

31.2 

99.0 

67.5 

52 

53 

73.4 

37.4 

01.9 

66.9 

32.4 

98.5 

65.1 

32.3 

1800.1 

68.6 

53 

54 

74.4 

38.5 

03.0 

68.0 

33.5 

99.6 

66.2 

33.4 

01.3 

69.8 

54 

55 

1275. 5 

1339. 6 

1404. 1 

1469. 1 

1534. 6 

1600.  7 

1667.  3 

1734. 5 

1802.  4 

1870. 9 

55 

56 

76.6 

40.6 

05.2 

70.2 

35.7 

01.8 

68.4 

35.7 

03.5 

72.1 

56 

57 

77.6 

41.7 

06.2 

71.3 

36.8 

02.9 

69.5 

36.8 

04.7 

73.2 

57 

58 

78.7 

42.8 

■  07.3 

72.4 

37.9 

04.0 

70.7 

37.9 

05.8 

74.4 

58 

59 

79.7 

43.8 

08.4 

73.5 

39.0 

05.1 

71.8 

39.1 

07.0 

75.5 

59 

M. 

20° 

21° 

22° 

28° 

24° 

26° 

26° 

27° 

28° 

29° 

M. 

TABLE  3. 

[Page  461    | 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp. 

1 

293.465 

M. 

80° 

31° 

82° 

38° 

34° 

35°              36° 

87° 

38° 

39° 

M. 

0 

1876.  7 

1946.  0 

2016. 0 

2086. 8 

2158.  4 

2230. 9 

2304. 2 

2378. 5 

2453.  8 

2530.  2 

0 

1 

77.8 

47.1 

17.2 

88.0 

59.6 

32.1 

05.5 

79.8 

55.1 

31.5 

1 

2 

79.0 

48.3 

18.3 

89.2 

60.8 

33.3 

06.7 

81.0 

56.4 

32.8 

2 

3 

80.1 

49.4 

19.5 

90.3 

62.0 

34.5 

07.9 

82.3 

57.6 

34.0 

3 

4 

81.3 

50.6 

20.7 

91.5 

63.2 

35.7 

09.2 

83.5 

58.9 

35.3 

4 

5 

1882. 4 

1951. 8 

2021.9 

2092.  7 

2164.4 

2236.  9 

2310. 4 

2384. 8 

2460. 2 

2536. 6 

5 

6 

83.6 

52.9 

23.0 

93.9 

65.6 

38.2 

11.6 

86.0 

61.4 

37.9 

6 

7 

84.7 

54.1 

24.2 

95.1 

66.8 

39.4 

12.9 

87.3 

62.7 

39.2 

7 

8 

85.9 

55.3 

25.4 

96.3 

68.0 

40.6 

14.1 

88.5 

64.0 

40.5 

8 

9 

87.0 

56.4 

26.6 

97.5 

69.2 

41.8 

15.3 

89.8 

65.2 

41.7 

9 

10 

1888. 2 

1957.  6 

2027.  7 

2098.  7 

2170. 4 

2243.0 

2316. 5 

2391.  0 

2466. 5 

2543. 0 

10 

11 

89.3 

58.7 

28.9 

99.8 

71.6 

44.2 

17.8 

92.3 

67.8 

44.3 

11 

12 

90.5 

59.9 

30.1 

2101. 0 

72.8 

45.5 

19.0 

93.5 

69.0 

45.6 

12 

13 

91.6 

61.1 

31.3 

02.2 

74.0 

46.7 

20.3 

94.8 

70.3 

46.9 

13 

14 

92.8 

62.2 

32.4 

03.4 

75.2 

47.9 

21.5 

96.0 

71.6 

48.2 

14 

15 

1893. 9 

1963. 4 

2033. 6 

2104. 6 

2176. 4 

2249. 1 

2322.  7 

2397.  3 

2472.  8 

2549. 5 

15 

16 

95.1 

64.6 

34.8 

05.8 

77.6 

50.3 

24.0 

98.5 

74.1 

50.7 

16 

17 

96.2 

65.7 

36.0 

07.0 

78.8 

51.6 

25.2 

99.8 

75.4 

52.0 

17 

18 

97.4 

66.9 

37.1 

08.2 

80.0 

52.8 

26.4 

2401. 0 

76.6 

53.3 

18 

19 

98.5 

68.1 

38.3 

09.4 

81.2 

54.0 

27.7 

02.3 

77.9 

54.6 

19 

20 

1899.  7 

1969.  2 

2039. 5 

2110. 6 

2182.  5 

2255. 2 

2328. 9 

2403. 5 

2479. 2 

2555. 9 

20 

21 

1900. 8 

70.4 

40.7 

11.8 

83.7 

56.4 

30.1 

04.8 

80.4 

57.2 

21 

22 

02.0 

71.5 

41.8 

12.9 

84.9 

57.7 

31.4 

06.0 

81.7 

58.5 

22 

23 

03.1 

72.7 

43.0 

14.1 

86.1 

58.9 

32.6 

07.3 

83.0 

59.8 

23 

24 

04.3 

73.9 

44.2 

15.3 

87.3 

60.1 

33.8 

08.5 

84.3 

61.0 

24 

25 

1905. 5 

1975. 0 

2045.4 

2116.5 

2188. 5 

2261. 3 

2335.1 

2409.  8 

2485. 5 

2562.  3 

25 

26 

06.6 

76.2 

46.6 

17.7 

89.7 

62.5 

36.3 

11.1 

86.8 

63.6 

26 

27 

07.8 

77.4 

47.7 

18.9 

90.9 

63.8 

37.6 

12.3 

88.1 

64.9 

27 

28 

08.9 

78.5 

48.9 

20.1 

92.1 

65.0 

38.8 

13.6 

89.3 

66.2 

28 

29 

10.1 

79.7 

50.1 

21.3 

93.3 

66.2 

40.0 

14.8 

90.6 

67.5 

29 

30 

1911.2 

1980.  9 

2051.  3 

2122. 5 

2194. 5 

2267. 4 

2341. 3 

2416. 1 

^91.9 

2568.  8 

30 

31 

12.4 

82.0 

52.5 

23.7 

95.7 

68.7 

42.5 

17.3 

^  93.2 

70.1 

31 

32 

13.5 

83.2 

53.6 

24.9 

96.9 

69.9 

43.7 

18.6 

94.4 

71.4 

32 

33 

14.7 

84.4 

54.8 

26.1 

98.1 

71.1 

45.0 

19.8 

95.7 

72.7 

33 

34 
35 

15.8 

85.5 

56.0 

27.3 

99.4 

72.3 

46.2 
2347. 5 

21.1 

97.0 

73.9 

34 

1917.0 

1986.  7 

2057. 2 

2128. 5 

2200.6 

2273. 5 

2422. 3 

2498.  3 

2575.  2 

35 

36 

18.2 

87.9 

58.4 

29.6 

01.8 

74.8 

48.7 

23.6 

99.5 

76.5 

36 

37 

19.3 

89.1 

59.5 

30.8 

03.0 

76.0 

49.9 

24.9 

2500.8 

77.8 

37 

38 

20.5 

90.2 

60.7 

32.0 

04.2 

77.2 

51.2 

26.1 

02.1 

79.1 

38 

39 

21.6 

91.4 

61.9 

33.2 

05.4 

78.4 

52.4 

27.4 

03.4 

80.4 

39 

40 

1922. 8 

1992.  6 

2063.1 

2134.  4 

2206.  6 

2279.  7 

2353.  7 

2428.  6 

2504.6 

2581.7 

40 

41 

23.9 

93.7 

64.3 

35.6 

07.8 

80.9 

54.9 

29.9 

05.9 

83.0 

41 

42 

25.1 

94.9 

65.5 

36.8 

09.0 

82.1 

56.1 

31.2 

07.2 

84.3 

42 

43 

26.3 

96.1 

66.6 

38.0 

10.2 

83.3 

57.4 

32.4 

08.5 

85.6 

43 

44 

27.4 

97.2 

67.8 

39.2 

11.5 

84.6 

58.6 

33.7 

09.7 

86.9 

44 

45 

1928.  6 

1998.  4 

2069.  0 

2140. 4 

2212.  7 

2285.  8 

2359. 9 

2434. 9 

2511. 0 

2588. 2 

45 

46 

29.7 

99.6 

70.2 

41.6 

13.9 

87.0 

61.1 

36.2 

12.3 

89.5 

46 

47 

30.9 

2000.7 

71.4 

42.8 

15.1 

88.3 

62.4 

37.4 

13.6 

90.8 

47 

48 

32.0 

01.9 

72.6 

44.0 

16.3 

89.5 

63.6 

38.7 

14.8 

92.1 

48 

49 

33.2 

03.1 

73.7 

45.2 

17.5 

90.7 

64.8 

40.0 

16.1 

93.4 

49 

50 

1934. 4 

2004.  3 

2074. 9 

2146.  4 

2218.  7 

2291.9 

2366. 1 

2441.2 

2517. 4 

2594. 7 

50 

51 

35.5 

05.4 

76.1 

47.6 

19.9 

93.2 

67.3 

42.5 

18.7 

96.0 

51 

52 

36.7 

06.6 

77.3 

48.8 

21.1 

94.4 

68.6 

43.7 

20.0 

97.3 

52 

53 

37.8 

07.8 

78.5 

50.0 

22.4 

95.6 

69.8 

45.0 

21.2 

98.5 

53 

54 

39.0 

08.9 

79.7 

51.2 

23.6 

96.9 

71.1 
2372. 3 

46.3 
2447.5 

22.5 

99.8 
2601. 1 

54 
55 

55 

1940. 2 

2010. 1 

2080.  8 

2152. 4 

2224.  8 

2298. 1 

2523.  8 

56 

41.3 

11.3 

82.0 

53.6 

26.0 

99.3 

-^73.6 

48.8 

25.1 

02.4 

56 

57 

42.5 

12.5 

83.2 

54.8 

27.2 

2300. 5 

74.8 

50.1 

26.4 

03.7 

57 

58 

43.6 

13.6 

84.4 

56.0 

28.4 

01.8 

76.1 

51.3 

27.6 

05.0 

58 

59 

44.8 

14.8 

85.6 

57.2 

29.6 

03.0 

77.3 

52.6 

28.9 

06.3 

59 

M, 

30° 

81° 

32° 

88° 

34° 

35° 

36° 

87° 

88° 

39° 

M. 

Page  462J 

TABLE  3. 

Meridional  Parts,  or  Increased  Latitudes. 

\ 

Con^P-  29065 

M. 

40° 

41° 

42° 

48° 

44° 

45° 

46° 

47° 

48° 

49° 

M. 

0 

2607.6 

2686.2 

2766. 0 

2847.1 

2929.5 

3013. 4 

3098.  7 

3185. 6 

3274. 1 

3364.  4 

0 

1 

08.9 

87.6 

67.4 

48.5 

30.9 

14.8 

3100.1 

87.1 

75.6 

65.9 

1 

2 

10.2 

88-9 

68.7 

49.9 

32.3 

16.2 

01.6         88.5 

77.1 

67.4 

2 

3 

11.5 

90.2 

70.1 

51.2 

33.7 

17.6 

03.0  !      90.0 

78.6 

69.0 

3 

4 

12.8 

91.5 

71.4 

52.6 

35.1 

19.0 

04.4 

91.4 

80.1 

70.5 

4 

5 

2614. 1 

2692.  8 

2772.  8 

2853. 9 

2936.  5 

3020.  4 

3105. 9 

3192. 9 

3281. 6 

3372.0 

5 

6 

15.4 

94.2 

74.1 

55.3 

37.9 

21.8 

07.3         94.4 

83.1 

73.5 

6 

7 

16.8 

95.5 

75.4 

56.  7         39. 3 

23.3 

08.8  i       95.8 

84.6 

75.1 

7 

8 

18.1 

96.8 

76.8 

58. 0         40. 6 

24.7 

10.2  ;       97.3 

86.1 

76.6 

8 

9 

19.4 

98.1 
2699. 5 

78.1 

59. 4         42. 0 

26.1 

11.  6  :       98.  8 

87.6 

78.1 

9 

10 

2620.  7 

2779. 5 

2860.8     2943.4 

3027. 5 

3113.1  1  3200.2 

3289. 0 

3379. 6 

10 

11 

22.0 

2700.8 

80.8 

62.1         44.8 

28.9 

14.5         01.7 

90.5 

81.2 

11 

12 

23.3 

02.1 

82.2 

63.5  I      46.2 

30.3 

16.0         03.2 

92.0 

82.7 

12 

13 

24.6 

03.4 

83.5 

64.9         47.6 

31.7 

17.4  ,      04.6 

93.5 

84.2 

13 

14 

25.9 
2627.2" 

04.8 

84.8 

66.2  1      49.0 

33.2 

18.8  1      06.1 

95.0 

85.7 

14 

15 

2706.1 

2786. 2 

2867. 6 

2950. 4 

3034. 6 

3120.  3     3207. 6 

3296.  5 

3387. 3 

15 

16 

28.5 

07.4 

87.5 

69.0 

51.8 

36.0 

21.7         09.0 

98.0 

88.8 

16 

17 

29.8 

08.7 

88.9 

70.3 

53.2 

37.4 

23.2         10.5 

99.5 

90.3 

17 

18 

31.1 

10.1 

90.2 

71.7 

54.5 

38.8 

24.6  j       12.0 

3301. 0 

91.8 

18 

19 
20 

32.4 

11.4 

91.6 

73.1 

55.9 

40.2 

26.0  1       13.4 

02.5 

93.4 

19 
20 

2633.  7 

2712.  7 

2792. 9 

2874.4  !  2957.3 

3041.  7 

3127.5  !  3214.9 

3304. 0 

3394. 9 

21 

35.0 

14.0 

94.3 

75.  8         58.  7 

43.1 

28.9 

16.4 

05.5 

96.4 

21 

22 

36.3 

15.4 

95.6 

77.2         60.1 

44.5 

30.4 

17.9 

07.0 

98.0 

22 

23 

37.6 

16.7 

97.0 

78.6 

61.5 

45.9 

31.8 

19.3 

08.5 

99.5 

23 

24 
25 

38.9 
2640.  2 

18.0 

98.3 

79.9 

62.9 

47.3 

33.3. 

20.8 

10.0 

3401.0 

24 
25 

2719. 3 

2799. 7 

2881. 3 

2964.3 

3048.  7 

3134.  7 

3222.  3 

3311.5 

3402.  6 

26 

41.6 

20.7 

2801.0 

82.7 

65.7 

50.2 

36.2 

23.7 

13.0 

04.1 

26 

27 

42.9 

22.0 

02.4 

84.0 

67.1 

51.6 

37.6 

25.2 

14.5 

05.6 

27 

28 

44.2 

23.3 

03.7 

85.4 

68.5 

53.0 

39.0 

26.7 

16.0 

07.2 

28 

29 

45.5 

24.7 

05.1 

86.8  i      69.9 

.  54.4 

40.5 

28.2 

17.5 

08.7 

29 
30 

30 

2646.  8 

2726. 0 

2806. 4 

2888.2     2971.3 

3055. 9 

3141. 9 

3229. 6 

3319. 0 

3410. 2 

31 

48.1 

27.3 

07.8 

89.5  1       72.7 

57.3 

43.4 

31.1 

20.5 

11.8 

31 

32 

49.4 

28.6 

09.1 

90.  9  1       74. 1 

58.7 

44.8 

32.6 

22.1 

13.3 

32 

33 

50.7 

30.0 

10.5 

92.3         75.5 

60.1 

46.3 

34.1 

23.6 

14.8 

33 

34 

52.0 

31.3 

11.8 

93.7 

76.9 

61.5 

47.7 

35.6 

25.1 

16.4 

34 

35 

2653.  3 

2732. 6 

2813.  2 

2895. 0 

2978. 3 

3063.  0 

3149. 2 

3237.  0 

3326.  6 

3417. 9 

35 

36 

54.7 

34.0 

14.5 

96.4 

79.7 

64.4 

50.6 

38.5 

28.1 

19.5 

36 

37 

56.0 

35.3 

15.9 

97.8 

81.1 

65.8 

52.1 

40.0 

29.6 

21.0 

37 

38 

57.3 

36.6 

17.2 

99.2  1       82.5 

67.2 

53.5 

41.5 

31.1 

22.5 

38 

39 

58.6 

38.0 

18.6 

2900.5         83.9 

68.7 

55.0 

42.9 

32.6 

24.1 

39 

40 

2659. 9 

2739.  3 

2820. 0 

2901.9     2985.3 

3070. 1 

3156. 4 

3244. 4 

3334. 1 

3425. 6 

40 

41 

61.2 

40.6 

21.3 

03.3         86.7 

71.5 

57.9 

45.9 

35.6 

27.2 

41 

42 

62.5 

42.0 

22.7 

04.  7         88. 1 

72.9 

59.4 

47.4 

37.1 

28.7 

42 

43 

63.9 

43.3 

24.0 

06.1         89.5 

74.4 

60.8 

48.9 

38.6 

30.2 

43 

44 

65.2 

44.6 

25.4 

07.4         90.9 

75.8 

62.3 

50.3 

40.2 

31.8 

44 

45 

2666. 5 

2746. 0 

2826.  7 

2908. 8     2992. 3 

3077.  2 

3163. 7 

3251.8 

3341. 7 

3433. 3 

45 

46 

67.8 

47.3 

28.1 

10.2         93.7 

78.7 

65.2 

53.3 

43.2 

34.9 

46 

47 

69.1 

48.6 

29.4 

11.6         95.1  !      80.1 

66.6 

54.8 

44.7 

36.4 

47 

48 

70.4 

50.0 

30.  8 

13.  0         96.  5 

81.5 

68.1 

56.3 

46.2 

38.0 

48 

49 

71.7 

51.3 

32.2 

14.3         97.9 

82.9 

69.5 

57.8 

47.7 

39.5 

49 

50 

2673. 1 

2752. 7 

2833.  5 

2915.  7     2999.  3 

3084. 4 

3171.0 

3259.  3 

3349. 2 

3441.0 

50 

51 

74.4 

54.0 

34.9 

17. 1  -  3000.  7 

85.8 

72.5 

60.7 

50.8 

42.6 

51 

52 

75.7 

55.3 

36.2 

18. 5         02. 1 

87.2 

73.9 

62.2 

52.3 

44.1 

52 

53 

77.0 

56.7 

37.6 

19.9  !      03.5 

88.7 

75.4 

63.7 

53.8 

45.7 

53 

54 

78.3 

58.0 

39.0 

21.2 
2922.  6 

04.9 

90.1 

76.8 

65.2 

55. 3 

47.2 

54 

55 

2679. 6 

2759. 3 

2840.  3 

3006.3 

3091.5 

3178.  3 

3266.  7 

3356. 8 

3448.  8 

55 

56 

81.0 

60.7 

41.7 

^4.0         07.7 

93.0 

79.7 

68.2 

58.  3 

50.3 

56 

57 

82.3 

62.0 

43.0 

25.4         09.2 

94.4 

81.2 

69.7 

59.9 

51.9 

57 

58 

83.6 

63.4 

44.4 

26.8  I       10.6 

95.8 

82.7 

71.1 

61.4 

53.4 

58 

59 

84.9 

64.7 

45.8 

28.2         12.0 

97.3 

84.1 

72.6 

62.9 

55.0 

59 

M. 

40° 

41° 

42° 

48°               44° 

46° 

46° 

47° 

48° 

49° 

M. 

TABLE  3. 

[Page  463    | 

Meridional  Parts,  or 

Increased  Latitudes. 

Com  p. 

1 

293.465 

M. 

50° 

51° 

62° 

58° 

54° 

55° 

56° 

67° 

58° 

59° 

M. 

0 

3456.  5 

3550. 6 

3646.  7 

3745. 1 

3845.  7 

3948.  8 

4054. 5 

4163. 0 

4274.  4 

4389. 1 

0 

1 

58.1 

52.2 

48.4 

46.7 

47.4 

50.5 

56.3 

64.8 

76.3 

91.0 

1 

2 

59.6 

53.8 

50.0 

48.4 

49.1 

52.3 

58.1 

66.6 

78.2 

92.9 

2 

3 

61.2 

55.4 

51.6 

50.0 

50.8 

54.0 

59.8 

68.5 

80.1 

94.9 

3 

4 

62.7 

56.9 

53.2 

51.7 

52.5 

55.7 

61.6 

70.3 

82.0 

96.8 

4 

5 

3464. 3 

3558.5 

3654. 8 

3753. 4 

3854.  2 

3957. 5 

4063. 4 

4172. 1 

4283. 9 

4398.  8 

5 

6 

65.9 

60.1 

56.5 

55.0 

55.9 

59.2 

65.2 

74.0 

85.7 

4400.  7 

6 

,7 

67.4 

61.7 

58.1 

56.7 

57.6 

61.0 

67.0 

75.8 

87.6 

02.6 

7 

8 

69.0 

63.3 

59.7 

58.3 

59.3 

62.7 

68.8 

77.7 

89.5 

04.6 

8 

9 

70.5 

64.9 

61.3 

60.0 

61.0 

64.5 

70.6 

79.5 

91.4 

06.5 

9 

10 

3472. 1 

3566. 5 

3663. 0 

3761. 7 

3862. 7 

3966. 2 

4072. 4 

4181.3 

4293.  3 

4408. 5 

10 

11 

73.6 

68.1 

64.6 

63.3 

64.4 

68.0 

74.2 

83.2 

95.2 

10.4 

11 

12 

75.2 

69.7 

66.2 

65.0 

66.1 

69.7 

76.0 

85.0 

97.1 

12.4 

12 

13 

76.7 

71.3 

67.9 

66.7 

67.8 

71.5 

77.7 

86.9 

99.0 

14.3 

13 

14 

78.3 

72.8 

69.5 

68.3 

69.5 

73.2 

79.5 

88.7 

4300.9 

16.3 

14 

15 

3479. 9 

3574. 4 

3671. 1 

3770. 0 

3871. 2 

3975. 0 

4081. 3 

4190. 6 

4302.  8 

4418. 2 

15 

16 

81.4 

76.0 

72.7 

71.7 

72.9 

76.7 

83.1 

92.4 

04.7 

20.2 

16 

17 

83.0 

77.6 

74.4 

73.3 

74.6 

78.5 

84.9 

94.2 

06.6 

22.1 

17 

18 

84.5 

79.2 

76.0 

75.0 

76.3 

80.2 

86.7 

96.1 

08.5 

24.1 

18 

19 

86.1 

80.8 

77.6 

76.7 

78.1 

82.0 

88.5 

97.9 

10.4 

26.1 

19. 

20 

3487.  7 

3582. 4 

3679.  3 

3778. 3 

3879. 8 

3983. 7 

4090.  3 

4199.  8 

4312.  3 

4428. 0 

20 

21 

89.2 

84.0 

80.9 

80.0 

81.5 

85.5 

92.1 

4201. 6 

14.2 

30.0 

21 

22 

90.8 

85.6 

82.5 

81.7 

83.2 

87.2 

93.9 

03.5 

16.1 

31.9 

22 

23 

92.4 

87.2 

84.2 

83.3 

84.9 

89.0 

95.7 

05.3 

18.0 

33.9 

23 

24 

93.9 

88.8 

85.8 

85.0 

86.6 

90.7 

97.5 

07.2 

19.9 

35.8 

24 

25 

3495.5 

3590.  4 

3687. 4 

3786. 7 

3888.  3 

3992. 5 

4099.3 

4209. 0 

4321.  8 

4437.  8 

25 

26 

97.1 

92.0 

89.1 

88.4 

90.0 

94.3 

4101.1 

10.9 

23.7 

39.8 

26 

27 

98.6 

93.6 

90.7 

90.0 

91.8 

96.0 

02.9 

12.8 

25.6 

41.7 

27 

28 

3500.  2 

95.2 

92.3 

91.7 

93.5 

97.8 

04.8 

14.6 

27.5 

43.7 

28 

29 

01.8 

96.8 

94.0 

93.4 

95.2 

99.5 

06.6 

16.5 

29.4 

45.7 

29 

30 

3503.  3 

3598.  4 

3695.  6 

3795. 1 

3896.  9 

4001.3 

4108. 4 

4218. 3 

4331. 3 

4447.6 

30 

31 

04.9 

3600. 0 

97.3 

96.8 

98.6 

03.1 

10.2 

20.2 

33.2 

49.6 

31 

32 

06.5 

01.6 

98.9 

98.4 

3900.4 

04.8 

12.0 

22.0 

35.2 

51.6 

32 

33 

08.0 

03.2 

3700. 5 

3800.1 

02.1 

06.6 

13.8 

23.9 

37.1 

53.5 

33 

34 

09.6 

04.8 

02.2 

01.8 

03.8 

08.3 

15.6 

25.8 

39.0 

55.5 

34 

35 

3511. 2 

3606.4 

3703. 8 

3803. 5 

3905.  5 

4010. 1 

4117.4 

4227. 6 

4340. 9 

4457. 5 

35 

36 

12.7 

08.0 

05.5 

05.1 

07.2 

11.9 

19.2 

29.5 

42.8 

59.4 

36 

37 

14.3 

09.6 

07.1 

06.8 

09.0 

13.6 

21.0 

31.3 

44.7 

61.4 

37 

38 

15.9 

11.2 

08.7 

08.5 

10.7 

15.4 

22.9 

33.2 

46.6 

63.4 

38 

39 

17.5 

12.8 

10.4 

10.2 

12.4 

17.2 

24.7 

35.1 

48.6 

65.4 

39 

40 

3519. 0 

3614. 5 

3712. 0 

3811. 9 

3914. 1 

4018. 9 

4126. 5 

4236. 9 

4350. 5 

4467. 3 

40 

41 

20.6 

16.1 

13.7 

13.6 

15.9 

20.7 

28.3 

38.8 

52.4 

69.3 

41 

42 

22.2 

17.7 

15.3 

15.2 

17.6 

22.5 

30.1 

40.7 

54.3 

71.3 

42 

43 

23.7 

19.3 

17.0 

17.0 

19.3 

24.3 

31.9 

42.5 

56.2 

73.3 

43 

44 

25.3 

20.9 

18.6 

18.6 

21.0 

26.0 

33.8 

44.4 

58.2 

75.3 

44 

45 

3526. 9 

3622. 5 

3720. 3 

3820.  3 

3922.  8 

4027. 8 

4135. 6 

4246.  3 

4360. 1 

4477.  2 

45 

46 

28.5 

24.1 

21.9 

22.0 

24.5 

29.6 

37.4 

48.1 

62.0 

79.2 

46 

47 

30.1 

25.7 

23.6 

23.7 

26.2 

31.4 

39.2 

50.0 

63.9 

81.2 

47 

48 

31.6 

27.3 

25.2 

25.4 

28.0 

33.1 

41.0 

51.9 

65.9 

83.2 

48 

49 

33.2 

29.0 

26.9 

27.1 

29.7 

34.9 

42.9 

53.8 

67.8 

85.2 

49 

50 

3534. 8 

3630. 6 

3728. 5 

3828. 7 

3931. 4 

4036.  7 

4144. 7 

4255. 6 

4369.  7 

4487. 2 

50 

51 

36.4 

32.2 

30.2 

30.4 

33.2 

38.5 

46.5 

57.5 

71.7 

89.1 

51 

52 

37.9 

33.8 

31.8 

32.1 

34.9 

40.2 

48.3 

59.4 

73.6 

91.1 

52 

53 

39.5 

35.4 

33.5 

33.8 

36.6 

42.0 

50.2 

61.3 

75.5 

93.1 

53 

54 

41.1 

37.0 

35.1 

35.5 

38.4 

43.8 

52.0 

63.1 

77.4 

95.1 

54 
55 

55 

3542. 7 

3638. 6 

3736. 8 

3837. 2 

3940. 1 

4045. 6 

4153. 8 

4265. 0 

4379.  4 

4497.1 

56 

44.3 

40.3 

38.4 

38.9 

41.8 

47.4 

55.7 

66.9 

81.3 

99.1 

56 

57 

45.9 

41.9 

40.1 

40.6 

43.6 

49.1 

57.5 

68.8 

83.2 

4501. 1 

57 

58 

47.4 

43.5 

41.7 

42.3 

45.3 

50.9 

59.3 

70.7 

85.2 

03.1 

58 

59 

49.0 

45.1 

43.4 

45.0 

47.0 

52.7 

61.1 

72.5 

87.1 

05.1 

59 

M. 

60° 

51° 

52° 

53° 

54° 

55° 

66° 

67° 

58° 

59° 

M. 

Page  464j 

TABLE  3. 

Meridional  Parts,  or 

Increased  Latitudes. 

Comp 

1 

293.46.5 

M. 

60° 

61° 

02° 

03° 

04° 

05° 

66° 

67° 

68° 

69° 

M. 

0 

4507. 1 

4628.  7 

4754. 3 

4884. 1 

5018.  4 

5157. 6 

5302. 1 

5452. 4 

5609. 1 

5772.  7 

0 

1 

09.1 

30.8 

56.4 

86.3 

20.6 

59.9 

04.6 

55.0 

11.8 

75.5 

1 

2 

11.1 

32^9 
34ri9 

58.6 

88.5 

22.9 

62.3 

07.0 

57.6 

14.4 

78.3 

2 

3 

13.1 

60.7 

90.7 

25.2 

64.7 

09.5 

60.1 

17.1 

81.1 

3 

4 

15.1 

37.0 

62.8 

92.9 

27.5 

67.0 

11.9 

62.7 

19.8 

83.8 

4 
5 

5 

4517.1 

4639. 0 

4764.9 

4895. 1 

5029.8 

5169. 4 

5314.  4 

5465. 2 

5622.  4 

5786.  6 

6 

19.1 

41.1 

67.1 

97.3 

32.1 

71.8 

16.9 

67.8 

25.1 

89.4 

6 

7 

21.1 

43.2 

69.2 

99.5 

34.3 

74.2 

19.3 

70.4 

27.8 

92.2 

/ 

8 

23.1 

45.2 

71.3 

4901.  7 

36.6 

76.5 

21.8 

72.9 

30.5 

95.1 

8 

9 

25.1 

47.3 

73.5 

03.9 

38.9 

78.9 

24.3 

75.5 

33.2 

9%Ji 

9 
10 

10 

4527. 1 

4649. 4 

4775. 6 

4906. 1 

5041. 2 

5181.  3 

5326.  7 

5477. 1 

5635. 9 

5800.7 

11 

29.1 

51.5 

77.8 

08.3 

43.5 

83.7 

29.2 

80.7 

38.5 

03.5 

11 

12 

31.1 

53.5 

79.9 

10.5 

45.8 

86.0 

31.7 

83.2 

41.2 

06.3 

12 

13 

33.1 

55.6 

82.0 

12.8 

48.1 

88.4 

34.2 

85.8 

43.9 

09.1 

13 

14 

35.1 

57.7 

84.2 

15.0 

50.4 

90.8 

36.6 

88.4 

46.6 

11.9 

14 

15 

4537.1 

4659.  7 

4786. 3 

4917.  2 

5052.  7 

5193. 2 

5339. 1 

5491.0 

5649. 3 

5814. 7 

15 

16 

39.2 

61.8 

88.5 

19.4 

55.0 

95.6 

41.6 

93.6 

52.0 

17.6 

16 

17 

41.2 

63.9 

90.6 

21.6 

57.3 

98.0 

44.1 

96.2 

54.7 

20.4 

17 

18 

43.2 

66.0 

92.8 

23.9 

59.6 

5200.4 

46.6 

98.7 

57.4 

23.2 

18 

19 
20 

45.2 

68.1 

94.9 

26.1 

61.9 

02.7 

49.1 

5501.  3 

60.1 

26.0 

19 

4547. 2 

4670. 1 

4797. 1 

4928.  3 

5064.2 

5205. 1 

5351. 5 

5503. 9 

5662.  8 

5828. 9 

20 

21 

49.2 

72.2 

99.2 

30.5 

66.5 

07.5 

54.0 

06.5 

65.5 

31.7 

21 

22 

51.3 

74.3 

4801.4 

32.8 

68.8 

09.9 

56.5 

09.1 

68.2 

34.5 

22 

23 

53.3 

76.4 

03.5 

35.0 

71.1 

12.3 

59.0 

11.7 

70.9 

37.4 

23 

24 

55.3 

78.5 

05.7 

37.2 

73.4 

14.7 

61.5 

14.3 

73.7 

40.2 

24 

25 

4557. 3 

4680.  6 

4807.  8 

4939. 4 

5075. 7 

5217. 1 

5364.  0 

5516. 9 

5676. 4 

5843. 0 

25 

26 

59.3 

82.6 

10.0 

41.7 

78.1 

19.5 

66.5 

19.5 

79.1 

45.9 

26 

27 

61.4 

84.7 

12.1 

43.9 

80.4 

21.9 

69.0 

22.1 

81.8 

48.7 

27 

28 

63.4 

86.8 

14.3 

46.1 

82.7 

24.3 

71.5 

24.7 

84.5 

51.6 

28 

29 

65.4 

88.9 

16.5 

48.4 

85.0 

26.7 

74.0 

27.3 

87.3 

54.4 

29 

30 

4567.  4 

4691. 0 

4818. 6 

4950.  6 

5087.  3 

5229. 1 

5376. 5 

5529.  9 

5690.  0 

5857.  3 

30 

31 

69.5 

93.1 

20.8 

52.9 

89.6 

•31.6 

79.0 

32.5 

92.7 

60.1 

31 

32 

71.5 

95.2 

23.0 

55.1 

92.0 

34.0 

81.5 

35.2 

95.4 

63.0 

32 

33 

73.5 

97.3 

25.1 

57.3 

94.3 

36.4 

84.0 

37.8 

98.2 

65.9 

33 

34 

75.6 

99.4 

27.3 

59.6 

96.6 

38.8 

86.5 

40.4 

5700. 9 

68.7 

34 

35 

4577. 6 

4701. 5 

4829. 5 

4961.8 

5098. 9 

5241. 2 

5389.  I 

5543. 0 

5703.  6 

5871. 6 

35 

36 

79.6 

03.6 

31.6 

64.1 

5101.3 

43.6 

91.6 

45.6 

06.4 

74.4 

36 

37 

81.7 

05.7 

33.8 

66.3 

03.6 

46.0 

94.1 

48.3 

09.1 

77.3 

37 

38 

83.7 

07.8 

36.0 

68.6 

05.9 

48.5 

96.6 

50.9 

11.9 

80.2 

38 

39 

85.7 

09.9 

38.1 

70.8 

08.3 

50.9 

99.1 

53.5 

14.6 

83.1 

39 

40 

4587. 8 

4712.  0 

4840. 3 

4973. 1 

5110. 6 

5253. 3 

5401. 6 

5556. 1 

5717. 3 

5885. 9 

40 

41 

89.8 

14.1 

42.5 

75.3 

12.9 

55.7 

04.2 

58.8 

20.1 

88.8 

41 

42 

91.8 

16.2 

44.7 

77.6 

15.3 

58.2 

06.7 

61.4 

22.8 

91.7 

42 

43 

93.9 

18.3 

46.8 

79.8 

17.6 

60.6 

09.2 

64.0 

25.6 

94.6 

43 

44 

95.9 

20.4 

49.0 

82.1 

19.9 

63.0 

11.8 

66.7 

28.3 

97.4 

44 

45 

4598. 0 

4722. 5 

4851. 2 

4984.  3 

5122. 3 

5265. 4 

5414.  3 

5569.3 

5731. 1 

5900. 3 

45 

46 

4600. 0 

24.6 

53.4 

86.6 

24.6 

67.9 

16.8 

71.9 

33.9 

03.2 

46 

47 

02.1 

26.7 

55.6 

88.9 

27.0 

70.3 

19.3 

74.6 

36.6 

06.1 

47 

48 

04.1 

28.9 

57.8 

91.1 

29.3 

72.8 

21.9 

77.2 

39.4 

09.0 

48 

49 
50 

06.1 

31.0 

59.9 

93.4 

31.7 

75.2 

24.4 

79.9 

42.1 

11.9 

49 

4608. 2 

4733. 1 

4862. 1 

4995. 6 

5134. 0 

5277. 6 

5427. 0 

5582.  5 

5744. 9 

5914.  8 

50 

51 

10.2 

35.2 

64.3 

97.9 

36.4 

80.1 

29.5 

85.2 

47.7 

17.7 

51 

52 

12.3 

37.3 

66.5 

5000.2 

38.7 

82.5 

32.0 

87.8 

50.4 

20.6 

52 

53 

14.3 

39.4 

68.7 

02.4 

41.1 

85.0 

34.6 

90.5 

53.2 

23.5 

53 

54 

16.4 

41.6 

70.9 

04.7 

43.4 

87.4 

37.1 

93.1 

56.0 

26.4 

54 

55 

4618. 5 

4743. 7 

4873. 1 

5007. 0 

5145. 8 

5289. 8 

5439.  7 

5595. 8 

5758. 8 

5929. 3 

55 

56 

20.5 

45.8 

75.3 

09.3 

48.1 

92.3 

42.2 

98.4 

61.5 

32.2 

56 

57 

22.6 

47.9 

77.5 

11.5 

50.5 

94.7 

44.8 

5601. 1 

64.3 

35.1 

57 

58 

24.6 

50.0 

79.7 

13.8 

52.8 

97.2 

47.3 

03.8 

67.1 

38.1 

58 

59 

26.7 

52.2 

81.9 

16.1 

55.2 

99.7 

49.9 

06.4 

69.9 

41.0 

59 

M. 

«0° 

61° 

62° 

68° 

64° 

65° 

66° 

67° 

68° 

09° 

M. 

TABLE  3. 

[Page 

465 

IMeridional  Parts,  or  Increased  Latitudes. 

Comp. 

1 

^ 

'293.4d5 

M. 

70° 

71° 

72° 

78° 

74°   1   75° 

76° 

77° 

78° 

79° 

M. 

0 

5943.  9 

6123. 5 

6312. 5 

6512. 0 

6723. 2 

6947.  7 

7187.  3 

7444.  4 

7721. 6 

8022.  7 

0 

1 

46.8 

26.6 

15.8 

15.4 

26.8 

51.6 

91.5 

48.8 

26.4 

27.9 

1 

2 

49.7 

29.7 

19.0 

18.9 

30.5 

55.4 

95.6 

53.3 

31.3 

33.2 

2 

3 

52.7 

32.8 

22.3 

22.3 

34.1 

59.3 

99.7 

57.7 

36.1 

38.5 

3 

4 

55.6 

35.8 

25.5 

25.7 

37.7 

63.2 

7203.  9 

62.2 

40.9 

43.7 

4 

5 

5958. 5 

6138. 9 

6328. 8 

6529. 1 

6741.4 

6967. 1 

7208. 0 

7466. 7 

7745. 8 

8049. 0 

5 

6 

61.5 

42.0 

32.0 

32.6 

45.0 

70.9 

12.2 

71.1 

50.6 

54.3 

6 

7 

64.4 

45.1 

35.3 

36.0 

48.7 

74.8 

16.4 

75.6 

55.5 

59.6 

7 

8 

67.3 

48.2 

38.5 

39. 5 

52.3 

78.7 

20.5 

80.1 

60.3 

64.9 

8 

9 

vj«.3 

51.3 

41.8 

42.9 

56.0  '   82.6 

24.7 

84.6 

65.2 

70.2 

9 

10 

5973. 2 

6154. 4 

6345. 0 

6546.  4 

6759. 7  6986. 5 

7228. 9 

7489. 1 

7770. 1 

8075. 5 

10 

11 

76.2 

57.5 

48.3 

49.8 

63.3    90.4 

33.1 

93.6 

74.9 

80.8 

11 

12 

79.1 

60.6 

51.6 

53.3 

67.0  :   94.3 

37.3 

98.1 

79.8 

86.1 

12 

13 

82.1 

63,7 

54.8 

56.7 

70.7  !   98.3 

41.5 

7502.  6 

84.7 

91.5 

13 

14 

85.0 

66.8 

58.1 

60.2 

74.3 

7002.2 

45.7 

07.1 

89.6 

96.8 

14 

15 

5988. 0 

6169. 9 

6361. 4 

6563.  7 

6778. 0 

7006.1 

7249. 9 

7511.7 

7794. 5 

8102. 2 

15 

16 

90.9 

73.0 

64.7 

67.1 

81.7 

10.0 

54.1 

16.2 

99.4 

07.5 

16 

17 

93.9 

76.1 

67.9 

70.6 

85.4 

14.0 

58.3 

20.7 

7804. 3 

12.9 

17 

18 

96.9 

79.2 

71.2 

74.1 

89.1 

17.9 

62.5 

25.3 

09.3 

18.3 

18 

19 

99.8 

82.3 

74.5 

77.6 

92.8 

21.8 

66.7 

29.8 

14.2 

23.7 

19 

20 

6002.8 

6185. 5 

6377. 8 

6581. 0 

6796.  5  7025.  8 

7270. 9 

7534.  4 

7819. 1 

8129. 1 

20 

21 

05.8 

88.6 

81.1 

84.5 

6800.2  :   29.7 

75.2 

38.9 

24.1 

34.5 

21 

22 

08.7 

91.7 

84.4 

88.0 

03. 9    33.  7 

79.4 

43.5 

29.0 

39.9 

22 

23 

11.7 

94.8 

87.7 

91.5 

07.6  !   37.7 

83.7 

48.1 

34.0 

45.3 

23 

24 

14.7 

98.0 

91.0 

95.0 

11.3    41.6 

87.9 

52.7 

39.0 

50.8 

24 

25 

6017.  7 

6201.1 

6394. 3 

6598. 5 

6815.0  7045.6 

7292.  2 

7557.  3 

7844. 0 

8156.  2 

25 

26 

20.7 

04.2 

97.6 

6602.  0 

18.8    49.6 

96.4 

61.8 

48.9 

61.6 

26 

27 

23.6 

07.4 

6400.  9 

05.5 

22. 5    53. 5 

7300.  7 

66.4 

53.9 

67.1 

27 

28 

26.6 

10.5 

04.3 

09.0 

26.  2    57.  5 

05.0 

71.0 

58.9 

72.6 

28 

29 

29.6 

13.7 

07.6 

12.5 

.30.0    61.5 

09.2 

75.7 

63.9 

78.0 

29 

30 

6032.  6 

6216. 8 

6410. 9 

6616. 1 

6833.  7  7065. 5 

7313. 5 

7580.  3 

7868.  9 

8183. 5 

30 

31 

35.6 

20.0 

14.2 

19.6 

37.4    69.5 

17.8 

84.9 

74.0 

89.0 

31 

32 

38.6 

23.1 

17.6 

23.1 

41.2    73.5 

22.1 

89.5 

79.0 

94.5 

32 

33 

41.6 

26.3 

20.9 

26.6 

44.9 

77.5 

26.4 

94.2 

84.0 

8200.0 

33 

34 

44.6 

29.4 

24.2 

30.2 

48.7 

81.5 

30.7 

98.8 

89.1 

05.5 

34 

35 

6047.  6 

6232.  6 

6427.6 

6633.  7 

6852. 4  7085. 5 

7335.0 

7603. 4 

7894. 1 

8211. 1 

35 

36 

50.6 

35.8 

30.9 

37.2 

56.  2    89. 5 

39.3 

08.1 

99.2 

16.6 

36 

37 

53.6 

38.9 

34.2 

40.8 

60.  0    93. 5 

43.6 

12.8 

7904. 2 

22.1 

37 

38 

56.6 

42.1 

37.6 

44.3 

63.7 

97.6 

47.9 

17.4 

09.3 

27.7 

38 

39 

59.7 

45.3 

40.9 

47.9 

67.5 

7101.6 

52.3 

22.1 

14.4 

33.3 

39 

40 

6062.7 

6248. 4 

6444.3 

6651.4 

6871. 3  7105. 6 

7356. 6 

7626.  8 

7919. 4 

8238.  8 

40 

41 

65.7 

51.6 

47.6 

55.0 

75.1 

09.7 

60.9 

31.4 

24.5 

44.4 

41 

42 

68.7 

54.8 

51.0 

58.5 

78.9 

13.7 

65.3 

36.1 

29.6 

50.0 

42 

43 

71.7 

58.0 

54.4 

62.1 

82.6 

17.8 

69.6 

40.8 

34.7 

55.6 

43 

44 
45 

74.8 

61.2 

57.7 

65.7 

86.4 

21.8 

74.0 

45.5 

39.9 

61.2 

44 

6077. 8 

6264. 4 

6461.1 

6669.2 

6890.  2 

7125. 9 

7378. 3 

7650. 2 

7945. 0 

8266.  8 

45 

46 

80.8 

67.6 

64.5 

72.8 

94.0 

29.9 

82.7 

55.0 

50.1 

72.4 

46 

47 

83.9 

70.8 

67.8 

76.4 

97.8 

34.0 

87.1 

59.7 

55.2 

78.1 

47 

48 

86.9 

74.0 

71.2 

80.0 

6901.  7 

38.1 

91.4 

64.4 

60.4 

83.7 

48 

49 

89.9 

77.2 

74.6 

83.5 

05.5 

42.2 

95.8 

69.1 

65.5 

89.3 

49 

50 

6093. 0 

6280.  4 

6478. 0 

6687. 1 

6909. 3 

7146.  2 

7400.  2 

7673. 9 

7970.  7 

8295. 0 

50 

51 

96.0 

83.6 

81.4 

90.7 

13.1 

50.3 

04.6 

78.6 

75.9 

8300. 7 

51 

52 

99.1 

86.8 

84.8 

94.3 

16.9 

54.4 

09.0 

83.4 

81.0 

06.4 

52 

53 

6102. 1 

90.0 

88.2 

97.9 

20.8 

58.5 

13.4 

88.1 

86.2 

12.0 

53 

54 

05.2 

93.2 

91.6 

6701. 5 

24.6 

62.6 

17.8 

92.9 

91.4 

17.7 

54 

55 

6108. 2 

6296. 4 

6495. 0 

6705. 1 

6928.  4 

7166.  7 

7422.  2 

7697.  7 

7996. 6 

8323.  4 

55 

56 

11.3 

99.6 

98.4 

08.7 

32.3 

70.8 

26.6 

7702. 5 

8001.8 

29.2 

56 

57 

14.3 

6302. 9 

6501.8 

12.4 

36.1 

75.0 

31.1 

07.2 

07.0 

34.9 

57 

58 

17.4 

06.1 

05.2 

16.0 

40.0 

79.1 

35.5 

12.0 

12.2 

40.6 

58 

59 

20.5 

09.3 

08.6 

19.6 

43.8 

83.2 

39.9 

16.8 

17.5 

46.4 

59 

M. 

70° 

71° 

72° 

78° 

74° 

75° 

76° 

77° 

78° 

79° 

M. 

22489—03- 


-BO- 


Page  466] 

TABLE  4. 

1 

Length  of 

a  Degree  in  Latitude  and  . 

Longitude. 

Degree  of  Long. 

Degree  of  Lat.                          1 

Lat. 

Naut.  miles. 

statute  miles. 

Meters. 

Naut.  miles. 

Statute  miles. 

Meters. 

0 

0 

60.068 

69. 172 

Ill  321 

59. 661 

68. 704 

110  567 

o 

0 

1 

0.059 

9.162 

1  304 

.661 

.704 

568 

1 

2 

0.^1 
59.  { 86 

9.130 

1  253 

.662 

.705 

569 

2 

3 

9.078 

1  169 

.663 

.706 

570 

3 

4 

9.922 

9.005 

1  051 

.664 

.708 

573 

4 

5 

59. 840 

68. 911 

110  900 

59. 666 

68.  710 

110  576 

5 

6 

9.741 

8.795 

0  715 

.668 

.712 

580 

6 

7 

9.622 

8.660 

0  497 

.670 

.715 

584 

7 

8 

9.487 

8.504 

0  245 

.673 

.718 

589 

8 

9 

9.333 

8.326 

109  959 

.676 

.721 

595 

9 

10 

59. 161 

68.129 

109  641 

59. 680 

68. 725 

110  601 

10 

11 

8.971 

7.910 

9  289 

.684 

.730 

608 

11 

12 

8.764 

7.670 

8  904 

.687 

.734 

616 

.   12 

13 

8.538 

7.410 

8  486 

.692 

.739 

624 

13 

14 

8.295 

7.131 

8  036 

.697 

.744 

633 

14 

15 

58. 034 

66.  830 

107  553 

59.  702 

68. 751 

110  643 

15 

16 

7.756 

6.510 

7  036 

.707 

.757 

653 

16 

17 

7.459 

6.169 

6  487 

.713 

.764 

663 

17 

18 

7.146 

5.808 

5  906 

.719 

.771 

675 

18 

19 

6.816 

5.427 

5  294 

.725 

.778 

686 

19 

20 

56. 468 

65.026 

104  649 

59. 732 

68. 786 

110  699 

20 

21 

6.102 

4.606 

3  972 

.739 

.794 

712 

21 

22 

5.720 

4.166 

3  264 

.746 

.802 

725 

22 

23 

5.321 

3.706 

2  524 

.754 

.811 

739 

23 

24 

4.905 

3.228 

1  754 

.761 

.820 
68.829 

753 

24 

25 

54. 473 

62.  729 

100  952 

59.  769 

110  768 

25 

26 

4.024 

2.212 

0  119 

•  .777 

.839 

783 

26 

27 

3.558 

1.676 

99  257 

.786 

.848 

799 

27 

28 

3.076 

1.122 

8  364 

.795 

.858 

815 

28 

29 

2.578 

0.548 

7  441 

.804 

.869 

832 

29 

30 

52.064 

59. 956 

96  488 

59. 813 

68. 879 

110  849 

30 

31 

1.534 

9.345 

5  506 

.822 

.890 

866 

31 

32 

0.989 

8.716 

4  495 

.831 

.901 

883 

32 

33 

0.428 

8.071 

3  455 

.841 

.912 

901 

33 

34 

49.851 

7.407 

2  387 

.851 

.923 

919 

34 

35 

49. 259 

56. 725 

91  290 

59. 861 

68. 935 

110  938 

35 

36 

8.653 

6.027 

0  166 

.871 

.946 

956 

36 

37 

8.031 

5.311 

89  014 

.881 

.958 

975 

37 

38 

7.395 

4:579 

7  835 

.891 

.969 

994 

38 

39 

6.744 

3.829 

6  629 

.902 

.981 

111  013 

39 

40 

46. 079 

53.063 

85  396 

59. 912 

68. 993 

111  033 

40 

41 

5.399 

2.281 

4  137 

.923 

69.006 

052 

41 

42 

4.706 

1.483 

2  853 

.933 

.018 

072 

42 

43 

4.000 

0.669 

1  543 

.944 

.030 

091 

43 

44 

3.280 

49. 840 

0  208 

.954 

.042 

111 

44 

45 

2.546 

8.995 

78  849 

.965 

.054 

131 

45 

TABLE  4. 

[Page  467    | 

Length  of 

a  Degree  in  Latitude  and  Longitude. 

Degree  of  Long. 

Degree  of  Lat. 

Lat. 

Naut.  miles. 

Statute  miles. 

Meters. 

Naut.  miles. 

Statute  miles. 

Meters. 

0 

46 

42. 546 

48. 995 

78  849 

59.  965 

69. 054 

Ill  131 

o 

45 

46 

1.801 

8.136 

7  466 

.976 

.066 

151 

46 

47 

1.041 

7.261 

6  058 

.987 

.079 

170 

47 

48 

0.268 

6.372 

4  628 

.997 

.091 

190 

48 

49 

39. 484 

5.469 

3  174 

60. 008 

.103 

210 

49 
50 

50 

38. 688 

44.552 

71  698 

60. 019 

69. 115 

111  229 

51 

7.880 

3.621 

0  200 

.029 

.127 

249 

51 

52 

7.060 

2.676 

68  680 

.039 

.139 

268 

52 

53 

6.229 

1.719 

7  140 

.050 

.151 

287 

53 

54 

5.386 

0.749 

5  578 

.060 

.163 

306 

54 

55 

34. 532 

39. 766 

63  996 

60.  070 

69. 175 

111  325 

55 

56 

3.668 

8.771 

2  395 

.080 

.086 

343 

56 

57. 

2.794 

7.764 

0  774 

.090 

.197 

362 

57 

58 

1.909 

6.745 

59  135 

.100 

.209 

380 

58 

59 

1.015 

5.716 

7  478 

.109 

.220 

397 

59 

60 

30. 110 

34.  674 

55  802 

60. 118 

69.  230 

111  415 

60 

61 

29. 197 

3.623 

4  110 

.128 

.241 

432 

61 

62 

8.275 

2.560 

2  400 

.137 

.251 

448 

62 

63 

7.344 

1.488 

0  675 

,145 

.261 

464 

63 

64 

6.404 

0.406 

48  934 

.154 

.271 

480 

64 

65 

25. 456 

29.  315 

47  177 

60.162 

69. 281 

111  496 

65 

66 

4.501 

8.215 

5  407 

.170 

.290 

511 

66 

67 

3.538 

7.106 

3  622 

.178 

.299 

525 

67 

68 

2.567 

5.988 

1  823 

.186 

.308 

539 

68 

69 

1.590 

4.862 

0  012 

.193 

.316 

553 

69 

70 

20.  606 

23.  729 

38  188 

60.200 

69. 324 

111  566 

70 

71 

19. 616 

2.589 

6  353 

.207 

.332 

578 

71 

72 

8.619 

1.441 

4  506 

.213 

.340 

590 

72 

73 

7.617 

0.287 

2  648 

.220 

.347 

602 

73 

74 

6.609 

19. 127 

0  781 

.225 

.354 

613 

74 

75 

15. 596 

17. 960 

28  903 

60. 231 

69. 360 

111  623 

75 

76 

4.578 

6.788 

7  017 

.236 

.366 

633 

76 

77 

3.556 

5.611 

5  123 

.241 

.372 

642 

77 

78 

2.529 

4.  428 

3  220 

.246 

.377 

650 

78 

79 

1.499 

3.242 

1  311 

.250 

.382 

658 

79 

80 

10. 465 

12. 051 

19  394 

60.254 

69. 386 

111  665 

80 

81 

9.428 

10.857 

7  472 

.257 

.390 

671 

81 

82 

8.388 

9.659 

5  545 

.260 

.394 

677 

82 

83 

7.345 

8.458 

3  612 

,263 

.397 

682 

83 

84 

6.300 

7.255 

1  675 

.265 

.400 

687 

84 

85 

5.253 

6.049 

9  735 

60.268 

69. 402 

111  691 

85 

86 

4.205 

4.842 

7  792 

.269 

.404 

694 

86 

87 

3.154 

3.632 

5  846 

.270 

,405 

696 

87 

88 

2.103 

2.422 

3  898 

.271 

,407 

698 

88 

89 

1.052 

1.211 

1  949 

.272 

.407 

699 

89 

90 

0 

0 

0 

.272- 

.407 

699 

90 

Page  468] 

TABLE 

5A. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

Difference  between  the  course  and  first  bearing?,  in 

points. 

the  course 

and  second 

bearing,  in 
points. 

2 

2K 

2H 

2 

% 

»      1 

8Ji 

^%            1 

3 

1.96 

1.09 

3i 

1.57 

0.94 

'2.19 

1.31 

3J 

1.32 

0.84 

1.76 

1.12 

2.42 

1.  58 

3f 

1.14 

0.76 

1.47 

0.99 

1.94 

1.30 

2.64 

1.77 

4 

1.00 

0.71 

1.27 

0.90 

1.62 

1.15 

2.12 

1.50 

2.85 

2.01 

% 

4i 

0.90 

0.66 

1.12 

0.83 

1.40 

1.04 

1.77 

1.31 

2.29 

1.69 

3.05 

2.26 

4J 

0.81 

0.63 

1.00 

0.77 

1.23 

0.95 

1.53 

1.18 

1.91 

1.48 

2.45 

1.90 

3.25 

2.51 

4| 

0.74 

0.60 

0.91 

0.73 

1.10 

0.89 

1.34 

1.08 

1.65 

1.32 

2.05 

1.65 

2.61 

2.10 

5 

0.69 

0.57 

0.83 

0.69 

1.00 

0.83 

1.20 

1.00 

1.45 

1.21 

1.77 

1.47 

2.19 

1.82 

5\ 

0.64 

0.55 

0.77 

0.66 

0.92 

0.79 

1.09 

0.94 

1.30 

1.11 

1.56 

1.34 

1.88 

1.62 

5J 

0.60 

0.53 

0.72 

0.63 

0.85 

0.75 

1.00 

0.88 

1.18 

1.04 

1.39 

1.23 

1.66 

1.46 

5| 

0.57 

0.52 

0.68 

0.61 

0.79 

0.72 

0.93 

0.84 

1.08 

0.98 

1.26 

1.14 

1.48 

1.34 

6 

0.54 

0.50 

0.64 

0.59 

0.74 

0.69 

0.86 

0.80 

1.00 

0.92 

1.16 

1.07 

1.35 

1.24 

6} 

0.52 

0.49 

0.60 

0.57 

0.70 

0.66 

0.81 

0.76 

0.93 

0.88 

1.07 

1.01 

1.23 

1.16 

6J 

0.50 

0.47 

0.58 

0.55 

0.67 

0.64 

0.77 

0.73 

0.88 

0.84 

1.00 

0.96 

1.14 

1.09 

6| 

0.48 

0.46 

0.55 

0.54 

0.64 

0.62 

0.73 

0.71 

0.83 

0.80 

0.94 

0.91 

1.06 

1.03 

7 

0.46 

0.45 

0.53 

0.52 

0.61 

0.60 

0.69 

0.68 

0.79 

0.77 

0.89 

0.87 

1.00 

0.98 

7k 

0.45 

0.44 

0.51 

0.51 

0.59 

0.58 

0.67 

0.66 

0.75 

0.74 

0.84 

0.83 

0.94 

0.93 

n 

0.43 

0.43 

0.50 

0.50 

0.57 

0.56 

0.64 

0.64 

0.72 

0.72 

0.80 

0.80 

0.90 

0.89 

n 

0.42 

0.42 

0.48 

0.48 

0.55 

0.55 

0.62 

0.62 

0.69 

0.69 

0.77 

0.77 

0.86 

0.86 

8 

0.41 

0.41 

0.47 

0.47 

0.  53 

0.53 

0.60 

0.60 

0.67 

0.67 

0.74 

0.74 

0.82 

0.82 

8J 

0.41 

0.41 

0.46 

0.46 

0.52 

0.52 

0.58 

0.58 

0.65 

0.65 

0.72 

0.72 

0.79 

0.79 

8J 

0.40 

0.40 

0.45 

0.45 

0.51 

0.51 

0.57 

0.57 

0.63 

0.63 

0.69 

0.69 

0.76 

0.76 

8f 

0.39 

0.39 

0.45 

0.44 

0.50 

0.50 

0.56 

0.55 

0.61 

.0.61 

0.68 

0.67 

0.74 

0.73 

9 

0.39 

0.38 

0.44 

0.43 

0.49 

0.48 

0.55 

0.54 

0.60 

0.59 

0.66 

0.65 

0.72 

0.71 

n 

0.39 

0.38 

0.44 

0.42 

0.49 

0.47 

0.54 

0.52 

0.59 

0.57 

0.64 

0.63 

0.70 

0.68 

n 

0.38 

0.37 

0.43 

0.41 

0.48 

0.46 

0.53 

0.  51 

0.58 

0.56 

0.63 

0.61 

0.69 

0.66 

91 

0.38 

0.36 

0.43 

0.40 

0.48 

0.45 

0.52 

0.49 

0.57 

0.54 

0.62 

0.59 

0.67 

0.63 

10 

0.38 

0.35 

0.43 

0.40 

0.47 

0.44 

0.52 

0.48 

0.57 

0.52 

0.61 

0.57 

0.66 

0.61 

lOJ- 

0.38 

0.35 

0.43 

0.39 

0.47 

0.43 

0.52 

0.47 

0.56  '\  0.51 

0.61 

0.55 

0.&5 

0.59 

m 

0.38 

0.34 

0.43 

0.38 

0.47 

0.42 

0.51 

0.45 

0.56 

0.49 

0.60 

0.53 

0.65 

0.57 

10| 

0.39 

0.33 

0.43 

0.37 

0.47 

0.40 

0.51 

0.44 

0.56 

0.48 

0.60 

0.51 

0.64 

0.55 

11 

0.39 

0.32 

0.43 

0.36 

0.47 

0.  39 

0.51 

0.43 

0.56 

0.46 

0.60 

0.50 

0.64 

0.53 

lU 

0.39 

0.31 

0.44 

0.35 

0.48 

0.38 

0.52 

0.41 

0.56 

0.45 

0.60 

0.48 

0.64 

0.51 

iij 

0.40 

0.31 

0.44 

0.34 

0.48 

0.37 

0.52 

0.40 

0.56 

0.43 

0.60 

0.46 

0.63 

0.49 

111 

0.41 

0.30 

0.45 

0.33 

0.49 

0.36 

0.52 

0.39 

0.56 

0.42 

0.60 

0.44 

0.64 

0.47 

12 

0.41 

0.29 

0.45 

0.32 

0.49 

0.  35 

0.53 

0.37 

0.57 

0.40 

0.60 

0.43 

0.64 

0.45 

12i 

0.42 

0.28 

0.46 

0.31 

0.50 

0.34 

0.54 

0.36 

0.57 

0.38 

0.61 

0.41 

0.64 

0.42 

12J 

0.43 

0.28 

0.47 

0.30 

0.51 

0.32 

0.55 

0.35 

0.58 

0.37 

0.61 

0.39 

0.65 

0.41 

12| 

0.45 

0.27 

0.48 

0.29 

0.52 

0.31 

0.56 

0.33 

0.59 

0.  35 

0.62 

0.37 

0.65 

0.39 

13 

0.46 

0.26 

0.50 

0.28 

0.53 

0.30 

0.57 

0.32 

0.60 

0.33 

0.63 

0.  35 

0.66 

0.37 

n\ 

0.48 

0.24 

0.51 

0.26 

0.  55 

0.28 

0.58 

0.30 

0.61 

0.32 

0.64 

0.33 

0.67 

0.35 

l^ 

0.50 

0.23 

0.53 

0.25 

0.57 

0.27 

0.60 

0.28 

0.63 

0.30 

0.66 

0.31 

0.69 

0.32 

13| 

0.52 

0.22 

0.55 

0.24 

0.59 

0.25 

0.62 

0.26 

0.65 

0.28 

0.68 

0.29 

0.70 

0.30 

14 

0.54 

0.21 

0.58 

0.22 

0.61 

0.  23 

0.64 

0.24 

0.67 

0.26 

0.69 

0.27 

0.72 

0.28 

TABLE 

5A. 

[Page  469    | 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 
the  course 

Difference  between  the  course  and  first  bearing,  in  points. 

and  second 

bearing,  in 

points. 

8K 

4 

*V* 

4M 

*r* 

5 

5K             1 

4f 

3.44 

2.76 

5 

2.76 

2.30 

3.62 

3.01 

5i 

2.31 

1.98 

2.91 

2.50 

3.80 

3.26 

5^ 

1.99 

1.76 

2.44 

2.15 

3.05 

2.69 

3.96 

3.49 

5f 

1.75 

1.59 

2.10 

1.90 

2.55 

2.31 

3.18 

2.88 

4.12 

3.72 

6 

1.57 

1.45 

1.85 

1.71 

2.20 

2.03 

2.66 

2.46 

3.31 

3.  05 

4.26 

.3.94 

6i 

1.42 

1.34 

1.65 

1.56 

1.94 

1.82 

2.29 

2.  16 

2.77 

2.61 

,3.42 

3.22 

4.40 

4.14 

6^ 

1.31 

1.25 

1.50 

1.44 

1.73 

1.66 

2.02 

1.93 

2.38 

2.28 

2.86 

2.74 

3.53 

3.38 

6| 

1.21 

1.17 

1.38 

1.33 

1.57 

1.  52 

1.81 

1.75 

2.10 

2.04 

2.47 

2.39 

2.95 

2.87 

7 

1.13 

1.11 

1.27 

1.25 

1.44 

1.41 

1.64 

1.61 

1.88 

1.84 

2.17 

2.13 

2.55 

2.50 

7i 

1.06 

1.05 

1. 19 

1.17 

1.33 

1.32 

1.50 

1.49 

1.70 

1.69 

1.94 

1.92 

2.24 

2.22 

7i 

1.00 

1.00 

1.11 

1.11 

1.24 

1.24 

1.39 

1.  38 

1.56 

1.55 

1.76 

1.76 

2.01 

2.00 

71 

0.95 

0.95 

1.05 

1.05 

1.17 

1.17 

1.30 

1.30 

1.45 

1.44 

1.62 

1.62 

1.82 

1.82 

8      ■ 

0.91 

0.91 

1.00 

1.00 

1.10 

1.10 

1.22 

1.22 

1.35 

1.35- 

1.50 

1.50 

1.67 

1.67 

8i 

0.87 

0.87 

0.95 

0.95 

1.05 

1.05 

1.15 

1.15 

1.27 

1.26 

1.40 

1.39 

1.54 

1.54 

8i 

0.84 

0.83 

0.91 

0.91 

1.00 

1.00 

1.09 

1.09 

1.20 

1.19 

1.31 

1.30 

1.44 

1.43 

8| 

0.81 

0.80 

0.88 

0.87 

0.96 

0.95 

1.04 

1.03 

1.14 

1.12 

1.24 

1.22 

1.35 

1.34 

9 

0.78 

0.77 

0.85 

0.83 

0.92 

0.90 

1.00 

0.98 

1.08 

1.06 

1.18 

1.15 

1.28 

1.25 

9i 

0.76 

0.74 

0.82 

0.80 

0.89 

0.86 

0.96 

0.93 

1.04 

1.01 

1.12 

1.09 

1.21 

1.18 

9i 

0.74 

0.71 

0.80 

0.77 

0.86 

0.83 

0.93 

0.89 

1.00 

0.96 

1.08 

1.03 

1.16 

1.11 

91 

0.73 

0.68 

0.78 

0.74 

0.84 

0.79 

0.90 

0.&5 

0.97 

0.91 

1.04 

0.97 

1.11 

1.04 

10 

0.71 

0.66 

0.77 

0.71 

0.82 

0.76 

0.88 

0.81 

0.94 

0.87 

1.00 

0.92 

1.07 

0.99 

lOi 

0.70 

0.63 

0.75 

0.68 

0.80 

0.72 

0.86 

0.77 

0.91 

0.82 

0.97 

0.88 

1.03 

0.93 

m 

0.69 

0.61 

0.74 

0.65 

0.79 

0.69 

0.84 

0.74 

0.89 

0.78 

0.94 

0.83 

1.00 

0.88 

101 

0.68 

0.59 

0.73 

0.63 

0.77 

0.66 

0.82 

0.70 

0.87 

0.75 

0.92 

0.79 

0.97 

0.83 

11 

0.68 

0.56 

0.72 

0.60 

0.76 

0.64 

0.81 

0.67 

0.85 

0.71 

0.90 

0.75 

0.95 

0.79 

lU 

0.67 

0.54 

0.71 

0.57 

0.76 

0.61 

0.80 

0.64 

0.84 

0.67 

0.88 

0.71 

0.93 

0.75 

lU 

0.67 

0.52 

0.71 

0.55 

0.75 

0.58 

0.79 

0.61 

0.83 

0.64 

0.87 

0.67 

0.91 

0.70 

111 

0.67 

0.50 

0.71 

0.52 

0.74 

0.55 

0.78 

0.58 

0.82 

0.61 

0.86 

0.64 

0.90 

0.66 

12 

0.67 

0.48 

0.71 

0.50 

0.74 

0.52 

0.78 

0.55 

0.81 

0.57 

0.85 

0.60 

0.88 

0.63 

12i 

0.67 

0.45 

0.71 

0.48 

0.74 

0.50 

0.77 

0.52 

0.81 

0.54 

0.84 

0.56 

0.87 

0.59 

m 

0.68 

0.43 

0.71 

0.45 

0.74 

0.47 

0.77 

0.49 

0.80 

0.51 

0.84 

0.53 

0.87 

0.55 

12| 

0.68 

0.41 

0.71 

0.43 

0.74 

0.44 

0.77 

0.46 

0.80 

0.48 

0.83 

0.50 

0.86 

0.51 

13 

0.69 

0.38 

0.72 

0.40 

0.75 

0.42 

0.78 

0.43 

0.80 

0.45 

0.83 

0.46 

0.86 

0.48 

131^ 

0.70 

0.36 

0.73 

0.37 

0.76 

0.39 

0.78 

0.40 

0.81 

0.41 

0.83 

0.43 

0.86 

0.44 

13J 

0.71 

0.34 

0.74 

0.  35 

0.76 

0.36 

0.79 

0.37 

0.81 

0.38 

0.84 

0.39 

0.86 

0.41 

131 

0.73 

0.31 

0.75 

0..32 

0.77 

0.33 

0.80 

0.34 

0.82 

0.35 

0.84 

0.36 

0.86 

0.37 

14 

0.74 

0.28 

0.77 

0.29 

0.79 

0.30 

0.81 

0.31 

0.83 

0.32 

0.85 

0.32 

0.87 

0.33 

o% 

oVa 

6 

«^ 

6^ 

6K 

'       1 

6J 

4.52 

4.33 

6| 

3.63 

3.52 

4.63 

4.49 

7 

3.04 

2.98 

3.72 

3.65 

4.74 

4.64 

7i 

2.62 

2.59 

3.11 

3.08 

3.80 

3.76 

4.83 

4.77 

7i 

2.30 

2.29 

2.68 

2.67 

3.18 

3.17 

3.87 

3.86 

4.91 

4.88 

7f 

2.06 

2.06 

2.36 

2.36 

2.74 

2.74 

3.24 

3.24 

3.94 

3.93 

4.97 

4.97 

8 

1.87 

1.87 

2.11 

2.11 

2.41 

2.41 

2.79 

2.79 

3.30 

3.30 

.3.99 

3.99 

5.03 

5.03 

8i 

1.72 

1.71 

1.92 

1.92 

2.16 

2.16 

2.46 

2.  46 

2.84 

2.84 

3.34 

3.34 

4.04 

4.03 

8^ 

1.59 

1.58 

1.76 

1.75 

1.96 

1.95 

2.20 

2.19 

2.50 

2.49 

2.88 

2.87 

3.38 

3.36 

8f 

1.48 

1.46 

1.63 

1.61 

1.80 

1.78 

2.00 

1.98 

2.24 

2.21 

2.53 

2.51 

2.91 

2.88 

9 

1.39 

1.36 

1.52 

1.49 

1.66 

1.63 

1.83 

1.80 

2.03 

1.99 

2.27 

2.23 

2.56 

2.51 

9i 

1.31 

1.27 

1.42 

1.38 

1.55 

1.50 

1.69 

1.64 

1.86 

1.81 

2.06 

2.00 

2.29 

2.23 

9^ 

1.25 

1.19 

1.35 

1.29 

1.46 

1.39 

1.58 

1.51 

1.72 

1.65 

1.89 

1.81 

2.08 

1.99 

9| 

1.19 

1.12 

1.28 

1.20 

1.38 

1.30 

1.48 

1.40 

1.61 

1.51 

1.75 

1.64 

1.91 

1.80 

10 

1.14 

1.05 

1.22 

1.13 

1.31 

1.21 

1.40 

1.30 

1.51 

1.39 

1.62 

1.50 

1.77 

1.63 

lOi 

1.10 

0.99 

1.17 

1.06 

1.25 

1.13 

1.33 

1.20 

1.42 

1.29 

1.53 

1.38 

1.65 

1.49 

lOi 

1.06 

0.94 

1.13 

0.99 

1.20 

1.05 

1.27 

1.12 

1.35 

1.19 

1.44 

1.27 

1.55 

1.36 

101 

1.03 

0.88 

1.09 

0.93 

1.15 

0.99 

1.22 

1.04 

1.29 

1.11 

1.37 

1.18 

1.46 

1.25 

11 

1.00 

0.83 

1.05 

0.88 

1.11 

0.92 

1.17 

0.97 

1.24 

1.03 

1.31 

1.09 

1.39 

1.15 

lU 

0.98 

0.78 

1.03 

0.82 

1.08 

0.87 

1.13 

0.91 

1.19 

0.96 

1.25 

1.01 

1.32 

1.06 

lU 

0.95 

0.73 

1.00 

0.77 

1.05 

0.81 

1.10 

0.85 

1.15 

0.89 

1.21 

0.93 

1.27 

0.98 

111 

0.94 

0.69 

0.98 

0.72 

1.02 

0.76 

1.07 

0.79 

1.12 

0.83 

1.17 

0.86 

1.22 

0.90 

12 

0.92 

0.65 

0.96 

0.68 

1.00 

0.71 

1.04 

0.73 

1.09 

0.77 

1.13 

0.80 

1.18 

0.83 

12i 

0.91 

0.61 

0.94 

0.63 

0.98 

0.66 

1.02 

0.68 

1.06 

0.71 

1.10 

0.74 

1.14 

0.77 

12J 

0.90 

0.57 

0.93 

0.59 

0.97 

0.61 

1.00 

0.63 

1.04 

0.66 

1.07 

0.68 

1.11 

0.71 

12| 

0.89 

0.53 

0.92 

0.55 

0.95 

0.57 

0.98 

0.59 

1.02 

0.61 

1.05 

0.63 

1.08 

0.65 

13 

0.89 

0.49 

0.91 

0.51 

0.94 

0.52 

0.97 

0.54 

1.00 

0.56 

1.03 

0.57 

1.06 

0.59 

13i 

0.88 

0.45 

0.91 

0.47 

0.93 

0.48 

0.96 

0.49 

0.99 

0.51 

1.01 

0.52 

1.04 

0.54 

13J 

0.88 

0.42 

0.91 

0.43 

0.93 

0.44 

0.95 

0.45 

0.98 

0.46 

1.00 

0.47 

1.02 

0.48 

13| 

0.88 

0.38 

0.90 

0.39 

0.92 

0.40 

0.95 

0.41 

0.97 

0.41 

0.99 

0.42 

1.01 

0.43 

14 

0.89 

0.34 

0.91 

0.35 

0.92 

0.35 

0.94 

0.36 

0.90 

0.37 

0.98 

0.38 

1.00 

0.38 

Page  470]                                             TABLE  5A. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 

Difference  between  the  course  and  first  bearing,  in  points. 

the  course 

and second 

bearing,  in 
points. 

IK 

J^ 

7K 

8 

W* 

»% 

m 

9 

8i 

5.07 

5.06 

• 

' 

8J 

4.07 

4.05 

5.10 

5.08 

8| 

3.41 

3.37 

4.10 

4.06 

5.12 

5.06 

9 

2.94 

2.88 

3.43 

3.36 

4.11 

4.03 

5.13 

5.03 

n 

2.58 

2.51 

2.95 

2.87 

3.44 

3.34 

4.12 

3.39 

5.12 

4.97 

H 

2.31 

2.21 

2.60 

2.49 

2.96 

2.84 

3.44 

3.30 

4.11 

3.93 

5.10 

4.88 

n 

2.10 

1.98 

2.33 

2.19 

2.61 

2.46 

2.97 

2.79 

3.44 

3.24 

4.10 

3.86 

5.07 

4.77 

10 

1.92 

1.78 

2.11 

1.95 

2.34 

2.16 

2.61 

2.41 

2.96 

2.74 

3.43 

3.17 

4.07 

3.76 

5.03 

4.64 

10^ 

1.78 

1.61 

1.93 

1.75 

2.12 

1.92 

2.34 

2.11 

2.61 

2.36 

2.95 

2.67 

3.41 

3.08 

4.04 

3.65 

10^ 

1.66 

1.46 

1.79 

1.58 

1.94 

1.71 

2.12 

1.87 

2.34 

2.06 

2.60 

2.29 

2.94 

2.59 

3.38 

2.98 

10| 

1.56 

1.34 

1.67 

1.43 

1.80 

1.54 

1.95 

1.67 

2.12 

1.82 

2.33 

2.00 

2.58 

2.22 

2.91 

2.50 

11 

1.47 

1.22 

1.57 

1.30 

1.68 

1.39 

1.80 

1.50 

1.94 

1.62 

2.11 

1.76 

2.31 

1.92 

2.56 

2.13 

lU 

1.40 

1.12 

1.48 

1.19 

1.57 

1.26 

1.68 

1.35 

1.80 

1.44 

1.93 

1.55 

2.10 

1.69 

2.29 

1.84 

lu 

1.34 

1.03 

1.41 

1.09 

1.49 

1.15 

1.58 

1.22 

1.68 

1.30 

1.79 

1.38 

1.92 

1.49 

2.08 

1.61 

111 

1.28 

0.95 

1.34 

1.00 

1.41 

1.05 

1.49 

1.10 

1.57 

1.17 

1.67 

1.24 

1.78 

1.32 

1.91 

1.41 

12 

1.23 

0.87 

1.29 

0.91 

1.35 

0.95 

1.41 

1.00 

1.49 

1.05 

1.57 

1.11 

1.66 

1.17 

1.77 

1.25 

m 

1.19 

0.80 

1.24 

0.83 

1.29 

0.87 

1.35 

0.91 

1.41 

0.95 

1.48 

1.00 

1.56 

1.05 

1.65 

1.11 

12i 

1.15 

0.73 

1.20 

0.76 

1.24 

0.79 

1.29 

0.82 

1.35 

0.86 

1.41 

0.89 

1.47 

0.93 

1.55 

0.98 

12| 

1.12 

0.67 

1.16 

0.69 

1.20 

0.72 

1.25 

0.74 

1.29 

0.77 

1.34 

0.80 

1.40 

0.83 

1.46 

0.87 

13 

1.09 

0.61 

1.13 

0.63 

1.16 

0.65 

1.20 

0.67 

1.24 

0.69 

1.29 

0.72 

1.34 

0.74 

1.39 

0.77 

m 

1.07 

0.55 

1.10 

0.57 

1.13 

0.58 

1.17 

0.60 

1.20 

0.62 

1.24 

0.64 

1.28 

0.66 

1.32 

0.68 

m 

1.05 

0.50 

1.08 

0.51 

1.10 

0.52 

1.13 

0.53 

1.16 

0.55 

1.20 

0.56 

1.23 

0.58 

1.27 

0.60 

131 

1.03 

0.44 

1.06 

0.45 

1.08 

0.46 

1.11 

0.47 

1.13 

0.48 

1.16 

0.50 

1.19 

0.51 

1.22 

0.52 

14 

1.02 

0.39 

1.04 

0.40 

1.06 

0.41 

1.08 

0.41 

1.10 

0.42 

1.13 

0.43 

1.15 

0.44 

1.18 

0.45 

»K 

95^ 

9% 

10 

lOK 

im 

lOK 

»     1 

lOi 

4.97 

4.50 

10^ 

3.99 

3.52 

4.91 

4.33 

101 

3.34 

2.87 

3.94 

3.38 

4.83 

4.14 

11 

2.88 

2.39 

3.30 

2.74 

3.87 

3.22 

4.74 

3.94 

lU 

2.53 

2.04 

2.84 

2.28 

3.24 

2.61 

3.80 

3.05 

4.63 

3.72 

lU 

2.27 

1.75 

2.50 

1.93 

2.79 

2.16 

3.18 

2.46 

3.72 

2.88 

4.52 

3.49 

111 

2.06 

1.52 

2.24 

1.66 

2.46 

1.82 

2.74 

2.03 

3.11 

2.31 

3.63 

2.69 

4.40 

3.20 

12 

1.89 

1.33 

2.03 

1.44 

2.20 

1.56 

2.41 

1.71 

2.68 

1.90 

3.04 

2.15 

3.53 

2.50 

4.26 

3.01 

m 

1.75 

1.18 

1.86 

1.25 

2.00 

1.34 

2.16 

1.45 

2.36 

1.59 

2.62 

1.76 

2.95 

1.98 

3.42 

2.30 

m 

1.62 

1.03 

1.72 

1.09 

1.83 

1.16 

1.96 

1.24 

2.11 

1..34 

2.30 

1.46 

2.55 

1.62 

2.86 

1.82 

121 

1.53 

0.91 

1.61 

0.96 

1.69 

1.01 

1.80 

1.07 

1.92 

1.14 

2.06 

1.23 

2.24 

1.34 

2.47 

1.47 

13 

1.44 

0.80 

1.51 

0.84 

1.58 

0.88 

1.66 

0.92 

1.76 

0.98 

1.87 

1.04 

2.01 

1.11 

2.17 

1.21 

m 

1.37 

0.71 

1.42 

0.73 

1.48 

0.76 

1.55 

0.80 

1.63 

0.84 

1.72 

0.88 

1.82 

0.94 

1.94 

1.00 

m 

1.31 

0.62 

1.35 

0.64 

1.40 

0.66 

1.46 

0.69 

1.52 

0.72 

1.59 

0.75 

1.67 

0.79 

1.76 

0.83 

13| 

1.25 

0.54 

1.29 

0.55 

1.33 

0.57 

1.38 

0.59 

1.42 

0.61 

1.48 

0.63 

1.54 

0.66 

1.62 

0.69 

14 

1.21 

0.46 

1.24 

0.47 

1.27 

0.49 

1.31 

0.50 

1.35 

0.52 

1.39 

0.53 

1.44 

0.55 

1.50 

0.57 

UK 

11 

'A 

llji 

12 

I'zy,       1 

t'2% 

12'/i 

u      1 

12i 

4.12 

2.77 

i 

m 

3.31 

2.10 

3.96 

2.51 

12| 

2.77 

1.65 

3.18 

1.90 

3.80 

2.26 

13 

2.38 

1.32 

2.66 

1.48 

3.05 

1.69 

3.62 

2.01 

m 

2.10 

1.08 

2.29 

1.18 

2.55 

1.31 

2.91 

1.50 

3.44 

1.77 

13i 

1.88 

0.89 

2.02 

0.95 

2.20 

1.04 

2.44 

1.15 

2.76 

1.30 

3.25 

1.53 

13| 

1.70 

0.73    1.81 

0.77 

1.94 

0.83 

2.10 

0.90 

2.31 

0.99 

2.61 

1.12 

3.05 

1.31 

14 

1.56 

0.60    1.64 

0.63 

1.73 

0.66 

1.85 

0.71 

1.99 

0.76 

2.19 

0.84 

2.45 

0.94 

2.85 

1.09 

TABLE 

5B. 

[Page  471    | 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

the  course 

and  second 

bearing. 

Difference  between  the  course  and  first  bearing. 

20° 

22° 

24° 

26° 

28° 

80° 

a 

2° 

30° 

1.97 

0.98 

32 

1.64 

0.87 

2.16 

1.14 

34 

1.41 

0.79 

1.80 

1.01 

2.34 

1.31 

36 

1.24 

0.73 

1.55 

0.91 

1.96 

1.15 

2.52 

1,48 

38 

1.11 

0.68 

1.36 

0.84 

1,68 

1.04 

2.11 

1,30 

2.70 

1.66 

40 

1.00 

0.64 

1.21 

0.78 

1.48 

0.95 

1.81 

1,16 

2.26 

1,45 

2.88 

1.85 

42 

0.91 

0.61 

1.10 

0.73 

1.32 

0.88 

1.59 

1.06 

1.94 

1,30 

2.40 

1.61 

3.05 

2,04 

44 

0.84 

0.58 

1.00 

0.69 

1.19 

0.83 

1.42 

0.98 

1.70 

1.18 

2.07 

1.44 

2.55 

1,77 

46 

0.78 

0.56 

0.92 

0.66 

1.09 

0.78 

1.28 

0.92 

1.52 

1.09 

1.81 

1.30 

2.19 

1,58 

48 

0.73 

0.54 

0.85 

0.64 

1.00 

0.74 

1.17 

0.87 

1.37 

1.02 

1.62 

1.20 

1,92 

1,43 

50 

0.68 

0.52 

0.80 

0.61 

0.93 

0.71 

1.08 

0.83 

1.25 

0.96 

1.46 

1.12 

1.71 

1.31 

52 

0.65 

0.51 

0.75 

0.59 

0.87 

0.68 

1.00 

0.79 

1.15 

0.91 

1.33 

1.05 

1.55 

1.22 

54 

0.61 

0.49 

0.71 

0.57 

0.81 

0.66 

0.93 

0.76 

1.07 

0.87 

1.23 

0.99 

1.41 

1.14 

56 

0.58 

0.48 

0.67 

0.56 

0.77 

0.64 

0.88 

0.73 

1.00 

0.83 

1.14 

0.95 

1.30 

1.08 

58 

0.56 

0.47 

0.64 

0.54 

0.73 

0.62 

0.83 

0.70 

0.94 

0.80 

1.07 

0.90 

1.21 

1.03 

60 

0.53 

0.46 

0.61 

0.53 

0.69 

0.60 

0.78 

0.68 

0.89 

0.77 

1.00 

0.87 

1.13 

0.98 

62 

0.51 

0.45 

0.58 

0.51 

0.66 

0.58 

0.75 

0.66 

0.84 

0,74 

0.94 

0.83 

1.06 

0.94 

64 

0.49 

0.44 

0.56 

0.50 

0.63 

0.57 

0.71 

0.64 

0.80 

0.72 

0.89 

0.80 

1.00 

0.90 

66 

0.48 

0.43 

0.54 

0.49 

0.61 

0.56 

0.68 

0.62 

0.76 

0.70 

0.85 

0.78 

0.95 

0.87 

68 

0.46 

0.43 

0.52 

0.48 

0.59 

0.54 

0.66 

0.61 

0,73 

0.68 

0.81 

0,75 

0.90 

0.84 

70 

0.45 

0.42 

0.50 

0.47 

0.57 

0.53 

0.63 

0.59 

0.70 

0.66 

0.78 

0.73 

0.86 

0.81 

72 

0.43 

0.41 

0.49 

0.47 

0.55 

0.52 

0.61 

0.58 

0.68 

0.64 

0.76 

0.71 

0.82 

0.78 

74 

0.42 

0.41 

0.48 

0.46 

0.53 

0.51 

0.59 

0.57 

0.65 

0.63 

0.72 

0.69 

0.79 

0.76 

76 

0.41 

0.40 

0.46 

0.45 

0.52 

0.50 

0.57 

0.56 

0.63 

0.61 

0.70 

0.67 

0.76 

0.74 

78 

0.40 

0.39 

0.45 

0.44 

0.50 

0.49 

0.56 

0.54 

0,61 

0.60 

0.67 

0.66 

0.74 

0.72 

80 

0.39 

0.39 

0.44 

0.44 

0.49 

0.48 

0.54 

0.53 

0.60 

0.59 

0.65 

0.64 

0.71 

0.70 

82 

0.39 

0.38 

0.43 

0.43 

0.48 

0.47 

0.53 

0.52 

0,58 

0,57 

0.63 

0,63 

0.69 

0.69 

84 

0.38 

0.38 

0.42 

0.42 

0.47 

0.47 

0.52 

0.51 

0.57 

0,56 

0.62 

0,61 

0.67 

0.67 

86 

0.37 

0.37 

0.42 

0.42 

0.46 

0.46 

0.51 

0.51 

0.55 

0.55 

0.60 

0,60 

0.66 

0.65 

88 

0.37 

0.37 

0.41 

0.41 

0.45 

0.45 

0.50 

0.50 

0.54 

0.54 

0.59 

0,59 

0.64 

0.64 

90 

0.36 

0.36 

0.40 

0.40 

0.45 

0.45 

0.49 

0.49 

0.53 

0.53 

0.58 

0.58 

0.62 

0.62 

92 

0.36 

0.36 

0.40 

0.40 

0.44 

0.44 

0.48 

0.48 

0.52 

0.52 

0.57 

0.57 

0.61 

0.61 

94 

0.36 

0.35 

0.39 

0.39 

0.43 

0.43 

0.47 

0.47 

0.51 

0.51 

0.56 

0.55 

0.60 

0.60 

96 

0.35 

0.35 

0.39 

0.39 

0.43 

0.43 

0.47 

0.46 

0.51 

0.50 

0.55 

0.54 

0.59 

0.59 

98 

0.35 

0.35 

0.39 

0.38 

0.42 

0.42 

0.46 

0.46 

0,50 

0.50 

0.54 

0.53 

0.58 

0.57 

100 

0.35 

0.34 

0.38 

0.38 

0.42 

0.41 

0.46 

0.45 

0,49 

0.49 

0.53 

0.52 

0.57 

0.56 

102 

0.35 

0.34 

0.38 

0.37 

0.42 

0.41 

0.45 

0.44 

0.49 

0.48 

0.53 

0.51 

0.56 

0.55 

104 

0.34 

0.33 

0.38 

0.37 

0.41 

0.40 

0.45 

0.43 

0.48 

0.47 

0.52 

0.50 

0.56 

0.54 

106 

0.34 

0.33 

0.38 

0.36 

0.41 

0.39 

0.45 

0.43 

0.48 

0.46 

0.52 

0.50 

0.55 

0.53 

108 

0.34 

0.32 

0.38 

0.36 

0.41 

0.39 

0.44 

0.42 

0.48 

0.45 

0.51 

0.49 

0.55 

0.52 

110 

0.34 

0.32 

0.37 

0.35 

0.41 

0.38 

0.44 

0.41 

0.47 

0.44 

0.51 

0.48 

0.54 

0,51 

112 

0.34 

0.32 

0.37 

0.35 

0.41 

0.38 

0.44 

0.41 

0,47 

0.44 

0.50 

0.47- 

0.54 

0,50 

114 

0.34 

0.31 

0.37 

0.34 

0.41 

0.37 

0.44 

0.40 

0,47 

0.43 

0:50 

0.46 

0.54 

0.49 

116 

0.34 

0.31 

0.38 

0.34 

0.41 

0.37 

0.44 

0.39 

0,47 

0.42 

0.50 

0.45 

0.53 

0.48 

118 

0.35 

0.31 

0.38 

0.33 

0.41 

0.36 

0.44 

0.39 

0.47 

0.41 

0.50 

0.44 

0.53 

0.47 

120 

0.35 

0.30 

0.38 

0.33 

0.41 

0.36 

0.44 

0.38 

0.47 

0.41 

0.50 

0.43 

0.53 

0,46 

122 

0.  35 

0.30 

0.38 

0.32 

0.41 

0.35 

0.44 

0.37 

0,47 

0,40 

0.50 

0.42 

0.53 

0,45 

124 

0.35 

0.29 

0.38 

0.32 

0.41 

0.34 

0.44 

0.37 

0.47 

0.39 

0.50 

0.42 

0.53 

0.44 

126 

0.36 

0.29 

0.39 

0.31 

0.42 

0.34 

0.45 

0.36 

0.47 

0.38 

0.50 

0,41 

0.53 

0.43 

128 

0.36 

0.28 

0.39 

0.31 

0.42 

0.33 

0.45 

0,35 

0.48 

0.38 

0.50 

0,40 

0.53 

0.42 

130 

0.36 

0.28 

0.39 

0.30 

0.42 

0.32 

0.45 

0.35 

0.48 

0.37 

0.51 

0.39 

0.54 

0.41 

132 

0.37 

0.27 

0.40 

0.30 

0,43 

0.32 

0.46 

0.34 

0.48 

0.36 

0.51 

0.38 

0.54 

0.40 

134 

0.37 

0.27 

0.40 

0.29 

0.43 

0.31 

0.46 

0.33 

0.49 

0.35 

0.52 

0.37 

0.54 

0.39 

136 

0.38 

0.26 

0.41 

0.28 

0.44 

0.30 

0.47 

0.32 

0.49 

0.34 

0.52 

0.36 

0.55 

0.38 

138 

0.39 

0.26 

0.42 

0.28 

0.45 

0.30 

0.47 

0.32 

0.50- 

0.  33 

0.53 

0.35 

0.55 

0.37 

140 

0.39 

0.25 

0.42 

0.27 

0.45 

0.29 

0.48 

0.31 

0.51 

0.  33 

0.53 

0.34 

0.56 

0.36 

142 

0.40 

0.25 

0.43 

0.27 

0.46 

0.28 

0.49 

0.30 

0.51 

0.32 

0.54 

0.33 

0.56 

0.35 

144 

0.41 

0.24 

0.44 

0.26 

0.47 

0.28 

0.50 

0.29 

0.52 

0.31 

0.55 

0.32 

0.57 

0.34 

146 

0.42 

0.24 

0.45 

0.25 

0.48 

0.27 

0.51 

0.28 

0.53 

0.30 

0.56 

0.31 

0.58 

0,32 

148 

0.43 

0  23 

0.46 

0.25 

0.49 

0.26 

0.52 

0.27 

0.54 

0.29 

0.57 

0,30 

0.59 

0.31 

150 

0.45 

0.22 

0.48 

0.24 

0.50 

0.25 

0.53 

0.26 

0.55 

0.28 

0.58 

0,29 

0.60 

0.30 

152 

0.46 

0.22 

0.49 

0.23 

0.52 

0.24 

0.54 

0.25 

0.57 

0.27 

0.59 

0,28 

0.61 

0.29 

154 

0.48 

0.21 

0.50 

0.22 

0.53 

0.23 

0.56 

0.24 

0.58 

0.25 

0.60 

0  26 

0.  62 

0.27 

156 

0.49 

0.20 

0.52 

0.21 

0.55 

0.22 

0.57 

0.23 

0.60 

0.24 

0.62 

0  25 

0.64 

0.26 

158 

0.51 

0.19 

0.54 

0.20 

0.57 

0.21 

0.59 

0.22 

0.61 

0.23 

0.63 

0.24 

0.66 

0.25 

160 

0.53 

0.18 

0.56 

0.19 

0.59 

0.20 

0.61 

0.21 

0.63 

0,22 

0.65 

0.22 

0.67 

0.23 

1    Page  472] 

TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 
between 
the  cours* 
and  secoiu 
bearing. 

Difference  between  the  course  and  first  bearing. 

a:° 

Z6° 

i> 

8° 

40° 

42° 

44° 

46° 

44° 

3.22 

i 
2.24 

46 

2.69^  1.93 

3.39 

2.43 

48 

2.31  1  1.72 

2.83 

2.10 

3.55 

2.63 

50 

2.  03  i  1. 55 

2.43 

1.86 

2.96 

2.27 

.3.70 

2.84 

52 

1.81  !  1.43 

2.13 

1.68 

2.54 

2.01 

3.09 

2.44 

3.85 

3.04 

54 

1.63|  1.32 

1.90 

1.54 

2.23 

1.81 

2.66 

2.15 

3.22 

2.60 

4.00 

3.24 

56 

1.49  1  1.24 

1.72 

1.42 

1.99 

1.65 

2.  .33 

1.93 

2.77 

2: 29 

3.34 

2.77 

4.14 

3.43 

58 

1.37 

1.17 

1.57 

1.33 

1.80 

1.53 

2.08 

1.76 

2.43 

2.06 

2.87 

2.44 

3.46 

2.93 

60 

1.28 

1.10 

1.45 

1.25 

1.64 

1.42 

1.88 

1.63 

2.17 

1.88 

2.52 

2.18 

2.97 

2.57 

62 

1.19 

1.05 

1.34 

1.18 

1.51 

1.34 

1.72 

1.52 

1.96 

1.73 

2.25 

1.98 

2.61 

2.30 

64 

1.12 

1.01 

1.25 

1.13 

1.40 

1.26 

1.58 

1.42 

1.79 

1.61 

2.03 

1.83 

2.33 

2.09 

66 

1.06 

0.96 

1.18 

1.07 

1.31 

1.20 

1.47 

1.34 

1.65 

1.51 

1.85 

1.69 

2.10 

1.92 

68 

1.00 

0.93 

1.11 

1.03 

1.23 

1.14 

1.37 

1.27 

1.53 

1.42 

1.71 

1.58 

1.92 

1.78 

70 

0.95 

0.89 

1.05 

0.99 

1.16 

1.09 

1.29 

1.21 

1.43 

1.34 

1.58 

1.49 

1.77 

1.66 

72 

0.91 

0.86 

1.00 

0.95 

1.10 

1.05 

1.21 

1.15 

1.34 

1.27 

1.48 

1.41 

1.64 

1.56 

74 

0.87 

0.84 

0.95 

0.92 

1.05 

1.01 

1.15 

1.10 

1.26 

1.21 

1.39 

1.34 

1.53 

1.47 

76 

0.84 

0.81 

0.91 

0.89 

1.00 

0.97 

1.09 

1.06 

1.20 

1.16 

1.31 

1.27 

1.44 

1.40 

78 

0.80 

0.79 

0.88 

0.86 

0.96 

0.94 

1.04 

1.02 

1.14 

1.11 

1.24 

1.22 

1.36 

1.33 

80 

0.78 

0.77 

0.85 

0.83 

0.92 

0.91 

1.00 

0.98 

1.09 

1.07 

1.18 

1.16 

1.28 

1.27 

82 

0.75 

0.75 

0.82 

0.81 

0.89 

0.88 

0.96 

0.95 

1.04 

1.03 

1.13 

1.12 

1.22 

1.21 

84 

0.73 

0.73 

0.79 

0.79 

0.86 

0.85 

0.93 

0.92 

1.00 

0.99 

1.08 

1.07 

1.17 

1.16 

86 

0.71 

0.71 

0.77 

0.77 

0.83 

0.83 

0.89 

0.89 

0.96 

0.96 

1.04 

1.04 

1.12 

1.12 

88 

0.69 

0.69 

0.75 

0.75 

0.80 

0.80 

0.86 

0.86 

0.93 

0.93 

1.00 

1.00 

1.08 

1.07 

90 

0.67 

0.67 

0.73 

0.73 

0.78 

0.78 

0.84 

0.84 

0.90 

0.90 

0.97 

0.97 

1.04 

1.04 

92 

0.66 

0.66 

0.71 

0.71 

0.76 

0.76 

0.82 

0.82 

0.87 

0.87 

0.93 

0.93 

1.00 

1.00 

94 

0.65 

0.64 

0.69 

0.69 

0.74 

0.74 

0.79 

0.79 

0.85 

0.85 

0.91 

0.90 

0.97 

0.97 

96 

0.63 

0.63 

0.68 

0.67 

0.73 

0.72 

0.78 

0.77 

0.83 

0.82 

0.88 

0.88 

0.94 

0.93 

98 

0.62 

0.62 

0.67 

0.66 

0.71 

0.70 

0.76 

0.75 

0.81 

0.80 

0.86 

0.85 

0.91 

0.90 

100 

0.61 

0.60 

0.65 

0.64 

0.70 

0.69 

0.74 

0.73 

0.79 

0.78 

0.84 

0.83 

0.89 

0.88 

102 

0. 60  '  0.  59 

0.64 

0.63 

0.68 

0.67 

0.73 

0.71 

0.77 

0.76 

0.82 

0.80 

0.87 

0.85 

104 

0.  60    0.  58 

0.63 

0.61 

0.67 

0.65 

0.72 

0.69 

0.76 

0.74 

0.80 

0.78 

0.85 

0.82 

106 

0.  59  1  0.  57 

0.63 

0.60 

0.66 

0.64 

0.70 

0.68 

0.74 

0.72 

0.79 

0.76 

0.83 

0.80 

108 

0. 58  '  0.  55 

0.62 

0.59 

0.66 

0.62 

0.69 

0.66 

0.73 

0.70 

0.77 

0.74 

0.81 

0.77 

110 

0. 58  1  0.  54 

0.61 

0.57 

0.65 

0.61 

0.68 

0.64 

0.72 

0.68 

0.76 

0.71 

0.80 

0.75 

112 

0. 57  1  0. 53 

0.61 

0.56 

0.64 

0.59 

0.-68 

0.63 

0.71 

0.66 

0.75 

0.69 

0.79 

0.73 

114 

0. 57  i  0.  52 

0.60 

0.55 

0.63 

0.58 

0.67 

0.61 

0.70 

0.64 

0.74 

0.68 

0.78 

0.71 

116 

0.  56  1  0.  51 

0.60 

0.54 

0.63 

0.57 

0.66 

0.60 

0.70 

0.63 

0.73 

0.66 

0.77 

0.69 

118 

0. 56  1  0.  50 

0.59 

0.52 

0.63 

0.55 

0.66 

0.58 

0.69 

0.61 

0.72 

0.64 

0.76 

0.67 

120 

0. 56  I  0.  49 

0.59 

0.51 

0.62 

0.54 

0.65 

0.57 

0.68 

0.59 

0.72 

0.62 

0.75 

0.65 

122 

0.56 

0.47 

0.59 

0.50 

0.62 

0.53 

0.65 

0.55 

0.68 

0.58 

0.71 

0.60 

0.74 

0.63 

124 

0.56 

0.46 

0.59 

0.49 

0.62 

0.51 

0.65 

0.54 

0.68 

0.56 

0.71 

0.58 

0.74 

0.61 

126 

0.  56    0. 45 

0.59 

0.48 

0.62 

0.50 

0.64 

0.52 

0.67 

0.54 

0.70 

0.57 

0.73 

0.59 

128 

0.56 

0.44 

0.59 

0.46 

0.62 

0.49 

0.64 

0.51 

0.67 

0.53 

0.70 

0.55 

0.73 

0.57 

130 

0.56 

0.43 

0.59 

0.45 

0.62 

0.47 

0.64 

0.49 

0.67 

0.51 

0.70 

0.53 

0.72 

0.55 

132 

0.56 

0.42 

0.59 

0.44 

0.62 

0.46 

0.64 

0.48 

0.67 

0.50 

0.70 

0.52 

0.72 

0.54 

134 

0.57 

0.41 

0.59 

0.43 

0.62 

0.45 

0.64 

0.46 

0.67 

0.48 

0.69 

0.50 

0.72 

0.52 

136 

0.57 

0.40 

0.60 

0.41 

0.62 

0.43 

0.65 

0.45 

0.67 

0.47 

0.70 

0.48 

0.72 

0.50 

138 

0. 58  :  0.  39 

0.60 

0.40 

0.63 

0.42 

0.65 

0.43 

0.67 

0.45 

0.70 

0.47 

0.72 

0.48 

140 

0.  58    0.  37 

0.61 

0.39 

0.63 

0.40 

0.65 

0.42 

0.68 

0.43 

0.70 

0.45 

0.72 

0.46 

142 

0.  59    0.  36 

0.61 

0.38 

0.63 

0.39 

0.66 

0.41 

0.68 

0.42 

0.70 

0.43 

0.72 

0.45 

144 

0.  60    0.  35 

0.62 

0.36 

0.64 

0.38 

0.66 

0.39 

0.68 

0.40 

0.71 

0.41 

0.73 

0.43 

146 

0.60 

0.34 

0.63 

0.35 

0.65 

0.36 

0.67 

0.37 

0.69 

0..39 

0.71 

0.40 

0.73 

0.41 

148 

0.61 

0.32 

0.63 

0.34 

0.66 

0..35 

0.68 

0.36 

0.70 

0.37 

0.72 

0.38 

0.74 

0.39' 

150 

0.62 

0.31 

0.64 

0.32 

0.66 

0.33 

0.68 

0.34 

0.70 

0.35 

0.72 

0.36 

0.74 

0.37 

152 

0.63 

0.30 

0.65 

0.31 

0.67 

0.32 

0.69 

0.33 

0.71 

0.33 

0.73 

0.34 

0.75 

0.35 

154 

0.65 

0.28 

0.67 

0.29 

0.68 

0.30 

0.70 

0.31 

0.72 

0.32 

0.74 

0.32 

0.76 

0.33 

156 

0.66 

0.27 

0.68 

0.28 

0.70 

0.28 

0.72 

0.29 

0.73 

0.30 

0.75 

0.30 

0.77 

0.31 

158 

0.67 

0.25 

0.69 

0.26 

0.71 

0.27 

0.73 

0.27 

0.74 

0.28 

0.76 

0.28 

0.78 

0.29 

160 

0.69 

0.24 

0.71 

0.24 

0.73 

0.25 

0.74 

0.25 

0.76 

0.26 

0.77 

0.26 

0.79 

0.27 

TABLE  5B. 

[Page  473    | 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

Difference  between  the  course  and  first  bearing. 

between 
the  course 
and  second 

bearing. 

48° 

50° 

5 

2° 

54° 

56° 

58° 

60° 

58° 

4.28 

3.63 

60 

3.57 

3.10 

4.41 

3.82 

62 

3.07 

2.71 

3.68 

3.25 

4.54 

4.01 

64 

2.70 

2.42 

3.17 

2.85 

3.79 

3.41 

4.66 

4.19 

66 

2.40 

2.20 

2.78 

2.54 

3.26 

2.98 

3.89 

3.55 

4.77 

4.36 

68 

2.17 

2.01 

2.48 

2.30 

2.86 

2.65 

3.34 

3.10 

3.99 

3.71 

4.88 

4.53 

70 

1.98 

1.86 

2.24 

2.10 

2.55 

2.39 

2.94 

2.76 

3.43 

3.22 

4.08 

3.83 

4.99 

4.69 

>72 

1.83 

1.74 

2.04 

1.94 

2.30 

2.19 

2.62 

2.49 

3.01 

2.86 

3.51 

3.33 

4.17 

3.96 

74 

1.70 

1.63 

1.88 

1.81 

2.10 

2.02 

2.37 

2.27 

2.68 

2.58 

3.08 

2.96 

3.58 

3.44 

76 

1.58 

1.54 

1.75 

1.70 

1.94 

1.88 

2.16 

2.10 

2.42 

2.35 

2.74 

2.66 

3.14 

3.05 

78 

1.49 

1.45 

1.63 

1.60 

1.80 

1.76 

1.99 

1.95 

2.21 

2.16 

2.48 

2.43 

2.80 

2.74 

80 

1.40 

1.38 

1.53 

1.51 

1.68 

1.65 

1.85 

1.82 

2.04 

2.01 

2.26 

2.23 

2.53 

2.49 

82 

1.33 

1.32 

1.45 

1.43 

1.58 

1.56 

1.72 

1.71 

1.89 

1.87 

2.08 

2.06 

2.31 

2.29 

84 

1.26 

1.26 

1.37 

1.36 

1.49 

1.48 

1.62 

1.61 

1.77 

1.76 

1.93 

1.92 

2.13 

2.12 

86 

1.21 

1.20 

1.30 

1..30 

1.41 

1.41 

1.53 

1.52 

1.66 

1.65 

1.81 

1.80 

1.98 

1.97 

88 

1.16 

1.16 

1.24 

1.24 

1.34 

1.34 

1.45 

1.45 

1.56 

1.56 

1.70 

1.70 

1.84 

1.84 

90 

1.11 

1.11 

1.19 

1.19 

1.28 

1.28 

1.38 

1.38 

1.48 

1.48 

1.60 

1.60 

1.73 

1.73 

92 

1.07 

1.07 

1.14 

1.14 

1.23 

1.23 

1.31 

1.31 

1.41 

1.41 

1.52 

1.52 

1.63 

1.63 

94 

1.03 

1.03 

1.10 

1.10 

1.18 

1.17 

1.26 

1.26 

1.35 

1.34 

1.44 

1.44 

1.55 

1.54 

96 

1.00 

0.99 

1.06 

1.06 

1.13 

1.13 

1.21 

1.20 

1.29 

1.28 

1.38 

1.37 

1.47 

1.47 

98 

0.97 

0.96 

1.03 

1.02 

1.10 

1.08 

1.16 

1.15 

1.24 

1.23 

1.32 

1.31 

1.41 

1.39 

100 

0.94 

0.93 

1.00 

0.98 

1.06 

1.04 

1.12 

1.11 

1.19 

1.18 

1.27 

1.25 

1.35 

1.33 

102 

0.92 

0.90 

0.97 

0.95 

1.03 

1.01 

1.09 

1.06 

1.15 

1.13 

1.22 

1.19 

1.29 

1.27 

104 

0.90 

0.87 

0.95 

0.92 

1.00 

0.97 

1.06 

1.02 

1.12 

1.08 

1.18 

1.14 

1.25 

1.21 

106 

0.88 

0.84 

0.92 

0.89 

0.97 

0.94 

1.03 

0.99 

1.09 

1.04 

1.14 

1.10 

1.20 

1.16 

108 

0.86 

0.82 

0.90 

0.86 

0.95 

0.90 

1.00 

0.95 

1.05 

1.00 

1.11 

1.05 

1.17 

1.11 

110 

0.84 

0.79 

0.88 

0.83 

0.93 

0.87 

0.98 

0.92 

1.02 

0.96 

1.08 

1.01 

1.13 

1.06 

112 

0.83 

0.77 

0.87 

0.80 

0.91 

0.84 

0.95 

0.88 

1.00 

0.93 

1.05 

0.97 

1.10 

1.02 

114 

0.81 

0.74 

0.85 

0.78 

0.89 

0.82 

0.93 

0.85 

0.98 

0.89 

1.02 

0.93 

1.07 

0.98 

116 

0.80 

0.72 

0.84 

0.75 

0.88 

0.79 

0.92 

0.82 

0.96 

0.85 

1.00 

0.90 

1.04 

0.94 

118 

0.79 

0.70 

0.83 

0.73 

0.86 

0.76 

0.90 

0.79 

0.94 

0.83 

0.98 

0.86 

1.02 

0.90 

J  20 

0.78 

0.68 

0.82 

0.71 

0.85 

0.74 

0.89 

0.77 

0.91 

0.80 

0.96 

0.83 

1.00 

0.87 

122 

0.77 

0.66 

0.81 

0.68 

0.84 

0.71 

0.87 

0.74 

0.90 

0.77 

0.95 

0.80 

0.98 

0.83 

124 

0.77 

0.63 

0.80 

0.66 

0.83 

0.69 

0.86 

0.71 

0.90 

0.74 

0.93 

0.77 

0.96 

0.80 

126 

0.76 

0.61 

0.79 

0.64 

0.82 

0.66 

0.85 

0.69 

0.88 

0.71 

0.91 

0.74 

0.95 

0.77 

128 

0.75 

0.59 

0.78 

0.62 

0.81 

0.64 

0.84 

0.66 

0.87 

0.69 

0.90 

0.71 

0.93 

0.74 

130 

0.75 

0.57 

0.78 

0.60 

0.81 

0.62 

0.83 

0.64 

0.86 

0.66 

0.89 

0.68 

0.92 

0.71 

132 

0.75 

0.56 

0.77 

0.57 

0.80 

0.59 

0.83 

0.61 

0.85 

0.64 

0.88 

0.66 

0.91 

0.68 

134 

0.74 

0.54 

0.77 

0.55 

0.80 

0.57 

0.82 

0.59 

0.85 

0.61 

0.87 

0.63 

0.90 

0.65 

136 

0.74 

0.52 

0.77 

0.53 

0.80 

0.55 

0.82 

0.57 

0.84 

0.58 

0.87 

0.60 

0.89 

0.62 

138 

0.74 

0.50 

0.77 

0.51 

0.79 

0.53 

0.81 

0.54 

0.84 

0.56 

0.86 

0.58 

0.89 

0.59 

140 

0.74 

0.48 

0.77 

0.49 

0.79 

0.51 

0.81 

0.52 

0.83 

0.54 

0.86 

0.55 

0.88 

0.57 

142 

0.74 

0.46 

0.77 

0.47 

0.79 

0.49 

0.81 

0.50 

0.83 

0.51 

0.85 

0.52 

0.87 

0.54 

144 

0.75 

0.44 

0.77 

0.45 

0.79 

0.46 

0.81 

0.48 

0.83 

0.49 

0.85 

0.50 

0.87 

0.51 

146 

0.75 

0.42 

0.77 

0.43 

0.79 

0.44 

0.81 

0.45 

0.83 

0.46 

0.85 

0.47 

0.87 

0.49 

148 

0.76 

0.40 

0.77 

0.41 

0.79 

0.42 

0.81 

0.43 

•0.83 

0.44 

0.85 

0.45 

0.87 

0.46 

150 

0.76 

0.38 

0.78 

0.39 

0.80 

0.40 

0.81 

0.41 

0.83 

0.42 

0.85 

0.42 

0.87 

0.43 

152 

0.77 

0.36 

0.78 

0.37 

0.80 

0.38 

0.82 

0.38 

0.83 

0.39 

0.85 

0.40 

0.87 

0.41 

154 

0.77 

0.34 

0.79 

0.35 

0.81 

0.35 

0.82 

0.36 

0.84 

0.37 

0.85 

0.37 

0.87 

0.38 

156 

0.78 

0.32 

0.80 

0.32 

0.81 

0.33 

0.83 

0.34 

0.84 

0.34 

0.86 

0.35 

0.87 

0.35 

158 

0.79 

0.30 

0.81 

0.30 

0.82 

0.31 

0.83 

0.31 

0.85 

0.32 

0.86 

0.32 

0.87 

0.33 

160 

0.80 

0.27 

0.82 

0.28 

0.83 

0.28 

0.84 

0.29 

0.85 

0.  29 

0.86 

0.30 

0.88 

0.30 

Page  474]                                            TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

the  course 

Difference  between  the  course  and  first  bearing. 

and  second 
bearing. 

62° 

«4° 

66° 

68° 

70° 

72° 

74° 

76° 

72° 

5.08 

i 
4.84 

\ 

74 

4.25 

4.08 

5.18 

4.98 

76 

3.65 

3.54 

4.32 

4.19 

5.26 

5.10 

78 

3.20 

3.13 

3.72 

3.63 

4.39 

4.30 

5.34 

5.22 

80 

2.86 

2.81 

3.26 

3.21 

3.78 

3.72 

4.46 

4.39 

5.41 

5.33 

82 

2.58 

2.56 

2.91 

2.88 

3.31 

3.28 

3.83 

3.80 

4.52 

4.48 

5.48 

5.  42 

84 

2.36 

2.34 

2.63 

2.61 

2.96 

2.94 

3.36 

3.35 

3.88 

3.86 

4.57 

4.55 

5.54 

5.51 

86 

2.17 

2.17 

2.40 

2.39 

2.67 

2.66 

3.00 

2.99 

3.41 

3.40 

3.  93 

3.92 

4.62 

4.61 

5.59 

5.57 

88 

2.01 

2.01 

2.21 

2.21 

2.44 

2.44 

2.71 

2.71 

3.04 

3.04 

3.45 

3.45 

3.97 

3.97 

4.67 

4.66 

90 

1.88 

1.88 

2.05 

2.05 

2.25 

2.25 

2.48 

2.48 

2.75 

2.75 

3.08 

3.08 

3.49 

3.49 

4.01 

4.01 

92 

1.77 

1.76 

1.91 

1.91 

2.08 

2.08 

2.28 

2.28 

2.51 

2.51 

2.78 

2.78 

3.11 

3.11 

3.52 

3.52 

94 

1.67 

1.66 

1.80 

1.79 

1.95 

1.94 

2.12 

2.11 

2.31 

2.30 

2.54 

2.53 

2.81 

2.80 

3.14 

3.13 

96 

1.58 

1.57 

1.70 

1.69 

1.83 

1.82 

1.97 

1.96 

2.14 

2.13 

2.34 

2.  33 

2.57 

2.55 

2.84 

2.82 

98 

1.50 

1.49 

1.61 

1.59 

1.72 

1.71 

1.85 

1.84 

2.00 

1.98 

2.17 

2.15 

2.36 

2.34 

2.59 

2.56 

100 

1.43 

1.41 

1.53 

1.51 

1.63 

1.61 

1.75 

1.72 

1.88 

1.85 

2.03 

2.00 

2.19 

2.16 

2.39 

2.35 

102 

1.37 

1.34 

1.46 

1.43 

1.55 

1.52 

1.66 

1.62 

1.77 

1.73 

1.90 

1.86 

2.05 

2.00 

2.21 

2.16 

104 

1.32 

1.28 

1.40 

1.36 

1.48 

1.44 

1.58 

1.53 

1.68 

1.63 

L79 

1.74 

1.92 

1.87 

2.07 

2.01 

106 

1.27 

1.22 

1.34 

1.29 

1.42 

1.37 

1.51 

1.45 

1.60 

1.54 

1.70 

1.63 

1.81 

1.74 

1.94 

1.87 

108 

1.23 

1.17 

1.29 

1.23 

1.37 

1.30 

1.44 

1.37 

1.53 

1.45 

1.62 

1.54 

1.72 

1.63 

1.83 

1.74 

110 

1.19 

1.12 

1.25 

1.17 

1.32 

1.24 

1.39 

1.30 

1.46 

1.37 

1.54 

1.45 

1.64 

1.54 

1.74 

1.63 

112 

1.15 

1.07 

1.21 

1.12 

1.27 

1.18 

1.33 

1.24 

1.40 

1.30 

1.48 

1.37 

1.56 

1.45 

1.65 

1.53 

114 

1.12 

1.02 

1.17 

1.07 

1.23 

1.12 

1.29 

1.18 

1.35 

1.24 

1.42 

1.30 

1.50 

1.37 

1.58 

1.44 

116 

1.09 

0.98 

1.14 

1.03 

1.19 

1.07 

1.25 

1.12 

1.31 

1.17 

1.37 

1.23 

1.44 

1.29 

1.51 

1.36 

118 

1.07 

0.94 

1.11 

0.98 

1.16 

1.02 

1.21 

1.07 

1.26 

1.12 

1.32 

1.17 

1.38 

1.22 

1.45 

1.28 

120 

1.04 

0.90 

1.08 

0.94 

1.13 

0.98 

1.18 

1.02 

1.23 

1.06 

1.28 

1.11 

1.34 

1.16 

1.40 

1.21 

122 

1.02 

0.86 

1.06 

0.90 

1.10 

0.93 

1.15 

0.97 

1.19 

1.01 

1.24 

1.05 

1.29 

1.10 

1.35 

1.14 

124 

1.00 

0.83 

1.04 

0.86 

1.08 

0.89 

1.12 

0.93 

1.16 

0.96 

1.21 

1.00 

1.25 

1.04 

1.31 

1.08 

126 

0.98 

0.79 

1.02 

0.82 

1.05 

0.85 

1.09 

0.88 

1.13 

0.92 

1.18 

0.95 

1.22 

0.99 

1.27 

1.02 

128 

0.97 

0.76 

1.00 

0.79 

1.03 

0.82 

1.07 

0.84 

1.11 

0.87 

1.  lo 

0.90 

1.19 

0.94 

1.23 

0.97 

130 

0.95 

0.73 

0.98 

0.75 

1.02 

0.78 

1.05 

0.80 

1.09 

0.83 

1.12 

0.  86 

1.16 

0.89 

1.20 

0.92 

132 

0.94 

0.70 

0.97 

0.72 

1.00 

0.74 

1.03 

0.77 

1.06 

0.79 

1.10 

0.82 

1.13 

0.84 

1.17 

0.87 

134 

0.93 

0.67 

0.96 

0.69 

0.99 

0.71 

1.01 

0.73 

1.04 

0.75 

1.08 

0.77 

1.11 

0.80 

1.14 

0.82 

136 

0.92 

0.64 

0.95 

0.  66 

0.97 

0.68 

1.00 

0.69 

1.03 

0.71 

1.  06 

0.74 

1.09 

0.  76 

1.12 

0.78 

138 

0.91 

0.61 

0.94 

0.63 

0.96 

0.64 

0.99 

0.66 

1.01 

0.68 

1.04 

0.70 

1.07 

0.72 

1.10 

0.74 

140 

0.90 

0.58 

0.93 

0.60 

0.95 

0.61 

0.97 

0.63 

1.00 

0.64 

1 .  03 

0.66 

1.05 

0.68 

1.08 

0.70 

142 

0.90 

0.55 

0.92 

0.57 

0.94 

0.58 

0.96 

0.59 

0.99 

0.61 

1.01 

0.62 

1.04 

0.64 

1.06 

0.65 

144 

0.89 

0.52 

0.91 

0.54 

0.93 

0.55 

0.96 

0.56 

0.98 

0.57 

1.00 

0.59 

1.02 

0.60 

1.05 

0.  62 

146 

0.89 

0.50 

0.91 

0.51 

0.93 

0.52 

0.95 

0.53 

0.97 

0.54 

0.99 

0.55 

1.01 

0.57 

1.03 

0.58 

148 

0.89 

0.47 

0.90 

0.48 

0.92 

0.49 

0.94 

0.50 

0.96 

0.51 

0.98 

0.52 

1.00 

0.53 

1.02 

0.54 

150 

0.88 

0.44 

0.90 

0.45 

0.92 

0.46 

0.94 

0.47 

0.95 

0.48 

0.97 

0.49 

0.99 

0.50 

1.01 

0.50 

152 

0.88 

0.41 

0.90 

0.42 

0.92 

0.43 

0.93 

0.44 

0.95 

0.45 

0.97 

0.45 

0.98 

0.46 

1.00 

0.47 

154 

0.88 

0.39 

0.90 

0.39 

0.91 

0.40 

0.93 

0.41 

0.94 

0.41 

0.96 

0.42 

0.98 

0.  43 

0.99 

0.43 

156 

0.89 

0.36 

0.90 

0.37 

0.91 

0.87 

0.93 

0.38 

0.94 

0.38 

0.96 

0.39 

0.97 

0.  39 

0.99 

0.40 

158 

0.89 

0.33 

0.90 

0.34 

0.91 

0.34 

0.93 

0.35 

0.94 

0.  35 

0.95 

0.  36 

0.97 

0.  36 

0.98 

0.37 

160 

0.89 

0.30 

0.90 

0.31 

0.91 

0.31 

0.93 

0.32 

0.94 

0.32 

0.95 

0.33 

0.96 

0.33 

0.98 

0.33 

TABLE  5B.                                           [Page 

475 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

Difference  between  the  course  and  first  bearing. 

between 

the  course 

and  second 

bearing. 

78° 

80° 

82° 

84° 

86° 

88° 

90° 

92° 

88° 

5.63 

5.63 

90 

4.70 

4.70 

5.67 

5.67 

92 

4.04 

4.04 

4.74 

4.73 

5.70 

5.70 

94 

3.55 

3.54 

4.07 

4.06 

4.76 

4.75 

5.73 

5.71 

96 

3.17 

3.15 

3.57 

3.55 

4.09 

4.07 

4.78 

4.76 

5.74 

5.71 

98 

2.86 

2.83 

3.19 

3.16 

3.59 

3.56 

4.11 

4.07 

4.80 

4.75 

5.76 

5.70 

100 

2.61 

2.57 

2.88 

2.84 

3.20 

3.16 

3.61 

3.55 

4.12 

4.06 

4.81 

4.73 

5.76 

5.67 

102 

2.40 

2.35 

2.63 

2.57 

2.90 

2.83 

3.22 

3.15 

3.62 

3.54 

4.13 

4.04 

4.81 

4.70 

5.76 

5.63 

104 

2.23 

2.16 

2.42 

2.35 

2.64 

2.56 

2.91 

2.82 

3.23 

3.13 

3.63 

3.52 

4.13 

4.01 

4.81 

4.66 

106 

2.08 

2.00 

2.25 

2.16 

2.43 

2.34 

2.65 

2.55 

2.92 

2.80 

3.23 

3.11 

3.63 

3.49 

4.13 

3.97 

108 

1.96 

1.86 

2.10 

2.00 

2.26 

2.15 

2.45 

2.33 

2.66 

2.53 

2.92 

2.78 

3.24 

3.08 

3.63 

3.45 

110 

1.85 

1.73 

1.97 

1.85 

2.11 

1.98 

2.27 

2.13 

2.45 

2.31 

2.67 

2.51 

2.92 

2.75 

3.23 

3.04 

112 

1.75 

1.62 

1.86 

1.72 

1.98 

1.83 

2.12 

1.96 

2.28 

2.11 

2.46 

2.28 

2.67 

2.48 

2.92 

2.71 

114 

1.66 

1.52 

1.76 

1.61 

1.87 

1.71 

1.99 

1.82 

2.12 

1.94 

2.28 

2.08 

2.46 

2.25 

2.67 

2.44 

116 

1.59 

1.43 

1.68 

1.51 

1.77 

1.59 

1.88 

1.69 

2.00 

1.79 

2.13 

1.91 

2.28 

2.05 

2.46 

2.21 

118 

1.52 

1.34 

1.60 

1.41 

1.68 

1.49 

1.78 

1.57 

1.88 

1.66 

2.00 

1.76 

2.13 

1.88 

2.28 

2.01 

120 

1.46 

1.27 

1.53 

1.33 

1.61 

1.39 

1.69 

1.47 

1.78 

1.54 

1.89 

1.63 

2.00 

1.73 

2.13 

1.84 

122 

1.41 

1.19 

1.47 

1.25 

1.54 

1.31 

1.62 

1.37 

1.70 

1.44 

1.79 

1.52 

1.89 

1.60 

2.00 

1.70 

124 

1.36 

1.13 

1.42 

1.18 

1.48 

1.23 

1.55 

1.28 

1.62 

1.34 

1.70 

1.41 

1.79 

1.48 

1.89 

1.56 

126 

1.32 

1.06 

1.37 

1.11 

1.43 

1.15 

1.48 

1.20 

1.55 

1.26 

1.62 

1.31 

1.70 

1.38 

1.79 

1.45 

128 

1.28 

1.01 

1.33 

1.04 

1.38 

1.08 

1.43 

1.13 

1.49 

1.17 

1.55 

1.23 

1.62 

1.28 

1.70 

1.34 

130 

1.24 

0.95 

1.29 

0.98 

1.33 

1.02 

1.38 

1.06 

1.44 

1.10 

1.49 

1.14 

1.56 

1.19 

1.62 

1.24 

132 

1.21 

0.90 

1.25 

0.93 

1.29 

0.96 

1.34 

0.99 

1.39 

1.03 

1.44 

1.07 

1.49 

1.11 

1.55 

1.16 

134 

1.18 

0.85 

1.22 

0.88 

1.26 

0.90 

1.30 

0.93 

1.34 

0.97 

1.39 

1.00 

1.44 

1.04 

1.49 

1.07 

136 

1.15 

0.80 

1.19 

0.83 

1.22 

0.85 

1.26 

0.88 

1.30 

0.90 

1.34 

0.93 

1.39 

0.97 

1.44 

1.00 

138 

1.13 

0.76 

1.16 

0.78 

1.19 

0.80 

1.23 

0.82 

1.27 

0.85 

1.30 

0.87 

1.35 

0.90 

1.39 

0.93 

140 

1.11 

0.71 

1.14 

0.73 

1.17 

0.75 

1.20 

0.77 

1.23 

0.79 

1.27 

0.82 

1.31 

0.84 

1.34 

0.86 

142 

1.09 

0.67 

1.12 

0.69 

1.14 

0.70 

1.17 

0.72 

1.20 

0.74 

1.24 

0.76 

1.27 

0.78 

1.30 

0.80 

144 

1.07 

0.63 

1.10 

0.64 

1.12 

0.66 

1.15 

0.67 

1.18 

0.69 

1.21 

0.71 

1.24 

0.73 

1.27 

0.75 

146 

1.05 

0.59 

1.08 

0.60 

1.10 

0.62 

1.13 

0.63 

1.15 

0.64 

1.18 

0.66 

1.21 

0.67 

1.24 

0.69 

148 

1.04 

0.55 

1.06 

0.56 

1.08 

0.57 

1.11 

0.59 

1.13 

0.60 

1.15 

0.61 

1.18 

0.62 

1.21 

0.64 

150 

1.03 

0.51 

1.05 

0.52 

1.07 

0.53 

1.09 

0.54 

1.11 

0.55 

1.13 

0.57 

1.15 

0.58 

1.18 

0.59 

152 

1.02 

0.48 

1.04 

0.49 

1.05 

0.49 

1.07 

0.50 

1.09 

0.51 

1.11 

0.52 

1.13 

0.53 

1.15 

0.54 

154 

1.01 

0.44 

1.02 

0.45 

1.04 

0.46 

1.06 

0.46 

1.08 

0.47 

1.09 

0.48 

1.11 

0.49 

1.13 

0.50 

156 

1.00 

0.41 

1.01 

0.41 

1.03 

0.42 

1.05 

0.43 

1.06 

0.43 

1.08 

0.44 

1.09 

0.45 

1.11 

0.45 

158 

0.99 

0.37 

1.01 

0.38 

1.02 

0.38 

1.03 

0.39 

1.05 

0.39 

1.06 

0.40 

1.08 

0.40 

1.09 

0.41 

160 

0.99 

0.34 

1.00 

0.34 

1.01 

0.35 

1.02 

0.35 

1.04 

0.35 

1.05 

0.36 

1.06 

0.36 

1.08 

0.37 

94° 

96° 

98° 

100° 

102° 

104° 

106° 

108°         1 

104° 

5.74 

5.57 

106 

4.80 

4.61 

5.78 

5.51 

108 

4.12 

3.92 

4.78 

4.55 

5,70 

5.42 

110 

3.62 

3.40 

4.11 

3.86 

4.76 

4.48 

5.67 

5.33 

112 

3.23 

2.99 

3.61 

3.35 

4.09 

3.80 

4.74 

4.40 

5.63 

5.22 

114 

2.92 

2.66 

3.22 

2.94 

3.59 

3.28 

4.07 

3.72 

4.70 

4.30 

5.59 

5.10 

116 

2.66 

2.39 

2.91 

2.61 

3.20 

2.88 

3.57 

3.21 

4.04 

3.63 

4.67 

4.19 

5.54 

4.98 

118 

2.45 

2.17 

2.65 

2.34 

2.90 

2.56 

3.19 

2.81 

3.55 

3.13 

4.01 

3.54 

4.62 

4.08 

5.48 

4.84 

120 

2.28 

1.97 

2.45 

2.12 

2.64 

2.29 

2.88 

2.49 

3.17 

2.74 

3.52 

3.05 

3.  97  !  3.  44 

4.57 

3.96 

122 

2.12 

1.80 

2.27 

1.92 

2.43 

2.06 

2.63 

2.23 

2.86 

2.43 

3.14 

2.66 

3.  49  1  2.  96 

3.93 

3.33 

124 

2.00 

1.65 

2.12 

1.76 

2.26 

1.87 

2.  42  i  2.  01 

2.61 

2.16 

2.84 

2.35 

3.11 

2.58 

3.45 

2.86 

126 

1.88 

1.52 

1.99 

1.61 

2.11 

1.71 

2.25 

1.82 

2.40 

1.95 

2.59 

2.10 

2.81 

2.27 

3.08 

2.49 

128 

1.78 

1.41 

1.88 

1.48 

1.98 

1.56 

2.10 

1.65 

2.23 

1.76 

2.39 

1.88 

2.57 

2.02 

2.78 

2.19 

130 

1.70 

1.30 

1.78 

1.36 

1.87 

1.43 

1.97 

1.51 

2.08 

1.60 

2.21 

1.70 

2.36 

1.81 

2.54 

1.94 

132 

1.62 

1.20 

1.69 

1.26 

1.77 

1.32 

1.86 

1.38 

1.96 

1.45 

2.07 

1.54 

2.19 

1.63 

2.34 

1.74 

134 

1.55 

1.12 

1.62 

1.16 

1.68 

1.21 

1.76 

1.27 

1.85 

1.33 

1.94 

1.40 

2.05 

1.47 

2.17 

1.56 

136 

1.49 

1.04 

1.55 

1.07 

1.61 

1.12 

1.68   1.16 

1.75 

1.22 

1.83 

1.27 

1.92 

1.34 

2.03 

1.41 

138 

1.44 

0.96 

1.49 

0.99 

1.54 

1.03 

1.60 

1.07 

1.66 

1.11 

1.74 

1.16 

1.81 

1.21 

1.90 

1.27 

140 

1.39 

0.89 

1.43 

0.92 

1.48 

0.95 

1.53 

0.98 

1.59 

1.02 

1.65 

1.06 

1.72 

1.10 

1.79 

1.15 

142 

1.34 

0.83 

1.38 

0.85 

1.43 

0.88 

1.47 

0.91 

1.52 

0.94 

1.58 

0.97 

1.64 

1.01 

1.70 

1.05 

144 

1.30 

0.77 

1.34 

0.79 

1.38 

0.81 

1.42 

0.83 

1.46 

0.86 

1.51 

0.89 

1.56 

0.92 

1.62 

0.95 

146 

1.27 

0.71 

1.30 

0.73 

1.33 

0.75 

1.37 

0.77 

1.41 

0.79 

1.45 

0.81 

1.50 

0.84 

1.54 

0.86 

148 

1.23 

0.65 

1.26 

0.67 

1.29 

0.69 

1.33 

0.70 

1.36 

0.72 

1.40 

0.74 

1.44 

0.76 

1.48 

0.78 

150 

1.20 

0.60 

1.23 

0.61 

1.  26  '  0.  63 

1.29 

0.64 

1.32 

0.66 

1.35 

0.67 

1.38 

0.69 

1.42 

0.71 

152 

1.18 

0.55 

1.20 

0.56 

1.22 

0.57 

1.  25  !  0.  59 

1.28 

0.60 

1.31 

0.61 

1.34 

0.63 

1.37 

0.64 

154 

1.15 

0.50 

1.17 

0.51 

1.19 

0.52 

1.  22  0.  53 

1.24 

0.54 

1.27 

0.56 

1.29 

0.57 

1.32 

0.58 

156 

1.13 

0.46 

1.15 

0.47 

1.17 

0.47 

1. 19  i  0.  48 

1.21 

0.49 

1.23 

0.50 

1.2510.51 

1.28 

0.52 

158 

1.11 

0.42 

1.13 

0.42 

1.14 

0.43 

1.16 

0.44 

1.18 

0.44 

1.20 

0.45 

1.22 

0.46 

1.24 

0.47 

160 

1.09 

0.37 

1.11 

0.38 

1.12 

0.38 

1.14 

0.39 

1.15 

0.39 

1.17 

0.40 

1.19 

0.41 

1.21, 

0.41 

Page  476J                                          TABLE  5B. 

Distance  of  an  Object  by  Two  Bearings. 

Difference 

between 

the  course 

and  second 

bearing. 

Difference  between  the  course  and  first  bearing. 

110° 

112° 

114° 

116° 

118° 

120° 

122° 

120° 

5.41 

4.69 

1 

' 

122 

4.52 

li 

5.34 

4.53 

124 

3.88 

4.46 

3.70 

15.26 

4.36 

126 

3.41 

2!  76 

3.83 

3.10 

14.39 

3.55 

5.18 

4.19 

128 

3.04 

2.40 

3.36 

2.65 

13.78 

2.98 

4.32 

3.41 

5.08 

4.01 

130 

2.75 

2.10 

3.00 

2.30 

3.31 

2.54 

3.72 

2.85 

4.25 

3.25 

4.99 

3.82 

132 

2.51 

1.86 

2.71 

2.01 

2.96 

2.20 

3.26 

2.42 

3.65 

2.71 

4.17 

3.10 

4.88 

3.63 

134 

2.31 

1.66 

2.48 

1.78 

2.67 

1.92 

2.91 

2.09 

3.20 

2.30 

3.58 

2.57 

4.08 

2.93 

136 

2.14 

1.49 

2.28 

1.58 

2.44 

1.69 

2.63 

1.83 

2.86 

1.98 

3.14 

2.18 

3.51 

2.44 

138 

2.00 

1.34 

2.12 

1.42 

2.25 

1.50 

2.40 

1.61 

2.58 

1.73 

2.80 

1.88 

3.08 

2.06 

140 

1.88 

1.21 

1.97 

1.27 

2.08 

1.34 

2.21 

1.42 

2.36 

1.52 

2.53 

1.63 

2.74 

1.76 

142 

1.77 

1.09 

1.85 

h  14 

1.95 

1.20 

2.05 

1.26 

2.17 

1.34 

2.31 

1.42 

2.48 

1.53 

144 

1.68 

0.99 

1.75 

1.03 

1.83 

1.07 

1.91 

1.13 

2.01 

1.18 

2.13 

1.25 

2.26 

1.33 

146 

1.60 

0.89 

1.66 

0.93 

1.72 

0.96 

1.80 

1.01 

1.88 

1.05 

1.98 

1.10 

2.08 

1.17 

148 

1.53 

0.81 

1.58 

0.84 

1.63 

0.87 

1.70 

0.90 

1.77 

0.94 

1.84 

0.98 

1.93 

1.03 

150 

1.46 

0.73 

1.51 

0.75 

1.55 

0.78 

1.61 

0.80 

.  1.  67 

0.83 

1.73 

0.87 

1.81 

0.90 

152 

1.40 

0.66 

1.44 

0.68 

1.48 

0.70 

1.53 

0.72 

1.58 

0.74 

1.63 

0.77 

1.70 

0.80 

154 

1.35 

0.59 

1.39 

0.61 

1.42 

0.62 

1.46 

0.64 

1.50 

0.66 

1.55 

0.68 

1.60 

0.70 

156 

1.31 

0.53 

1.33 

0.54 

1.37 

0.56 

1.40 

0.57 

1.43 

0.58 

1.47 

0.60 

1.52 

0.62 

158 

1.26 

0.47 

1.29 

0.48 

1.32 

0.49 

1.34 

0.50 

1.37 

0.51 

1.41  1  0.53 

1.44 

0.54 

160 

1.23 

0.42 

1.25 

0.43 

1.27 

0.43 

1.29 

0.44 

1.  32 

0.45 

1.35  1  0.46 

1.38 

0.47 

124° 

126° 

128° 

130° 

132° 

134° 

136°            1 

134° 

4.77 

3.43 

136 

3.99 

2.77 

4.66 

3.23 

138 

3.43 

2.29 

3.89 

2.60 

4.54 

3.04 

140 

3.01 

1.93 

3.34 

2.15 

3.79 

2.44 

4.41 

2.84 

142 

2.68 

1.65 

2.94 

1.81 

3.26 

2.01 

3.68 

2.27 

4.28 

2.63 

144 

2.42 

1.42 

2.62 

1.54 

2.86 

1.68 

3.17 

1.86 

3.57 

2.10 

4.14 

2.43 

146 

2.21 

1.24 

2.37 

1.32 

2.55 

1.43 

2.78 

1.55 

3.07 

1.72 

3.46 

1.93 

4.00 

2.24 

148 

2.04 

1.08 

2.16 

1.14 

2.30 

1.22 

2.48 

1.31 

2.70 

1.43 

2.97 

1.58 

3.34 

1.77 

150 

1.89 

0.95 

1.99 

0.99 

2.10 

1.05 

2.24 

1.12 

2.40 

1.20 

2.61 

1.30 

2.87 

1.44 

152 

1.77 

0.83 

1.85 

0.87 

1.94 

0.91 

2.04 

0.96 

2.17 

1.02 

2.33 

1.09 

2.52 

1.18 

154 

1.66 

0.73 

1.72 

0.76 

1.80 

0.79 

1.88 

0.83 

1.98 

0.87 

2.10 

0.92 

2.25 

0.99 

156 

1.56 

0.64 

1.62 

0.66 

1.68 

0.68 

1.75 

0.71 

1.83 

0.74 

1.92 

0.78 

2.03 

0.83 

158 

1.48 

0.56 

1.53 

0.57 

1.58 

0.59 

1.63 

0.61 

1.70 

0.64 

1.77 

0.66 

1.85 

0.69 

160 

1.41 

0.48 

1.45 

0.49 

1.49 

0.51 

1.53 

0.52 

1.58 

0.54 

1.64 

0.56 

1.71 

0.58 

138° 

140°         ;           142° 

144°           1            14«° 

148° 

150°            1 

148° 

3.85 

2.04 

150 

3.22 

1.61 

3.70 

1.85 

152 

2.77 

1.30 

3.09 

1.45 

3.55     1.66 

154 

2.43 

1.06 

2.66 

1.16 

2. 96  ;  1.  30 

3.38 

1.48 

156 

2.17 

0.88 

2.33 

0.95 

2.  54  :  1. 04 

2.83 

1.15 

3.22 

1.31 

158 

1.96 

0.73 

2.08 

0.78 

2.23    0.84 

2.43 

0.91 

2.69 

1.01 

3.05 

1.14 

160 

1.79 

0.61 

1.88 

0.64 

1.99    0.68 

2.13 

0.73 

2.31 

0.79 

2.55 

0.87 

2.88      0.98    1 

TABLE 

6. 

[Page  477 

Distance  of  Visibility  of  Objects  at  Sea. 

Height, 

Nautical 

statute 

Height, 

Nautical 

Statute 

Height, 

Nautical 

statute 

feet. 

miles. 

miles. 

feet. 

miles. 

miles. 

feet. 

miles. 

miles. 

1 

1.1 

1.3 

100 

11.5 

13.2 

760 

31.6 

36.4 

2 

1.7 

1.9 

105 

11.7 

13.5 

780 

32.0 

36.9 

3 

2.0 

2.3 

110 

12.0 

13.8 

800 

32.4 

37.3 

4 

2.3 

2.6 

115 

12.3 

14.1 

820 

32.8 

37.8 

5 

2.5 

2.9 

120 

12.6 

14.5 

840 

33.2 

38.3 

6 

2.8 

3.2 

125 

12.9 

14.8 

860 

33.6 

38.7 

7 

2.9 

3.5 

130 

13.1 

15.1 

880 

34.0 

39.2 

8 

3.1 

3.7 

135 

13.3 

15.3 

900 

34.4 

39.6 

9 

3.5 

4.0 

140 

13.6 

15.6 

920 

34.7 

40.0 

10 

3.6 

4.2 

145 

13.8 

15.9 

940 

35.2 

40.5 

11 

3.8 

4.4 

150 

14.1 

16.2 

960 

35.5 

40.9 

12 

4.0 

4.6 

160 

14.5 

16.7 

980 

35.9 

41.3 

13 

4.2 

4.8 

170 

14.9 

17.2 

1,000 

36.2 

41.7 

14 

4.3 

4.9 

180 

15.4 

17.7 

1,100 

38.0 

4.3.8 

15 

4.4 

5.1 

190 

15.8 

18.2 

1,200 

39.6 

45.6 

16 

4.6 

5.3 

200 

16.2 

18.7 

1,300 

41.3 

47.6 

17 

4.7 

5.4 

210 

16.6 

19.1 

1,400 

42.9 

49.4 

18 

4.9 

5.6 

220 

17.0 

19.6 

1,500 

44.4 

51.1 

19 

5.0 

5.8 

230 

17.4 

20.0 

1,600 

45.8 

52.8 

20 

5.1 

5.9 

240 

17.7 

20.4 

1,700 

47.2 

54.4 

21 

5.3 

6.1 

250 

18.2 

20.9 

1,800 

48.6 

56.0 

22 

5.4 

6.2 

260 

18.5 

21.3 

1,900 

49.9 

57.5 

23 

5.5 

6.3 

270 

18.9 

21.7 

2,000 

51.2 

59.0 

24 

5.6 

6.5 

280 

19.2 

22.1 

2, 100 

52.5 

60.5 

25 

5.7 

6.6 

290 

19.6 

22.5 

2,200 

53.8 

61.9 

26 

5.8 

6.7 

300 

19.9 

22.9 

2,300 

55.0 

63.3 

27 

6.0 

6.9 

310 

20.1 

23.2 

2,400 

56.2 

64.7 

28 

6.1 

7.0 

320 

20.5 

23.6 

2,500 

57.3 

66.0 

29 

6.2 

7.1 

330 

20.8 

24.0 

2,600 

58.5 

67.3 

30 

6.3 

7.2 

340 

21.1 

24.3 

2,700 

59.6 

68.6 

31 

6.4 

7.3 

350 

21.5 

24.7 

2,800 

60.6 

69.8 

32 

6.5 

7.5 

360 

21.7 

25.0 

2,900 

61.8 

71.1 

33 

6.6 

7.6 

370 

22.1 

25.4 

3,000 

62.8 

72.3 

34 

6.7 

7.7 

380 

22.3 

25.7 

3,100 

63.8 

73.5 

35 

6.8 

7.8 

390 

22.7 

26.1 

3,200 

64.9 

74.7 

36 

6.9 

7.9 

400 

22.9 

26.4 

3,300 

65.9 

75.9 

37 

6.9 

8.0 

410 

23.2 

26.7 

3,400 

66.9 

77.0 

38 

7.0 

8.1 

420 

23.5 

27.1 

3,500 

67.  8 

78.1 

39 

7.1 

8.2 

430 

23.8 

27.4 

3,600 

68.  8 

79.2 

40 

7.2 

8.3 

440 

24.1 

27.7 

3,700 

69.7 

80.3 

41 

7.3 

8.4 

450 

24.3 

28.0 

3, 800 

70.7 

81.4 

42 

7.4 

8.5 

460 

24.6 

28.3 

3,900 

71.6 

82.4 

43 

7.5 

8.7 

470 

24.8 

28.6 

4,000 

72.5 

83.5 

44 

7.6 

8.8 

480 

25.1 

28.9 

4,100 

73.4 

84.5 

45 

7.7 

8.9 

490 

25.4 

29.2 

4,200 

74.3 

85.6 

46 

7.8 

9.0 

500 

25.6 

29.5 

4,300 

75.2 

86.6 

47 

7.9 

9.0 

520 

26.1 

30.1 

4,400 

76.1 

87.6 

48 

7.9 

9.1 

540 

26.7 

30.7 

4, 500 

76.9 

88.5 

49 

8.0 

9.2 

560 

27.1 

31.2 

4,600 

77.7 

89.5 

50 

8.1 

9.3 

580 

27.6 

31.8 

4,700 

78.6 

90.5 

55 

8.5 

9.8 

600 

28.0 

32.3 

4,800 

79.4 

91.4 

60 

8.9 

10.2 

620 

'28.6 

32.9 

4,900 

80.2 

92.4 

65 

9.2 

10.6 

640 

29.0 

33.4 

5,000 

81.0 

93.3 

70 

9.6 

11.0 

660 

29.4 

33.9 

6,000 

88.8 

102.2 

75 

9.9 

11.4 

680 

29.9 

34.4 

7,000 

96.0 

110.5 

80 

10.3 

11.8 

700 

30.3 

34.9 

8,000 

102.6 

118.1 

85 

10.6 

12.2 

720 

30.7 

35.4 

9,000 

108.  7 

125.2 

90 

10.9 

12.5 

740 

31.1 

35.9 

10,000 

114.6 

132.0 

95 

11.2 

12.9 

Page  478] 

TABLE  7 

For  converting  Arc  into  Time, 

and  the  reverse. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

o 

H.  M. 

' 

M.  S. 

/ 

M.  S. 

' 

M.  S. 

' 

M.  S. 

' 

M.  S. 

/ 

M.  S. 

II 

s.  ^ 

" 

s.  A 

II 

s.  A 

" 

8.  A 

" 

s.  A 

II 

S.  rfB 

1 

0  4 

61 

4  4 

121 

8  4 

181 

12  4 

241 

16  4 

301 

20  4 

2 

0  8 

62 

4  8 

122 

8  8 

182 

12  8 

242 

16  8 

302 

20  8 

3 

0  12 

h, 

4  12 

123 

8  12 

183 

12  12 

243 

16  12 

303 

20  12 

4 

0  16 

64 

4  16 

124 

8  16 

184 

12  16 

244 

16  16 

304 

20  16 

5 

0  20 

65 

4  20 

125 

8  20 

185 

12  20 

245 

16  20 

305 

20  20 

6 

0  24 

66 

4  24 

126 

8  24 

186 

12  24 

246 

16  24 

306 

20  24 

7 

0  28 

67 

4  28 

127 

8  28 

187 

12  28 

247 

16  28 

307 

20  28 

8 

0  32 

68 

4  32 

128 

8  32 

188 

12  32 

248 

16  32 

308 

20  32 

9 

0  36 

69 

4  36 

129 

8  36 

189 

12  36 

249 

16  36 

309 

20  36 

10 

0  40 

70 

4  40 

130 

8  40 

190 

12  40 

250 

16  40 

310 

20  40 

11 

0  44 

71 

4  44 

131 

8  44 

191 

12  44 

251 

16  44 

311 

20  44 

12 

0  48 

72 

4  48 

132 

8  48 

192 

12  48 

252 

16  48 

312 

20  48 

13 

0  52 

73 

4  52 

133 

8  52 

193 

12  52 

253 

16  52 

313 

20  52 

14 

0  56 

74 

4  56 

134 

8  56 

194 

12  56 

254 

16  56 

314 

20  56 

15 

1  0 

75 

5  0 

135 

9  0 

195 

13  0 

255 

17  0 

315 

21  0 

16 

1  4 

76 

5  4 

136 

9  4 

196 

13  4 

256 

17  4 

316 

21  4 

17 

1  8 

77 

5  8 

137 

9  8 

197 

13  8 

257 

17  8 

317 

21  8 

18 

1  12 

78 

5  12 

138 

9  12 

198 

13  12 

258 

17  12 

318 

21  12 

19 

1  16 

79 

5  16 

139 

9  16 

199 

13  16 

259 

17  16 

319 

21  16 

20 

1  20 

80 

5  20 

140 

9  20 

200 

13  20 

260 

17  20 

320 

21  20 

21 

1  24 

81 

5  24 

141 

9  24 

201 

13  24 

261 

17  24 

321 

21  24 

22 

1  28 

82 

5  28 

142 

9  28 

202 

13  28 

262 

17  28 

322 

21  28 

23 

1  32 

83 

5  32 

143 

9  32 

203 

13  32 

263 

17  32 

323 

21  32 

24 

1  36 

84 

5  36 

144 

9  36 

204 

13  36 

264 

17  36 

324 

21  36 

25 

1  40 

85 

5  40 

145 

9  40 

205 

13  40 

265 

17  40 

325 

21  40 

26 

1  44 

86 

5  44 

146 

9  44 

206 

13  44 

266 

17  44 

326 

21  44 

27 

1  48 

87 

5  48 

147 

9  48 

207 

13  48 

267 

17  48 

327 

21  48 

28 

1  52 

88 

5  52 

148 

9  52 

208 

13  52 

268 

17  52 

328 

21  52 

29 

1  56 

89 

5  56 

149 

9  56 

209 

13  56 

269 

17  56 

329 

21  56 

30 

2  0 

90 

6  0 

150 

10  0 

210 

14  0 

270 

18  0 

330 

22  0 

31 

2  4 

91 

6  4 

151 

10  4 

211 

14  4 

271 

18  4 

331 

22  4 

32 

2  8 

92 

6  8 

152 

aO  8 

212 

14  8 

272 

18  8 

332 

22  8 

33 

2  12 

93 

6  12 

153 

10  12 

213 

14  12 

273 

18  12 

333 

22  12 

34 

2  16 

94 

6  16 

154 

10  16 

214 

14  16 

274 

18  16 

334 

22  16 

35 

2  20 

95 

6  20 

155 

10  20 

215 

14  20 

275 

18  20 

335 

22  20 

36 

2  24 

96 

6  24 

156 

10  24 

216 

14  24 

276 

18  24 

336 

22  24 

37 

2  28 

97 

6  28 

157 

10  28 

217 

14  28 

277 

18  28 

337 

22  28 

38 

2  32 

98 

6  32 

158 

10  32 

218 

14  32 

278 

18  32 

338 

22  32 

39 

2  36 

99 

6  36 

159 

10  36 

219 

14  36 

279 

18  36 

339 

22  36 

40 

2  40 

100 

6  40 

160 

10  40 

220 
221 

14  40 
14  44 

280 

18  40 

340 

22  40 

41 

2  44 

101 

6  44 

161 

10  44 

281 

18  44 

341 

22  44 

42 

2  48 

102 

6  48 

162 

10  48 

222 

14  48 

282 

18  48 

342 

22  48 

43 

2  52 

103 

6  52 

163 

10  52 

223 

14  52 

283 

18  52 

343 

22  52 

44 

2  56 

104 

6  56 

164 

10  56 

224 

14  56 

284 

18  56 

344 

22  56 

45 

3  0 

105 

7  0 

165 

11  0 

225 

15  0 

285 

19  0 

345 

23  0 

46 

3  4 

106 

7  4 

166 

11  4 

226 

15  4 

286 

19  4 

346 

23  4 

47 

3  8 

107 

7  8 

167 

11  8 

227 

15  8 

287 

19  8 

347 

23  8 

48 

3  12 

108 

7  12 

168 

11  12 

228 

15  12 

288 

19  12 

348 

23  12 

49 

3  16 

109 

7  16 

169 

11  16 

229 

15  16 

289 

19  16 

349 

23  16 

50 
51 

3  20 

110 

7  20 

170 

11  20 

230 

15  20 

290 

19  20 

350 

23  20 

3  24 

111 

7  24 

171 

11  24 

231 

15  24 

291 

19  24 

351 

23  24 

52 

3  28 

112 

7  28 

172 

11  28 

232 

15  28 

292 

19  28 

352 

23  28 

53 

3  32 

113 

7  32 

173 

11  32 

233 

15  32 

293 

19  32 

353 

23  32 

54 

3  36 

114 

7  36 

174 

11  36 

234 

15  36 

294 

19  36 

354 

23  36 

55 

3  40 

115 

7  40 

175 

11  40 

235 

15  40 

295 

19  40 

355 

23  40 

56 

3  44 

116 

7  44 

176 

11  44 

236 

15  44 

296 

19  44 

356 

23  44 

57 

3  48 

117 

7  48 

177 

11  48 

237 

15  48 

297 

19  48 

357 

23  48 

58 

3  52 

118 

7  52 

178 

11  52 

238 

15  52 

298 

19  52 

358 

23  52 

59 

3  56 

119 

7  56 

179 

11  56 

239 

15  56 

299 

19  56 

359 

23  56 

60 

4  0 

120 

8  0 

180 

12  0 

240 

16  0 

300 

20  0 

360 

24  0 

Note. — When  turning  seconds  of  arc  into  time,  and  vice  versa,  it  should  be  remembered  that  the  fractions  are  sixtieths; 
thufi,  the  value  in  time  oi  42"  is  not  2^48,  but  2»U=2".8. 


TABLE  8. 

[Page  479 

Sidereal  into  Mean  Solar  Time. 

"3 

To  be  subtracted  from  a  sidereal  time  interval. 

Oh 

Ih 

2. 

Sh 

4h 

oh 

6" 

7" 

For  seconds. 

m. 

in.    8. 

TO.    «. 

m.      «. 

TO.    8. 

TO.    S. 

TO.    8. 

TO. 

8. 

m.   8. 

8. 

8. 

0 

0  0.000 

0  9.830 

0  19.659 

0  29.  489 

0  39. 318 

0  49. 148 

0  58. 977 

1  8. 807 

1 

0  0. 164 

0  9.993 

0  19.823  0  29.653 

0  39.482 

0  49.  312 

0 

59. 141 

1  8. 971 

1 

0.003 

2 

0  0. 328 

0  10.  157 

0  19. 987  0  29.  816  0  39. 646 

0  49. 475 

0  59.  305 

1  9. 135 

2 

.005 

3 

0  0.  491 

0  10.  321 

0  20. 151 

0  29. 980 

0  39. 810 

0  49. 639 

0  59. 469 

1  9. 298 

3 

.008 

4 

0  0.  655 

0  10.485 

0  20.  314 

0  30. 144 

0  39.  974 

0  49.  803 

0 
0 

59.  633 

1  9.462 

4 

.011 

5 

0  0.  819 

0  10.649 

0  20.  478 

0  30. 308 

0  40. 137 

0  49. 967 

59.  796 

1  9.626 

5 

.014 

6 

0  0.  983 

0  10.  813 

0  20. 642 

0  30.  472 

0  40.  301 

0  50. 131 

0  59. 960 

1  9.790 

6 

.016 

7 

0  1. 147 

0  10.976 

0  20.  806 

0  30. 635 

0  40. 465 

0  50.  295 

0.124 

1  9. 954 

7 

.019 

8 

0  1.311 

0  11. 140 

0  20.  970 

0  30. 799 

0  40.  629 

0  50.  458 

0.288 

1  10.118 

8 

.022 

9 
10 

0  1.474 

0  11. 304 

0  21. 134 

0  30.  963 

0  40.  793 

0  50. 622 

0.452 

1  10.281 

9 

.025 

0  1.638 

0  11.468 

0  21. 297 

0  31. 127 

0  40.  956 

0  50.  786 

0.616 

1  10.445 

10 

.027 

11 

0  1.802 

0  11.  632 

0  21.461  i  0  31.291 

0  41. 120 

0  50. 950 

0.779 

1  10.609 

11 

.030 

12 

0  1.966 

0  11.  795 

0  21. 625  0  31. 455 

0  41.  284 

0  51. 114 

0.943 

1  10.773 

12 

.033 

13 

0  2. 130 

0  11.959 

0  21.789  1  0  31.618 

0  41.  448 

0  51.  278 

1.107 

1  10.  937 

13 

.035 

14 

0  2.  294 

0  12. 123 

0  21. 953  0  31.  782 

0  41.612 

0  51.441 

1.271 

1  11.100 

14 

.038 

15 

0  2. 457 

0  12.  287 

0  22. 117  1  0  31. 946 

0  41. 776 

0  51.  605 

1.435 

1  11.264 

15 

.041 

16 

0  2.  621 

0  12.  451 

0  22.  280  0  32. 110  0  41.  939 

0  51.  769 

1.599 

1  11.428 

16 

.044 

17 

0  2.  785 

0  12.  615 

0  22. 444  0  32.  274  i  0  42. 103 

0  51. 933 

1.762 

1  11.592 

17 

.046 

18 

0  2.  949 

0  12.  778  0  22. 608  0  32.  438  i  0  42.  267 

0  52.  097 

1.926 

1  11.756 

18 

.049 

19 

0  3. 113 

0  12.  942  1  0  22.  772  i  0  32.  601  I  0  42.  431 

0  52.  260 

2.090 

1  11.920 

19 

.052 

20 

0  3.277 

0  13. 106 

0  22.  936  i  0  32.  765 

0  42. 595 

0  52. 424 

2.254 

1  12.083 

20 

.055 

21 

0  3.  440 

0  13. 270 

0  23.  099  i  0  32. 929 

0  42.  759 

0  52. 588 

2.418 

1  12.247 

21 

.057 

22 

0  3. 604 

0  13.434 

0  23.  263  ;  0  33.  093 

0  42.  922 

0  52.  752 

2.582 

1  12.411 

22 

.060 

23 

0  3.  768 

0  13.598 

0  23.  427 

0  33.  257 

0  43. 086 

0  52. 916 

2.745 

1  12.575 

23 

.063 

24 

0  3. 932 

0  13.  761 

0  23.  591 

0  33.  420 

0  43.  250 

0  53. 080 

2.909 

1  12.739 

24 

.066 

25 

0  4. 096 

0  13.925 

0  23.  755 

0  33.  584 

0  43.  414 

0  53. 243 

3.073 

1  12.903 

25 

.068 

26 

0  4. 259 

0  14.089 

0  23. 919 

0  33.  748 

0  43.  578 

0  53. 407 

3.237 

1  13.066 

26 

.071 

27 

0  4. 423 

0  14. 253 

0  24. 082 

0  33.  912 

0  43.  742 

0  53. 571 

3.401 

1  13.230 

27 

.074 

28 

0  4. 587 

0  14.417 

0  24.  246 

0  34.  076 

0  43.905 

0  53. 735 

3.564 

1  13.394 

28 

.076 

29 

0  4.  751 

0  14.581 

0  24.  410 

0  34.  240 

0  44. 069 

0  53.  899 
0  54.  063 

3.728 

1  13.558 

29 

.079 

30 

0  4.915 

0  14.  744 

0  24. 574 

0  34. 403 

0  44.  233 

3.892 

1  13.722 

30 

.082 

31 

0  5. 079 

0  14.908 

0  24.  738 

0  34.  567 

0  44. 397 

0  54.  226 

4.056 

1  13.886 

31 

.085 

32 

0  5. 242 

0  15.072 

0  24.  902 

0  34. 731 

0  44.  561 

0  54.  390 

4.220 

1  14.049 

32 

.087 

33 

0  5. 406 

0  15.236 

0  25.065 

0  34. 895 

0  44.  724 

0  54.  554 

4.384 

1  14.213 

33 

.090 

34 

0  5. 570 

0  15.400 

0  25.  229 

0  35. 059 

0  44.  888 

0  54.  718 

4.547 

1  14.377 

34 
35' 

.093 
.096 

35 

0  5.  734 

0  15. 563 

0  25.  393 

0  35.  223 

0  45.  052 

0  54.  882 

4.711 

1  14.541 

36 

0  5.  898 

0  15.  727 

0  25. 557 

0  35.  386 

0  45.  216 

0  55.  046 

4.875 

1  14.705 

36 

.098 

37 

0  6.062 

0  15. 891 

0  25.  721 

0  35. 550 

0  45.  380 

0  55.  209 

5.039 

1  14.868 

37 

.101 

38 

0  6. 225 

0  16. 055 

0  25.  885 

0  35.  714 

0  45.  544 

0  55.  373 

5.203 

1  15.032 

38 

.104 

39 

0  6.  389 

0  16. 219 
0  16.383 

0  26. 048 

0  35.  878 

0  45.  707 

0  55.  537 

5.367 

1  15.196 

39 

.106 

40 

0  6. 553 

0  26.  212 

0  36. 042 

0  45.  871 

0  55. 701 

5.530 

1  15.360 

40 

.109 

41 

0  6.  717 

0  16.546 

0  26.  376 

0  36.  206 

0  46. 035 

0  55.  865 

5.694 

1  15.524 

41 

.112 

42 

0  6.  881 

0  16.  710 

0  26. 540 

0  36.  369 

0  46. 199 

0  56. 028 

5.858 

1  15.688 

42 

.115 

43 

0  7.045 

0  16. 874 

0  26.  704 

0  36.  533 

0  46.  363 

0  56. 192 

6.022 

1  15.851 

43 

.117 

44 

0  7.  208 

0  17.038 

0  26.  867 

0  36.  697 

0  46.  527 

0  56.  356 

6.186 

1  16.015 

44 

.120 

45 

0  7.372 

0  17.202 

0  27. 031 

0  36. 861 

0  46. 690 

0  56. 520 

6.350 

1  16.179 

45 

.123 

46 

0  7.536 

0  17.366 

0  27. 195 

0  37. 025 

0  46.  854 

0  56. 684 

6.513 

1  16.343 

46 

.126 

47 

0  7.  700 

0  17.  529 

0  27.  359 

0  37. 188 

0  47. 018 

0  56.  848 

6.677 

1  16.507 

47 

.128 

48 

0  7.864 

0  17.693 

0  27.  523 

0  37.  352 

0  47. 182 

0  57.  Oil 

6.841 

1  16.671 

48 

.131 

49 

0  8.  027 

0  17.857 

0  27. 687 

0  37.  516 

0  47.  346 

0  57. 175 

7.005 

1  16.834 

49 

.134 

50 

0  8. 191 

0  18.021 

0  27.  850 

0  37.680 

0  47. 510 

0  57.  339 

7.169 

1  16.998 

50 

.137 

51 

0  8.355 

0  18. 185 

0  28.014 

0  37.  844 

0  47.  673 

0  57.  503 

7.332 

1  17. 162 

51 

.139 

52 

0  8.519 

0  18. 349 

0  28. 178 

0  38. 008 

0  47.  837 

0  57.  667 

7.496 

1  17.326 

52 

.142 

53 

0  8.  683 

0  18. 512 

0  28.  342 

0  38. 171 

0  48. 001 

0  57.  831 

7.660 

1  17.490 

53 

.145 

54 

0  8.  847 

0  18.676 

0  28. 506 

0  38.  335 
0  38.499 

0  48. 165 

0  57.  994 

7.824 

1  17.654 

54 

.147 

55 

0  9. 010 

0  18. 840 

0  28.  670 

0  48.  329 

0  58. 158 

7.988 

1  17.817 

55 

.150 

56 

0  9. 174 

0  19.004 

0  28.  833 

0  38.  663 

0  48.  492 

0  58.  322 

8.152 

1  17.981 

56 

.153 

57 

0  9.  338 

0  19. 168 

0  28. 997 

0  38.  827 

0  48.  656 

0  58. 486 

8.315 

1  18.145 

57 

.156 

58 

0  9. 502 

0  19.  331 

0  29. 161 

0  38. 991 

0  48.  820 

0  58. 650 

8.479 

1  18.309 

58 

.158 

59 

0  9.  666 

0  19. 495 

0  29.  325 

0  39. 154 

0  48.  984 

0  58. 814 

8.643 

1  18.473 

59 

0.161 

Page  480] 

TABLE  8. 

Sidereal  into  Mean  Solar  Time. 

S 

To  be  subtracted  from  a  sidereal  time  interval. 

8h 

flh 

lOi- 

llh 

Igk 

18* 

14h 

IS" 

For  seconds.! 

m. 

VI.        s. 

TO.    S. 

m.      ». 

m.      s. 

TO. 

8. 

VI.          D. 

TO.    «. 

TO.    S. 

s. 

«. 

0 

1  18.636 

1  28.466 

1  38.296 

1  48. 125 

57. 955 

2  7. 784 

2  17. 614 

2  27.443 

1 

1  18.800 

1  28.630 

1  38.459 

1  48.289 

58. 119 

2  7. 948  2  17.  778 

2  27.  607 

1 

0.003 

2 

1  18.964 

1  28.t94 

1  38.623 

1  48.453 

58. 282 

2  8.112  2  17.941 

2  27.  771 

2 

.005 

3 

1  19.128 

1  28.958 

1  38.787 

1  48.617 

58. 446 

2  8.  276  2  18. 105 

2  27.  935 

3 

.008 

4 

1  19.292 

1  29. 121 

1  38.951 

1  48.  780 
1  48.944 

58.  610 
58. 774 

2  8.440  1  2  18.269 
2  8.603  2  18.433 

2  28.  099 
2  28.  263 

4 
5 

.011 
.014 

5 

1  19.456 

1  29.285 

1  39. 115 

6 

1  19.619 

1  29.449 

1  39.279 

1  49. 108 

58. 938 

2  8. 767  2  18. 597 

2  28.  426 

6 

.016 

7 

1  19.783 

1  29.  613 

1  39.442 

1  49.272  !  1 

59. 101 

2  8.931 

2  18.  761 

2  28.  590 

7 

.019 

8 

1  19.947 

1  29.  777 

1  39.606 

1  49.436  1 

59. 265 

2  9.095 

2  18. 924 

2  28. 754 

8 

.022 

9 

1  20.111 

1  29.940 
1  30. 104 

1  39. 770 

1  49.600  1 
1  49.  763  1 

59. 429 
59. 593 

2  9.259  2  19.088 

2  28.  918 

9 

.025 

10:  1  20,275 

1  39.934 

2  9.423  2  19.252 

2  29.  082 

10 

.027 

11  1  20. 439 

1  30.268 

1  40.098 

1  49.927  1 

59. 757 

2  9.586  2  19.416 

2  29. 245 

11 

.030 

12  1  20.602 

1  30.432 

1  40.261 

1  50.091  1 

59. 921 

2  9.750  2  19.580 

2  29. 409 

12 

.033 

13  1  20.  766 

1  30.596 

1  40.425  1  1  50.255  2 

0.084 

2  9. 914  2  19.  744 

2  29. 573 

13 

.035 

14  1  20.930 

1  30.760 

1  40.589  1  1  50.419  2 

0.248 

2  10.078  2  19.907 

2  29.  737 

14 

.038 

15  1  T  21. 094 

1  30.923 

1  40.  753  1  50.  583  2 

0.412 

2  10.  242  t  2  20.  071 

2  29.901 

15 

.041 

16  1  21.258 

1  31.  087 

1  40. 917  1  50.  746  2 

0.576 

2  10. 405  2  20.  235 

2  30.065 

16 

.044 

T7 

i  21.422 

1  31.  251 

1  41.081  1  50.910  2 

0.740 

2  10.  569  2  20.  399 

2  30. 228 

17 

.046 

18 

i  21.585 

1  31.415 

1  41.244  1  51.074  2 

0.904 

2  10.  733  2  20.  563 

2  30. 392  18 

.049 

19  1  21.749 

1  31.579 

1  41.408  1  51.233  2 

1.067 

2  10.  897  i  2  20.  727 
2  11.061  2  20.890 

2  30. 556 

19 

.052 

20  1  21.913 

1  31.  743 

1  41.572  1  51.402  2 

1.231 

2  30. 720 

20 

.055 

21  1  1  22. 077 

1  31.906 

1  41.736  1  51.565  2 

1.  395 

2  11.  225  2  21.  054 

2  30. 884 

21 

.057 

22!  1  22.241 

1  32.  070 

1  41.900  1  51.729  2 

1.559 

2  11. 388  ;  2  21.  218 

2  31.  048 

22 

.060 

23  1  1  22.404 

1  32. 234 

1  42.  064  1  51. 893  2 

1.723 

2  11.552  2  21.382 

2  31.211 

23 

.063 

24  !  1  22.  568 

1  32.398 

1  42.227  1  52.057 

2 
2 

1.887 
2.050 

2  11. 716  2  21.  546 
2  11.  880  2  21.  709 

2  31.  375 
2  31. 539 

24 

.066 

25  i  1  22.  732 

1  32.  562 

1  42.  391   1  52. 221 

25 

.068 

26  1  1  22.  896 

1  32.726 

1  42.  555  1  52.  385  2 

2.214 

2  12.044  2  21.873 

2  31.  703 

26 

.071 

27  1  1  23.  060 

1  32.889 

1  42.  719  1  52.  548  2 

2.378 

2  12.208  2  22.037 

2  31.867 

27 

.074 

28  1  1  23.224 

1  33.053 

1  42. 883  1  52.  712  2 

2.542 

2  12.371  2  22.201 

2  32. 031 

28 

.076 

29 
30 

1  23.387 
1  23.551 

1  33.217 
1  33.381 

1  43.  047  1  52.  876  2 

2.706 

2  12.535 

2  22.  365 

2  32. 194 

29 

.079 

1  43.210  1  53.040  .  2 

2.869 

2  12.699 

2  22.529 

2  32.  358 

30 

.082 

31 

1  23.  715 

1  33.545 

1  43. 374  1  53.  204  2 

3.033 

2  12.863 

2  22.  692 

2  32.  522 

31 

.085 

32 

1  23.879 

1  33.  708 

1  43. 538  :  1  53.  368  2 

3.197 

2  13.  027  i  2  22.  856 

2  32. 686 

32 

.087 

33 

1  24.043 

1  33.872 

1  43. 702  i  1  53. 531  2 

3.361 

2  13. 191  1  2  23.  020 

2  32. 850 

33 

.090 

34 

1  24.207 

1  34.036 

1  43.866 

1  53.695 

2 

3.525 

2  13.354 

2  23. 184 

2  33.013 

34 

.093 

35 

1  24.370 

1  34.200 

1  44.  029 

1  53.859 

2 

3.689 

2  13.518 

2  23.  348 

2  33. 177 

35 

.096 

36 

1  24.  534 

1  34.364 

1  44.193 

1  54.023 

2 

3.  852 

2  13.682 

2  23.512 

2  33.341 

36 

.098 

37 

1  24.698 

1  34.528 

1  44.  357 

1  54. 187  2 

4.016 

2  13.846 

2  23.675 

2  33.505 

37 

.101 

38 

1  24.862 

1  34.691 

1  44.521 

1  54.351  2 

4.180 

2  14.010 

2  23. 839 

2  33.669 

38 

.104 

39 

1  25.026 

1  34.855 

1  44. 685 

1  54.514  2 

4.344 

2  14.173 
2  14.337 

2  24.  003 
2  24. 167 

2  33. 833 

39 

.106 

40 

1  25. 190 

1  35.019 

1  44.849 

1  54.  678  2 

4.508 

2  33. 996 

40 

.109 

41 

1  25.353 

1  35. 183 

1  45.012 

1  54.842 

2 

4.672 

2  14.501 

2  24.  331 

2  34. 160 

41 

.112 

42 

1  25.517 

1  35.347 

1  45.176 

1  55.006 

2 

4.  835 

2  14. 665  !  2  24.  495 

2  34. 324 

42 

.115 

43 

1  25.681 

1  35.511 

1  45.340 

1  55. 170 

2 

4.999 

2  14.  829  i  2  24.  658 

2  .34.  488 

43 

.117 

44 

1  25.845 

1  35.674 

1  45.504 

1  55.333 

2 

5.163 

2  14. 993  i  2  24.  822 

2  34. 652 

44 

.120 

45 

1  26.009 

1  35.838 

1  45.668 

1  55.497 

2 

5.327 

2  15. 156 

2  24.  986 

2  34.  816 

45 

.123 

46 

1  26. 172 

1  36.002 

1  45.832 

1  55.661 

2 

5.491 

2  15. 320 

2  25. 150 

2  34. 979 

46 

.126 

47 

1  26.336 

1  36. 166 

1  45.995 

1  55.825 

2 

5.655 

2  15.484 

2  25. 314 

2  35. 143 

47 

.128 

48 

1  26.500 

1  36.330 

1  46. 159 

1  55.989 

2 

5.818 

2  15.648 

2  25.477 

2  35.  307 

48 

.131 

49 

1  26.664 

1  36.493 

1  46.323 

1  56. 153 

2 

5.982 

2  15.812 

2  25. 641 

2  35.  471 

49 

.134 

50 

1  26.  828 

1  36.657 

1  46.487 

1  56.316 

2 

6.146 

2  15.976 

2  25.  805 

2  35. 635 

50 

.137 

51 

1  26.992 

1  36.821 

1  46.651 

1  56.480 

2 

6.310 

2  16.139  2  25.969 

2  35.  798 

51 

.139 

52 

1  27. 155 

1  36.985 

1  46.815 

1  56.644 

2 

6.474 

2  16.303 

2  26. 133 

2  35.  962 

52 

.142 

53 

1  27.  319 

1  37. 149 

1  46.978 

1  56.808 

2 

6.637 

2  16.467 

2  26. 297 

2  36.126 

53 

.145 

54 

1  27.483 

1  37.313 

1  47.142 

1  56.972 

2 

6.801 

2  16.631 

2  26.460 

2  36. 290 

64 

.147 

55 

1  27.647 

1  37.476 

1  47.306 

1  57.136 

2 

6.965 

2  16.  795 

2  26.  624 

2  36. 454 

55 

.150 

56 

1  27.811 

1  37.  640 

1  47. 470  i  1  57.  299 

2 

7.129 

2  16.959 

2  26.  788 

2  36.618 

56 

.153 

57 

1  27.975 

1  37.804 

1  47.634  1  57.463 

2 

7.293 

2  17. 122 

2  26. 952 

2  36.  781 

57 

.156 

58 

1  28. 138 

1  37.968 

1  47.797  1  57.627 

2 

7.457 

2  17.286 

2  27. 116 

2  36.  945 

58 

.158 

59 

1  28.302 

1  38. 132 

1  47. 961  1  57.  791 

2 

7.620 

2  17.450 

2  27. 280 

2  37. 109 

59 

0.161 

TABLE  8. 

[Page  481 

Sidereal  into  Mean  Solar  Time. 

"3 
2 

"2 

m. 
0 

1 

2 
3 
4 
5 
6 
7 
8 
9 

To  be  subtracted  from  a  sidereal  time  interval. 

m.       s. 
2  37.  273 
2  37.  437 
2  37.  601 
2  37.  764 
2  37.  928 
2  38.  092 
2  38.  256 
2  38. 420 
2  38.  584 
2  38. 747 

17h 

m.   s. 
2  47.  102 
2  47.  266 
2  47.  430 
2  47.  594 
2  47.  758 
2  47.  922 
2  48. 085 
2  48.249 
2  48.  413 
2  48.  577 

181- 

19«> 

ao" 

•21h 

2  SI" 

2S^ 

For  seconds.! 

m.       s. 
2  56.  932 
2  57.  096 
2  57.  260 
2  57.424 
2  57. 587 

m. 
3 
3 
3 
3 
3 

6.762 
6.925 
7.089 
7.253 
7.417 

m.       s. 
3  16.591 
3  16. 755 
3  16.919 
3  17.083 
3  17.246 

m.   8. 
3  26.421 
3  26.  585 
3  26.  748 
3  26.  912 
3  27.  076 

TO.    8. 

3  36. 250 
3  367414 
3  36.  578 
3  36. 742 
3  36.906 

TO.    «. 

3  46. 080 
3  46.  244 
3  46. 407 
3  46. 571 
3  46.  735 

1 
2 

3 
4 

8. 

0. 003 
.005 
.008 
.011 

2  57. 751 
2  57.915 
2  58. 079 
2  58.  243 
2  58.  406 

3 
3 
3 
3 
3 

7.581 
7.745 
7.908 
8.072 
8.236 

3  17.410 
3  17.574 
3  17.  738 
3  17.902 
3  18.066 

3  27.  240 
3  27.404 
3  27.568 
3  27.  731 
3  27.895 

3  37. 069 
3  37.  233 
3  37.397 
3  37.561 
3  37.  725 

3  46. 899 
3  47. 063 
3  47.  227 
3  47.  390 
3  47.  554 

5 
6 
7 
8 
9 

.014 
.016 
.019 
.022 
.025 

10 
11 
12 
13 
14 

2  38. 911 
2  39. 075 
2  39.  239 
2  39.  403 
2  39.  566 

2  48.  741 
2  48.  905 
2  49.  068 
2  49. 232 
2  49.  396 

2  58. 570 
2  58. 734 
2  58.  898 
2  59. 062 
2  59. 226 

3 
3 
3 
3 
3 

8.400 
8.564 
8.728 
8.891 
9.055 

3  18.229 
3  18.393 
3  18.557 
3  18. 721 
3  18.885 

3  28.  059 
3  28. 223 
3  28. 387 
3  28. 550 
3  28.  714 

3  37.  889 
3  38. 052 
3  38.  216 
3  38. 380 
3  38. 544 

3  47.  718 
3  47.  882 
3  48.  046 
3  48. 210 
3  48. 373 

10 
11 
12 
13 
14 

.027 
.030 
.033 
.035 
.038 

15 
16 
17 
18 
19 

2  39. 730 
2  39.894 
2  40. 058 
2  40. 222 
2  40.  386 

2  49.560 
2  49. 724 
2  49. 888 
2  50. 051 
2  50.  215 

2  59.  389 
2  59. 553 
2  59. 717 

2  59.881 

3  0.045 

3 
3 
3 
3 
3 

9.219 
9.383 
9.547 
9.710 
9.874 

3  19.049 
3  19.212 
3  19.  376 
3  19.540 
3  19.  704 

3  28.878 
3  29.042 
3  29.  206 
3  29.  370 
3  29. 533 

3  38.  708 
3  38. 871 
3  39.035 
3  39. 199 
3  39.  363 

3  48. 537 
3  48. 701 
3  48.  865 
3  49. 029 
3  49. 193 

15 
16 
17 
18 
19 

.041 
.044 
.046 
.049 
.052 

20 
21 
22 
23 
24 

2  40.  549 
2  40. 713 
2  40.  877 
2  41.041 
2  41.  205 

2  50.  379 
2  50. 543 
2  50.  707 
2  50. 870 
2  51. 034 

3 
3 
3 
3 
3 

0.209 
0.372 
0.  536 
0.700 
0.864 

3 
3 
3 
3 
3 

10. 038 
10. 202 
10. 366 
10. 530 
10.  693 

3  19.868 
3  20.032 
3  20. 195 
3  20.  359 
3  20. 523 

3  29. 697 
3  29.  861 
3  30.025 
3  30. 189 
3  30.  353 

3  39.527 
3  39. 691 
3  39.  854 
3  40.  018 
3  40. 182 

3  49.  356 
3  49.  520 
3  49.  684 
3  49. 848 
3  50.012 

20 
21 
22 
23 
24 

.055 
.057 
.060 
.063 
.066 

25 

26 
27 

28 
29 

2  41.369 
2  41.532 
2  41.696 
2  41.860 
2  42. 024 

2  51. 198 
2  51.  362 
2  51.526 
2  51. 690 
2  51.853 

3 
3 
3 
3 
3 

1.028 
1.192 
1.  355 
1.519 
1.683 

3 
3 
3 
3 
3 

10.  857 
11. 021 
11. 185 

11.  349 
11.513 

3  20.687 
3  20.  851 
3  21.014 
3  21. 178 
3  21. 342 

3  30.  516 
3  30. 680 
3  30. 844 
3  31.008 
3  31. 172 

3  40.346 
3  40. 510 
3  40. 674 
3  40. 837 
3  41.001 

3  50. 175 
3  50.  339 
3  50. 503 
3  50. 667 
3  50.  831 

25 
26 
27 

28 
29 

.068 
.071 
.074 
.076 
.079 

30 
31 
32 
33 
34 

2  42. 188 
2  42.  352 
2  42.  515 
2  42.  679 
2  42.  843 

2  52.017 
2  52. 181 
2  52. 345 
2  52. 509 
2  52.  673 

3 
3 
3 
3 
3 

1.847 
2.011 
2.174 
2.338 
2.502 

3 
3 
3 
3 
3 

11.676 
11. 840 
12.  004 
12. 168 
12.  332 

3  21.  506 
3  21.  670 
3  21. 834 
3  21.  997 
3  22. 161 

3  31.  336 
3  31.499 
3  31.  663 
3  31.  827 
3  31.991 

3  41. 165 
3  41.  329 
3  41.  493 
3  41. 657 
3  41.  820 

3  50. 995 
3  51. 158 
3  51. 322 
3  51. 486 
3  51.  650 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

.082 
.085 
.087 
.090 
.093 

35 
36 
37 
38 
39 

2  43.  007 
2  43. 171 
2  43.  334 
2  43. 498 
2  43.  662 

2  52.  836 
2  53. 000 
2  53. 164 
2  53.  328 
2  53. 492 

3 
3 
3 
3 
3 

2.666 
2.830 
2.994 
3.  157 
3.321 

3 
3 
3 
3 
3 

12. 496 
12.  659 
12.  823 
12.  987 
13. 151 

3  22.  325 
3  22. 489 
3  22.  653 
3  22.817 
3  22. 980 

3  32. 155 
3  32.  318 
3  32. 482 
3  32.  646 
3  32.  810 

3  41. 984 
3  42. 148 
3  42.  312 
3  42. 476 
3  42.  639 

3  51.814 
3  51.  978 
3  52. 141 
3  52. 305 
3  52.  469 

.096 
.098 
.101 
.104 
.106 

40 
41 
42 
43 
44 

2  43.  826 
2  43.990 
2  44. 154 
2  44. 317 
2  44.  481 

2  53.  656 
2  53.  819 
2  53. 983 
2  54. 147 
2  54.  311 

3 
3 
3 
3 
3 

3.  485 
3.  649 
3.813 
3.977 
4.140 

3 
3 
3 
3 
3 

13.  315 
13. 478 
13.  642 
13. 806 
13.  970 

3  23. 144 
3  23. 308 
3  23. 472 
3  23.636 
3  23. 800 

3  32.974 
3  33. 138 
3  33.  301 
3  33.465 
3  33.  629 

3  42.  803 
3  42. 967 
3  43. 131 
3  43. 295 
3  43.  459 

3  52. 633 
3  52.  797 
3  52.  961 
3  53. 124 
3  53.  288 
3  53. 452 
3  53. 616 
3  53. 780 
3  53. 943 
3  54. 107 

40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

.109 
.112 
.115 
.117 
.120 
.123 
.126 
.128 
.131 
.134 

45 
46 
47 
48 
49 

2  44. 645 
2  44. 809 
2  44. 973 
2  45. 137 
2  45.  300 

2  54.  475 
2  54.  638 
2  54.  802 
2  54.  966 
2  55. 130 

3 
3 
3 
3 
3 

4.304 
4.468 
4.632 
4.796 
4.960 

3 
3 
3 
3 
3 

14. 134 
14.298 
14.461 
14. 625 
14. 789 

3  23.963 
3  24.127 
3  24.  291 
3  24.  455 
3  24.  619 

3  33.  793 
3  33.  957 
3  34. 121 
3  34.  284 
3  34.  448 

3  43.622 
3  43.  786 
3  43. 950 
3  44. 114 
3  44. 278 

50 
51 
52 
53 
54 

2  45.464 
2  45. 628 
2  45. 792 
2  45. 956 
2  46. 120 

2  55. 294 
2  55. 458 
2  55.  621 
2  55. 785 
2  55.949 

3 
3 
3 
3 
3 

5.123 
5.287 
5.451 
5.615 
5.779 

3 
3 
3 
3 
3 
3 
3 
3 
3 
3 

14.  953 
15. 117 
15. 281 

15.  444 
15.608 
15. 772 
15. 936 
16. 100 
16. 264 
16. 427 

3  24.  782 
3  24.946 
3  25.110 
3  25. 274 
3  25. 438 

3  34. 612 
3  34.  776 
3  34.940 
3  35. 104 
3  35. 267 

3  44. 442 
3  44.  605 
3  44.  769 
3  44.  933 
3  45.097 

3  54. 271 
3  54. 435 
3  54. 599 
3  54. 763 
3  54. 926 

50 
51 
52 
53 
54 

.137 
.139 
.142 
.145 
.147 

55 
56 

57 
58 
59 

2  46.283 
2  46. 447 
2  46.  611 
2  46.  755 
2  46.  939 

2  56. 113 
2  56. 277 
2  56.  441 
2  56.  604 
2  56. 768 

3 
3 
3 
3 
3 

5.942 
6.106 
6.270 
6.434 
6.598 

3  25.602 
3  25. 765 
3  25.929 
3  26. 093 
3  26.  257 

3  35.431 
3  35. 595 
3  35.  759 
3  35.  923 
3  36. 086 

3  45. 261 
3  45.  425 

3  45.  588 
3  45. 752 
3  45. 916 

3  55. 090 
3  55. 254 
3  55. 418 
3  55.  582 
3  55. 746 

55 
56 

57 
58 
59 

.150 
.153 
.156 
.158 
0.161 

22489—03- 


-31 


Page  482]                  TABLE  9. 

Mean  Solar  into  Sidereal  Time. 

To  be  added  to  a  mean  time  interval.                            1 

Oh 

Ik 

21.        8" 

4b 

oh 

[«" 

Jh 

For  seconds.  1 

m. 
0 

1 

2 
3 
4 

m. 
0 
0 
0 
0 
0 

0.000 
0.164 
0.  329 
0.493 
0.657 

m.     B. 
0  9.856 
0  10.021 
0  la  185 
0  10.349 
0  10.514 

m.     s. 
0  19. 713 
0  19.877 
0  20. 041 
0  20.  206 
0  20.  370 

m.     s. 
0  29.  569 
0  29.  734 
0  29. 898 
0  30.  062 
0  30.  227 

m.     s. 
0  39. 426 
0  39.590 
0  39.  754 
0  39.919 
0  40.  083 
0  40.  247 
0  40.  412 
0  40. 576 
0  40.  740 
0  40. 904 

in.     s. 
0  49.  282 
0  49.  447 
0  49. 611 
0  49. 775 
0  49. 939 

m.     s. 
0  59. 139 
0  59. 303 
0  59.  467 
0  59. 632 
0  59.  796 

TO.   8. 

1  8.995 
1  9.160 
1  9. 324 
1  9. 488 
1  9. 652 

s. 

1 
2 

.3 
4 

s. 

0.003 
.005 
.008 
.011 

5 
6 

7 
8 
9 

0 
0 
0 
0 
0 

0.821 
0.986 
1.150 
1.314 

1.478 

0  10.678 
0  10.842 
0  11.006 
0  11.171 
0  11.  335 

0  20.  534 
0  20.699 
0  20.  863 
0  21.  027 
0  21. 191 

0  30. 391 
0  30.  555 
0  30.  719 
0  30.  884 
0  31.048 

0  50. 104 
0  50. 268 
0  50. 432 
0  50.  597 
0  50.  761 

0  59. 960 

1  0. 124 
1  0. 289 
1  0. 453 
1  0.617 

1  9. 817 
1  9.981 
1  10.145 
1  10.310 
1  10.474 

5 
6 

7 
8 
9 

.014 
.016 
.019 
.022 
.025 

10 
11 
12 
13 
14 

0 
0 
0 
0 
0 

1.643 
1.807 
1.971 
2.136 
2.300 

0  11.499 
0  11.663 
0  11.828 
0  11.992 
0  12. 156 

0  21.356 
0  21.520 
0  21.  684 
0  21.  849 
0  22.  013 

0  31.212 
0  31. 376 
0  31. 541 
0  3i.  705 
0  31.  869 

0  41.  069 
0  41.  233 
0  41. 397 
0  41:561 
0  41. 726 

0  50. 925 
0  51.089 
0  51. 254 
0  51.418 
0  51. 582 

0.782 
0.946 
1.110 
1.274 
1. 439 

1  10.638 
1  10.802 
1  10.967 
1  11.131 
1  11.295 

10 
11 
12 
13 
14 

.027 
.030 
.033 
.036 
.038 

15 
16 
17 
18 
19 

0 
0 
0 
0 
0 

2.464 
2.628 
2.  793 
2.957 
3.121 

0  12.321 
0  12.485 
0  12. 649 
0  12.813 
0  12. 978 

0  22. 177 
0  22.  341 
0  22.  506 
0  22.  670 
0  22. 834 

0  32. 034 
0  32. 198 
0  32.  362 
0  32.  526 
0  32.  691 

0  41.  890 
0  42.  054 
0  42.  219 
0  42.  383 
0  42. 547 

0  51.  746 
0  51.911 
0  52.  075 
0  52.  239 
0  52. 404 
0  52. 568 
0  52. 732 
0  52.  896 
0  53. 061 
0  53.  225 
0  53.  389 
0  53. 554 
0  53. 718 
0  53.  882 
0  54. 046 

^- 

1.603 
1.767 
1.932 
2.096 
2.260 

1  11.459 
1  11.624 
1  11.788 
1  11.952 
1  12.117 
1  12.281 
1  12.445 
1  12.609 
1  12.774 
1  12.938 
1  13.102 
1  13.266 
1  13.431 
1  13.595 
1  13.759 

15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25" 
26 
27 
28 
29 

.041 
.044 
.047 
.049 
.052 
.6.55 
.057 
.060 
.063 
.066 
.068 
.071 
.074 
.077 
.079 

20 
21 
22 
23 
24 

0 

0 
0 
0 
0 

3.285 
3.450 
3.614 
3.778 
3.943 

0  13. 142 
0  13.306 
0  13.471 
0  13.635 
0  13. 799 

0  22.  998 
0  23. 163 
0  23. 327 
0  23. 491 
0  23. 656 

0  32.  855 
0  33.  019 
0  33. 183 
0  33. 348 
0  33.512 

0  42.  711 
0  42.  876 
0  43. 040 
0  43. 204 
0  43.  368 

2.424 
2.589 
2.753 
2.917 
3.081 

25 
26 

27 
28 
29 

0 
0 
0 
0 
0 

4.107 
4.271 
4.435 
4.600 
4.764 

0  13.963 
0  14. 128 
0  14.292 
0  14.456 
0  14.620 

0  23.  820 
0  23.  984 
0  24. 148 
0  24.  313 
0  24. 477 

0  33.  676 
0  33.  841 
0  34.005 
0  34. 169 
0  34.  333 

0  43.  533 
0  43.  697 
0  43.  861 
0  44.  026 
0  44. 190 

1 

3.246 
3. 410 
3.574 
3.739 
3.903 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

4.928 
5.093 
5.257 
5. 421 
5.585 
5.  750 
5. 914 
6.078 
6.242 
6.407 

0  14.785 
0  14.949 
0  15. 113 
0  15.278 
0  15.442 

0  24. 641 
0  24.  805 
0  24. 970 
0  25. 134 
0  25. 298 

0  34. 498 
0  34.  662 
0  34.  826 
0  34. 990 
0  35. 155 

0  44.  354 
0  44.518 
0  44.  683 
0  44. 847 
0  45.  Oil 
0  45. 176 
0  45. 340 
0  45. 504 
0  45.  668 
0  45. 833 

0  54. 211 
0  54. 375 
0  54.  539 
0  54. 703 
0  54.  868 

-^- 

4.067 
4.231 
4.396 
4.  560 

4.724 

1  13.924 
1  14.088 
1  14.252 
1  14.416 
1  14.581 
1  14.745 
1  14.909 
1  15.073 
1  15.238 
1  15.402 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

.082 
.085 
.088 
.090 
.093 
.096 
.099 
.101 
.104 
.107 

0  15.606 
0  15. 770 
0  15.935 
0  16.099 
0  16.  263 

0  25.463 
0  25.  627 
0  25. 791 
0  25. 955 
0  26. 120 
0  26. 284 
0  26.  448 
0  26.  612 
0  26.  777 
0  26.941 

0  35.  319 
0  35.  483 
0  35.  648 
0  35.  812 
0  35. 976 

0  55.  032 
0  55. 196 
0  55. 361 
0  55. 525 
0  55.  689 

4.888 
5.053 
5.217 
5.381 
5.546 

40 
41 
42 
43 
44 

0 
0 
0 
0 
0 

6.571 
6.735 
6.900 
7.064 

7.228 

0  16.427 
0  16.  592 
0  16.  756 
0  16.920 
0  17. 085 

0  36. 140 
0  36. 305 
0  36.469 
0  36.  633 
0  36. 798 

0  45.  997 
0  46. 161 
0  46.  325 
0  46.  490 
0  46.  654 

0  55.  853 
0  56.  018 
0  56. 182 
0  56.  346 
0  56.  510 

5.710 
5.874 
6.038 
6. 203 
6.367 

1  15.566 
1  15.731 
1  1.5.895 
1  16.059 
1  16.223 

40 
41 
42 
43 
44 

.110 
.112 
.115 
.118 
.120 

45 
46 
47 
48 
49 

0 
0 
0 
0 
0 

7.392 
7.557 
7.721 

7.885 
8.049 

0  17.249 
0  17.413 
0  17.  577 
0  17.  742 
0  17.906 
0  18.070 
0  18. 234 
0  18.399 
0  18.563 
0  18. 727 
0  18.  892 
0  19.056 
0  19.  220 
0  19.  .384 
0  19.549 

0  27. 105 
0  27. 270 
0  27.434 
0  27. 598 
0  27.  762 

0  36.962 
0  37. 126 
0  37. 290 
0  37.  455 
0  37.  619 

0  46.  818 
0  46.  983 
0  47. 147 
0  47.  311 
0  47. 475 

0  56.  675 
0  56. 839 
0  57. 003 
0  57. 168 
0  57. 332 
0  57. 496 
0  57. 660 
0  57. 825 
0  57. 989 
0  58. 153 

6.531 
6.695 
6.860 
7.024 

7.188 

1  16.388 
1  16.552 
1  16.716 
1  16.881 
1  17.045 

45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

.123 
.126 
.129 
.131 
.134 
.137 
.140 
.142 
.145 
.148 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 

0 
0 
0 
0 

0 

8.214 
8.378 
8.542 
8.707 
8.871 

0  27.  927 
0  28.  091 
0  28. 255 
0  28.420 
0  28. 584 
0  28.  748 
0  28. 912 
0  29.077 
0  29.  241 
0  29.  405 

0  37.  783 
0  37.  947 
0  38. 112 
0  .38.  276 
0  38. 440 
0  38.  605 
0  38.  769 
0  .38.  933 
0  39. 097 
0  39. 262 

0  47.  640 
0  47.  804 
0  47.  968 
0  48. 132 
0  48.  297 
0'  48. 461 
0  48. 625 
0  48. 790 
0  48.  954 
0  49. 118 

7.353 
7.517 
7.681 
7.845 
8.010 

1  17.209 
1  17.373 
1  17.538 
1  17.702 
1  17.866 

0 
0 
0 
0 
0 

9.035 
9.199 
9.364 
9.528 
9.692 

0  58.317 
0  58. 482 
0  58. 646 
0  58. 810 
0  58.975 

8.174 
8.338 
8.502 
8.667 
8.  831 

1  18.0.30 
1  18.195 
1  18. 359 
1  18.523 
1  18.688 

55 
56 

57 
58 
59 

.151 
.153 
.156 
.159 
0.162 

TABLE  9. 

[Page  483 

Mean  Solar  into  Sidereal  Time. 

c 
g 
S 

To  be  added  to 

a  mean  time  interval. 

8h 

flh 

lOh 

lli> 

12h 

ISh 

14h 

15'' 

For  seconds.! 

m. 

m.     s. 

m.    8. 

m.      s. 

7/1.    S. 

m. 

s. 

m. 

8. 

m.     s. 

m.     s. 

s. 

s. 

0 

1   18.852 

1  28.708 

1  38.565 

1  48.421 

1 

58. 278 

2 

8.134 

2   17.991 

2  27.  847 

1 

1  19.016 

1  28.873 

1  38. 729 

1  48.585 

1 

58.  442 

2 

8.298 

2  18. 155 

2  28.011 

1 

0.003 

2 

1  19.180 

1  29.037 

1  38.893 

1  48.750 

1 

58. 606 

2 

8.463 

2  18.319 

2  28. 176 

2 

.005 

3 

1  19.345 

1  29.201 

1  39.058 

1  48.914 

1 

58.  771 

2 

8.627 

2  18.483 

2  28.340 

3 

.008 

4 
5 

1  19.509 
1  19.673 

1  29.365 
1  29.530 

1  39.222 
1  39.386 

1  49.078 
1  49.  243 

1 

1 

58. 935 
59.099 

2 
2 

8.791 
8.956 

2  18.648 
2  18.812 

2  28. 504 
2  28.  668 

4 
5 

.011 

.014 

() 

1  19.837 

1  29.694 

1  39.550 

1  49.407 

1 

59. 263 

2 

9.120 

2  18.976 

2  28. 833 

6 

.016 

7 

1  20.002 

1  29.858 

1  39.715 

1  49.571 

1 

59. 428 

2 

9.284 

2  19.141 

2  28.  997 

7 

.019 

8 

1  20.166 

1  30.022 

1  39.879 

1  49. 735 

1 

59. 592 

2 

9.448 

2  19.305 

2  29. 161 

8 

.022 

9 

1  20.330 

1  30. 187 

1  40.043 

1  49.900 

1 

59. 756 

2 

9.613 

2  19.469 

2  29.  326 

9 

.025 

10 

1  20.495 

1  30.351 

1  40.207 

1  50.064 

1 

59. 920 

2 

9.777 

2  19.633 

2  29.  490 

10 

.027 

11 

1  20.659 

1  30.515 

1  40.372 

1  50.  228 

2 

0.085 

2 

9.941 

2  19,798 

2  29.654 

11 

.030 

12 

1  20.823 

1  30.680 

1  40.536 

1  50.  393 

2 

0.249 

2 

10. 105 

2  19.962 

2  29. 818 

12 

.033 

13 

1  20.987 

1  30.844 

1  40.  700 

1  50.557 

2 

0.413 

2 

10.  270 

2  20. 126 

2  29. 983 

13 

.036 

14 

1  21.152 

1  31.008 

1  40.865 
1  41.029 

1  50.721 
1  50.  885 

2 

0.578 
0.742 

2 

10.  434 

2  20. 290 

2  30. 147 

14 

.  038 

15 

1  21.  316 

1  31.172 

2 

10. 598 

2  20.455 

2  30. 311 

15 

.041 

16 

1  21.480 

1  31.337 

1  41. 193 

1  51.050 

2 

0.906 

2   10.763 

2  20. 619 

2  30. 476 

16 

.044 

17 

1  21.644 

1  31.501 

1  41.357 

1  51.214 

2 

1.070 

2 

10.  927 

2  20.  783 

2  30.  640 

17 

.047 

18 

1  21.809 

1  31.665 

1  41.522 

1  51.378 

2 

1.235 

2 

11.091 

2  20.  948 

2  30.  804 

18 

.049 

19 

20 

1  21.973 

1  31.  829 
1  31.994 

1  41.686 

1  51.542 

2 

1.399 

2 

11.255 

2  21.112 

2  30. 968 
2  31. 133 

19 
20 

.052 
.055 

1  22.137 

1  41.  850 

1  51.  707 

2 

1. 563 

2 

11.  420 

2  21.276 

21 

1  22.302 

1  32. 158 

1  42.015 

1  51.871 

2 

1.727 

2 

11.584 

2  21.  440 

2  31. 297 

21 

.057 

22 

1  22.466 

1  32.322 

1  42. 179 

1  52.035 

2 

1.892 

2 

11. 748 

2  21.605 

2  31.461 

22 

.060 

23 

1  22.630 

1  32.487 

1  42.343 

1  52.200 

2 

2.056 

2 

11.912 

2  21.  769 

2  31.625 

23 

.063 

24 
25 

1  22. 794 
1  22.959 

1  32.651 

1  42.  507 
1  42.672 

1  52. 364 

2 

2.220 

2 

12. 077 

2  21. 933 

2  31. 790 

24 
25 

.066 

1  32.815 

1  52.528 

2 

2.385  ;  2 

12. 241 

2  22.  098 

2  31.954 

.068 

2(5 

1  23.123 

1  32.979 

1  42.836 

1  52.692 

2 

2.549  2 

12.  405 

2  22.  262 

2  32. 118 

26 

.071 

27 

1  23.287 

1  33. 144 

1  43.000 

1  52.857 

2 

2. 713  2 

12. 570 

2  22. 426 

2  32. 283 

27 

.074 

28 

1  23.451 

1  33.308 

1  43. 164 

1  53.021 

2 

2.877  '  2 

12.  734 

2  22.590 

2  32.  447 

28 

.077 

29 
30 

1  23.616 

1  33.472 

1  43.329 
1  43.493 

1  53. 185 

2 

3.042  ,  2 

12.  898 

2  22. 755 

2  32. 611 

29 

.079 

1  23.780 

1  33.637 

1  53.349 

2 

3.206  1  2 

13. 062 

2  22.  919 

2  32. 775 

30 

.082 

31 

1  23.944 

1  33. 801 

1  43.657 

1  53.514 

2 

3.370  2 

13.  227 

2  23. 083 

2  32.940 

31 

.085 

32 

1  24. 109 

1  33.965 

1  43.822 

1  53.678  2 

3.534  2 

13.  391 

2  23.  247 

2  33. 104 

32 

.088 

33 

1  24.273 

1  34. 129 

1  43.986 

1  53.  842  i  2 

3.699  2 

13.  555 

2  23. 412 

2  33.  268 

33 

.090 

34 
35 

1  24.437 
1  24.601 

1  34.  294 
1  34.458 

1  44. 150 
1  44. 314 

1  54.007  ;  2 
1  54. 171  ;  2 

3.863  2 

13. 720 

2  23.  576 

2  33.432 

34 
35 

.093 

4.027  2 

13.  884 

2  23.  740 

2  33. 597 

.096 

36 

1  24.766 

1  34.622 

1  44.479 

1  54.335  2 

4.192  2 

14. 048 

2  23.  905 

2  33. 761 

36 

.099 

37 

1  24.930 

1  34. 786 

1  44.643   1  54.499  2 

4.356  2 

14.212 

2  24.069 

2  33.  925 

37 

.101 

38 

1  25.094 

1  34.951 

1  44.807 

1  54.664 

2 

4.520 

2 

14.  377 

2  24.  233 

2  34.090 

38 

.104 

39 
40 

1  25.259 

1  35. 115 

1  44.  971 

1  54.828 

2 

4.684 

2 

14.  541 

2  24.  397 

2  34.  254 
2  34.418 

39 

.107 

1  25.423 

1  35.279 

1  45. 136 

1  54.  992 

2 

4.849 

2 

14. 705 

2  24. 562 

40 

.110 

41 

1  25.  587 

1  35.444 

1  45.300 

1  55. 156 

2 

5.013 

2 

14.  869 

2  24.  726 

2  34.  582 

41 

.112 

42 

1  25. 751 

1  35.608 

1  45.464 

1  55. 321 

2 

5.177  i  2 

15. 034 

2  24.  890 

2  34.  747 

42 

.115 

43 

1  25.916 

1  35.  772 

1  45. 629 

1  55.  485 

2 

5.342  !  2 

15. 198 

2  25. 054 

2  34.911 

43 

.118 

44 
45 

1  26.080 
1  26.244 

1  35.936 
1  36. 101 

1  45.  793 
1  45.957 

1  55. 649 

1  55. 814 

2 
2 

5. 506  1  2  15.  362 
5.670  2  15.527 

2  25.219 
2  25.  383 

2  35. 075 
2  35.239 

44 

.120 

45 

.123 

46 

1  26.408 

1  36.265 

1  46. 121 

1  55.978 

2 

5. 834  2 

15.  691 

2  25. 547 

2  35. 404 

46 

.126 

47 

1  26.573 

1  36.429 

1  46.286 

1  56. 142 

2 

5. 999 

2 

15. 855 

2  25.  712 

2  35. 568 

47 

.129 

48 

1  26.737 

1  36.593 

1  46.450 

1  56. 306 

2 

6.163 

2 

16. 019 

2  25. 876 

2  35. 732 

48 

.131 

49 

1  26.901 

1  36.  758 
1  36.  922 

1  46.614 
1  46.  778 

1  56.471 

2 

6.327 

2 

16. 184 

2  26.  040 

2  35. 897 

49 
50 

.134 

50 

1  27.066 

1  56.6;^ 

2 

6.491 

2 

16. 348 

2  26.  204 

2  36. 061 

.137 

51 

1  27.230 

1  37.086 

1  46.943 

1  56.  799 

2 

6.656 

2 

16.512 

2  26.  369 

2  36. 225 

51 

.140 

52 

1  27.394 

1  37.251 

1  47.107 

1  56.964 

2 

6.820 

2 

16.  676 

2  26.  533 

2  36. 389 

52 

.142 

53 

1  27.558 

1  37.415 

1  47.  271 

1  57. 128 

2 

6.984 

2 

16.  841 

2  26.  697 

2  36.554 

53 

.145 

54 

1  27.  723 

1  37.579 

1  47.436 

1  57.292 

2 

7.149 

2 
2 

17.005 
17. 169 

2  26.  861 
2  27. 026 

2  36.  718 

54 

.148 

55 

1  27.887 

1  37.  743 

1  47.  600 

1  57.456 

2 

7.313 

2  36. 882 

55 

.151 

56 

1  28. 051 

1  37.908 

1  47.  764 

1  57.621 

2 

7.477 

2 

17.  334 

2  27. 190 

2  37. 047 

56 

.153 

57 

1  28.215  1  38.072 

1  47.928 

1  57. 785 

2 

7.641 

2 

17.  498 

2  27. 354 

2  37.211 

57 

.156 

58 

1  28.380  1  38.236 

1  48.093 

1  57. 949 

2 

7.806 

2 

17.  662 

2  27.519 

2  37.  375 

58 

.159 

59 

1  28.544  1  38.400 

1  48.257 

1  58. 113 

2 

7.970 

o 

17.  826 

2  27.683 

2  37.5.39 

59 

0.162 

Page  484j 

TABLE  0. 
Mean  Solar  into  Sidereal  time. 

c 

ai 

To  be  added  to  a  mean  time  Interval. 

leh 

l**" 

ISh 

ISk 

20'J 

211. 
in.      s. 

22h 

ash 

For  seconds. 

m. 

m.      s. 

m.  8. 

m. 

s. 

m.      s. 

TO.   8. 

m.     8. 

tn.     8. 

8. 

!   8. 

0 

2   37.  704 

2  47.  560 

2 

57. 417 

3  7.273 

3  17. 129 

3  26.986 

3  36.842 

3  46.  699 

1 

2  37.  868 

2  4^.  724 

2  57. 581 

3  7. 437 

3  17.294 

3  27.  150 

3  37.007 

3  46. 863 

1 

i  0.  003 

2 

2  38.032 

2  47.  889 

2  57.  745 

3  7.602 

3  17.458 

3  27.315 

3  37. 171 

3  47. 027 

2 

.005 

3 

2  38. 196 

2  48. 053 

2  57.909 

3  7.766 

3  17. 622 

3  27.  479 

3  37.  335 

3  47. 192 

3 

.008 

4 

2  38.  361 

2  48.  217 

2  58. 074 

3  7. 930 

3  17.  787 

3  27.  643 

3  37. 500 

3  47.  356 
3  47.520 

4 
5 

i  .011 

:oi4 

5 

2  38. 525 

2  48. 381 

2  58. 238 

3  8.094 

3  17.951 

3  27.807 

3  37. 664 

6 

2  38.689 

2  48.  546 

2  58. 402 

3  8.259 

3  18. 115 

3  27.972 

3  37.  828 

3  47.  685 

6 

!  .016 

7 

2  38. 854 

2  48. 710 

2  58. 566 

3  8.423 

3  18.279 

3  28. 136 

3  37.992 

3  47. 849 

7 

.019 

8 

2  39.  018 

2  48.  874 

2  58. 731 

3  8.587 

3  18.444 

3  28.300 

3  38. 157 

3  48.013 

8 

.022 

9 

2  39. 182 

2  49.  039 

2  58. 895 

3  8.751 

3  18.608 

3  28.464 

3  38. 321 

3  48. 177 

9 

.025 

10 

2  39.  346 

2  49. 203 

2  59. 059 

3  8.916 

3  18. 772 

3  28.  629 

3  38. 485 

3  48.  342 

10 

j  .027 

11 

2  39.511 

2  49. 367 

2  59.  224 

3  9.080 

3  18.937 

3  28.  793 

3  38. 649 

3  48.  506 

11 

!  .030 

12 

2  39.  675 

2  49. 531 

2  59. 388 

3  9.244 

3  19. 101 

3  28.957 

3  38. 814 

3  48. 670 

12 

!  .033 

13 

2  39.839 

2  49.  696 

2  59. 552 

3  9.409 

3  19.265 

3  29. 122 

3  38.  978 

3  48. 834 

13 

;  .036 

14 
15 

2  40.003 

2  49. 860 

2  59.  716 

3  9.573 

3  19.429 

3  29.  286 

3  39. 142 
3  39. 307 

3  48.  999 

14 

i  .038 

2  40. 168 

2  50.  024 

2 

59. 881 

3  9.737 

3  19.594 

3  29.  450 

3  49.  163 

15 

.041 

16 

2  40.  332 

2  50. 188 

3 

0.045 

3  9.901 

3  19.  758 

3  29.  614 

3  39.471 

3  49. 327 

W 

.044 

17 

2  40. 496 

2  50. 353 

3 

0.209 

3  10.066 

3  19.922 

3  29.  779 

3  39.635 

3  49. 492 

17 

.047 

18 

2  40.  661 

2  50.  517 

3 

0.373 

3  10.230 

3  20.086 

3  29.943 

3  39. 799 

3  49.  6;56 

18 

.049 

19 

2  40.  825 

2  50. 681 
2  50. 846 

3 

0.538 

3  10.  394 

3  20.251 

3  30. 107 
3  30.  271 

3  39.  964 
3  40. 128 

3  49.820 
3  49.  984 

19 

.052 

20 

2  40.  989 

3 

0.702 

3  10.559 

3  20.415 

20 

.  055 

21 

2  41. 153 

2  51.010 

3 

0.866 

3  10.723 

3  20. 579 

3  30.436 

3  40.  292 

3  50. 149 

21 

:  .057 

22 

2  41.318 

2  51. 174 

3 

1.031 

3  10.887 

3  20.  744 

3  30.  600 

3  40.  456 

3  50. 313 

22 

.060 

23 

2  41.  482 

2  51. 338 

3 

1.195 

3  11.051 

3  20. 908 

3  30.  764 

3  40.  621 

3  50. 477 

23 

.063 

24 

2  41.  646 

2  51. 503 

3 

1.359 

3  11.216 

3  21.072 

3  30. 929 

3  40. 785 
3  40.949 

3  50. 642 
3  50.806 

24 
25 

.066 

25 

2  41.810 

2  51. 667 

3 

1.523 

3  11.380 

3  21.236 

3  31.  093 

:  .068 

26 

2  41.975 

2  51. 831 

3 

1.688 

3  11.544 

3  21. 401 

3  31.257 

3  41.114 

3  50.  970 

26 

.071 

27 

2  42. 139 

2  51.995 

3 

1.852 

3  11.708 

3  21.  565 

3  31.421 

3  41.278 

3  51.134 

27 

.074 

28 

2  42. 303 

2  52. 160 

3 

2.016 

3  11.873 

3  21.  729 

3  31.  586 

3  41.442 

3  51. 299 

28 

.077 

29 

2  42.  468 

2  52. 324 

3 

2.181 

3  12.037 

3  21. 893 

3  31.  750 

3  41.  606 
3  41.771 

3  51.463 

29 

.079 

30 

2  42.  632 

2  52.488 

3 

2.345 

3  12.201 

3  22.058 

3  31.914 

3  51.627 

30 

.082 

31 

2  42.  796 

2  52. 653 

3 

2.509 

3  12.366 

3  22.222 

3  32.  078 

3  41.935 

3  51. 791 

31 

.085 

32 

2  42.  960 

2  52. 817 

3 

2.673 

3  12.530 

3  22.386 

3  32.243 

3  42. 099 

3  51. 956 

32 

.088 

33 

2  43. 125 

2  52.  981 

3 

2.838 

3  12.694 

3  22.551 

3  32.407 

3  42. 264 

3  52. 120 

33 

.090 

34 

2  43.  289 

2  53.145 

3 

3.002 

3  12.858 

3  22.715 

3  32.571 

3  42.  428 

3  52.  284 

34 

.093 

35 

2  43.453 

2  53.310 

3 

3.166 

3  13.023 

3  22.  879 

3  32. 736 

3  42.  592 

3  52.  449 

35 

.096 

36 

2  43.  617 

2  53.  474 

3 

3.  330 

3  13. 187 

3  23.043 

3  32.900 

3  42.  756 

3  52. 613 

36 

.099 

37 

2  43.  782 

2  53.  638 

3 

3.495 

3  13.351 

3  23.208 

3  33.064 

3  42.  921 

3  52. 777 

37 

.101 

38 

2  43. 946 

2  53. 803 

3 

3.659 

3  13.515 

3  23.372 

3  33.  228 

3  43. 085 

3  52. 941 

38 

.104 

39 
40 

2  44. 110 
2  44. 275 

2  53.  967 

3 

3.823 

3  13.680 

3  23. 536 

3  33. 393 

3  43.  249 

3  53. 106 

39 
40 

.107 
.110 

2  54. 131 

3 

3.988 

3  13.844 

3  23.  7UU 

3  33.557 

3  43.  413 

3  53. 270 

41 

2  44.  439 

2  54. 295 

3 

4.152 

3  14.008 

3  23.  865 

3  33.  721 

3  43.578 

3  53.434 

41 

.112 

42 

2  44.  603 

2  54.  460 

3 

4.316 

3  14. 173 

3  24. 029 

3  33.  886 

3  43.  742 

3  53. 598 

42 

.115 

43 

2  44.  767 

2  54.  624 

3 

4.480 

3  14.337 

3  24. 193 

3  34. 050 

3  43.  906 

3  53.  763 

43 

.118 

44 

2  44.  932 

2  54. 788 

3 

4.645 

3  14.501 

3  24.  358 

3  34. 214 

3  44.  071 

3  53. 927 
3  54. 091 

44 
45 

.120 
.123 

45 

2  45.  096 

2  54.  952 

3 

4.809 

3  14.665 

3  24.  522 

3  34.  378 

3  44.  235 

46 

2  45.  260 

2  55.117 

3 

4.973 

3  14.830 

3  24.  686 

3  34.  543 

3  44.  399 

3  54.  256 

46 

.126 

47 

2  45.  425 

2  55. 281 

3 

5.137 

3  14.994 

3  24.  850 

3  34.  707 

3  44. 563 

3  54.420 

47 

.129 

48 

2  45.  589 

2  55.  445 

3 

5.  302 

3  15. 158 

3  25.  015 

3  34.871 

3  44.  728 

3  54. 584 

48 

.  131 

49 

2  45. 753 

2  55.  610 

3 

5. 466 

3  15.322 

3  25. 179 

3  35. 035 

3  44. 892 

3  54. 748 
3  54.913 

49 
50 

.134 
.137 

50 

2  45'.  917 

2  55. 774 

3 

5.  630 

3  15.487 

3  25.  343 

3  35.  200 

3  45.  056 

51 

2  46.  082 

2  55. 938 

3 

5.  795 

3  15.651 

3  25. 508 

3  35. 364 

3  45.  220 

3  55. 077 

51 

.140 

52 

2  46.  246 

2  56. 102 

3 

5.959 

3  15.815 

3  25.  672 

3  35.  528 

3  45. 385 

3  55.  241 

52 

.142 

53 

2  46.  410 

2  56. 267 

3 

6.123 

3  15.980 

3  25.  836 

3  35. 693 

3  45.549 

3  55. 405 

53 

.145 

54 

2  46. 574 

2  56.  431 

3 

6.287 

3  16: 144 

3  26.  000 

3  35.  857 

3  45. 713 

3  55. 570 

54 
55 

.148 

55 

2  46.  739 

2  56.595 

3 

6.452 

3  16.308 

3  26.  165 

3  36. 021 

3  45.  878 

3  55. 734 

.  151 

56 

2  46.  903 

2  56.  759 

3 

6.616 

3  16.472 

3  26.  329 

3  36.  185 

3  46.  042 

3  55. 898 

56 

.153 

57 

2  47.  067 

2  56.  924 

3 

6.780 

3  16.637 

3  26.493 

3  36.  350 

3  46.  206 

3  56. 063 

57 

.156 

58 

2  47.  232 

2  57. 088 

'J 

6.944 

3  16.801 

3  26.  657 

3  36.  514 

3  46.  370 

3  56. 227 

58 

.159 

59 

2  47.  396 

2  57. 252 

3 

7.109 

3  16.965 

3  26.822 

3  36.  678 

3  46.  535 

3  56.  391 

59 

0.162 

^   3 


^  -i 


2 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  486 


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Page  486] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


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in  to  in  to  in  to  in  to  in  to 


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ooo»t~i-iiniN'<i<'^(Nin 

'  CO  rH  "^  I— t  ^  tH  ^  rH  ^ 

intointointointointo 


<NtOi-l00O>O>00iHr~lN 
<NeOC<COr-(CO>H'*r1T}< 

intointointointointo 


tO')<'<llinCOtOINOO.HO> 
iNCOINCOe^COINeOlNCO 

intointointointointo 


oc^oocot-'^tominto 

COCOiNCOiNCOC^COC5cO 

intointointointointo 


COO>iNO<-It-IOC-IC:»CO 
COINCOCOCOCOCOCOCMCO 

intointointointointo 


i^r^tpocinooi<a>coQ 
co<Neoc5eoc^coiNcoco 

intointointointointo 


i-f  in  o  to  oi  to  Gci 


)COC4COI^ 

5  in  to  in  to 


inco'*-(<co-*coiniN 


in  to  in 


INt)<1N 

to  in  to 


•*»i(Nt)<S 

inointo 


«00©00Q 

in  rH  in  th  in 
iintointom 


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rH  TJi  i-(  T}<  C^ 

to  in  to  in  to 


toin  in  in  in  in 
in  rH  in  i—(  in  rH 

in  to  in  to  in  to 


jgto-*tO 

in  to  in  to 


■^t- cor- CO 

in  rH  in  rH  in 

in  to  in  to  in 


00  CO  00 -*  aj -"ji 
in  to  in  to  in  to 


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in  to  in  to 


JrHlNrH^JrHC^i-KNrHlNrHINrHCOi-ieO 


:OrHOrHO 
a  to  to  to  to  to 


rHOrHO 

to  to  to  to  to 


OrHOrHOrH 

to  to  to  to  to  to 


rH  CO  O  CO 
OrnSrH 

to  to  to  to 


.grHgrHg 
^  CO  CO  CO  CO  CO 


i-lOrHOrH 
CO  CO  CO  CO  CO 


COrHeOrHeCi-HCOi-ICO(N 


OiHOrHOrH 

CO  CD  CO  CO  CO  CO 


OrHOr-1 
COCO  COCO 


t^  CO  00  C^  00 


t^iocpioco»ccpcococo 

iCrHiOrHiCrHiOrHiOrH 
iOCOOCO»CCOiOcOiOcO 


to  to  to  to  to 


38383 

to  to  to  to  to 


coiNcoc^cooicoe^coc^ 


O  ?H  S  rt  S 
^  CO  CO  CO  CO 


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CO  CO  CO  CO  CD 


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'T" 


00      ^   ^^^    .-      c^i      CO     -^     in 
?5c^co       cococococo 


OOOOOrHt-rHt-C^ItO 


in  toin 


c^-riN 

to  into 


into  in  to 


(NQ0C^0>rH05rHOOO 


OrHin 

in  to  in 


inrH 

to  in  to 


ine<iS(N 

in  to  in  to 


to  to  in 
Jo  I— ( in 

in  to  in 


toin  to 

to  in  to 


in  to  in  to 


l-iJ'OJ-^C 
S  rH  in  rH  t 

jtoin  tou 


OrHO 

to  to  to 


iNgiN 

to  to  to 


to  to  to  to 


O5o5o5c»05c»05cc05a} 


to        i^        05        Ol         C3 

M        CO        CO        CO        TT 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  487 


12; 


.^^ 


•xoaddy 


•xojddv 


-^        C>1        cc 


(^aifiiaafiicapiaifiitn  oj  cc  pj  cc  P4  cc  pj  co  pj  oq 


g'MCOlN'^fil'i-l'i'r-llC 


OiOOOOOiOOiOi— I 


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^  ^  t^  ^  t^  ^  t^  ^  t^  ^  t^ 


5  c<i  ir4  o»  C4  M  CJ  e 


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pjasp:;c»QHaQpH!»McQ 


•r  th e<5 c^  M M M e<3 1-1  ■*  i-i>oooino-*i-icoc^ 
coaocoGOcoxccxcccc;ccoo  c«ra>  c^  a»  c^  os  c-i  ai 


MOOCOCOCOOOCOXCOTO 


rHT(IO^OinOlS>ftO 


— <inicooo-i'c<ioooo 


f-H'^OiOiCO'iT'i-IWr-l 


or-ecrH05-^L':5airHcooi:^i-tc^:oi^»-Hcoioooos"^nr-iiooit^t^ 


eot^cooocooocococooo 


MOOCOOOCOOOWQOCOOO 


■<JI  rl  M  tH  «  i-l  « 


» lO  r- CO  m  o  c^  I 
rfi  •<ji  t^ -^  t~  •*  t~ - 


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01INC^O)C^eOrHMr-ITr 


50C^C^C^<NMC>)COi-l05 


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sss 


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■^r-IC0i-l«lr-ICOC^M<N 


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>>0(NcocOrtico>r- 


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lOOiOOfO-^r-ITl'i-l 


SsooeooooiOMO 

■*t~eOt~M00M00COO0 


JOCOiOt^QC 
<OiCiOiCiSC 


■rf*r»T}<t^-<ti-*cot>oooo 


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COQOMOOCOOOCOQOWOO 


moor-ic^t-toiMQaoio 

r-IOTi-l'^O'^OlOiniiS 


COOOOiOCJOOOOCO 


»-i  (M  rococo  OS  OS  ccior* 

~)C<3i-I«i-CMO-^Ot)< 


r-o-^QOiNr-t^coi-i 

NOJMOTC^  CO  1-IOT  !-(■<}> 


-iOi-it<i-^aot~500co 


T  O -Tf  rH  CO 

CO  00  CO  CO  CO  00  ec 


T-(eo<N 

xcooo 


SC<ltOt^02JiCQpOSCO 
■<J<t~COt~COO0CO00CO00 


GOlO  ^  Q 

©■^ois 


OJiCtM 
cot- CO 


00  CO  CO 


eooiS 


H  I^  OJ  C^  CO  O)  CO  i-H  ^ ^^ 


-        £!  ■ 

o-rou 


Tfr--* 


00  CO  1-1  p  iQ  t- 00 

rH  CO  e^  «  N  e^  oS 

t-  Tj<  |>  ■*  t^  ^  t~ 


coc^ostCiOosiH-^r-^os 


t^OiUJi-tCOCO^H? 


t- It  t- ■*  r~ -^  r- 


g"  ^  !-»  2  00  OO  p  --O 
iH -r  O -f  o  55  o 


SoS 


— ■lOCO'TiOe^tOiHOOC 
Si-ITf<rH-*i-C^i-C^< 


;osoooi-ir~cou5'^»j<o 

-         —         ^         —  -"Jlr-IT)" 


SOS  o  00 1-t  r*  CO  lo 
iH  •>»' 1-1  ■*  1-1  ^  T-l 


!ii«t~eoooMpfHT 
S  (M  CO  c5  CO  6j  ^  e^ ' 


Sc5SlNCO 


t^iootoi^r^^os 


iNCoSc 

iC?o»o  t 


SsjcocOcO 
j;  lO  to  lO  «0 


C^NrHCOQ'^OQUJ 


S*  t^  OS  to  OS  ki 
C0lMeOC4C 
^iC  to  iC  to  u 


<r-IC2  0» 
3  CO  CO  CO 

5tOiO  to 


COiOi-H^OSOStOiH- 
0U50    -    -    -  ^  - 

lO  tOkO 


.    _    _  toiHifeo 

lO  >A  iC  lO  O  kO  o 
to  T)<  to  Tt<  t- -Tji  t- 


tOr-ICOCOOtOt-OS-^C^iHOI^CTi 
•^i-|-*rH-*r-ICO<HCOMCOCJC^t^ 


c5coc 


(NtOOSQOr^i-t-^COrHtO 
-  "Oil'i-lrJliH-^rH 

t>.  ^  t^  ■^  t>.  ^  t>. 


00  1-1  to 
OiOO 

iCtOiO 


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to  iC  to  IC  to  iC  to 


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(Nt^oos^i-n^eom- 


iHrfrl 
lOtOi/S 


lO  O  tC  O  ^ 
to  kC  to  lO  to  iC  to 


sss 

intoio 


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r-li*iH 
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ii<  rt  Tji  i-(  ■»  iH  Cn 

to  lA  to  lO  to  iC  to 


SOS  p  t-  CO  in  >o 
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to  ■<J<  t»  ■^  t~  ■^  t» 


lOtOiO 


■*  to  to  s  00  53  p 
o  in  to  in  to  lO  r» 


C^^C^^C4'tT-(^iH^ 

lOtointointointoioto 


1-ITjlrH 

iintoio 


OS  C^  rH  O  N  go -V 
•^  rH  in  r^  lO  P  in 

to  in  to  in  to  in  to 


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Si-ieoe^eociiMeoojeo 


incoM  to 

Tfr-cairH 


OS  OS  to  c 
COrHrtC 


inp'Vi-i 


t>-co-^ 


to^oo 
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—  mom 


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m  torn  to 


sss? 

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r^totor^mos-^pc^rH 
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mtomtomtomtomto 


s^joototor^-mos 

stomtomtomto 


COpi-l(N 

mtomto 


omo 
m  torn 


CQCCCCOOCQCOCCOOCOOO 


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liO  coo  CO  lO  o 


gS2S2 

,c;m  to  mto 


CO  00  CO 

m  1-1  in 
mtom 


r-imi-l 

torn  to 


g'Qomoom 
m  1—1  m  rH 

.fl*  m  to  m  to 


QO  moo  t 
mtom  t 


oocor"COt>.T»<tommm 
mtomtomtomtomto 


r-ostooti-'coc^c^'* 

(MCOIM- 

m  tom  t 


CO  3;  cj  in  T^ 

CO  CO  CO 

mtom 


p  00  OS  OS 
CO  CO  CO  CO  CO  C^  CO 

tom  tom  tom  to 


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mtomto 


t~oom 

m  tom 


Scorj 
i-im 

tomto 


H  in  CO  CO 
:mtom 


I- j^to 
tom  to 


3  .H  t^  (N  to  CO  m  a; 

iCOCOCOCOCOCOCO 

stomtomtomto 


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cococoeoc 

m  to  m  to  L 


5  CO  e^  CO 

^tomto 


m  to -^  to  CO  t^  CO  00  c^  OS 


caosoioi-ioi-i.-ii-irt 
mT-imc^m(NmMmc>i 

mtomtomtomtomto 


mSmc 
m  tom  t 


5  OS  CO  00  t 

>mtom  to 


TtOI-VCO 

m  tomo 


poo>-<occ^r-co 


CO  CO  CO 

mtom 


CO  CO  CO 

tomto 


mtomto 


tomm 
II  Si-* 

mtom 


tomt~. 

tomto 


t^tot^tOI^t^tOt^tOt^ 

mrHm»— imi— <mi-^mr- 1 

mtomtomtomtomto 


X  in  00  u^.  00  »«  o> 


\0'^^'£> 


^^ 


*z 


g  g  oj  g  ca 

^  to  to  to  to 


gCO'NC 
r-(Or 

to  to  to  t 


IC^COOJCOOICOi-tCOi-tCO 
jOi-lOi-lOrHOi-lOrt 

itotototototototo  to  to 


rH       OJ      CO      -^      m        to 

-*      -^r      KS<      ■*      ■*    I    -T 


05  02  a;  03  05  CO  Pf  03  05  OQ 


1-hCO^HOO— ^COi-H^i— (■"J* 


Oi-l  O 
to  to  to 


i-IOi-i 

to  to  to 


Oi-lOi-l 

to  to  to  to 


1-1  •*P'* 

Oi-iOi-l 

to  to  to  to 


g3g 

OtOtO 


mpm 

^-*  O  1— I 

to  to  to 


05o3'o5oco5a}pjo305o3bjaQ05os05;cOiGCQ5o3 


X         OS         P  r-         ^'l         CO         -"t        l?f"^|     t$^    (^     ^5         OS         p^ 

^^m      mi-'^mmmmmmmto 


Page  488] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


Xi     u. 


^z 


o      T-i      c^      ec 


'xojdd V 


iO<oi-*ooci       Oi-tc^eo 


li^       to       I^       CO        o 


C^xQ^aiP^cGP^cctfcd,94%p^cctfcctic/ipHcdOiJccOi$cfi0cioc^vj^ 


S*C»«OOS(C5itpcyi«pai«P    04!03050X)<©CC«DCO«P 


ootpao<£>oo'^op?©oo«p 


QO^oo^aD'^aotpao^ootp 


CiCCaiaOOJOOOiCOOiOO 


aOqOX'OOQOOOODXXQOCCOC 


jsQCCOaOQGOQQCOXOOSQOiQOaOa'-OiOs 


00OG0Q00Q00O0Di-HQ0»-i 


iCtOiOOiC^CiC^DiCO 


GCC^OOC^CCC^XCOt^CCI^CC 


^iC^iCCOiOCOiC^iCtO 


iCCOiOOiC^dCtOiCtO 


co^oot'-t^r*t^t^r*oocox 


g^ai50asr*QOt^Gcoo 


gt^QOOOQOOO^QOO 


t^Or-r-l?Oi-f!CC^iOC^iCCO 


O^OOOSOOOi-tOCM 
iC^iCiOiOtOiJStD»C<y3 


Or-iQ<Na>iMXCOOD'<1* 


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iC^iCtOificOiCOi^^OiCtO 


TTi-ITf^i-C'S'rHTri-l-^i-H-Tfr 


^iCCCiCtOiCtCi»0^«C^  ,iCcOiCtOiCcO»C«vC«D 


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fliOtOiCCOiCeOiO«OiO^ 


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.  icoiJ5oicoicoi?5i-i 


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1— it^QODOiOoOOt^i— I 
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SS2 


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lOi-llCrHiCC^lCC^liSC^ 

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lOtC 


r*  toto^«•- 
•*  c^-^iN- 
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iCtOtOtOLCtOintOlCtO 


lOtO 


lO  tOiC  to 


marl—' 

^  CO  ^  CO 
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■^  coco  CO  CO  CO  CO  CO  CO  coco -T 

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2-^' 


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i-(id-iin.-i 

to  iC  to  lA  to 


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lOtoioto 


5  CO  t~  C4  OS 
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tO-^iCtOCOOOrHOsasrHt^CO 

cocococococococooa^c^-* 
lOtoictointointointoiCto 


•VC^COOJ 

in  to  in  to 


t^QiCIN 

CO  CO  CO  CO 

in  to  lO  to 


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COCOCOCOCOCOC^COfN-^lN*^ 

intointointoiotointointo 


r  in  o 
".  lOto 


in  oui 
intoic 


.t>-intot~'«)'ooc^o>-<c^Oicot^intor--^ai!N'-i 

J  to  in  to 


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to  in  to  in  to 


>  in  to  in  to 


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in  to  in  to 


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CO  ?1  CO  CO 

in  to  in  to 


QC^OOrftOtO-^CCC^OOC^ 
COCOC-<COI^COC^CO(N'*C^'» 

intointointointointointo 


pixXxQiaicixoiai\ci!XiciiK(A^Xx!^wm^fiiixaiwXi^x<£mcDaixa^X!jiOia^oi^ 


"^^  ^     m     ^,    ^a 


to      l~      X 


O         ^^"^     1-H 


in     to     t^     X 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  489 


a  ^ 


s 

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^iCiCidOiCiCiOiCiCiC    lOiOiO^Ci^UtiiOiOiCiC   »0  iC  »C-  iC  tC  tO  iC  lO  iCiC  j»C  lO  »C  iC  i-C  iC  iC  iC  iC  «c 


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ccoiNOCMi-irH^^c^'orNoeoaiocoi'^cO'^ 


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S'co:ocor-2^r*c^corHosooidoaoi-ir^Mr*co 
■V^H'Tf<T-C«»"i-t'^r-('^rHhtT-ieOC^COC^CCC^COC^ 


COC^Ct5c^COC^CQCMCCW|CCC^CO?JCOCCC^«1^»CO 


-^rt'^1-H^c^'^c^'^^^coc^coc^«^^coc^cOl^J^coe^cc?1ccc^cc«ccco54eoc<^otc^ccc^« 


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Page  490] 


^ 


N    a 


3  o 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


^'^ 


•xoiddv     Q"^ 


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pdaQpHOQpjaQpjastfcceiHCCpHail^aS^ceOicnpiScAQjaiojcoOHCCPdai 


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*2:  BJxMcccs'uaaJccaSoiiQiaoaSMSJxaJccaia!  aJaJaJxaSaiMcfiaSM 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  491 


p    a 


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Page  492] 


TABLE  10. 
'Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


S^ 


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r-lrHi-lT-<rH,-lr-li-(<NS 

CO  ic  CO  .ire  CO  ire  CO  ire  CO  ire 


c^r-roco-^ireco-^t— ro 
coirecoirecDirecoirecoire 


Oi-tf-HOfNosrooo-^t- 

i-HOJi-lJirHi-HrtT-HMT-l 

coirecoirecoirecoirecoire 


Scococoiret-»ret— -^coco 
ireroireccireroireroireco 

^ireirevcireicireireireireio 


o»rooe^©'-ii-iQ£io  ccosTcocvrer-irecocoire 

icirecoirecoirecoirecoiccoirecoirecoirecoirecoire 


OCOiScCiScOtCCO 


COiCCO'^a>'^OCOOC^Ii-ii-*OI'-*COOCOO>^OQ 
iScO»CCOiCCOOCCOCOOCOOCOOCOOC^O?S 


t'-'^aOCO^C^Of-lrHO 


SCO  CO 

^  lO  O 


lO'n'iCCOiCCOiSCO 


cc t-* r» r>- r- <© 00 «e cc ic  oi-^o-^^co^coc^c^ 

lO  CO  iC  CO  iC  CO  iC  CO  iC  CO   iCCO  oco  oco  o  coocc 


ocoocooeooiMOc^ 


COC^'^C^'«J<i-i»Cii-f 


iCn'iOTpiCCOiCCOiCCOiCCOiScOiCOOiCCCOCO 


8»CiHTj<C^"^CMC0C0C^ 
COOCOOCOOCOOCO 


Sc^iCc^iOcO'^coTrcoco 
i£i-rr  — " ■ " 

,^  iC  1/5 


iC  ^  iC  ■^  lO  -^ 


l-^CO'^C^'^C^»CCJiOt-tCpi-'^OI"«Ot^OSOOps 
jiO'^UO'J'iC'^iO'^iO^   iC'^irt'^iOTOCOiCCO 

if5  lOiOiC^iCidOiAkC  iCiftiCiCtCOidOiOUi 


[iCCOiCCOiCCOOCOOCO 


CO  O  CO  iC  CO  lO '^  lO  •3' lO    ^ '<*■  ^  CO  »A  CO  ift  CO  lij  c^ 
lO -^  iC  ■^  kO  ■^  lO  ^i  lO -^    iC  ^  lO  ^  lO  T  iC -^  iQ  ** 


^  iC  o 


SOS  rH  a>  r-l  O  1-1  00 
^  iC  -^  iC*^  iC  ^ 


i-iXi-HQO(NooiMooc^ooc^t^dr*cor-cot^coco 


■xojdd  V 


SCI  Q(M 
iC  lO  iC 

i/S  iC  lO  Id 


is  ic  i!5  ic 


O*  ■'J*  Oi  "^ 


0>  ^  OS  ^ 
lO  iC  id  ^ 


gi-lQrHi-Hi-«r^.-t^i-t    ^iH^i-Hi-HQi-HQfNO 
iC  i?ti  lO  lO  iCiCiCiO  O   iC  iC  lOiC  lO  ift  iC  ut  iCui 


lO  iQ  iC  "^  iO  "^  ij3 
iC  iC  iC  »0  iCiC  iC 


^iCiC 


00  <0  00  CO 

•^  ic  "^  iS 

iC  iC  lO  lO 


00  to  00  «o 
^  iC  ^  lO 


Q^!XiC^u^Oi<rJX':r^Oi^ 


2^ 


o      w      6»      S      M      S 


00  «p  00  t*  00  t 


oor*ooi^oot>-oot--oot>- 


C  iC  iC  lO  »C  »C  iCi  lOiCiC   iC  iCift  tO  iC  »0  iCiO  iC  lO 


&H95pt^C»Q^CX2p4c»tf  GO  pC^CGpjxPjCOpCHCOtfU^  Oh  C»  Qh  GO  C^h  C/5  P4  CC  P^  CC 


OO  OS 


SCOOCOOCOQ 
iC  lO  lC  iC  lO  lC  ^ 


oot^oot^t^i^r^t^t^r* 


«£>      r*      oQ      OS      Q       r-t      eg      c9      '^      uS"^  ^0      r* 
wcJCiJico       cococococo       coco 


•^ 


u^ 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  493 


x  o  I  d  d  V 


tftBpSwpjoopjtnBia! 


sjuipjcnKaiQjcnpjGCi 


Oi  ZD  fiiUl  Pi  ViOi'Xi  fix  a^  CC  P4  en  p4  I»  (4  GO  M  r» 


S*^«^r*OiO<o-^wr^os  ^ «o »c c^ as oo co -^ t* o>  ^j lO !>•  o 5? -^ co o> co cc  ©t^t^o-^coc<»o^«p 
i-lMf-l?IC^C^C^(NC^»H   COi-ICCi-ICOO-^O-^iC   tCOiOiOO-VOCCi-tCO   rlC^C^C^COr-C^OlOtS 


c^      CO      ■^      in       to      t~ 

lO      ic      »o      1/5       »c      ic 


iOO>Cli-c<1>r-CT<riM,fl?»IOC-l-r>-liCOOio 

xci5Gccoaoc030Mooco'»«accooo«aoe<5a>c^ 


OCCOMi-HiNi-IHr-IC^ 


iCOOir^c^coooQO  '^c^oor^cocoooooMfio 
.-(l^^I-lI-l6^■-^l^^l-lMO«lOcOlC■^lO■*^lO■^ 


S'lOOOr-iCOMMOOt^ 
iOCOiOOSOMOS60(N 


iC-^»COOiOCOiCCOOCO 


fJiH<Mi-(MiHCOO  MO  hi*  iO'q«>Oin'>5'U5T»<ClcOiOCCi-lI^C^i-l  041-1050 

i«t^'*t-'*i>-*t~-*i~ect~cot~e<5t-eoooeoooe<3XMooei5aocOQOc<5 


Ol'riN-^iOt^OtMO 
OC^r-IC^rti-li-lr-imi-l 


cooceoioo>iNc^«om 


00400)004 


gt-^-^^HOicr-oj'^oi 
»50eOi-(Oli-(r-(04i-l 

t^MOOCCOOeOOOMOOM 


04  O  CO  O  CO  >i5  «  ift  ■*  ■*  ■* -Wi  to  CO  O  OS  O  04  iH  « 
l>  •*  t~  ■*  t~  CO  C~  05  t~  CO  t^  05  l~  05  00  05  00  05  ao  CO 


a>t-H05ooi^^f-Ho»ciC 

rti-IO)0  04  005  005u5 
t~rl't^'>J<t^'<J(t^-.)lt-05 


t^O)005CO«0:OCOg>0    04«OtD050»O>05  iCt—rH    04t*tOOI»-tr>"t^OI0150 
i0  05O01O04O04O0)rHr-(rHr-lrHO05O0IO    05>O05lO'9'-<J<'*"T>C05 

:0'^r^'»i<»^'^t^*^t^"^  |I>'i^t-»ra«t^'^t»'^l^^    t*O5t^O5t^O5t^O5t*O0 


OO'OiOQOtpiOOjaQ 
-.J'iC'^'^iO-^iiScOOOS 

t^eor-o5r-o5i>coooo5 


!SOt^01ir5T)<05t^r-ia!00 


>-t'c9i^i-ipaoo5iC'!eMg5ooo5>otOi-(Ooo 

5iC05iCC0O0)O0l|O0)Or-lr-lr-li-(i-l03O 


S<O.-C00WOr-Oli(5iC05 
CCiCCC'^-^"^^"^"^'^ 


t^^a>OD04<:p»C05t^O 

^■^■^coir5co»r5o5iC05 


gr-cofto-^oooeO'* 
04C50400JrH.-ir-li-l 


■^^000^05iO00OC0»O 

oiooiiocciocc*-*-* 

t^'.tt^COI^COt^COt^CO 


iHr-l0»O<NO0jS05ift 

t^'*t~'^i>-^r-o5t^eo 


cOllO'fCO^THQQOiOt^ 
S05iOCO'C05iOCO'niTj"'<9> 


S'0»0>Ot^01U5-1*'^^01 
Ol4O«0iO05ifta5iC05iO 


oiiO-foot~i-ias  JO 04 to 

•^"^•^•^■'J^'^M'COiOCO 

tO^tO'^tO'^tO'^tOTj* 


305t~OOt-05T)<t-.rH'Ot^»J"»'t~Or-ltOtOe3 
OimCOO  04  004  004    -Hr-(r-lrHr1rH04  0  04  0 

■^'*itO'*r-'*t>-'*t-'5"'r-'^t~'*t-'^t»'*t-"i' 


0CQO0p04t0-^C0t^^ 


OT«0>tO'*05f-pOI^05-tt^i-lOt>-'*'*000 
■^05>OCOiraCOK5eOOOJ004004rHr-lr-lrHr-Ci-l 

o-*tO'^to-*tO'*r»'^t^'*t>-'*r-'^r-Tj<r»Ti< 


;lOCOtOi-IQOO»OOOrH 


wSeoS  :oi 


S0400400IIO 

rfjtoiotoift-a-^to'^to-^ 


■^O05r*r-n3ao^.-tto 

iCCOOCOU^CO-^"^-^ 


tDt)<tO'*tO'*tO-.J<0'* 


.3"^tooiooa»i-it>-'^-*t>T-ioaoMioto>-iooo 

T»'-4'»J'-^'*05ir505in05>(5  05O04O04O04rHi-( 

o.s<;o-*tO'j'tO'^tO'^tO'*t^"rt-'Vf-'^r-->!(< 


gO4t~05u'5iO-1<tOO400.H 
010040040040010 

^tOlCtOiOtOiCtO»OtOifl 


Sooi-ioo^aocor^-ric 
iHr-(04rH040040010 

^tOtOtOiOtOlOtOiOtOtC 


O>ai-jr»05tou9"jit^oi 

04ir5CO»i5CC005»CCOii5 

to-j'-js-^to-^to-^to-^ 


05  0r-IOOCOlOin0500i-l'rt00  05l(5t0  04a>5>04tO 

io5ira-*'«'^-^'*'<>'-^'^|ioeoiC05iSo5ir504  0  04 

i*^^t0^t0^t0^tO^'t0^t0^tO'T<t0^t*^ 


:o^r^oio>THO^c^^ 

040040040COiOCO>0 

tOiCOiCtOiOtO-^tO-^ 


Tfi  to  to  ■.f  00  Ol  00  04  t^ 

o5ioeoioeoio-3>0'*^ 
to^to-^to^o^to^ 


lCiCr»04Q004t>-i5'<J' 

tO'^tO-^tO-n'tO^tO'^ 


ift»(5tD^0005a>i-tOO|040^C0r^iC^t03<00C0 


erHi-lrHT-lr-(rti-(TH04i-( 

.dtOLCtoiCtootoictoic 


i^ooiooiSoiioiS 

:0»ntOiC!0»00»CtOiO 


!o>i-i'H©coaoi!itof-'^ 

M0  05  0COii5cOiC05iA 
tOiOtOiCtO-^tO-^tO"^ 


3>04^0)o5r-to>caooj 
to^to^to.s*to^to^ 


tfOlOS05»'*»'t^tOtOt^U5 
,fl*  to  iC  to  iC  to  »C  to  iC  '^  lO 


00^0>0IO.-IJ4O05® 
tOtCtOiCtOiCtOiCtOiO 


S005004i-lrH04po50> 
00)i-l04rH04>-l04i-(r-( 

^tOir5tOiCtO>CtOi/5tOiC 


■'j'ooicr^totoooicos'.^ 

tOi(5:OiOtOiOtOiCOir5 


iOt~tOlS00-J<O3I4.HQ 
010040040040050 

tOiOtOiOtOiOtOiOtOiO 


055C";tOt^-fa»O4O4p 

o5iSo5"005ioe«5in-^iS 

tO'*tO'»)<tO'T"0'<1"tO^ 


ooii-i.-1050'^gotot^ 

04  r-l04i-l  04^04  004  0 

tolOtOlCtOU5tOtOtOtO 


l--i(5O105i-IO4O5pi<50O 
010040050050050 

tOiOtOiCtOiiStOirttO'^ 


- 1- 1^  *"c  gi  ic  < 


-    , >giic^-* 

I004004004004 

^tOiAtOiCtOLCtOiCtOlC 


O05rH^01.H05O'*0> 
i-(04i-IO4i-104i-l04r-li-H 

tOtOtOiCtOiCtOlCtOtC 


t^t^OOtOOstOOCO 
rlrlrli-lr-lr-COlr-t 

tOU5tO»OtO»CtO>(5 


oioiccoi0^f^*oo»o 

04r-C01i-l04  0  04  0  04  0 

totntotctotctoictoio 


a3'043<r-llOQtOOt001 
S:OC00050C0005004 

.C^tOiOtOLf5tOtCtOiOtOLC 


SoogcoQO»r«a»tooio 
O4001001004r-(04 

tOiCtOiCtOiCtOiOtOiC 


:005005J5050050» 
;tOvatOiOtOi/5tOiCtOir5,tOiCtOlCeOiOtOiOtO»C 


oi  05  cool 

rt  OliH  04 
tOiOtOiO 


IHO4I-I04 
tOiO  to  iC 


t^osoot*csto^ir50ico 


oooa^x^r^oto 

004  004  0  041-104 

©lAtOiCtOiOtOiC 


-HlC01-T05CO-»'J4tOi-l 
r-(O4i-IOli-104i-104i-l04 

tOkCtOiCtOiAtOiCtOiO 


:»0-^iCCOli5  05ir5COiOCO 


.■|C'^l5'*tp-9<tOT)'tOCO 
«tniAiOiOLCL£5iOiCOiA 


goo-HoOf-ir^oir^oito 
COOCOOCOOCOOCO 

to  iC  to  vC  to  lO  to  lO  to  lO 


'tom 


ssss 


ocftoco 


§ooa> 


o«o«oco©ecoe5 


~     t*  lO  ■^  »0  "^  lO  ■^  lO  Tf< 


•xojddy 


aocooeoocoQccoco 


-  lO  r^  "5  '^ 
r  lo  Tj<  lit)  ■^ 

5  iC  lO  iC  lO 


lO  ■^  lO  ^ 


©050COQCOQCOOCC 
I0»0i0i0i0i00»0i0i0 


iC  lO  iCi  iC 


tOGOtOQOtoccoostoqs 


3  lO  tO  lO  tC 


O  lO  ^  lO 


Pi  CB  C^  cc  p4  03  p4  02  P:5  CO  '  tf'  oi  P5 !»  pi  OQ  Ph'  cc  pti  cc  c4  o^ 


Page  494] 


TABLE  10. 
Mean  Time  of  Suit's  Visible  Rising  and  Setting. 


^    -S 


1^         w 

.15    3 


^^ 


•xojddv 


xoiddy 


5"^ 


^OQpjinadcQcdaOP^aQ 


^  ■«<  rt  •g<  rH -^  1-1 -a"  1-1  ^  .H    -31  r-l  CO  T-l  eO  1-1  eC  r-l  CC  r-l 
SSi-HOrHOrHOr-lOi-l    O  1-1  O  i-(  O  r-l  O  ■-(  O  rt 


pjaQPjtspjccQjcntf  cQ  pd  co  P4  %  pj  cc  tf  «:  cj  c»  pj  co  pj  aa  oj  oi  PJ  en  pj  co  SIh  co 


$SOr-tOrHOt-IOT-»Ot-(    Or-tOi— lOr^OfHOi— I 


O-HOrlOrHOr-lOrH 
?0  O  <D  *0  50  ^  ^  O  ^  !0 


S'lCcoinNioojioc^to'M 
Or-IOi-lOrtOrHOi-l 


©>-IOT-lOiHO.-40rH 
CO  ^  ^  CO  >0  CO  O  to  CO  CO 


OrHOiHOr-cOi-lOrt 

COCOCOCOCOCOCOCOCOCO 


S"cc-<j<t~Ti<r.-.jit^«ct^c<5,ooeoacc<occo)acc^a>oi 
OrHOi-IOr-(OrHOi-lOi-IOrHOT-IOi-IOr-l 

.tfCOCOCOCOCOcOCOcOCOCOcOCOCOCOCOCOCOCOcocO 


Oi-IOi-IOr-IOi-HOrHOi-lOr-l,-lrti-li-lr-(iH 
^COCOCOCOCOCOCOCOCOCO.COCOCOCOCOCOCOCOCOCO 


.:  00  CO  30  ic  01 10  a>  •<»<  a»  ■*  o -.»<  o  «  ^h  m  ih  co  i-m  oj  c^  c^  .-i « i-i  co  o  ■*  o 

SOr-IOi-IO-HOr-IO.-l    T-HtHr-lrtr-lrHrtT-lrHr-l    •Hi-HrHi-li-li-li-li-lrHi-t 
^COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO 


Si-ieO»HC0^«THeCi-IC«i-HrorHM^«i-IMrHeCrf 
.HOr-IO.-tOr-IOrHlc5i-(Oi-IO^Oi-IOrtOrt 

COCOCOCOCOCOCOCOCOCCCOCOCOCOCOCOCOCOCOCOCOCO 


rtOrtOrHOi-lOrHOTH 

cocococococococococococo 


CO  C^  CO  C^  CO  t-l  t^  r-l  r^  r-l    t^  r-(  r*  rH  t^  O  1^  O  t^  O  t^  O 

OrHOi-IOi-lOi-lOrH    O  1-I  O  f-H  O  i-H  O  ■-I  O  tH  O  rH 

COCOCOCOCOCOCOCOCOCO  cocococococococococococo 


Or.lOr-lSr-l©i-lO.HOTHOrHOi-(OrHi-lrHi-li-l 
COCOCOCOCOCOCOCOCOCOCOCO  CO  COCOCOCOCOCOCOCOCO 


Y-(0!-lrti-trHi-(rHTH,.Hi-(r-li-liHOr-lOr-tOi-'0 
COCOCOCOCOCOCOCOCOCO   CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


rH  (N  .-I  >-l  ^  1-1  C^  •-I  C^  O    MOMOC5  0sC0»'^^-^cr0 
1-1  i-H  rH  r-(  rH  1-1  iH  r-l  i-H  rH    rH  i-t  >-l  i-l  rH  O  r-l  O  rH  O  rH  O 

CO  CO  CO  cococococococo  cocococococococococococo 


~;xc0«iC00si0O>OO-*N-l'^'-'=^^"C^C^50^Wi-l'*r^-*OiCOiffiS    COWCOOOt^aOt^l^OOt^QCCO 
SOr-IOr-<0"-li-tt-li-li-li-lr-<rtrHi-lT-lT-lT-lrti-lii-li-li-lTHrHr-irHi-lr-.0    i-IOr-IOrHOi-IO.-(Oi-IO 

^COCOCOCOCOCOCOCOCOCO  CO  cococococococococococococococococococococococococococococococo 


■»J<OiCOSiOCC»COOCOOOCOt^ 
rtOiHOi-(Oi-IOrHOTHO 

CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


g"oii^ocDo>o.Hic^-*c^-*c<i«iMMccc^-^i-ilin>-i>oocoocoo>t^gji^ooooQoa>t^aj«50cooin 
^COCOCOCOCOCOCOCOCOCO  cocococococococococococococococococococolcocococococococococococo 


ss 


05I^OCO-HCOi-liOO)iC|J^'*CO-*Tt<05-*CliCrH|COi-ICOOt^OX35CCX|Oi9COH^OCO.HvOC<liCN- 


lOC^OlMOM  O 

^COCOCOCOCOCOCOCOCOCO  cocococococococococolcocococococococococo'cocococococococococococo 


;O00»-Ht~-HCO(NCOlNiO 


^COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO 


OTT)iT*<'^iOCOiCC-4CO-H 


COCOCOCOCOCOCOCOCOCO  cocococococococococococo 


iOOOTHt^i-ICOC^COCOiCl'»3**rJ<Tj*cO»CC^cOC^t^i-IOOOaiOsascOOI^r-it^ 


4 


COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO 


OOOrHt^O)t^CCCO-^iO 


^COCOCOCOCOCOCOCOCOCO 


-JOOOtHl>-cNI>COcO-.l<iO 


^COCOCOCOCOCOCOCOCOCO 


c»OODrHt^C^COMiCTj«-.JH    iCCOCOC^t^T-iODOaiOS 


^COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO 


[COCOCOCOCOCOCOCOCOCO 


rHCpiM'Cm3<'*C0>OI^CO<N 

cocococococococococococo 


iC^iCCCcOC^t^^XO 


CO  CO  COCDCOCOCOCOCOCO 


iC^coMt^lNXrtOO 


COCOCOCOCOCOCOCOCOCO 


gOXr-lt^C^COCOtO-c)<-*   COeOr-lNXi-l0500g 
^  COCOCOCOCOCOCOCOCOCO    CO  COCOCOCOCOCOCOCOCO 


oiopoi^x 


SOI  ^  X  J<  I^  C^  CO 
OOJOOIOC^  o 

:cococococococo>o 


Oi^OXr-H^C-lCpCOlC 
COCOCOCOCOCOCOCOCOCO 


OXi-ll-»!NCpCCiO"*-J< 
C^OCIOC-IOC^OMO 

COCOCOCOCOCOCOCOCOCO 


COCOCOCOCOCOCOCOCOCO 


g'OXC^t^MCC^iOiC-* 

^COCOCOCOCOCOCOCOCOCO 


gOX'-icos^incOTj'Tjico 

^COCOCOCOCOCOCOCOCOCO 


l^r-ICO<NiCMOT-crC^ 


^COCOCOCOCOCOCOCOCOCO 


COC^t^r-IXOSJiOlrHCC 
iHr-li-l.-liH.H.-IO(NO 

COCOCOCOCOCOCOCOCOCO 


COm-^'»'>CCOCOClt^>-lXrH 
COCOCOCOCOCOCOCOCOOCOCO 


-»(<  T)<  lO  CO  CO  C^  t- T 


r^OCMOlMOC^OlNOC^liO 

cocococococococococDcoic 


lOMCOC^XiHOlQOCnT-HX 


C02)t~i-l0>pO0Ji-<t~C^cp 

c^oc^oc^ocoincoiocoiS 

COCOCOCOCOCOCOlOCO^COlC 


oj  t^  eo  CO -o"  I©  lO  CO  CO  cj  ao  "H  01  p  Q  op  T-H  t~  CO  CD  ■*  lO 
c^oc<ioc^Of5[oc^o  ?SoMoeouicoiOcoi25co3 

COCOCOCOCOCOCOCOCOCO    COCOCOCOCOlCCOiOCOlCCOlC 


COC»l^i-IXOiOsX.-lt~ 


COCOCOCOCOCOCOCOCOCO 


C0rHt^OXX05t^i-tCp 
i-(rH,-lrHrHOtHOC^O 

COCOCOCOCOCOCOCOCOCO 


)  c^  in  ■«  ■*  ic  CO 


OICPC<MC-*COCOC^t^rtlciQCTiOXTHCOC.--,     ,      . 

S^OC^OMOC^OMO  l5  iC  CO  vO  CO  ift  CO  iC  ci  16  CO  lO 

COCOCOCOCOCOCOCOCOCO   coiCCOiCCOiCCOlOCOiCCOiC 


c^iccocoioricopxos 

COCOCOCOCOCOCOCOCOtC 


0>I^OCC{N>CCOCOiOC^cOQ 
C^iCCOiCCOiCCOlCCOincOlS 

COiCCOiOCOiCCOlCcOiCCOiO 


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coin  CO  in  CO  in 


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coin  CO  in  coin  coin  CO  in 


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coincoincoincoincoincoin 


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m      CO     i~     X 


l~       X       era 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  495 


^   a 


M   a 


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■xoiddy 


HB3 


13    ?3 


C^        Cn|        C^        C^I        M 


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cc      as      o    ,  ^-      CI      CO      -7"      ic       '—      1^      00      d      o 


Page  496] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


o3       to 

*-   a 


0)        CI 

O    II 


5 


^z 


o    5 


-^     cj     eo 


■xojddv     S=» 


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to  -.o  o  to  o  <o 


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to  to  to  to  to  to 
to  to  to  to  to  to 


I— <  O  1— I  O  1— t  O  rH 

to  to  to  to  to  to  to  to 

Sot~o  tot'-o 
pH  O  I-.  O  >— '  O  I-* 

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totototototototo 


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to  '-O  to  to 

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to  to   to  to  t 

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in    I  lo     in 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  497 


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22489—03- 


-32 


Page  498] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


C3       » 


s  a  a 


3   s 


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s  xr 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Kising  and  Setting. 


[Page  499 


•xoiddy 


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5^        -^tp^tpS        iC»bift»cS        SiOioiOeo 


Page  600] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


J 


S 

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c^xSE^xfiSMQ^coC^yJoix 


:'^iaiOiOiOiCi«>C«JiO    lOJSiriiCtCiCiOiftiOiO    OtOi«iOiC>0"3»QiCiO    iOiC?2>ClCift04t5u5iOiO»C 
aiftiCiOiCiCidCiOiCiO  lOiCJiOiOiCiOiCiOiCiO   uOiOiCtOidOiOiCiftiC   iC^»ftiftiC»CiOutiiC»f5iCiC 


;  i35  iC  »c  3  lO  i« 
»  lif  »0  lO  lO  i'^  lO 


»  ^^  0>  W  Ol  C^  OS 

:  ifl  ic  lO  lo  »c  iC 
;  lO  iC  lO  »CiC  iC 


iCtOiOift  kOiOiO^iCiOiCiQiOiO  liOiC^»?l»«iOiOiOi/i;ift    iCi«»QiC»CidOiOiC»OtOiO 


:  C^  Q  00  Q  CO  o 


e  lO  CO  O  ^  l£2  to 


'^0'^oiijo»oos^Oioa>--ooo-^ccr*r*Gor^GO?pootolaoooi';oasioai>coiftQ'^ 

»0  O  »C  O  kO  0»0»0»C»CiCiCiOiC    lOOiOiCvOiOiOiCiOiO  |»C  iOiOiC!>0>0»CiOOiOOiC 
iCtOi0^iC^idOiOiCiOiO»0»0  V5iO»OidCiCiOiO»CiO   iOiOiCiOiOidOtCOiOtOiC 


•  »0  1^  lO  O  i«  o 


lOOiOOUCOiOiCLOiOiCiOiOiO    iCiOiOiOiCiOiC*COiQ 
iCOiC^OiOcOiOiOiOiOiOiCidC   >CiCiOiCiCiCi»C>iC50ift 


OicoicoifboiiS^iicoiib 

tOiOtOi^OiOCOiOtOiC^iC 


iiccoic^coM 

;  40  O  iC  O  >«  O 
»  lO  CO  tC  CD  iC  CO 


OiCO  kCOiCOiOiOiCiCidC    OiOOiCOiCOiQOiCiO'OOiOOiCOvftOiOOiO 

ii550»C^»CtOin«0^iC^iCiOiO    ?OiCCOiC«OiCOiO:0»cUoiO«Oi0^inO»0«OiC<OiC 


s^ 


;  ?o  "g*  IX)  sc  r-  M 
:  lO  O  lC  OO  O 

;  iT-  o  to  50  lO  to 


t>-  (N  35  '-' 
lOOiCO 


iooi00oooico55 

lO^OiOCO^OO^tC^iO 


«;t^if5r*TfGio«QOcoasc^ 

giOOmOiOOLOOiOO 
-£ii050iCtDiO:OiCO»C^ 


-;t^iCQO-3*as^aicooco 

StOOiSOiCOiOOOO 

-iiceoiosoiAcoiCOOco 


oooooi>ooic 

?0'iO(OC050«00':OOiC 


OOOOOOOOOvO 

C0':0«0C0C0'OOOc0iC 


"^acc^i^coh*coco-*5ol'g«»oiCioo-Tr'»'COi>?or^(N 

&iOOiCOiOO»COiO'0»CO>COiCOiOOiCOiO 
C0i0t0iC<OO'0iC?0i0,':0iC<0»0«0iC«0in<0»C«0iC 


wxTtt>-Tfr^icOipohP'f^t^>0'Xi"^oDcc(^c^O'r) 
Oi.cou:>oiooi?5o»ooiooiooi6oinoici-iic 

?OiO«0»COiCcOiOOiC«0»0«OiC<0»COiC50»ncOiC 


SXi^t^Cpt^b^'^Ot^iC 
iCOiCOiCOiCiOtO 

oioo»c?oiO':oir5!Oin 


g*X?pOl»CQiCQ^'-<C0 
iSou^OOOOOOO 

^iCOtO^CO^^OtOCO 


oi>oi>oooooin 

OCOOtO^^OO^OiC 


-JOO^OfOtOO^OtOtOtO 


Soot^r'-GOt^^co^iO 
iOOiCO»COiCO>C 

OiOtOiCcOiCOiC^iO 


tOiOOiOtOiCtOiCCOiO^OiO 


r-HiOrHii5i-H»OrH4jOi-HtC^-*iC 

io»0!OiOtoic^»coio«Oir; 


~  —   —   —  —     -     ^iCOuOOtOi— tiftrHlOr-tlOi—^irai— liOrHiCi-HlOi—t^ 


:otoococo;o:ocotOiO 


:Oooooooooo 

i^o^ooto^ootoocoo 


oooi>oooooic 


tOiriSOiOtOOtOiC^OiC   Oi-O^iO^^tOiCCOiC^OiC 


eoooooooooo 

^50:00^t0'^50^^<0 


iCCCOiMt^t-tCCOOsCi 

ooooooooouo 

iO:OtOOO!:OOOcOiO 


OGCi-Ht^iMtOCOiC'^Tt'    iOCCOC^GO'-ia>QO<?lr--CC 
rliOi— 'lOrHlOrHiSrHiO    rHiOi-HOi-HOi-tiCC^'^lM^ 

to  vO  ^  »0  O  vO  to  1/5  I©  iC    O  iC  «0  ift  O  iC  O  »C  «0  lO  O  lO 


S*  ^  a>  c^i  00  CO  r^  ■:**  ^  If:  iC 
oooooooooo 

^tocooco^co^^^oco 


oooooooooo 

^^tootoooco^oto 


Scoi^'^ioD'-H^ooas 
OO&OOOOf-iiC 

tOO^O'lOOtD'OOOiC 


i-(oO!Nr^cO'y3iC»oO'fh*coaoc^ai005i'>iaccor* 

!0»C^mOU^«0iCtDiC  'COiC^iCOiCtOiC^iOtOO 


r^coxc^^t-tOQC^o 

OOOOOOiHOr-iiC 

COeO«0?0«0«0^?0'-OiC 


«i*!MOCCCO'^t^iC'©cpiC 

$:0i-(00000000 

^CO«OOtOX>0';OtOCO«0 


COTff^COO"— 'i-HOCOOi 
OOOOrHOiHOrHiC 

OCO^OO'^OOtOiC 


coQO'^i^tccoso**'t^co  c^MOT-^.-40ic^a0'^r^ic*o 

CO»OOiOCOt0^i0^iC  ;?OO^iOOvO:OiOOtCO>C 


'^0D»0t-«0»0G0'^0lC0Oi-<?1QC0aC'^t-':0:0t^»C 
?OiO«OiCOiOtOiO:0»okoiOOi/iCOiOOiO^»C^»0 


■I  O  ■*  Oi  iC  Xi  O  : 


^^  :o  to 


OOOOOOO 
to  to  to  CO  to  CO  to 


S'^OCOi-Hi-HC^Q-^OS 
Or-tO—lOi-tOr-llC 

UotOtOtOtOtOtOtCtOiC 


tCGCtotocciCOscooirjIc^Qcoaiior-totoooioascc 

tOiOtOiOtDiOtO»i^tOiC  ,tOiOtOiOtOiCtOiCtO»r5tOiC 


»i^o-:l*a?i^qot£>teG£ju5iq>5?o<N'r^r-tcoo^oo 
itototototototototoo 


:iti-(0 

*  to  to  to 


OOOOOOO 

to  to  to  to  to  to  to 


ior^wioaj-^oc^iMrH 

r-tiCr-tiOr-liCC^iCi'MiC 

tOlCtOiCtOiCtOiTJtOiC 


gSSS 

f' CO  CO  CO 


o>  o  t^  t^  CO  go  ^ 
oooooSo 

CO  CO  CO  CO  CO  CO  CO 


fHOi— tOt-<0»— (iC»— liO 
COCOCOCOCOCOCOiCCOiO 


t^-COOC^OOTrHi-ICOO 
COiOCOlOCOlOCO^CCOiCi 


sgs§ 

^COCOCO 


GO  »c  r^  ^  iC  GO  "^ 

ooooooo 

CO  CO  CO  CO  CO  CO  CO 


OOrH 
CO  CO  CO 


— I  C^  OS  ^  GO  lO  CO 
O  rH  to  r-t  iC  •— *  »0 

CO  CO  to  CD  O  CO  IC 


moiiOoocococcioo>co.-icq 

COtCCOiOCOLOCOtCCOiCCOtC 


COLOCOtOCOtCCOlCCOLnCOtO 


CO  lC  CO  >0  CO  to  CO  to  CO  to    CO  to  CO  to  CO  to  CO  tO  CO  to  CO  tO 


SooS 
^cococo 


t^*^  CO  CO    -  -     -. 

ooooooo 

CO  CO  CO  CO  CO  CO  CO 


lO  t-  CO   0>  iH  rt 

ioOrt 

:COCOCO 


CO  CO  tO  CO  to  CO  to 


r~coo»iNp©c^«'*co  CO  to  t^  M  g>  rH  .-I  o  ec  GO  to  CO 
■-HtOr-iiorii/sc^'j'c^'V  ijTfffqTjifjTrco-^coaSoiSm 

COtOCOtOCOtOCOtOCOtO   COtOCOtOCOtOCOtOCOtOCOtO 


S'OGOrH 
©oo 

^- CO  CO  CO 


gg3gg§g 

to  to  to  to  to  to  to 


S8S 

CO  CO  CO 


lO  to  iC  to  iC  to  ift 


gsss 


S^^  CO  CO  rH  -^  OS 
OOOOOiO 

CO  to  CO  to  to  CO  ^ 


§ioS 
CO  toco 


coo-*-^  r)«0 

tO  r-t  tO  r-<  tO  f— I  tO 
tO  CO  to  CO  tO  CO  tO 


p^QQMcQpi^aaQjaQajco  pijaopiJcApjoBp^aop^oD  adxp^xajoopfcfip^co 


COi-HOOOOOOflcOCC-^   lOC^t^OOJOO—'l^COiOiQCO 
COtOCOtOCOtOCOtOCOtO   cOiOCOtOCOtOCOtOCOtOCOtO 


ioo»r-t~ootoococ^c^i'?'OcooOGCcoQtCJe^'*o 

CO  to  CO  to  CO  lO  CO  lO  CO  to  CO  to  CO  to  CO  to  CO  tO  CO  tO  CO  to 


OHCcp^oopjQQp^cnp^ccMai 


a  o 

&  .2 

OQ  el 

0  S 

1  3 


5    r 


^ 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  501 


•xojdd  V 


^^ 


r^ 


C^        Cvj        CJ 


IN        C^        M        C^        CO 


CO      '^      la       <©      i-^      Qi 

CO      CO      00       CO      CO      o 


PJOQP^XP^CIQQJ^^CIQ 


QHXpijxp^coQ^coc^GCpi^xpiHaQPi^oDQi^cQp^x  QjcQp^asp^GCP<ccp:^7^ 


g*C0iCC0iCc0iOC0»O^»C 


1— (tCrH;0.-^:pi-ft^— lO 


rHCDr-('Or-ILQT-liCi-*lO    f-HlCKNiCi'NlCOlu 

lO  lO  iC  lO  iC  iQ  tC  iC  iCiC  lO  lO  lO  ^  iCiC  C^  lO  iC  lO 

lO  lO  iC  kO  lO  vC  iC  lO  »d^  lO  iC  iC  iC  iC  lO  lO  iC  lO  lO 

'^■«*'^-^iC'«5*0'q"iCCOiOCO^CO;pC050CO(DCO 


t^  ^  I"*  ^  t^  CO  (^  CO  t^  CO 


>Q0^G0"r!*OS'^(J>C0QCO 


i^-}(,HCOC^CO^C^?^CSl 


gCOQC^Q'MrHCqr-IW 


QOCOCOCOOOC^OO'MOiNOSTHOrHQi-lOf-iOO 


OiOOiCOiOOiOOiO 


COOi-^Oi-^Oi-3'OOiCCO 


COC^COrHCOi-f^fH-^Q 


-^COCOCOC<l^(M^i-*lOrH 


OOi-l'^M'^COCOCO'N 


goa>osi340>oooooot^ 


i-i<oc^O(N»ceoin'^'^ 


OOtO^^tCtOiO^U^ 


"xo  add  V 


S*^^rHOC^0>C005C0G0 


a> '^  QO  »o  op  «o  c* 
iC  o  ic  «o  vC  <o  iC 


i-tooc^opc^t^coo-^<p]iCiCi02J^cor^coooc^ 


tOiO'^iCtOiCtOiCtOiC 


i-H-^t'.-c^^^iMCOC^CO 


^t^iCt^iCtO^iCt^iC 


tO^Ot^iOOO-^OiCOOCO 


Q0^05C0OC^Ot-lT-tO 


C^OiC000'^r>-iO(D<©iO 

C^CO!NCOC^COC^0OiMCO 


C^'<fC^'**'CS'*WCOC^CO 


!X)i-^r*?CQOiQOi"^Qco 

CMC0C^C0C^ICO(NCOeOCO 


sgiCOi^ooiN^r^ootpoxo 


lO  CO  lO  ic  ic  ;o  ic 


OSiCp'^^COMC^COtH 
:OiC«OiCCOiC«OiCtOiC 


<N^05COMCOCMCO?^CO 


;gt*OOGOr*Oa«OOiOi-H^I<NCOCO!M-^^iCO'Ogi 


a  eOiC  CO  U 


COiCCOiO«OiO«OiOCOiO 


l>QQQ0r^Q*.O^iOC^CO 

c^coc^cococococococo 

.(OU5COiCCOiOCOiO«OiC 


0»C— I'^S^COCOf-H^O 

cocococococOcococOco 

tOiCtO»C«OiCcOincOiC 


coc<ii2r-*coot^oQait* 

COCOCOCOCOCOCOCnCOC^ 

;OiCOtCcOtC<;OiCCOiC 


»pOOi-Hr>;C^<OC^'^Tf*Cp!vpC<l«5rHl 
a  CO  lA  CO  t 


*  IN  "*  C^  -^  CS  Tf  ^ 

3  ic  «o  m  CO  lO  CO  ic 


i-icO!N»r5co3;>ococO'-' 
cocococococOcocococo 

COiCCOvCCOiCcOiCCOiC 


it^QOipOt>-C^COCO'^ 

]COCOCOC^'<»'CStJ<N'^N 

COiCCOiOCOiCCOiCcOiO 


a  COiC  CO 


CO  "^  iCiQ  CO  t^  IN 
Tj*  (N --J*  <N -^  C^ -^ 

lA  COlCCO^  CO^ 


a'<«*<cOiOi«cOCOOOiNOiO 

:o4^c^    —    ■■  -■    -  --    - 

«  CO  lC  CO 


2co'^r*coosc^pO'NOi 
:in^(Ntpc^'^cO'^coco 

aCOlOCOlCCOlO^^COLC 


)»-l  OiOQCirHt 


S  CO  CO  CO  CO  CO 
5  CO  ITS  CO  lO  «0  iCi 


5  CO  CO  cO 
SiOcOiC 


cot^^jioco-^ 

CO  CO  CO  CO  CO  CO 
CO»CCOiC  COiO 


sOOCOOiNi-HOCOO-^t^ 

:*^-^eo-^cO'^c'5cococo 

•  COlOcOlCcOiCcOlO^^ 


»OWNOCOO>iCt*t>a 

•  CO^CO^COCOCOCOOOCO 

aCOtOCOvOCOlOCOiOCOiA 


CQ  CC  CC 


CC  CO  CO  CO  CC  CO 


cococococococcco 


ooi-it^eo«c-^-*ocot^-^ 


CO  CO  CO 

toicto 


.-I  00  CO  to 

toiotDin 


tda<:DiCcOLCOiCO^ 
lOiCtOCOOOC^OOi-HOO 

ko»OtOiO«DiC;Oi^(0»0 


tOiOCO 


OJCOt- 


to  ic  to  in 


ooc^<50iN05'<ri^tc4C 

•»f<CSSC<linr-(iCi-li5r-( 
tOiOtOiOtOLOtOifitCiC 


to  t^iO 
CO  CO  CO 

lO  tOiO 


oocoOi-HC^g 

CO  CO  ^  CO  ^  CO 
tOiO  t0  4C  to  iC 


1  1-1  r-l  CO  »  in  00 
5  ■.ji  CO  ■*  OJ  "#  ?1 

;  to  in  to  ir;>  to  in 


>e^Qts>inr»t>-toos'.ji 
:co^cocococococococo 

itointointoiotointoin 


«  CO  -^  CO 

5  in  to  in 


■.I*  a>  to  t^  t-*  in 

■*  CM -9"  ?J  ■■»' cJi 

to  in  to  in  to  in 


s  t>-t~-in 
>  in  to  in 


to  in  coin 


CMO'^OOtOtOCC'^OCM 
inCMiOrlinrHinrHSi-l 

toictointointoint^in 


to  to  op 
to  in  to 


in  to  in 


c-Jr-i-5io> 
inNinrH 

to  in  to  in 


iCOiccoicr^ict^iot^tc 


OSC0.-li-HCOOa»CQ0r-CO 
COiCCOtCcOiOCOiAcOiC 


o>*rr-ii-tcoaicpt>-GO"3< 

iCi-(OrHOOOOOO 
COiCt^iCI>iCI>iCI.^iC 


iCOCOCOCOCOCOCOcO^CO 

IcOiOCOiOCOiOCOiCCOift 


)in-J3in 


to  to  00  •>»<  o  c< 
■<>•  CM  ■«"  CM  35  CM 

to  in  to  in  to  in 


COiCcOiCcOiCCOiCt>-iC 


lO  O  CO  c^  p 
1/2 1^  lO  r»  ic 


jiCcOr-iCOiCOp^iNp 

-cocococococo^co'^c^ 

aCOiCCOiCCOiCcOlCCO^ 


»f*^OQMPOC^OD^CO 
:COCOCOCO"*COTfC^'^<N 

IcO^COiCCOiOCOiCCOiC 


«  r-.cO*C 
«C^'*  IN 

5  1/5  CO  iC 


Gc  CO  p  i-H  e^j  OS 

CO  iC  CO  »0  CO  iC 


-^I>.cOu^04C0i— ii-rcO^ 
lAi— (iCrHiCrHOT-<PP 

coiccoiccoior^ici^ic 


gS2 

t~ini^ 


.-J  CO  ^in  to 

OrHlC  THl?5 

lO  r- ■.»<  t^  Tji 


>  in  to  in 


SOCMOC^tO 
CMinrHinrH 

to  in  to  in  to  lO 


t^-^o»CMf-<oacot^tpin 
inr-iini-ioooooo 

tointoint^int^int^in 


oo 
c-in 


-Hoeo 

1— I  O  »-l 

i>int^ 


r^  to-^  oi  CM 
in  r-H  in  I— '  in 

TT  t-  Tf  l-   ■<»< 


»t**-(a>a>»-it^coininco 
:cceocofjTt<cM-*(N'*CM, 

Jtointointointointoin 


l-CMTTrH 

5  in  to  in 


>-H  to  CO  ■'J' in  CM 
to  in  to  in  to  in 


Soot^-coininc^ooQ 
-hOOOOOOOO 

toint^int^ini>int^in 


ot^cointocM^Oij^to 


f-linr-l 


in«  tji  fM  ■ 

^  l^  ^  t^  TJI 


"tOOQOOtOO-^CMCM'Tj'O 
:COCMeOCM-^CM-*CMTj<CM 

itointointointointoin 


toooooint5cOMr-(ino> 
^T-H'^T— tin.— iici— (tno 

tointointointointoin 


i^toO'<>cMr-iino>r~tp 
inoooooomoin 

tcini>'ini>.int»'.jit>-^ 


|0  -^  CO  ^  to 

U-HinT-iini-i 

|t>.  Tji  r»  rji  t- 


00  05  in  pi  CM 

■*  —  TfCM  -91 

■.}*  t^  Tji  r* -^ 


91       I 


tfcQrtccpiHCCpaccffJccOHCoeJaQDJodKoDpHCO 


tfcoPJaQP^cntfuipHCCP^oaPJastfaQpjcoCdcQ 


CMNcMCMCQ  CMCM^flCO 


Page  502] 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


S 

CO 

o 


1 


•xojddv 


•xojddv 


^^ 


5S 


5 


in      to     t- 


«!»pl5M«OptfCO(J5M 


St^  t^  t^  r^  r^  t^  t^  QO  r*  00  r*  cc  r*  go  t^  ao  t^  cc  so  ao 
TI"  iC  ■<)' IC -^  >0 -"t  "3  tC  iO  -^  >C -^  is  Tf>  iS  TP  is -^  i3 

^»CiOlC»C»OlOiO»OidCiO»OiCiOif5iOiniC»CiC 


S     3 


lO       o 


dHaQpHSOpjcQpjcfifriJaQ 


pcJagPnOQpcJcopdccpjaQ 


iOiO»OiOiOiCidCift»fl 


^» 


l>        00        a        Q 
lO       lO       »0        CD 


e^ccp^ccf:cjcof:^ci!}p^cG 


iC  iC  »C  lO  *C  iC  lO  lO  iQ  iC  lO  lO  iC  iC  iC  lO  »C  »C  lO  »5i 


Ma»0*GOCCGOCCt^-3«t^ 


O-^O-rr  OtI^O-"?*©^    rH 'Tf  i-i  tJ«  rH  tP  rH '^  rH  Tf* 


i-HCOT-twSrHCOi-lCOiHW 
-OiCcOiCOiOCOin<^iO 


(N  C^  CCiM  ■<*«  1-^ -^  O  »C  Ol  1:0  go  t^  CC  00  1^  00  CO  OitO 
to  »0  «0  lO  ?D  iC  CO  iC  O  iC  :0  iC  !0  iC  CD  iC  CO  lO  CO  lO 


COiOcOiOCOiC-COiCCOiC 


t^ccoooOiJit^aicoOic  i-H"»tccc«5Tfc^ir5t-<cOQ 

r-toSi-HCCrHCOi— ICCMCOC^CCCJCOC^CCC^COC^CO 
CDiOCOiCCOiOCOiOcOid  pOiCcOiOcO»OCD»CCOiC 


-  Oicor^ 

SiCcOKO 


OS  CO  1-H  lO  C^  00 

CDiCCOiC  COiC 


C^i^CO-^-^CCiftiMCOi-H 
CDiCcOiCCDiOcOiOCOiC 


GO<MOl.-IOOrHGOC^t^ 


cOiCc 


a  CO  CO  CO  c^  CO  cs 

;  CD  iC  CD  if5  CO  iC 


CO  Oi  '^  r^  lit)  CD  i-"-  iC 


COC4COCNCO<N 

'O  iC  CD  lO  CO  lO 


r^OOiOiOGOf-'I-^tNiO 
C^COC^tNCOfNCO-MCOiM 

^DiCcOiOCDiiOcOiCcOiO 


sc^coc^ 
51OC01C 


t^  iH  00  OS  O  t- 
CO  C^  CO  f-l -^  tH 

COiC  COiC  COiO 


COC^  COC^C0!NCO?5 
COiCCOiCcOiOcOiC 


asc^i-iocooi'<**r*cDir:' 

COC^'^C^Tj'i-l-^r-l-^r-1 

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icoc5 

3CDiC 


CDiCCOiCCOiCcOiC 


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COiCCD 


i-HiOfHiCrH 
liT  CD  iC  CO  iC 


gcooot^r^aicoo"^-Hco 
COC^COC^CO(N'^(N'^<M 

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I  ^  i-( -^  iH  L(5  rl 

S  CO  lO  CD  lO  CO  iC 


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^COiOCOiCCDvCCDiCcOiC 


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COiCcOiOcOiCcOu^^iiO 


COrH  10 
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ooco01-<(^^ol^I•>. 


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iOGCt^iCasC0<Mi-H-«I<c 


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5iC  COLO 


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CO  iCl^  lO  t^  Tj* 


3000 

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t-ooot.cD'M^'^c^r-ai 


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t-H  lO  »— I  lO  I— I 

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i-tCDiCO'^iCC^t-^OOiOO'-HC 


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(N-^fNTj^cN-^CO-^OOOO   O0CO'^C<l'<^CN-^C>linTH 

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10  Clio 


-*<00t)I 


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00-*  00-^ 


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lOi-HOOOOr-liBiHlC 

t^-a<00'*«'-^ODCOOOCO 


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-INTt<(NTj<COCOCOCOO0CO    --rC^-^fN-^rHinrHiOT-t 

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rioa>ootOi-i(Nioosooio 

jINCOCJCOCOCOOOiNeOlN 


P^ccPhcqPhcoP^coPJco 


sss 


SCOlO  c 
i-H  lO  r 

I  -^  ooco  c 


iNiN«500Q-*'^roOliO 


QHQQPjCQI^OQpljUipHOQ 


'Ti' 


•»»•        "^        iC 


00-*  00 


10  ■*  Oi  O  ■*  ^3  00 
in  rH -T  C^  •^  IN  CO 

CO  00  CO  00  CO  00  CO 


!iC<NO 

HiniNio 
3000000 


ooeoic  t^ciQ 

O)  "J*  CO  CO  ■^00 
00  CO  00  CO  00  CO 


c5^m' 


1 1^ -T< -^  1-^  C^  0> 
'  00  CO -^  (N  in  rH 

1 00  00  00  CO  00  00 


>t^t^OTf<coc<inrttp 

5COCOeOT)>(Ninr-lOO 

)ooooccoococococnc<5 


Sr-tp-^t^oinoo-^ai 
sco^c^Tj^^^LOooin 

iOOOOCOOOCOODCOOSC^ 


Oi5t»p4=op!3a6c4(»Wc»picotfa3pi;ooa3a3pia> 


rt        IN        C3        ■^        tQ      ^S       '""        OS     "^ 

ininininin      inuoinin 


TABLE  10. 

Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  503 


o    a 


•xoaddy 


P5  aj  03  CO  «  73  rt  cfj  rt  CO 


Wco'McoCKHCBPiccMccPSMtfcoPiGdrtccOHCC 


:iCOiooiao-*OTjio 


n 


coocoocoocoocco 


d:h  cd  piH  CO  a;  cc  jii  aJ  si  X*  Cij  x' 


C^?1C5cCC^CQN0trHCCi-IC0 


;ooo 


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iC  CC  iC  CC  »d 


>OG0C5giC5Ot;THO_<N 


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TttCCCO'^'N^prHt^asCO 

coiC«»AcoiScCiOc^i3 


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to  iC  O  iC  O  lO  CO 


Ou^  CO  iC  O  iC  O 


-MiCi— i^pOOOOsOiI^OCOC^ 


O  i-H  O  f-l  ,-1  ,-(  rl 
CO  lO  CO  iC  CO  vC  CO 


3010000I^'-'CO(N 
-CC^CCiCWiOCOiO 


»poc 


CO-^COiCCOiOCOiC 


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coiccoiAcoiCcoiS 


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cOC^iOCO'^'tCOiC'McO.— tl 


lO  CO  iC  CO  o 


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f- CM  rococo 

COiCCOiOCO 


COiCCOiO 
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t»o»c 


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jcoiCcOiCcoiScoiC.  coo 

'lO  iQiCiCiCidTSiOiCCO 


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lO  CO  Iff  cOiC 


CI  CO  CO  »C  tJ*  lO  iC 

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CO  lO  CO  lO  CO  lO  CO 


5  CC  t~-  CO  I-  -^  CO  iC 


Scoin 

iff  tff  iC 


'-fcocoi^cococMOir^ai 

COiffCOiffCOiffCOiffCOO 
iffiffiffiOiffiffiffiffiffiff 


OOQ^  OS 
COOCOOCM 

Iff  CO  >ff  CO  Iff 


O  OC  CI  t>-  CO  t^  -^ 

O  CM  O  Ct  O  CI  O 

CO  iff  CO  Iff  CO  Iff  CO 


71  CO  00  CO  00 
CO  iff  CO  iff  CO 

iff  Iff  Iff  Ifflff 


S  CO  iff 
Iff  Iff  iff 


CO  Iff 


cocoiffr^-t'^-cooccoaa 

COiffCOiffCOiffCOiffCOiff 
ifflfflfflfflfflfflfflfflfflff 


I01CJO»-*^^0.— I^CJCICO 


CO  Iff  CO 

iff  Iff  iff  CO  iff 


OCOO  CI  OCMO 
CO  Iff  CO  iff  CO  iff  CO 


Tf  S«iff  CO 
iff  iff  CO  Iff  iff 


Oicoo^'^oQ'^r^iff 
iff  Iff 


iff  o5  Iff 


I"-  CO  CO  CO  CO  1--  Iff  30  -^  00 
iCOiffCOiffCOiffCOiffCOiff 
Ifflfflfflfflfflfflfflfflfflff 


^  Oi  CO  d  CI 

CO  iff  CO  iff  CO 

iff  ■  Iff  lO  Iff  Iff 


SCJ  rH  -H  ^  ,-.  CM 
CO  O  CO  Occ  o 

CO  iff  CO  Iff  CO  Iff  CO 


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aCO  rH  ^ 

:  TPiff  ' 


j^  CM^  C^CM 

>*  iff  rr  Iff  ■«1«  Iff 

D  iff  Iff  iff  iff  iff 


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iff  iff  iff  iff  iff 


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Iff  Iff 


t>-co»^r»cot-.cooo 

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CM         CO        Tt 


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iff  Iff  Iff  Iff  Iff 


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Iff  •*  iff  'Tiff 

iff  Iff  Iff  Iff  iff 


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iff  ■^  Iff 
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— ^  iff  ■^  Iff 

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Iff        CO        t^        X         OS        o 


Page  504] 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


i  § 

V  so 

01  O 

5  I 


O^      II 

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3       55 


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SXCCOtC-HTfCOCOiC 
C^iOCOiCCOiCCOiOCO 


1— It^OsCll-^i— (iCCOCOiC 

iCC0'<rcO'^-«*'«Ti'^'«^Tp 


c^iO»-Ht^csQor^O'x>c^ 

OC^OC^iC(N»OCOt?5cO 


iCCOiOCOiCCOrf'CO'^'^ 


iCcoco-^c^cpor^OiOs 

iC?0»CtO»CtOiCcO^?D 


lOCOiCCOOCOiCCOiOCO 


TfT^-COiCr-ltOOaOCftOS 


t^O«Pi-HiCCOCO'^C<l!C 


CSiOC^iCCOiCCOiOCO 


?  OS  Ol  GC  O  t^  "H 

>  lO  ?o  iC  ^  iC  ^ 


COC^uOCO'^'^CO'X'C^t-* 
i0(0iO(0iC«0iCC0iO':0 


OOOOlOlCCi-Mt^MiOCO 


:  c^  oc<io 


iC  ^  iC  to  iC  CO 


OiiH00Cm>C0«O"^idO 
iCCOiCtOiCCOiCtOiOtO 


>'CiCiCiC"^^COt^<NQ0 
:C^OC^OC^O(NOC^O 

iictoictoictoiocoicto 


iiCCOiCCOiCcOiLCCOiitjCO 


THa>ooa>i-HQOc^i>.co 

iCcOiCOiOOiOOiOcO 


COtOCMt>.i-IXOai^i-* 
i-tiHi-ti-li-trHr-lrHOC^ 

iCCCiCcO^COiAtOiOCO 


tO"*j<ic»0'<!t<«ocor>.c^x 

THrHi-l»-lrHrHr->«-1i-1i-l 
iCtOiCOiO':OiO<;OiO«0 


•<ficc^cOr-(aoaiasQOi-t 

OC^OiNOOIiCC^iccO 

iCCOifSCOiOCO-^CO-^CO 


OOC^COCOtOiCCOCCiNt^ 
0<NO(NOCsiO[NOiM 

lOCDiCCOiC^iOCOiCCO 


i-'iHrH(M0(N0c50CS 

iCCOiCCOiCCOiOtOiO^ 


'^r*coqowa>i-HOp'-i 


OsC^GOCOt^-^COiOiCtO 
rHrHi-lrHrHTHr-(i-(r-li-l 

iCCOiCtOiCcDiCCOiOCO 


'^t^COOOlNOS— lOOtH 
r-()-(i-lrHi-lr-(i-l(NT-ICS 

OCOiO^OlOCOiCCOiflCO 


ICOOS^OO'^t^iO 


*QCOfliCOOS^*^  ^.^-„^  .-_^ ^ 

jiTDtOiCXi'iCOiC^i-t'O  i-C^iO:OiCcOiCOiOcD 


3  T^  ^  CO  OS 


>c^T-i?qc^^coQcoO'«*'  ai'^ai»ooQcpi>r*tDt>- 

:COOCOOCOOCOOCOO   C^OtMOC^OiMOC^O 

^iC^iCtCiCcOiO'-Ot^tC   iCtOiCCOiCcOiCtOiCcO 


JjOJNi-I^C^OC^OSCO 

iCeOiOcOiCOiOcOift-co 


•OOOiCOlTf*OCOOCO^-l 
lOCOiOcDiCcDiCCOiOtC 


oOTfr^io?D^iCt^-^oo 


i^OiOOiCtOiCCDiCCO 


iC?OiCCDiCtOiCtOiCCO 


»ift^-lTj<.— |-^<NCOC^COCO    C^COfN-^r-''g<Q>COCO 

:cooccocoocoocoo,coocoocoocoocoo 

BiC(DiC:OiCcCiCOiCcOiCOiC:OiC:OiC!^iCCO 


OicpOSt^OOCCt^QOcOOi 


tOOiCi-H-t^CO(MCOCO 
tCt0iC«0»CC0iOtOiC«O 


jr^Q'-OQCOi-Hifii-liOCq.iC^'^C^-^COCOCOCO'^ 

:coocoocoocoocoO:Coocoocoocoocoo 

JiCcDiO':OiCOif5cDi^50   lOOiOcOiOCOiCcOiCCO 


ri  -^  CI  tc  1-1 
cooeooco 

iC  CO  iC  O  iC 


COQcpOl^ 

owocoo 

CDiC  CO  lA  CO 


Sr*aoGOooast^a>t^o 

iCCOiOcOiC^OiCCOiOCO 


*55aiaiOiCiQCOQQO»HQOrHt^i— (t^C^^OC<|yDM 

:c*tOcoiCcoocoocoocoocoocoocoocoo 

iiOiOiCvdCcO'CcOiftiCO  iC  cOiCcOiOcOOcOiOcO 


COCOiCCOiQ 
CO  O  CO  O  CO 

irj  CO  iC  CO  iC 


OCOOCOC5 

CO  »C  COiC  CO 


•^■^"fJ^lOCOlCCOcOC^COrHt^^r* 
" COOCOOCCOCOOCOO 

lOcOiCcOiCCOiCCOiCcO 


ii-H!Xn-HQ0»-l0a.-H0SOaS|O0".  OQOiOOaQOi^-t 
S-TftCTriiS-'fiO'^iCi'^iCj-^iO-^OCOOCOOCOO 

*iOidCiO»COtCiCidOU3iCu0c0iCCOiCC0iCC0 


coocoococ 

lO  COiC  CO  lO  C 


t^cccococc^iCTriCto 
ccocoocoocoocoo 

iCcDiCcDiCcOiCcOi^CO 


j-^Qc-^GO'^aO'^X'COGOcooDcoasc^aiMasc^o 


iCCOiC  ?o  iC 


COiC  cOiC  CO 


»co^*cot^co^*co^*col^^ct^lCGOlCQplCaclftap 


lC  LO  iC  iC  lC 


00  ^  qo  ^  X' 
lO  '^  O  ^  lO 

iC  lO  tO  iC  lO 


rH^HOr-IO-MCl^JOSCil 
■^O'^O'^OCOOCOO 

iCCOiCCOiCcOiOCOiC.^ 


-'*«OS'*OiTt<O>C0CSC0Oi 


iOS^OC'COQOCOXCOOOCpCOCOCOt^ODl^OOr^GOt* 


D  t>- 00 1^  00 1>- 00  r^  00 1^  00  r^  00 1^  t^  t^  t-.  r-- r^  f* 


lC  lO  lO  ^  lA 


iC^  iC  ^  »c 
iC  iC  ^  lO  iC 


WcoPtHCoOiccPtHCcPtHCop^ai^tfc/itfa^SiccCtHaDD^cotfo^QScdCd 


rt         C^         CO 


c^      5^      ri      cs 


tr^    CO      r-      X      31      o     ^th"   (M      CO      Hf^'^'p 

C4  C^rJC^JC^CO  COCOCOCOCO 


PcHCoPCHxP^ccP^GCPcHa^ 


CD^    l^      ^^"^    ^         O 

CO        CO        CO        CO        Tf* 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  505 


s  i 


.H     e^     CO 


5 


^ 


00      Oi      <5-^      N      CO      ■^      "CMC 


•xojddy 


s     I 


aixaiaici^oixxx  qjccq^ccpihssOhccp^hoq 


tf-fcoo*-Di^ocofaioc»rec^iO'^0'--'-'ic^o 


iC       lO       lO       o 


rt  aj  OS  cc  03  CO  pi  aj  OS  aj  ra  aj  DJ  MJ  pi  02  c4  as  as  cc 


■*i-<COC-<r4CJC^CO.-l-f    O'TOiCiOO'^iHCOC-l 

COODCOCOCOXCOJOCOOc'c030COOOC^Oir-40sC^01 


c^?5iHSi-HCOrHeoo-*!o-*3-*iniO-*in-*ocooeortS>H4^?5r-icoocoo->j'iOirtTi'Ocoi-i 

,^-^t^'^i^'^r*'^t^Tj*t^-^t^cot^cor^coi^coGCcooocooocooocooocooocoaDcoaowoonciriOi 


^•^t>-^r*-^t^-^t^-^t^  -^i^-^t^cot^cct^cor* 


■^iCCOOCOOMi-Ht^Ni-HC^OCOS-TiSiS-^iO 

cot~coaocoocco«co«'co»coooc^aoo4aoc^oc 


M 1-1  e^ >-< i-i  1-1  ^ c^  1-H  c^  oc5ocoocoincoio-* 

.^  Tjl  t>.  ^  t~  ■^  t~  ^  I^  ■*  t>.   'J' t^  ■>>•  t^  ■*  t~  CO  t^  CO  t~ 


rfS  Tj"  b- -.jf  i> 


-3ir5  3'  __       _ 

<e^io^JOMOcoineo 


■>j"^'<i<iOcoiScooc^o5i>-ir-iNo6j3coin'* 
?5t>-coc-eot-coaoco«.coaoeoooeoaoe^ace<co 


O'r^'^-^iCCOlOeOOplOC^r-lrHrHOeqOCO 

cot*coi>coi>cor*cooocooDcooocOQOcoaocoao 


S'QQoQcoiC'OC^wocs^iireiC'Nooosc^iOiONOiaocoeot^OJC^Tf^Oi—  hjitoooe^j^gceof^c^ 
«o?ioc4oe^OrtrH  !-n-i«T-(Oc^oc^oc4>cco>ocO'^-*-*Ti<eoiocoiBc^o6)Oi-ii-iC>c^i 

^■<j"i>-^r~'^t^-^c»Tft~-T)<t>-'^t~Tj<t-'^i>'*r~cot-cot-cot~cor»eot~eot~coaccoQOeoooeooD 


S*CO»OrH000QQ^COC^^ 
coiocoinfioMOOJO 


peoiceoocoin5)iO<No 


:tj<-^CO-^CO»CCOiCCOiO 


SiOeocomor-ooostocj 
•^■^-^•v^-^co-^coic 


0»3a«5C^COiOOOit^Ca    COtOO>OiC"*QOOOCON-i005CCOQO>'*'^OCr-l 
i-(Or-irH>-lrHrtrtOO)    O0)l0C0lOe0iBC0'*'»J<h»"5<C0mC0iCI^Or^r-l 

T)<  t^  ■*  t^  ■*  i>  "^  t- ■*  t^  Tj<  t~  CO  t~  CO  r~  CO  t~  CO  t^  CO  t»  CO  t^  CO  t^  CO  GO  eo  00 


■"j'S'T-itooO'^iccocqtOiOOOiOcortt^t^-^coiOlooocoiOocorJicc-i-i 

<N  O  (N  O  1-1  O  rH  i-H -^  rH  O  r-l  O  C^  O  N  iC  CO  lO  CO  ■!»<  ■*  ■*  ■ni  CO  is  CO  lO  i^  O 

■^r*'^c^*^t^'^i>Tt<t^'^t^'^t^Ti«r*cot^cor^cot^cot^cot^cot^cox 


OsOiCOi-ICO'^Ot^t^O 


CJiOCJOC^OC^O 


■*C0i-<t~t»pa''^O0Q 


■«-^r-i^oooi-^Mcoic'oooi^'-c'*'*ot>.f-'jS'Sooo>'^'^o>o>'»eo 

COlOCOlOC^iCC^OlNO    C^Oi-ti-lr-frHi-tf-(OC^    OC^iOC^lCCO'^COTP'^ 

^co*^^£)-<j<tO'^t*'^t^  ■^t^-^t^'^r^-^t^'^t*  ^t^cor^cot^cot^coc^ 


iCCOlCCO'^'^'^'^COlO 

cot~coc~cot~cot~cot- 


c?ooo5^^"^coc^icot^  oposepc^co-^^t^ocoihoc^coioogct^i-ico^  ox'-pC'4c^«C'i^»-'CO"3 
STf<co-*-*-4'*Tii-^T)i'fl<  S'^eoiocoiceoicc^iCMoncSc^Or-ir-irHi-i  »-<t-ioc^oc^iCco»ftco 

.^•^tO'^CO^tO'^^O'^^    Tf<CO'^'©"^'£''^^'^CoU3*t^*^t^'^l^"^t^'<J*t^   -^t^-^i^-^t^coi^cot^ 


S'oi»OC>t^oso>t^»-'iftcocoiOf-<t^a»ai?oc^Tti*t'l^«oo»05co2?^^S59£'^^^wic^os»£co^r^ 
iCCOiCCO-^CO'^^'^'VTf-^Tf-^CO'^COiCCOiO    COiCfNUS'NOC^OC^Or-lf-ti-tr-tOfHOWOC^ 


S^CNiO^COiCClt^OOl 
OCOlCCOtCCOiOCOiOCO 


aoo»<N3'3;<Nt^ooa 


S'i-l0>0»QCCC^t0C0i0iOC0tOrt00  05Or~C^>O3' 
OM>oeo3eoiftco>ocO|iOcoinm'^'^')'-*^'s" 


COlOCOiCCOiS«lCC^Opl«55SOr1r1i-lri.-ci-l 


^^•^TTCOiCCO^COkO 


r-<o>002iiC>2'-iac«t-i 

C04C?IOC50PJOi-lr-( 


Soc^oc^oc-ioco»ccoSco35o5»5winwiO'^i-^'rr^^'n<-^'n''n'-^u5jwir5S535coSc^oc^o 


t^ 

0 

1-1 

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IH 

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S'OSC^OOCOt'-lft^SD'^t^CO^i— 'QQC^GC'^^^K^t^COOS^HrHOiCOt^lS 
oe-)Ocsloc5oc^ONOoiOMoeoiScoiocoioco>ncoio-^'*'*'*'<j< 


■*^Ti>-<i<^iOcoiAeoi/5 


c?e00SC^O»-4^O'N0S*^Q0l0<0t0in00C00i^i-l    QC^O>iJit>-OiCC^COO>iiHrHO>COt^iO»CODCOO 

grHS-iriSi-ce^Ssqoc^oMoc^oe^iotNoco  oeoiocoiocoincoineo  i/5irii'-*ir-*ifv*S 


S't^eoi^r^toociftWcoo 
l-li-ii-lr-lr-(r1i-lrHi-l(M 


f)i-<?4r-ICgi-li-li-li-li-l 


•xojddv     q"" 


S' to  1-1  lO -H  lO  IN  ■»»<  CO  CO  •«<  ca  ■«*" '^  lO  1-1  to  p  t~  o>  00 
C^i-lfJi-dNr-lMi-ifJi-l    i^i-lC^i-IIMi-lSi-li-li-i 

^iC  too  tCiC  tOiO  tO^  to   in  to  lC  to  iA  to  O  to  lO  to 


I^-HiHNO-U'OJiQt'O 

i-ie^i-ie^-^cjoiNOc< 

latOiCtOiCtOiCtOiOtO 


?SofJOcoocooco 

U3tOiCtO»Oto»OtoiCto 


t^OOtOOiiCp^^COC^ 
rt^l-l1-.rt?4lHC^llH^^ 

iCtCiCtOiCtDLCtOiCtO 


C4'^i-liQOtOOOI^l--a> 
iCtOii^tOiC'-OiCtOtAtO 


SiCtor-'^osci^Qeo 
coiccoiftcom-rio-* 

■^tO-OitO-TtO-JitO-litO 

lin.QS'C^Mcoputact^ 
oeoocoocoocoicco 

lOtOiCtOiCtOiCtO^tO 


COOSt^PiOf-l'^C^COCO 
rHi-li-l«i-CCMi-l6<i-l'M 

lOtointoiatoiotoioto 


ojiOi-itDmc-gpostp<5 
lO  to  iC  to'io  to  »c  to  iC  to 


S*i-iODOCOO>050500Qi-ir*^^t^C^tOC^iOCOiO-^ 
eOOCOS!NO!Ni-l?i— ik^i-KNi-KNi-iOJi-iC^i^ 

.^iCtOiStOiOtOiCtOiCtOiOtOiCtOtOtOiCtOiOtO 


rJ-iOCOtOC^t^i-IOOpoO 
iCtOiOtOiOtOifltOiCtO 


aiQ>OT}'iO"5>tccot^coi^;jt^MoC'-gpogjQO 

fteoocooeoocoocoo  coocoocoocoOMi-i 

^iCtOiCtOLStOiCtOiCtO    OtOtCtOiCtOiCtOtOtO 


3»oa>i-iocc^t^c^tceo 

5Ni-(C^i-tC^^HC4i-t!N^ 
iCtOiStOiStO»J^tOi/ttO 


i-l?iiHC^i-ICMi-loSi-l(N 

lOtOlfttOiOtOiOtOiCtO 

tO-^iCO'^tCCOt^I^OO 

|C<i-iCJi-ie^i-i04^oii-i 

ifitOiOtOiCtOiCtOiCtO 


•  qj  CO  OJ  CO  30  eo  0 


"t^iCtOiCtOtOtot 


:5sScooSocOocoocoocooc%ocooco 

,^iStOi/5tOiCtOiCtO»OtC    iCtOiCtOiCtOiOtOiOtO 


iCtOiSt^-^t^-^QpCOGO 
COOCOOCOOCOOCOO 

ictoictoiotoiotointo 


CC  O  CQ  ^H  CQ  i-H  CQ  ^^  CQ  1—* 


lO^OCCOCOOlC^ 


ccoSSocoocoocco 


QnScCP^CfiP^Xp^ODp^CO 


0^  CA  0^  X  pc^  (X  (3Q  X  ^'  CC 


tDaO'Saoi:oqo«DOi?paa 


aiHCJDO^CCp^OQQ^aD^^ClQ 


a^xp5co:rfaipfHXQiJj2 


iCiOiOiftiCiLQiftiiCtOO 


Page  506] 


^   a 


.t^    ^ 


^ 


J3      B 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


•xojddy 


Of-HCaCO"^         irttSI^OOOi         Or^C^M-^         lO«Ot>-0DO^C^ 


peic»P<aQpic»0:4a:ip4aQ  odcopiacaiaQP'i'Xtf  oi  tf  cd  P<  od  oi  x  OS  cc  d  oo  p^ccPE^aip^ccp^coa^JoQoicc 


SO^SrH5--lO^Or-lO.->Or-lO.->OrHOr-lOrHO.-IOiHOrHOi-10r-cOrHC5-<Or-lO^Ort 


-SineoiOMinMiCccioco  niM^'W^'Mico^"-*'  ^jTfjp-^^j-.fMTj.to-* 

gO.-'Oi-'O'— •Ot-'O'— I    Or- tOi— lOf— <0»-.0t-t|0i— lOrHOrHOi— iOr-1 


0^0'-<OrHO.-Oi-iO--c 

-^  ;o  ;s  o  «o  o  o  o  ^  to  o  -o 


O^OrHOi-lOrtOr-lOi-l 
:OOtD^COtC^OtC^OCO 


g3i-tO'— lOT-tOf-'Oi— t    Oi-HOrHOi— tOr-tOi-lOrHOi-iOi-HOr-tOf— t 


ec  t^  eo  i^  ru^  M 1^  ?j  w  CI  00 

Oi-HOr-lO  — OrHOi-lOm 

t05CCO:00:0^:0?0:wO?0 


ftOr^Oi-iO'-tOr^Or-tjOi-HOr-tOr^Ot-lOrH 


gortO-'0-^Or-i0r-.5rHSr-lOT-lOr-<0rH 


St^^r-Mt-wooccooi^ooMOi'-icii-ioi-'Ot-io 
i-IOr-lO>HOrlO>-IOi-IO.-lO.-lO>-IOnOC^ 

^!0?00?OCOtO?OtO?0  l?0<0-OtO'-0  0':CCSO:0:OCO 


Oi-(Oi-iOrHOSo55jOMOMO(NOOJOC10C^ 
^  O  O  O  O  ^  ^  O  ^  ^    5©  ^  5fl  ^^  ^  C3  ;5  tc  CO  !0  O  ^ 


Or-«©f-tOi-'Oi-tOi^ 


S  O  rH  O  r-(  O  tH  O  rt  O  1-1  O  i-H  O  ?5  O  C^  O  C^  O  6l 

^  ?0  CO  O  to  <:0  O  ^  O  ?S  ^  ;0  to  CO  ^  CO  O  to  O  ?0  O 


i-HOrHOr-^Oi-tOi-l 


COOOOIOCOtOCO^CO    tOCOO^OCOCOCOCOCOOiOCO 


cooox'O^ioaaico-3'O 

CDCOCOCO^COtOtOCOO 


CO«00<OtOCO«OtDOO   OCOCOCOCOtOOCOi^cOtCCO 


^ocococococo'^oococo  :oococococo:oocoo 


COcOtOcO^OcOtOOCOO  iCOOCOCOiOOiCOti^COiCO 


CO  C*5  ^  Tf  C^  iC  r-f  CO  Q  O  Q  r^  asi-*30  00  t^  31  t^O  CO  o 
OCJ  OC^  CXN  OC^  O  CJ  O  tMiC  C^OC^iC  (N»0  CCiC  cc 

1^  CO  CO  CO  ^  CO  CO  CO  CO  CO  CO  CO  >0  CO  lO  CO  iC  CO  i«  CO  O  CO 


-aOoO^OOasOiCCOt^OCOfHC 


I  »C  (M  -^  CO  CO  ■* 


^cocococococococococo'cocococococococococo 


-iOCO^QCdOiOUOl'-O   cOi— tcp?^*cco-^^coiO 
^COCOCOCOCOCOCOCOCOCO   COCOCOCOCOCOCOCOCOCO 


rJ-TfClif^f-iCOpl-QX   a>XXail:^OCOi-iiO'-"CM 
OCIOCMOC^OC^OC^   iO<NiC<MuOCO»OCOiCCOiOCO 

CO  CO  CO  CO  CO'CO  COCOCOCO   iCCOlCCOiCcOiCcOOCOi^CO 


OCOCOCOCOCOCOCOiOCO 


fiO  «  O  OSOl  OiOO  O  t^  <— '  CO  C^  CO  CO  iC -^ -^i  »C  CO  CO 
^  to  CO  CO  CO  ^  CO  CO  CD  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


p**oxooioiooo»-it-ri  ■cpcoicco'^'^coicijco 

g^;iHrti-(OCSIOC^OMjOCMOC10C^OC-JOC^ 

^COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO 


XOt^OCOr-lil^C^'^CO'^"^ 
iCCOiCCOiCCOiCCOiOCOiOCO 

iCCOiOCOK^COiCcOi^COiTicO 


c^coi-tr*ox^^XO  I'-i-icpiMicco-^'^cooc^co 

OC4OiNO?SiCOliSc0   tOCOi5cO>OCOiCCOiCCOiCCO 

cOcOCOCOCOCOiCcOvOCOOcOvCCOOCOiOCOiOCOiCCO 


OC^Oc5»C(MiOcOiOCO 

COCOCOCOtOcOiOCOiOCO 


t^»H    COC^lC 


co'^'^coiC'McO'-ir^ 

iCCOiOCOiOCOiCCOiOCOiOCO 
iCcO»CCOiOCOiOCOiCCO»i5CO 


-;oxa>o»xpt>-'-H  coiM  ic  co^ -rcoic^co^t- ; 

p^  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO    COCOCOCOCOCOCOCOCOCO 


Sco-^-^cococ^t^i-^xoci 
COiAcCiOCOiCCOiCCOiOCO 

kocOtCCOiOcOiCCOtCCOiCcO 


ptfCOCOCOCOcOcOcOCOtOCO 


^COCOCOCOCOCOCOCOCOCO    COCOCOCOCOCOCOCOCOCO 


lOCO-^-^COCOC^t^rHX 
COCOCOCOCOCOCOCOCOCO 


SaiOSOXrHCOC^lCCC 
C^iOCOiOCOiOCOiOCO 

COCCiCcOiCcOOcOvOcO 


■^Tj^coicc^t^i-'ocoiaixo 

iCCO»OCOiCCOiCCO"^CC"rp-^ 
iCCOiOCOu^COiOCOiCCOiOCO 


OiQXf-'t-C^iOCOTP-rf 
iCCOiCCOiCCOOCOiCCO 

lOCOiOCOiCcOiOcOi^CO 


jxaioaxi-ico-M 


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^COCOCOCOCOCOCOCOCOCO 


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CO  CO  CO  CO  CO  CO  CO  CO  iC  CO 


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^cocococococococococolcocococococo»cico>cco 


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CO  coo 


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cootT^'^^Q*^'^'^ 


ic  cmS 


C^  lO  CM  S  C^  TJ^  CM 

CO  iC  CO  iC  «0  lO  CO 


l^  X  CO  o  ^ 
lOcOiOCOiCcOiCcOiCco 


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OlCO^'T^  CO 
CO  CM'*  CM  ^ 

CO  vO  CD»C  CO 


r^  one  1-i  CO  CO  r-i 

CM  CM  <N  CO  CM  CO  CM 
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CO  rH  CO  ^-(  CO 
coo  CO  lO  CO 


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cS"^~^h"    cm         CO         -^  ifl         XD         t^         x"*    Oi         p 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


[Page  507 


a 


s 


C^        C<        iM        M 


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totototstootootoo 


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lO  toio  o 


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CO 

ic  to  in  to  lO  to 


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CO  ■'J'  CO 

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CO ^  CO  "^  "^  ^  ""S^  ^  ^   -"  ~       "       "  — 

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lOtou^toiCtointoicto 


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in  t^  in  t^ 


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MOi-lOrHOrH,-lr-lf-l 

int*int»im--int^int» 


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t-*in  t>-in  t^ 


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to  in  to  in  to 


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in  to  in  to  in  r*  in  t^  in  t^ 


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to  in  to  in  to 


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c^ine5inr-ioi-iorHo 

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tomtom 


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to  m  to  m  to 


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r^m  rH  m 

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Page  508] 


J3  ! 


•^  s. 


^  a 


TABLE  10. 
Mean  Time  of  Sun's  Visible  Rising  and  Setting. 


.iSaJ 


cojdd 


dv 


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TABLE  11. 

[Page  509 

For  reducing  the  Time  of  the  Moon's  passage  over  the  Meridian  of  Greenwich  to  the  Time  of  its 

pass-  1 

age 

over  anv  other  Meridian.     The  numbers  taken  from  this  Table  are  to  be  added  to  the  Time  at  1 

Greenwich  in  West  Longitude, 

subtracted  in 

East  Longitude. 

Longi- 
tude. 

Daily  variation  of  the 

moon's  pa.ssing 

the  meridian. 

Longi- 
tude. 

40" 

42m 

44m^ 

46m 

48™ 

oO-»        52" 

64m 

66" 

68" 

60"    1 

62"    i 

64" 

66" 

o 

m. 

m. 

m. 

m. 

■m. 

TO.               TO. 

TO. 

TO. 

TO. 

TO. 

TO.       1 

TO. 

TO. 

o 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0  ! 

0  : 

0 

0 

0 

5 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1  1 

1  1 

1 

1 

5 

10 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2  1 

2  ■■ 

2 

2 

10 

15 

2 

2 

2 

3 

2 

2 

2 

2 

2 

2 

2 

3 

3 

3 

15 

20 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

3 

3 

4 

4 

20 

25 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4 

5 

25 

30 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

30 

35 

4 

4 

4 

4 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

35 

40 

4 

5 

5 

5 

5 

6 

6 

6 

6 

6 

7 

7 

7 

7 

40 

45 

5 

5 

5 

6 

6 

6 

6 

7 

7 

7 

7 

8 

8 

8 

45 

50 

6 

6 

6 

6 

7 

7 

7 

7 

8 

8 

8 

9 

9 

9 

50 

55 

6 

6 

7 

7 

7 

8 

8 

8 

9 

9 

9 

9 

10 

10 

55 

60 

7 

7 

7 

8 

8 

8 

9 

9 

9 

10 

10 

10 

11 

11 

60 

65 

7 

8 

8 

8 

9 

9 

9 

10 

10 

10 

11 

11 

12 

12 

65 

70 

8 

8 

9 

9 

9 

10 

10 

10 

11 

11 

12 

12 

12 

13 

70 

75 

8 

9 

9 

10 

10 

10 

11 

11 

12 

12 

12 

13 

13 

14 

75 

80 

9 

9 

10 

10 

11 

11 

12 

12 

12 

13 

13 

14 

14 

15 

80 

85 

9 

10 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

15 

16 

85 

90 

10 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

15 

16 

16 

90 

95 

11 

11 

12 

12 

13 

13 

14 

14 

15 

15 

16 

16 

17 

17 

95 

100 

11 

12 

12 

13 

13 

14 

14 

15 

16 

16 

17 

17 

18 

18 

100 

105 

12 

12 

13 

13 

14 

15 

15 

16 

16 

17 

17 

18 

19 

19 

105 

110 

12 

13 

13 

14 

15 

15 

16 

16 

17 

18 

18 

19 

20 

20 

110 

115 

13 

13 

14 

15 

15 

16 

17 

17 

18 

19 

19 

20 

20 

21 

115 

120 

13 

14 

15 

15 

16 

17 

17 

18 

19 

19 

20 

21 

21 

22 

120 

125 

14 

15 

15 

16 

17 

17 

18 

19 

19 

20 

21 

22 

22 

23 

125 

130 

14 

15 

16 

17 

17 

18 

19 

19 

20 

21 

22 

22 

23 

24 

130 

135 

15 

16 

16 

17 

18 

19 

19 

20  i      21 

22 

22 

23 

24 

25 

135 

140 

16 

16 

17 

18 

19 

19 

20 

21  1      22 

23 

23 

24 

25 

26 

140 

145 

16 

17 

18 

19 

19 

20 

21 

22  '      23 

23 

24 

25 

26 

27 

145 

150 

17 

17 

18 

19 

20 

21 

22 

22  i      23 

24 

25 

26 

27 

27 

150 

155 
160 

17 

18 

19 

20 

21 
21 

22 

22 

23  i      24 

25 

26 

27 

28 

28 

155 

18 

19 

20 

20 

22 

23 

24  1      25 

26 

27 

28 

28 

29 

160 

165 

18 

19 

20 

21 

22 

23 

24 

1      25  i      26 

i      27 

27 

28 

29 

30 

165 

170 

19 

20 

21 

22 

23 

24 

25 

25         26 

27 

28 

29 

30 

31 

170 

175 

19 

20 

21 

22 

23 

24 

25 

26         27 

1      28 

29 

30 

31 

32 

175 

180 

20 

21 

22 

23 

24 

25         26 

!      27         28 

1       29 

1 

30 

31 

32 

33 

180 

40m 

42in 

1    44". 

1    46"- 

4S"> 

1    60"        52" 

64"    I     66" 

1     68" 

60" 

62" 

64" 

66" 

Page  510]                                            TABLE  12. 

For  finding  the  Variation  of  the  Sun'e  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.     Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Horary  motion. 

M. 

1" 

2" 

8" 

.4" 

5" 

6" 

7" 

8" 

9" 

10" 

11" 

12" 

13" 

14" 

15" 

16" 

17" 

18" 

19" 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 
4 

0 
0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 

0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
6 
6 
6 
6 
6 
6 

0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 
5 
5 
6 
6 
6 
6 
6 
6 
6 
6 
7 
7 
7 
7 
7 

0 

0 

0 
-. 

1 

2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5. 
5 
5 
5 
6 
6 
6 
6 
6 
6 
6 
7 
7 
7 
7 
7 
7 
7 
7 
8 
8 
8 
8 

0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 
6 
6 
6 
6 
6 
6 
6 
7 
7 
7 
7 
7 
7 
8 
8 
8 
8 
8 
8 
8 
9 
9 
9 
9 

0 
0 

2 
2 

I 

2 
2 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 

t 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9. 
10 
10 
10 
10 

0 
0 

2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
4 

0 
0 

2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
4 
4 
4 

0 
0 

1 
1 
1 
1 

2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
4 
4 
4 
4 

0 
0 

1 
1 
1 
1 

2 
2 
2 
2 
3 
3 
3 
3 
4 
4 
4 
4 
4 
5 

0 

1 
1 
1 

1 

2 

2 
2 
2 
3 

0 
1 
1 
1 
1 
2 
2 
2 
2 
3 

0 
1 
1 
1 
1 

0 

1 

1 
1 

2 

0 
1 
1 
1 
2 
2 
2 
3 
3 
3 
3 
4 
4 
4 
5 

1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 

17    • 
18 
19 
20 

2 
2 
2 
3 
3 

2 
2 
2 
3 
3 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 
0 

1 
1 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 

3 
3 
3 
4 
4 
4 
4 
5 
5 
5 

3 
3 
3 
4 
4 

3 
3 

4 
4 
4 

3 
4 
4 
4 
5 

4 
5 
5 
5 
5 

5 
5 
5 

5 
6 

5 
5 

5 
6 
6 

5 
5 
6 
6 
6 

4 

4 

4 

4 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

4 

4 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

12 

12 

12 

5 
5 
5 
5 
5 
6 
6 
6 
6 
7 
7 
7 
7 
7 
8 
8 
8 
8 
8 
9 
9 
9 
9 

10 
10 
10 
10 
10 
11 
11 
11 
11 
11 
12 
12 
12 
12 
13 
13 
13 

-  5 
5 

5 

6 

6 

6 

6 

7 

7 

7 

7 

7 

8 

8 

8 

8 

9 

9 

9 

9 

10 

10 

10 

10 

11 

11 

11 

11 

11 

12 

12 

12 

12 

13 

13 

13 

13 

14 

14 

14 

5 

6 

6 

6 

6 

7 

7 

7 

7 

8 

8 

8 

8 

9 

9 

9 

9 

10 

10 

10 

10 

11 

11 

11 

11 

12 

12 

12 

12 

13 

13 

13 

13 

14 

14 

14 

14 

15 

15 

15 

6 
6 
6 
6 

7 

7 

7 

7- 

8 

8 

8 

9 

9 

9 

9 
10 
10 
10 
10 
11 
11 
11 
11 
12 
12 

6 
6 

7 
7 
7 

6 

7 
7 
7 
8 

7 
7 
7 
8 
8 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

26 

27 
28 
29 
30 

0 
0 
0 
0 

7 
8 
8 
8 
9 

8 
8 
8 
9 
9 

8 
9 
9 
9 
10 

31 
32 
33 
34 
35 

9 
9 
9 
10 
10 
10 
10 
11 
11 
11 

9 
10 
10 
10 
11 

10 
10 
10 

11 
11 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

11 
11 
11 
12 
12 

11 
12 

12 
12 
13 

36 
37 
38 
39 
40 
41 
42 
43 
44 
45 

41 
42 
43 
44 
45 

•} 

2 

2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 

12 
12 
12 
12 
13 

12 
13 
13 
13 
14 

13 
13 
14 
14 
14 

46 

47 

48 

49- 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 

12 
13 
13 
13 
13 
14 
14 
14 
14 
15 
15 
15 
15 
16 
16 

13 
13 
14 
14 
14 

14 
14 
14 
15 
15 

15 
15 
15 
16 
16 
16 
16 
17 
17 
17 

46 

47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

14 
15 
15 
15 
16 
16 
16 
16 
17 
17 

15 
16 
16 
16 
17 

17 
17 
17 
18 
18 

18 
18 
18 
19 
19 

TABLE  12.                  [Page  511 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

20" 

21" 

22" 

23" 

24" 

25" 

26" 

27" 

28" 

29" 

80" 

81" 

82" 

88" 

84" 

85" 

86" 

1 
2 
3 
4 
5 

0 
1 
1 
1 

2 
2 

3 
3 
3 

0 
1 
1 
1 
2 
2 
2 
3 
3 
4 

0 

1 
1 
1 

2 
2 
3 
3 
3 
4 

0 
1 
1 
2 
2 
2 
3 
3 
3 
4 

0 

1 
1 

2 
2 
2 
3 
3 
4 
4 

0 

1 

1 

2 
2 
3 
3 
3 
4 
4 

0 
1 
1 
2 
2 
3" 
3 
3 
4 
4 

0 

1 
1 

2 
2 

0 

1 
1 
2 

2 

0 

1 
1 

2 
2 

1 
1 
2 

2 
3 

1 
1 
2 
2 
3 

1 
1 
2 

2 
3 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
1 
2 
2 
3 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

3 
3 
4 
4 
5 

3 
3 

4 
4 
5 

3 
3 
4 
4 
5 

3 
4 
4 
5 
5 

3 
4 
4 
5 
5 

3 
4 
4 
5 
5 

3 
4 
4 
5 
6 

3 
4 
5 
5 
6 

4 
4 
5 
5 
6 

4 

4 
5 
5 
6 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

4 
4 
4 
5 
5 
5 
6 
6 
6 
7 

4 

4 

5 

5 

5 

6 

6 

6 

7 

7 

7 

8 

8 

8 

9 

9 

9 

10 

10 

11 

11 

11 

12 

12 

12 

13 

13 

13 

14 

14 

4 

4 

5 

5 

6 

6 

6 

7 

7 

7 

8 

8 

8 

9 

9 

10 

10 

10 

11 

11 

11 

12 

12 

12 

13 

13 

14 

14 

14 

15 

15 

15 

16 

16 

17 

17 

17 

18 

18 

18 

19 

19 

19 

20 

20 

4 
5 

5 
5 
6 

4 
5 
5 
6 
6 

5 
5 
5 
6 
6 

5 

5 
6 
6 

7 

0 

5 
6 
6 

7 

5 

6 
6 

7 

7 

5 
6 
6 

7 

7 

6 
6 

7 
7 
8 

6 
6 

7 
7 
8 

6 
6 

7 
7 
8 

6 

7 
7 
8 
8 

6 

7 
7 
8 
9 

6 

7 
8 
8 
9 

7 
7 
8 
8 
9 

11 
12 
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Page  512]                  TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

I 
2 
3 
4 
5 
6 
7 
8 
9 
10 

87" 

88" 

89" 

1 
1 
2 
3 
3 

40" 

1 

1 

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21 

22 

23 

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41" 

42" 

48" 

44" 

45" 

46" 

47" 

48" 

49" 

50" 

51" 

52" 

58" 

1 
2 
3 
4 
5 

1 
1 
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1 
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36 
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41 
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49 
50 

34 
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36 
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"38 
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36 
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41 
42 

37 
37 
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42 
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37 
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56 
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42 
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56 
57 
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59 
60 

TABLE  12. 

[Page  513 

For  finding  the  Variation  of  the  Sun's  Kight  Ascension  or  Declination,  or 

of  the 

Equation  of  Time,  in  1 

any  number  of  minutes  of  time,  the 

Horary  Motion  bemg  given  at  the  top  of  the  page  in  seconds,  | 

and 'the  number  of  minutes  of  time 

in  the  side  column. 

Also  for  finding 

the  Variation  of  the  1 

Moon's  Declination  or  Right  Ascension  in 

seconds  of  time. 

the  motion 

in  one  minute  being  given  1 

at  the  top,  and  the  numbers  in  the  side  column  being 

taken  for  seconds 

1 

M. 

Horary  motion 

M. 

54" 

66" 
1 

66" 

1 

1 

5S" 

1 

69" 

1 

60" 

61" 

02" 

6S" 

64" 

65" 

66" 

67" 

68" 

69" 

70" 

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22489 -(18- 


Page  514]                 TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

71" 

72" 

1 

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TABLE  12.                  [Page  515 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 

.  and  the  number  of  minutes  of  time  in  the  side  cohmm.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension,  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion.                                1 

M. 

88" 

89" 

90" 

91" 

92" 

98" 

94" 

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96"  1  97" 

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73 
74 

68 
70 
72 
73 
75 

69 
71 
72 
74 
76 

70 
71 
73 
75 

77 

70 
72 
74 
76 

77 

71 
73 

75 
76 

78 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

67 
69 
70 
72 
73 

71 
73 

74 
76 

78 
79 
81 
82 
84 
85 
87 
88 
90 
91 
93 

72 
74 
75 

77 

78 

80" 

81 

83 

85 

86 

88 

89 

91 

92 

94 

73 
74 
76 

78 
79 

74 

75 
77 
78 
80 

74 
76 
78 
79 
81 

75 

77 
78 
80 
82 

76 
78 
79 
81 
83 

77 
78 
80 
82 
83 
85 
87 
88 
90 
92 

77 
79 
81 
82 
84 

78 
80 
82 
83 
85 

79 
81 

82 
84 
86 

80 
81 
83 

85 
87 

46 
47 
48 
49 
50 
51 
52 
53 
54 
55 

51 
52 
53 

54 
55 
56 
57 
58 
59 
60 

75 
76 
78 
79 
81 
82 
84 
85 
87 
88 

76 
77 
79 
80 
82 
83 
85 
86 
88 
89 

77 
78 
80 
81 
83 
84 
86 
87 
89 
90 

77 
79 
80 
82 
83 
85 
86 
88 
90 
91 

81 
82 
84 
86 
87 

82 
83 
85 
86 
88 

82 
84 
86 
87 
89 

83 
85 
87 
88 
90 

84 
86 
87 
89 
91 

86 
88 
89 
91 
93 

87 
88 
90 
92 
94 

88 
89 
91 
93 
94 

88 
90 
92 
94 
95 

8J 
90 
92 
93 
95 

90 
91 
93 
94 
96 

91 
92 
94 
95 

97 

91 
93 

95 
96 

98 

92 
94 
96 
97 
99 

93 
95 
97 

98 
100 

94 
96 
98 
99 
101 

95 

97 

99 

100 

102 

96 

98 

100 

101 

103 

97 

99 

101 

102 

104 

56 
57 
58 
59 
60 

Page  516]                 TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
anH  the  number  of  minutes  of  time  in  tlie  side  column.  Also  for  finding  the  Variatior  of  the 
Moon's  Declination  or  Right  Ascension,  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

1 
2 
3 
4 
5 

Horary  motion. 

M. 

105" 

106" 

107" 

108" 

109"  1  110"  f  111"    112" 

113" 

114" 

115" 

116" 

117" 

118" 

2 
4 
5 

7 
9 

2 
4 
5 
7 
9 

2 
4 
5 

7 
9 

•  2 
4 
5 
7 
9 

2 

4 
5 

7 
9 

2 
4 
6 

7 
9 

2 
4 
6 

7 
9 

2 
4 
6 

7 
9 

2 
4 
6 
8 
9 

2 

4 

6 

8 

10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

1 
2 
3 
4 
5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

11 
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16 
18 

11 
12 
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12 
14 
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12 
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15 
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16 
18 
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6 

7 

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21 
23 
25 
27 
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21 
23 
25 
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21 
23 
25 
27 
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22 
24 
26 
28 
30 

n 

12 
13 
14 
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19 
20 

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33 
35 

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34 
35 

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30 
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34 
36 

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31 
32 
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36 

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37 

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35 
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31 
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31 
33 
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16 
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18 
19 
20 

21 
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23 
24 
25 

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21 
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23 
24 
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26 
27 
28 
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30 

46 
47 
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51 
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26 
27 
28 
29 
30 
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32 
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34 
35 

31 
32 
33 
34 
35 

54 
56 
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61 
63 
65 
67 
68 
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55 
57 
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66 

59 
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67 

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60 
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64 
66 
68 

60 
62 
64 
66 

68 

61 
63 
65 
67 
69 

36 
37 
38 
39 
40 

64 
65 
67 
69 
71 

64 
66 
68 
70 
71 

65 
67 
68 
70 
72 
74 
76 
77 
79 
81 

65 
67 
69 
71 
73 

66 
68 
70 
72 
73 

67 
68 
70 
72 
74 

67 
69 
71 
73 
75 

68 
70 
72 
73 
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68 
70 
72 
74 
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71 
73 
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72 
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70 
72 
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71 
73 

75 
77 
79 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

72 
74 
75 
77 
79 

72 
74 
76 
78 
80 

73 
75 

77 
78 
80 

74 

76 
78 
80 
82 

75 

77 
79 
81 
83 

76 

78 
80 
81 
83 

77 
78 
80 
82 
84 

77 
79 
81 
83 
85 

78 
80 
82 
84 
86 

79 
81 
82 
84 
86 

79 
81 
83 

85 
87 

80 

82 
84 
86 
88 

81 
83 

85 
87 
89 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

81 
82 
84 
86 
88 

81 

83 
85 
87 
88 

82 
84 
86 
87 
89 

83 
85 
86 
88 
90 

84 
85 
87 
89 
91 

84 
86 
88 
90 
92 

85 
87 
89 
91 
93 

86 
88 
90 
91 
93 

87 
89 
90 
92 
94 

87 
89 
91 
93 
95 

88 
90 
92 
94 
96 

89 
91 
93 
95 
97 

90 
92 
94 
96 
98 

90 
92 
94 
96 

98 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

89 

91 

93 

95 

96 

98 

100 

102 

103 

105 

90 

92 

94 

95 

97 

99 

101 

102 

104 

106 

91 
93 
95 
96 
98 

92 
94 
95 
97 
99 

93 
94 
96 
98 
100 

94 
95 
97 
99 
101 

94 

96 

98 

100 

102 

95 

97 

99 

101 

103 

96 

98 

100 

102 

104 

97 

99 

101 

103 

105 

98 
100 
102 
104 
105 

99 
101 
102 
104 
106 

99 
101 
103 
105 
107 

100 
102 
104 
106 
108 

51. 

52 

53 

54 

55 

56 
57 
58 
59 
60 

100 
102 
103 
105 
107 

101 
103 
104 
106 
108 

102 
104 
105 
107 
109 

103 
105 
106 
108 
110 

104 
105 
107 
109 
111 

105 
106 
108 
110 

112 

105 
107 
109 
111 
113 

106 
108 
110 
112 
114 

107 
109 
111 
113 
115 

108 
110 
112 
114 
116 

109 
111 
113 
115 
117 

110 
112 
114 
116 
118 

56 
57 
58 
59 
60 

TABLE  12.                  [Page  517 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

119" 

120" 

121" 

122" 

123" 

124" 

126" 

126" 

127" 

128" 

129" 

180" 

131" 

132" 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

2 
4 
6 
8 
10 

2 

4 

6 

8 

10 

2 
4 
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8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
10 

2 
4 
6 
8 
11 

2 
4 
6 
8 
11 

2 
4 
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9 
11 

2 
4 
6 
9 
11 

2 

4 

7 

9 

11 

2 
4 

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11 

2 

4 

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11 

1 
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13 
15 
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13 
15 

18 
20 
22 

11 
12 
13 
14 
15 

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26 

28 
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24 
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22 
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33 
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51 

23 
25 

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25 

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26 

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24 
26 
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26 
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33 

24 
26 
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31 
33 

24 
26 
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31 
33 

11 
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32 
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36 
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46 
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61 
63 
65 
67 
69 

32 
34 
36 
38 
40 
42 
44 
46 
48 
50 

32 
34 
36 
38 
40 
42 
44 
46 
48 
50 

33 
35 
37 
39 
41 
43 
45 
47 
49 
51 

33 
35 
37 
39 
41 

33 
35 
38 
40 
42 

34 
36 
38 
40 
42 

34 
36 
38 
40 
42 

34 
36 
38 
41 
43 

34 
37 
39 
41 
43 

35 
37 
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41 
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35 
37 
39 
41 
44 

35 
37 
40 
42 
44- 

16 
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18 
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45 

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46 
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21 
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72 
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55 
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61 
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66 

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64 
66 

26 
27 
28 
29 
30 

62 
64 
66 
68 
70 

63 
65 
67 
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71 

63 
65 
67 
69 
71 

64 
66 
68 
70 
72 

64 
66 
68 
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72 

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67 
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73 

66 
68 
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73 
75 

67 
69 
71 
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67 
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72 
74 
76 

68 
70 
72 
74 
76 

68 
70 
73 
75 

77 

31 
32 
33 
34 
35 

36 
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38 
39 
40 
41 
42 
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44 
45 

71 
73 
75 

77 
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72 
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80 

73 
75 

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81 

73 
75 

77 

79 

81 

83 

85 

87 

89 

92 

94" 

96 

98 

100 

102 

104 

106 

108 

110 

112 

74 
76 

78 

80 

82 

84 

86 

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100 

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107 

109 

111 

113 

74 
76 
79 
81 
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75 

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83 

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83 

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79 
81 
83 
85 

u 
80 
82 
84 
86 

78 
80 
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79 
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83 

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81 
84 
86 
88 

36 
37 
38 
39 
40 

81 
83 
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82 
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83 
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89 
91 

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92 
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97 

89 
91 
93 
95 
98 

90 
92 
94 
96 
98 

90 

92 

95 

97 

99 

101 

103 

106 

108 

110 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 
51 
52 
53 
54 
55 

91 

93 

95 

97 

99 

101 

103 

105 

107 

109 

92 
94 
96 
98 
100 

93 
95 
97 
99 
101 

95 

97 

99 

101 

103 

96 

98 
100 
102 
104 

97 

99 

101 

103 

105 

97 

99 

102 

104 

106 

98 
100 
102 
105 
107 

99 
101 
103 
105 
108 

100 
102 
104 
106 
108 

100 
103 
105 
107 
109 

46 
47 
48 
49 
50 

102 
104 
106 
108 
110 

103 
105 
107 
109 
111 

105 
107 
110 
112 
114 

106 
108 
110 
113 
115 

107 
109 
111 
113 
116 

108 
110 
112 
114 
116 

109 
111 
113 
115 
117 

110 
112 
114 
116 
118 

111 
113 
115 
117 
119 

111 
114 
116 
118 
120 

112 
114 
117 
119 
121 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

56 
57 
58 
59 
60 

111 
113 
115 
117 
119 

112 
114 
116 
118 
120 

113 
115 
117 
119 
121 

114 
116 
118 
120 
122 

115 
117 
119 
121 
123 

116 
118 
120 
122 
124 

117 
119 
121 
123 
125 

118 
120 
122 
124 
126 

119 
121 
123 
125 
127 

119 
122 
124 
126 

128 

120 
123 
125 
127 
129 

121 
124 
126 
128 
130 

122 
124 
127 
129 
131 

123 
125 
128 
130 
132 

Page  618]                  TABLE  12. 

For  finding  the  Variation  of  the  Sun's  Right  Ascension  or  Declination,  or  of  the  Equation  of  Time,  in 
any  number  of  minutes  of  time,  the  Horary  Motion  l)eing  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  cohimn.  Also  for  findmg  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

188" 

134" 

2 
4 
7 
9 
11 

185" 

186" 

4 

187" 

188" 

189" 

140" 

141" 

142" 

148" 

144" 

145" 

146" 

1 
2 
3 
4 
5 

2 
4 
7 
9 
11 

2 
5 
7 
9 
11 

2 
5 
7 
9 
11 

2 

5 

7 

9 

11 

2 
5 
7 
9 
12 

2 
5 

7 

9 

12 

2 
5 
7 
9 
12 

2 
5 

7 

9 

12 

2 
5 
7 
9 
12 

2 
5 
7 

10 
12 

2 

5 

7 

10 

12 

2 

5 

7 

10 

12 

2 

5 

7 

10 

12 

1 
2 
3 
4 
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6 

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16 
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20 
22 

13 

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21 
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14 
17 
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14 
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14 
17 
19 
22 
24 

15 
17 
19 
22 

24 

15 
17 
19 
22 

24 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

24 
27 
29 
31 
33 

25 
27 
29 
31 
34 

25 
27 
29 
32 
34 

25 
27 
29 
32 
34 

25 
27 
30 
32 
34 

25 
28 
30 
32 
35 

25 
28 
30 
32 
35 

26 
28 
30 
33 
35 

26 
28 
31 
33 
35 

26 
28 
31 
33 
36 

26 
29 
31 
33 
36 

26 
29 
31 
34 
36 

27 
29 
31 
34 
36 

27 
29 
32 
34 
37 

11 
12 
13 
14 

15 

16 
17 
18 
19 
20 

35 
38 
40 
42 
44 

36 
38 
40 
42 
45 

36 
38 
41 
43 
45 

36 
39 
41 
43 
45 

37 
39 
41 
43 
46 

37 
39 
41 
44 
46 

37 
39 
42 
44 
46 

37 
40 
42 
44 

47 

38 
40 
42 
45 
47 

38 
40 
43 
45 
47 

38 
41 
43 

45 

48 

38 
41 
43 
46 

48 

39 
41 
44 
46 

48 

39 
41 
44 
46 
49 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

47 
49 
51 
53 
55 

47 
49 
51 
54 
56 

47 
50 
52 
54 
56 

48 
50 
52 
54 
57 

48 
50 
53 
55 
57 

48 
51 
53 
55 

58 

49 
51 
53 

56 

58 

49 
51 
54 

56 

58 

49 
52 
54 
56 
59 

50 
52 
54 
57 
59 

.  50 
52 
55 
57 
60 

50 
53 
55 
58 
60 

51 
53 
56 
58 
60 

51 
54 
56 
58 
61 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 

26 
27 
28 
29 
30 

58 
60 
62 
64 
67 

58 
60 
63 
65 
67 

59 
61 
63 
65 
68 

59 
61 
63 
66 

68 

59 
62 
64 
66 
69 

60 
62 
64 
67 
69 

60 
63 
65 
67 
70 

61 
63 
65 
68 
70 

61 
63 
66 

68 
71 

62 
64 
66 
69 
71 

62 
64 
67 
69 
72 

62 
65 
67 
70 
72 

63 
65 
68 
70 
73 

63 
66 
68 
71 
73 

31 
32 
33 
34 
35 

69 
71 
73 

75 
78 

69 
71 
74 

76 

78 

70 

72 
74 
77 
79 

70 
73 
75 

77 
79 

71 
73 
75 

78 
80 

71 
74 
76 

78 
81 

72 
74 
76 
79 
81 

72 
75 
77 
79 
82 

73 
75 

78 
80 
82 

73 
76 
78 
80 
83 

74 
76 
79 
81 
83 

74 

77 
79 
82 
84 

75 

77 
80 
82 
85 

75 
78 
80 
83 
85 

36 
37 
38 
39 
40 

80 
82 
84 
86 
89 

80 
83 
85 
87 
89 

81 
83 
86 
88 
90 

82 
84 
86 
88 
91 

82 
84 
87 
89 
91 

83 
85 
87 
90 
92 

83 
86 
88 
90 
93 

84 
86 
89 
91 
93 

85 
87 
89 
92 
94 

85 
88 
90 
92 
95 

86 
88 
91 
93 
95 

86 
89 
91 
94 
96 

87 
89 
92 
94 
97 

88 
90 
92 
95 
97 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

91 
93 
95 
98 
100 

92 
94 
96 
98 
101 

92 
95 
97 
99 
101 

93 

95 

97 

100 

102 

94 

96 

98 

100 

103 

94 

97 

99 

101 

104 

95 

97 

100 

102 

104 

96 

98 

100 

103 

105 

96 

99 

101 

103 

106 

97 

99 

102 

104 

107 

98 
100 
102 
105 
107 

98 
101 
103 
106 
108 

99 
102 
104 
106 
109 

100 
102 
105 
107 
110 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

102 
104 
106 
109 
111 

103 
105 
107 
109 
112 

104 
106 
108 
110 
113 

104 
107 
109 
111 
113 

105 
107 
110 
112 
114 

106 
108 
110 
113 
115 

107 
109 
111 
114 
116 

107 
110 
112 
114 
117 

108 
110 
113 
115 
118 

109 
111 
114 
116 
118 

110 
112 
114 
117 
119 

110 
113 
115 
118 
120 

111 
114 
116 
118 
121 

112 
114 
117 
119 
122 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

113 
115 
117 
120 
122 

114 
116 
118 
121 
123 

115 
117 
119 
122 
124 

116 
118 
120 
122 
125 

116 
119 
121 
123 
126 

117 
120 
122 
124 
127 

118 
120 
123 
125 
127 

119 
121 
124 
126 
128 

120 
122 
125 
127 
129 

121 
123 
125 
128 
130 

122 
124 
126 
129 
131 

122 
125 
127 
130 
132 

123 
126 
128 
131 
133 

124 
127 
129 
131 
134 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

56 
57 
58 
59 
60 

124 
126 
129 
131 
133 

125 
127 
130 
132 
134 

126 
128 
131 
133 
135 

127 
129 
131 
134 
136 

128 
130 
132 
135 
137 

129 
131 
133 
136 
138 

130 
132 
134 
137 
139 

131 
133 
135 
138 
140 

132 
134 
136 
139 
141 

133 
135 
137 
140 
142 

133 
136 
138 
141 
143 

134 
137 
139 
142 
144 

135 
138 
140 
143 
145 

136 
139 
141 
144 
146 

TABLE  12.                  [Page  519 

For  finding  the  Variation  of  the  Sun's  Right  Ascension,  or  Declination,  or  of  the  Equation  of  Time  in 
any  number  of  minutes  of  time,  the  Horary  Motion  being  given  at  the  top  of  the  page  in  seconds, 
and  the  number  of  minutes  of  time  in  the  side  column.  Also  for  finding  the  Variation  of  the 
Moon's  Declination  or  Right  Ascension  in  seconds  of  time,  the  motion  in  one  minute  being  given 
at  the  top,  and  the  numbers  in  the  side  column  being  taken  for  seconds. 

M. 

Horary  motion. 

M. 

147" 

148" 

149" 

160" 

161" 

152" 

153" 

164" 

166" 

166" 

157" 

168" 

169" 

160" 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

2 

5 

7 

10 

12 

2 

5 

7 
10 
12 

2 

5 

7 

10 

12 

3 
5 
8 

10 
13 

3 
5 
8 

10 
13 

3 
5 
8 

10 
13 

3 

5 

8 

10 

13 

3 

5 

8 

10 

13 

3 

5 

8 

10 

13 

3 

5 

8 

10 

13 

3 
5 

8 

10 
13 

3 

5 

8 

11 

13 

3 

5 

8 

11 

13 

3 

5 

8 

11 

13 

1 
2 
3 
4 
5 

15 
17 
20 
22 
25 

15 
17 
20 
22 
25 

15 
17 
20 
22 
25 

15 
18 
20 
23 
25 

15 
18 
20 
23 
25 

15 
18 
20 
23 
25 

15 
18 
20 
23 
26 

15 
18 
21 
23 
26 

16 
18 
21 
23 
26 

16 
18 
21 
23 
26 

16 
18 
21 
24 
26 

16 
18 
21 
24 
26 

16 
19 
21 
24 
27 

16 
19 
21 
24 
27 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

11 
12 
13 
14 
15 

27 
29 
32 
34 
37 

27 
30 
32 
35 
37 

27 
30 
32 
35 
37 

28 
30 
33 
35 
38 

28 
30 
33 
35 
38 

28 
30 
33 
35 
38 

28 
31 
33 
36 
38 

28 
31 
33 
36 
39 

28 
31 
34 
36 
39 

29 
31 
34 
36 
39 

29 
31 
34 
37 
39 

29 
32 
34 
37 
40 

29 
32 
34 
37 
40 

29 
32 
35 
37 
40 

16 
17 
18 
19 
20 

39 
42 
44 
47 
49 

39 
42 
44 
47 
49 

40 
42 
45 
47 
50 

40 
43 

45 
48 
50 

40 
43 
45 
48 
50 

41 
43 
46 
48 
51 

41 
43 
46 

48 
51 

41 
44 
46 
49 
51 

41 
44 
47 
49 
52 

42 
44 
47 
49 
52 

42 
44 
47 
50 
52 

42 
45 
47 
50 
53 

42 
45 
48 
50 
53 

43 
45 
48 
51 
53 

16 
17 
18 
19 
20 

21 
22 
23 
24 

25 

51 
54 
56 
59 
61 

52 
54 
57 
59 
62 

52 
55 
57 
60 
62 

53 
55 

58 
60 
63 

53 
55 
58 
60 
63 

53 
56 
58 
61 
63 

54 
56 
59 
61 
64 

54 
56 
59 
62 
64 

54 
57 
59 
62 
65 

55 
57 
60 
62 
65 

55 
58 
60 
63 
65 

55 
58 
61 
63 
66 

56 
58 
61 
64 
66 

56 
59 
61 
64 
67 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 

26 
27 
28 
29 
30 

64 
66 
69 
71 
74 

64 
67 
69 

72 
74 

65 
67 
70 
72 

75 

65 
68 
70 
73 
75 

65 
68 
70 
73 
76 

66 
68 
71 
73 
76 
79 
81 
84 
86 
89 

66 
69 
71 
74 

77 

67 
69 

72 
74 

77 

67 
70 
72 
75 

78 

68 
70 
73 

75 

78 

68 
71 
73 
76 
79 

68 
71 
74 
76 
79 

69 
72 
74 

77 
80 

69 
72 
75 

77 
80 

31 
32 
33 
34 
35 

76 

78 
81 
83 
86 

76 

79 
81 
84 
86 

77 
79 
82 
84 
87 

78 
80 

83 
85 
88 

78 
81 
83 
86 
88 

79 
82 
84 
87 
89 

80 
82 
85 
87 
90 

80 
83 
85 
88 
90 

81 
83 
86 
88 
91 

81 
84 
86 
89 
92 

82 
84 
87 
90 
92 

82 
85 
87 
90 
93 

83 
85 
88 
91 
93 

36 
37 
38 
39 
40 

88 
91 
93 
96 

98 

89 
91 
94 
96 
99 

89 
92 
94 
97 
99 

90 
93 
95 
98 
100 

91 
93 
96 
98 
101 

91 
94 
96 
99 
101 

92 
94 
97 
99 
102 

92 

95 

98 

100 

103 

93 

96 

98 

101 

103 

94 

96 

99 

101 

104 

94 

97 

99 

102 

105 

95 

97 

100 

103 

105 

95 

98 

101 

103 

106 

96 

99 

101 

104 

107 

36 
37 

38 
39 
40 

1  41 
42 
43 
44 
45 

41 
42 
43 
44 
45 

100 
103 
105 
108 
110 

101 
104 
106 
109 
111 

102 
104 
107 
109 
112 

103 
105 
108 
110 
113 
115 
118 
120 
123 
125 
128 
130 
133 
135 
138 

103 
106 
108 
111 
113 

104 
106 
109 
111 
114 

105 
107 
110 
112 
115 

105 
108 
110 
113 
116 

106 
109 
111 
114 
116 

107 
109 
112 
114 
117 

107 
110 
113 
115 

118 

108 
111 
113 
116 
119 

109 
111 
114 
117 
119 

109 
112 
115 
117 
120 

46 
47 
48 
49 
50 
51 
52 
53 
54 
55 

113 
115 
118 
120 
123 

113 
116 
118 
121 
123 

114 
117 
119 
122 
124 
127 
129 
132 
134 
137 

116 
118 
121 
123 
126 

117 
119 
122 
124 
127 

117 
120 
122 
125 
128 

118 
121 
123 
126 
128 

119 
121 
124 
127 
129 

120 
122 
125 
127 
130 

120 
123 
126 

128 
131 

121 
124 
126 
129 
132 

122 
125 
127 
130 
133 

123 
125 
128 
131 
133 

46 
47 
48 
49 
50 
51 
52 
53 
54 
55 

125 
127 
130 
132 
135 

126 
128 
131 
133 
136 

128 
131 
133 
136 
138 

129 
132 
134 
137 
139 

130 
133 
135 
138 
140 

131 
133 
136 
139 
141 

132 
134 
137 
140 
142 

133 
135 
138 
140 
143 

133 
136 
139 
141 
144 

134 
137 
140 
142 
145 

135 

138 
140 
143 
146 

136 
139 
141 
144 
147 

56 

57 
58 
59 
60 

137 
140 
142 
145 
147 

138 
141 
143 
146 

148 

139 
142 
144 
147 
149 

140 
143 
145 
148 
150 

141 
143 
146 
148 
151 

142 
144 
147 
149 
152 

143 
145 
148 
150 
153 

144 
146 
149 
151 
154 

145 
147 
150 
152 
155 

146 
148 
151 
153 
156 

147 
149 
152 
154 
157 

147 
150 
153 
155 
158 

148 
151 
154 
156 
159 

149 
152 
155 
157 
160 

56 

57 
58 
59 
60 

Page  520] 

TABLE  13. 

For  finding  the  Su 

a's  change  of  Right  Ascension  for  any  given  number  of  hours.                  1 

Hourly 

Number  of  hours 

Hourly 

tion. 

1 

2 

3 

4 

5             6 

7 

8 

0 

10      j      11      1      12 

tion. 

8. 

«. 

s. 

s. 

B. 

g.                  8. 

s. 

c. 

*. 

«.                   8.          !        8. 

8. 

8.50 

8.5 

17.0 

25.5 

34.0 

42.  b 

51.0 

59.5 

68.0 

76.5 

85.0 

93.5 

102.0 

8.50 

8.55 

8.6 

17.1 

25.7 

34.2 

42.8 

51.3 

59.9 

68.4 

77.0 

85.5 

94.1 

102.6 

8.55 

8.60 

8.6 

17.2 

.25.  8 

34.4 

43.0 

51.6 

60.2 

68.8 

77.4 

86.0 

94.  6 

103.2 

8.60 

8.65 

8.7 

17.3 

•26.0 

34.6 

43.3 

51.9 

60.6 

69.2 

77.9 

86.5 

95.2 

103.8 

8.65 

8.70 

8.7 
8.8 

17.4 
1775 

26.1 
26:3" 

34.8 
35.0' 

43.5 

43.  8 

52.2 
52.5 

60.9 
61.3 

69.6 
70.  0 

78.3 

7"8.8 

87.0 

87.5 

95.7 
96.3 

104.4 
105. 0 

8.70 
8.75 

8.75 

8.80 

8.8 

17.6 

26.4 

35.2 

44.0 

52.8 

61.6 

70.4 

79.2 

88.0 

96.8 

105.  6 

8.80 

8.85 

8.9 

17.7 

26.6 

35.4 

44.3 

53.1 

62.0 

70.8 

79.7 

88.5 

97.4 

106.2 

8.85 

8.90 

8.9 

17.8 

26.7 

35.6 

44.5 

53.4 

62.3 

71.2 

80.1 

89.0 

97.9 

106.8 

8.90 

8.95 

9.0 
9.0 

17.9 
18.0 

26.9 
27.0 

35.8 
36.0 

44.8 

53.7 

62.7 
63.0 

71.6 

80.6 
81.0 

89.5 

98.5 
99.0" 

107.4 

8.95 
9.  00 

9.00 

45.0 

54.0 

72.0 

90.0 

108.0 

9.05 

9.1 

18.1 

27.2 

36.2 

45.3 

54.3 

63.4 

72.4 

81.5 

90.5 

99.6 

108.6 

9.05 

9.10 

9.1 

18.2 

27.3 

36.4 

45.5 

54.6 

63.7 

72.8 

81.9 

91.0 

100.1 

109.2 

9.10 

9.15 

9.2 

18.3 

27.5 

36.6 

45.8 

54.9 

64.1 

73.2 

82.4 

91.5 

100.7 

109.8 

9.15 

9.20 
9.25 

9.2 
9.3 

18.4 
18.5 

27.6 

27.8 

36.8 
37.0 

46.0 

55.2 

64.4 
64.8 

73.6 

82.8 
83.3 

92.0 

101.2 
101.8 

110.4 
111.0 

9.20 
9:25 

46.3 

55.5 

74.0 

92.5 

9.30 

9.3 

18.6 

27.9 

37.2 

46.5 

.55.8 

65.1 

74.4 

83.7 

93.0 

102.3 

111.6 

9.30 

9.35 

9.4 

18.7 

28.1 

37.4 

46.8 

56.1 

65.5 

74.8 

84.2 

93.5 

102.9 

112.2 

9.35 

9.40 

9.4 

18.8 

28.2 

37.6 

47.0 

56.4 

65.8 

75.2 

84.6 

94.0 

103.4 

112.8 

9.40 

9.45 

9.5 

18.9 
19.0 

28.4 

37.8 

47.3 
47.5 

56.7 
57.0 

66.2 

75.6 

85.1 

94.5 

104.0 
104. 5 

113.4 

9.45 

9.50 

9.5 

28.5 

38.0 

66.5 

76.0 

85.5 

95.0 

114.0 

9.50 

9.55 

9.6 

19.1 

28.7 

38.2 

47.8 

57.3 

66.9 

76.4 

86.0 

95.5 

105.1 

114.6 

9.55 

9.60 

9.6 

19.2 

28.8 

38.4 

48.0 

57.6 

67.2 

76.8 

86.4 

96.0 

105.6 

115.2 

9.60 

9.65 

9.7 

19.3 

29.0 

38.6 

48.3 

57.9 

67.6 

77.2 

86.9 

96.5 

106.2 

115.  8 

9.65 

9.70 

9.7 

19.4 

29.1 
29.3 

38.8 
39.0 

48.5 

58.2 
58.5 

67.9 

77.6 

87.-3 

87.8 

97.0 

106.7 

116.4 

9.70 

9.75 

9.8 

19.5 

48.8 

68.3 

78.0 

97.5 

107.3 

117.0 

9.75 

9.80 

9.8 

19.6 

29.4 

39.2 

49.0 

58.8 

68.6 

78.4 

88.2 

98.0 

107.8 

117.6 

9.80 

9.85 

9.9 

19.7 

29.6 

.39.4 

49.3 

59.1 

69.0 

78.8 

88.7 

98.5 

108.4 

118.2 

9.85 

9.90 

9.9 

19.8 

29.7 

39.6 

49.5 

59.4 

69.3 

79.2 

89.1 

99.0 

108.9 

118.8 

9.90 

9.95 

10.0 

19.9 
20.0 

29.9 

39.8 

49.8 
50.0 

59.7 
60.0 

69.7 
70.0 

79.6 
80.0 

89.6 
90.0" 

99.5 

109.5 

119.4 

9.95 

10.00 

10.0 

30.0 

40.0 

100.0 

110.0 

120.0 

10.00 

10.05 

10.1 

20.1 

30.2 

40.2 

50.3 

60.3 

70.4 

80.4 

90.5 

100.5 

110.6 

120.6 

10. 05 

10.10 

10.1 

20.2 

30.3 

40.4 

50.5 

60.6 

70.7 

80.8 

90.9 

101.0 

111.1 

121.2 

10.10 

10.15 

10.2 

20.3 

30.5 

40.6 

50.8 

60.9 

71.1 

81.2 

91.4 

101.5 

111.7 

121.8 

10. 15 

10.20 

10.2 
10.3 

20.4 

30.6 

40.8 
41.0 

51.0 

61.2 

71.4 

81.6 

91.8 
92.  3 

102.0 
102.5 

112.2 

122.4 

10.20 

10.25 

20.5 

30.8 

51.3 

61.5 

71.8 

82.0 

112.8 

123.0 

10.  25 

10.30 

10.3 

20.6 

30.9 

41.2 

51.5 

61.8 

72.1 

82.4 

92.7 

103.0 

113.3 

123.6 

10.30 

10.35 

10.4 

20.7 

31.1 

41.4 

51.8 

62.1 

72.5 

82.8 

93.2 

103.5 

113.9 

124.2 

10.  35 

10.40 

10.4 

20.8 

31.2 

41.6 

52.0 

62.4 

72.8 

83.2 

93.6 

104.0 

114.4 

124.8 

10.40 

10.45 

10.5 

20.9 

31.4 

41.8 

52.3 
52.5 

62.7 
6.3.0 

73.2 
73.5 

83.6 

94.1 
94.5 

104.5 
105. 0' 

115.0 
115.5 

125.4 
126.0 

10. 45 

10.50 

10.5 

21.0 

31.5 

42.0 

84.0 

10.50 

10.  55 

10.6 

21.1 

31.7 

42.2 

52.8 

63.3 

73.9 

84.4 

95.0 

105.5 

116.1 

126.6 

10.  55 

10.60 

10.6 

21.2 

31.8 

42.4 

53.0 

63.6 

74.2 

84.8 

95.4 

106.0 

116.6 

127.2 

10.60 

10.65 

10.7 

21.3 

32.0 

42.6 

53.3 

63.9 

74.6 

85.2 

95.9 

106.5 

117.2 

127.8 

10.  65 

10.70 

10.7 

21.4 

32.1 
32.3 

42.8 
43.0 

5.3.5 

53.8 

64.2 

74.9 

85.6 
86.0 

96.3 
96.8 

107.0 
107.5 

117.7 
118.3 

128.4 
129.0 

10.70 

10.75 

1Q.8 

21.5 

64.5 

75.3 

10.75 

10.80 

10.8 

21.6 

32.4 

43.2 

54.0 

64.8 

75.6 

86.4 

97.2 

108.0 

118.8 

129.6 

10.80 

10.  85 

10.9 

21.7 

32.6 

43.4 

54.3 

65.1 

76.0 

86.8 

97.7 

108.5 

119.4 

130.2 

10.85 

10.90 

10.9 

21.8 

32.7 

43.6 

54.5 

65.4 

76.3 

87.2 

98.1 

109.0 

119.9 

130.8 

10.90 

10.95 

11.0 

21.9 
22.0 

32.9 

43.8 
44.0 

54.8 
55.0 

65.7 
66.0" 

76.7 
77.0 

87.6 
88.0 

98.6 

109.5 
110.0 

120. 5 
121.0 

131.4 

10.  95 
11.00 

11.00 

11.0 

33.0 

99.0 

132.0 

11.05 

11.1 

22.1 

33.2 

44.2 

55.3 

66.3 

77.4 

88.4 

99.5 

110.5 

121.6 

132.6 

11.05 

11.10 

11.1 

22.2 

.33.3 

44.4 

55.  5 

66.6 

77.  7 

88.8 

99.9 

111.0 

122.  1 

133.2 

11.10 

11.15 

11.2 

22.3 

33.5 

44.6 

55.8 

66.9 

78.1 

89.2 

100.4 

111.5 

122.7 

133.8 

11.15 

11.20 

11.2 
11.3 

22.4 

33.6 
33.8 

44.8 
45.0 

56.0 
56.3 

67.2 
67.5 

78.4 

89.6 

100.8 
101.3 

112.0 
112.5 

123.2 
123.8 

134.4 

11.20 

11.25 

22.5 

78.8 

90.0 

135.0 

11.25 

11.30 

11.3 

22.6 

33.9 

45.2 

56.5 

67.8 

79.1 

90.4 

101.7 

113.  0 

124.3 

135.6 

11.30 

11.35 

11.4 

22.7 

34.1 

45.4 

56.8 

68.1 

79.5 

90.8 

102.2 

113.5 

124.9 

136.2 

11.35 

11.40 

11.4 

22.8 

.34.2 

45.6 

57.0 

68.4 

79.8 

91.2 

102.  6 

114.0 

125.4 

136.8 

11.40 

11.45 

11.5 

22.9 

34.4 

45.8 

57.3 

68.7 

80.2 

91.6 

103.1 

114.5 

126.0 

137.4 

11.45 

TABLE  13.                                             [Page  521 

For  finding  the  Sun's  change  of  Right  Ascension  for  any  given  number  of  hours. 

Hourly 
varia- 
tion. 

Number  of  hours. 

Hourly 
varia- 
tion. 

13 

14 

15 

16       1      17 

18 

19 

20 

21 

s. 

22 

23 

24 

s. 

s. 

s. 

s. 

.«.             s. 

*. 

s. 

s. 

s. 

s, 

s. 

s. 

8.50 

110.5 

119.0 

127.5 

136.0 

144.5 

153.0 

161.5 

170.0 

178.5 

187.0 

195.5 

204.0 

8.50 

8.55 

111.2 

119.7 

128.  3 

136.8 

145.4 

153.  9 

162.5 

171.0 

179.6 

188.1 

196.7 

205.2 

8.55 

8.60 

111.8 

120.4 

129.0 

137.  6 

146.2 

154.8 

163.4 

172.0 

180.6 

189.2 

197.8 

206.4 

8.60 

8.65 

112.5 

121.1 

129.8 

138.4 

147.1 

155.  7 

164.4 

173.0 

181.7 

190.3 

199.0 

207.6 

8.65 

8.70 

113.1 

121.8 
122.5 

130.5 
131.3 

139.2 

147.9 

156.6 
157.5 

165.3 
166.3 

174.0 
175.0 

182.7 
183.  8 

191.4 
192.  5^ 

200.1 
201.3 

208.8 

8.70 
8.75 

8.75 

113.8 

140.0 

148.8 

210.0 

8.80 

114.4 

123.  2 

132.  0 

140.8 

149.6 

158.  4 

167.2 

176.0 

184.8 

193.  6 

202.4 

211.2 

8.80 

8.85 

115.1 

123.9 

132.8 

141.6 

150.5 

159.3 

168.2 

177.0 

185.9 

194.7 

203.6 

212.4 

8.85 

8.90 

115.  7 

124.6 

133.5 

142.4 

151.3 

160.2 

169.1 

178.0 

186.9 

195.8 

204.7 

213.6 

8.90 

8.95 
9.00 

116.4 
117.0 

125.  3 

134.3 
135.  0 

143.2 
144.0 

152.2 
153.0 

161.1 
162.0 

170.1 
171.0 

179.0 

188.0 

196.9 

205.  9 

214.8 

8.95 

126.0 

180.0 

189.0 

198.  0 

207.0 

216.0 

9.00 

9.05 

117.7 

126.7 

135.8 

144.8 

153.9 

162.  9 

172.0 

181.0 

190.1 

199.1 

208.2 

217.2 

9.05 

9.10 

118.3 

127.4 

136.5 

145.6 

154.7 

163.  8 

172.9 

182.0 

191.1 

200.2 

209.3 

218.4 

9.10 

9.15 

119.0 

128.1 

137.3 

146.4 

155.6 

164.7 

173.9 

183.0 

192.2 

201.  3 

210.5 

219.6 

9.15 

9.20 

119.6 
120.3 

128.8 

138.0 

147.2 

148.0 

156.4 
157. 3 

165.6 
166.5 

174.8 
175.8 

184.0 
185.0 

193.2 
194.  3 

202.4 
203.5 

211.6 

220.8 

9.20 

9.25 

129.5 

138.  8 

212.8 

222.0 

9.25 

9.30 

120.9 

130.  2 

139.5 

148.8 

158.1 

167.4 

176.7 

186.0 

195. 3 

204.6 

213.9 

223.2 

9.30 

9.  35 

121.6 

130.9 

140.3 

149.  6 

159.  0 

168.3 

177.7 

187.0 

196.4 

205.7 

215.1 

224.4 

9.35 

9.40 

122.2 

131.6 

141.0 

150.  4 

159.8 

169.2 

178.6 

188.0 

197.4 

206.8 

216.2 

225.6 

9.40 

9. 45 
9.50 

122.9 

132.3 
133.0 

141.8 

151.2 

160.7 
161.5 

170.1 
171.0 

179.6 
180.5 

189.0 
190.0 

198.5 
199.5 

207.9 
209.0 

217.4 

226.8 

9.45 

123.5 

142.5 

152.0 

218.  5 

228.0 

9.50 

9.55 

124.2 

133.7 

143.3 

152.  8 

162.4 

171.9 

181.5 

191.0 

200.6 

210.1 

219.7 

229.2 

9.55 

9.60 

124.8 

134.4 

144.0 

153.6 

163.2 

172.8 

182.4 

192.0 

201.6 

211.2 

220.8 

230.4 

9.60 

9.65 

125. 5 

135.1 

144.8 

154.4 

164.1 

173.7 

183.4 

193.0 

202.7 

212.3 

222.0 

231.6 

9.65 

9.70 

126.1 

135.8 
136.5 

145.5 
146.3 

155.2 
156.0 

164.9 
165.8 

174.6 
175.5 

184.3 
185.3 

194.0 

203.7 
204.8 

213.4 

223.1 

232.8 

9.70 

9.75 

126.8 

195.0 

214.5 

224.3 

-234.0 

9.75 

9.80 

127.4 

137.2 

147.0 

156.8 

166.6 

176.4 

186.2 

196.0 

205.8 

215.6 

225.4 

235.  2 

9.80 

9.85 

128.1 

137.9 

147.8 

157.6 

167.5 

177.3 

187.2 

197.0 

206.9 

216.7 

226.6 

236.4 

9.85 

9.90 

128.7 

138.6 

148.5 

158.  4 

168.3 

178.2 

188.1 

198.0 

207.9 

217.8 

227.7 

237.6 

9.90 

9.95 

129.4 

139.3 
140.0 

149.3 
150.0 

159.2 
160.0 

169.2 
170.0 

179.1 

189.1 

199.0 
200.0 

209.0 
210.0 

218.9 
220.0 

228.9 
230.  0 

238.8 

9.95 

10.00 

130.0 

180.0 

190.0 

240.0 

10.00 

10.05 

130.7 

140.7 

150.8 

160.8 

170.9 

180.9 

191.0 

201.0 

211.1 

221.1 

231.2 

241.2 

10.05 

10.10 

131.3 

141.4 

151.5 

161.6 

171.7 

181.8 

191.9 

202.0 

212.1 

222.2 

232.3 

242.4 

10.10 

10. 15 

132.0 

142.1 

152.3 

162.4 

172.6 

182.7 

192.9 

203.0 

213.2 

223.3 

233.5 

243.6 

10.15 

10.20 

132.6 

142.8 

153.0 

163.2 

173.  4 
174.3 

183.6 
184.5 

193.8 
194.8 

204.0 
205.0 

214.2 
215.3 

224.4 
225.5 

234.6 
235.  8 

244.8 

10.20 

10.25 

133.3 

143.5 

153.  8 

164.0 

246.0 

10.25 

10.30 

133.9 

144.2 

154.5 

164.8 

175.1 

185.4 

195.7 

206.0 

216.3 

226.6 

236.9 

247.2 

10.30 

10.  35 

134.6 

144.9 

155.  3 

165.6 

176.0 

186.3 

196.7 

207.0 

217.4 

227.7 

238.1 

248.4 

10.35 

10.40 

135.2 

145.6 

156.0 

166.4 

176.  8 

187.2 

197.6 

208.0 

218.4 

228.8 

239.2 

249.6 

10.40 

10.45 
10.50 

135.9 
136.5 

146.3 
147.0 

156.8 

167.2 

177.7 
-178.5 

188.1 

198.6 
199.5 

209.0 
210.0 

219.5 

229.9 
231.0 

240.4 

250.  8 
252.0 

10.45 

157. 5 

168.0 

189.0 

220.5 

241.5 

10.50 

10.55 

137.  2 

147.7 

158.  3 

168.8 

179.4 

189.9 

200.5 

211.0 

221.6 

232. 1 

242.7 

253.2 

10.55 

10.60 

137.8 

148.4 

159.0 

169.6 

180.2 

190.8 

201.4 

212.0 

222.6 

233.2 

243.8 

254.4 

10.60 

10.65 

138.5 

149.1 

159.8 

170.4 

181.1 

191.7 

202.4 

213.0 

223.  7 

234.  3 

245.0 

255.6 

10.  65 

10.70 

139.1 

149.8 
150.5 

160.5 

171.2 

181.9 
182.8 

192.6 
193.5 

203.3 
204.3 

214.0 

224.7 

235.4 
236.5 

246.1 
247.3 

256.8 

10.70 

10.75 

139.  8 

161.3 

172.0 

215.0 

225.8 

258.0 

10.75 

10.80 

140.4 

151.2 

162.0 

172.8 

183.6 

194.4 

205.2 

216.0 

226.8 

237.6 

248.4 

259.2 

10.80 

10.85 

141.1 

151.9 

162.8 

173.6 

184.5 

195.3 

206.2 

217.0 

227.9 

238.7 

249.6 

260.4 

10.85 

10.90 

141.7 

152.6 

163.  5 

174.4 

185.3 

196.2 

207.1 

218.0 

228.9 

239.8 

250.7 

261.6 

10.90 

10.  95 

142.4 

153.3 

164.3 
165.0 

175.2 

186.2 

197.1 
198.0 

208.1 
209.0 

219.0 

230.0 

240.9 
242.  0 

251.9 
253.  0 

262.8 

10.95 

11.00 

143.0 

154.0 

176.0 

187.0 

220.0 

231.0 

264.0 

11.00 

11.05 

143.7 

154.7 

165.  8 

176.8 

187.9 

198.9 

210.0 

221.0 

232.1 

243.1 

254.2 

265.2 

11.05 

11.10 

144.3 

155.  4 

166.5 

177.6 

188.7 

199.8 

210.9 

222.0 

233. 1 

244.2 

255.  3 

266.4 

11.10 

11.15 

145.0 

156.1 

167.  3 

178.4 

189.6 

200.7 

211.9 

223.0 

234.2 

245.3 

256.  5 

267.6 

11.15 

11.20 

145.6 
146.3 

156.8 
157.5 

168.0 

179.2 
180.0 

190.4 

201.6 

212.8 

224.0 

235.2 

246.4 
247.5 

257.6 

258.8 

268.8 
270.0 

11.20 

11.25 

168.8 

191.  3 

202.5 

213.8 

225.0 

236.3 

11.25 

11.30 

146.9 

158.2 

169.5 

180.8 

192.1 

203.4 

214.7 

226.0 

237.3 

248.6 

259.9 

271.2 

11.30 

11.35 

147.6 

158.9 

170.3 

181.6 

193.0 

204.3 

215.7 

227.0 

238.4 

249.7 

261.1 

272.4 

11.35 

11.40 

148.2 

159.6 

171.0 

182.4 

193.  8 

205.  2 

216.6 

228.0 

239.4 

250.8 

262.2 

273.  6 

11.40 

11.45 

148.  9 

160.  3 

171.  8 

183.  2 

194.7 

206.1 

217.6 

229.0 

240.5 

251.9 

263.4 

274.8 

11.45 

Page  522] 


TABLES  14,  15,  16. 


TABLE  14. 

Dip  of  the  Sea 
Horizon. 


Height  of  Dip  of  the 
the  Eye.     Horizon 


Feet. 


0  59 


2 

1  23 

3 

1  42 

4 

1  58 

5 

2  11 

6 

2  24 

7 

2  36 

8 

2  46 

9 

2  56 

10 

3  06 

11 

3  15 

12 

3  24 

13 

3  32 

14 

3  40 

15 

3  48 

16 

3  55 

17 

4  02 

18 

4  09 

19 

4  16 

20 

4  23 

21 

4  29 

22 

4  36 

23 

4  42 

24 

4  48 

25 

4  54 

26 

5  00 

27 

5  06 

28 

5  11 

29 

5  17 

30 

5  22 

31 

5  27 

32 

5  33 

33 

5  38 

34 

5  43 

35 

5  48 

36 

5  53 

37 

5  58 

38 

6  02 

39 

6  07 

40 

1  6  12 

45 

6  36 

50 

6  56 

55 

7  16 

60 

7  35 

65 

7  54 

70 

8  12 

75 

8  29 

80 

8  46 

85 

9  02 

90 

9  18 

95 

9  33 

100 

;  9  48 

Dlst.  of 

Land  in 

Sea  Miles. 


TABLE  15. 
Dip  of  the  Sea  at  different  Distances  from  the  Observer. 


u 
n 

2 
2J 


3 

H 

4 

5 


10 


11 
6 
4 
3 


23 
12 


Height  of  the  Eye  above  the  Sea  in  Feet. 
80        I 


15 


34 
17 
12 


20 


45 
23 
15 
12 


10 

8 


26 


57 

28 
19 
15 


12 
10 


85 


34 
23 
17 


14 
12 


40 
27 
20 


16 
14 
11 


6 


40 


91 
45 
30 
23 


19 
16 
12 
10 


Note  to  Table  15. — The  numbers  of  this  Table  below  the  black  lines 
are  the  same  as  are  given  in  Table  14,  the  visible  horizon  corresponding 
to  those  heights  not  being  so  far  distant  as  the  land. 


TABLE  16. 

The  Sun's  Parallax 

in  Altitude. 

Altitude. 

Parallax. 

o 

// 

0 

9 

10 

9 

20 

8 

30 

8 

40 

7 

50 

6 

55 

5 

60 

4 

65 

4 

70 

3 

75 

2 

80 

2 

85 

1 

90 

0 

TABLE  17. 

Parallax  in  Altitude  of  a  Planet. 

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Page  524]                                       TABLES  18,  19. 

TABLE  18. 
Augmentation  of  the  Moon's  Semidiameter. 

TABLE  19, 

Augmentation  of  the  Moon's 
Horizontal  Parallax. 

CO 

SS  • 
< 

J)'s  Semidiameter. 

o  ob 

OJ  > 

S^  o 
o 

0 
2 
4 

6 
8 

J)  's  Hor.  Parallax. 

W 

•            !»' 

16' 

17' 

1 

80" 

0" 

80" 

0" 

80" 

0" 

53' 

57'                81'        1 
1 

o 

0 
2 
4 
6 
8 

// 
0.1 
0.6 
1.0 
1.5 
2.0 

// 

0.1 
0.6 
1.1 
1.6 
2.1 

0.1 
0.7 
1.2 
1.7 
2.3 

// 

0.1 
0.7 
1.3 
1.9 
2.4 

II 

0.2 
0.8 
1.4 
2.0 
2.6 

II 

0.2 
0.8 
1.5 
2.1 
2.7 

II 
0.0 
0.0 
0.1 
0.1 
0.2 

// 

0.0 
0,0 
0.1 
0.1 
0.2 

II 

0,0 
0.0 
0.1 
0.1 
0.2 

10 
12 
14 

16 

18 

2.4 
2.9 
3.4 
3.8 
4.3 

2.6 
3.1 
3.6 
4.1 
4.6 

2.8 
3.3 
3.9 
4.4 
4.9 

3.0 
3.6 
4.1 
4.7 
5.2 

3.2 
3.8 
4.4 
5.0 
5,6 

3.4 
4.0 
4.7 
5.3 
5.9 

10 
12 
14 
16 
18 

0.3 
0.5 
0.6 
0.8 
1.0 

0.3 
0.5 
0.7 
0.9 
1.1 

0.4 
0.5 
0.7 
0.9 
1.1 

20 
22 
24 
26 

28 

4.7 
5.2 
5.6 
6.0 
6.5 

5.1 
5.5 
6.0 
6.5 
6.9 

5.4 
5.9 
6.4 
6.9 
7.4 

5.8 
6.3 
6.8 
7.4 
7.9 

6.1 
6.7 
7.3 

7.8 
8.4 

6.5 
7.1 

7.  7 
8.3 
8.9 

20 
22 
24 
26 

28 

1.2 
1.5 
1.7 
2.0 
2.3 

1.3 
L6 
1.9 
2.2 
2.5 

1.4 
1.7 
2.0 
2.3 
2.6 

30 
32 
34 
36 
38 

6.9 
7.3 

7.7 
8.1 
8.4 

7.3 

7.8 
8.2 
8.6 
9.0 

7.9 
8.3 
8.8 
9.2 
9.7 

8.4 
8.9 
9.4 
9.8 
10.3 

8.9 

9.4 

10.0 

10.5 

10.9 

9.5 
10.0 
10.6 
11.1 
11.6 

30 
32 
34 
36 
38 

2.6 
2.9 
3.3 
3.6 
4.0 

2.8 
3.1 
3.5 
3.9 
4.3 

3.0 
3.4 
3.8 
4.1 
4.6 

40 
42 
44 
46 
48 

8.8 
9.2 
9.5 
9.8 
10.2 

9.4 

9.8 

10.2 

10.5 

10.9 

10.1 
10.5 
10.9 
11.3 
11.6 

10.7 
11.2 
11.6 
12.0 
12.4 

11.4 
11.9 
12.3 
12.8 
13.2 

12.1 
12.6 
13.1 
13.6 
14.0 

40 
42 
44 
46 

48 

4.3 
4.7 
5.0 
5.4 

5.8 

4.6 
5.0 

5.4 
5.8 
6.2 

5.0 
5.4 

5.8 
6.2 
6.6 

50 
52 
54 
56 

58 

10.5 
10.8 
11.1 
11.3 
11.6 

11.2 
11.5 
11.8 
12.1 
12.4 

12.0 
12.3 
12.7 
13.0 
13.3 

12.8 
13.1 
13.5 
13.8 
14.1 

13.6 
14.0 
14.4 
14.7 
15.1 

14.4 
14.9 
15.3 
15.6 
16.0 

50 
52 
54 
56 

58 

6.1 
6.5 
6.8 
7.2 
7.5 

6.6 
7.0 
7.4 

7.7 
8.1 

7.1 
7.5 
7.9 
8.3 
8.6 

60 
62 
64 
66 
68 

11.8 
12.1 
12.3 
12.5 
12.7 

12.7 
12.9 
13.2 
13.4 
13.6 

13.5 
13.8 
14.1 
14.3 
14.5 

14.4 
14.7 
15.0 
15.2 
15.5 

15.4 
15.7 
16.0 
16.2 
16.5 

16.3 
16.6 
16.9 
17.2 
17.5 

60 
62 
64 
66 
68 

7.8 
8.1 
8.4 
8.7 
9.0 

8.4 
8.8 
9.1 
9.4 
9,7 

9.0 

9.4 

9.7 

10.0 

10.3 

70 
72 
74 

76 

78 

12.9 
13.0 
13.1 
13.3 
13.4 

13.8 
13.9 
14.1 
14.2 
14.3 

14.7 
14.9 
15.0 
15.2 
15.3 

15.7 
15.9 
16.0 
16.2 
16.3 

16.7 
16.9 
17.1 
17.2 
17.4 

17.7 
17.9 
18.1 
18.3 
18.4 

70 

72 
74 
76 
78 

9.2 

9.5 

9.7 

9.8 

10.0 

9,9 
10.2 
10.4 
10.6 
10.8 

10.6 
10.9 
11.1 
11.3 
11.5 

80 
82 
84 
86 
88 

13.5 
13.5 
13.6 
13.6 
13.7 

14.4 
14.5 
14.6 
14.6 
14.6 

15.4 
15.5 
15.6 
15.6 
15.6 

16.4 
16.5 
16.6 
16.6 
16.7 

17.5 
17.6 
17.6 
17.7 

17.7 

18.6 
18.7 
18.7 
18.8 
18.8 

80 

82 
84 
86 
88 

10.1 
10.3 
10.3 
10.4 
10.4 

10.9 
11.0 
11.1 
11.2 
11.2 

11.7 
11.8 
11.9 
12.0 
12.0 

90 

13.7 

14.6 

15.6 

16.7 

17.7 

18.8 

90 

10.5 

11.3 

12.0 

TABLE  20A. 

[Page  525    | 

Mean  Refraction. 

[Barometer,  30  inches.    Fahrenheit's  Thermometer, 

50°.J 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 

Mean  Re- 

Apparent 
Altitude. 

Mean  Re- 

Altitude. 

fraction. 

Altitude. 

fraction. 

Altitude. 

fraction. 

Altitude. 

fraction. 

fraction. 

o       / 

' 

o        / 

9  30 

5  35.  1 

o        / 

15  00 

3  34.1 

o      / 

25  00 

2     4.4 

42  00 

1  04.7 

0  00 

36  29.  4 

35 

5  32.4 

10 

3  31.7 

10 

2     3.4 

20 

1  03.9 

1  00 

24  53. 6 

40 

5  29.  6 

20 

3  29.4 

20 

2     2.5 

40 

1  03.2 

2  00 

18  25. 5 

45 

5  27.0 

30 

3  27.1 

30 

2     1.6 

43  00 

1  02.4 

3  00 

14  25. 1 

50 

5  24.3 

40 

3  24.8 

40 

2    0.7 

20 

1  01.7 

4  00 

11  44.4 

55 

5  21.7 

50 

3  22.6 

50 

1  59.8 

40 

1  01.0 

5  00 

9  52.0 

10  00 

5  19.2 

16  00 

3  20.5 

26  00 

1  58.9 

44  00 

1  00.3 

06 

9  44.0 

05 

5  16.7 

10 

3  18.4 

10 

1  58.1 

20 

0  59.  6 

10 

9  36.2 

10 

5  14.2 

20 

3  16.3 

20 

1  57.2 

40 

0  58.9 

15 

9  28.6 

15 

5  11.7 

30 

3  14.2 

30 

1  56.4 

45  00 

0  58.2 

20 

9  21.2 

20 

5    9.3 

40 

3  12.2 

40 

1  55.5 

20 

0  57.6 

25 

9  14.0 

25 

5    6.9 

50 

3  10.3 

50 

1  54.7 

40 

0  56.9 

5  30 

9     7.0 

10  30 

5    4.6 

17  00 

3    8.3 

27  00 

1  53.9 

46  00 

0  56.2 

35 

9     0.1 

35 

5    2.3 

10 

3    6.4 

10 

1  53.1 

20 

0  66.6 

40 

8  53.4 

40 

5    0.0 

20 

3    4.6 

20 

1  52.3 

40 

0  55.0 

45 

8  46.8 

45 

4  57.8 

30 

3    2.8 

30 

1  61.5 

47  00 

0  54.3 

50 

8  40.4 

50 

4  55.6 

40 

3    1.0 

40 

1  50.7 

20 

0  53.7 

55 

8  34.2 

55 

4  53.4 

50 

2  59.2 

50 

1  50.0 

40 

0  53.1 

6  00 

8  28.0 

11  00 

4  51.2 

18  00 

2  57.5 

28  00 

1  49.2 

48  00 

0  62.5 

05 

8  22.1 

05 

4  49.1 

10 

2  55.8 

20 

1  47.7 

49  00 

0  50.6 

10 

8  16.2 

10 

4  47.0 

20 

2  54.1 

40 

1  46.2 

50  00 

0  48.9 

15 

8  10.5 

15 

4  44.9 

30 

2  52.4 

29  00 

1  44.8 

51  00 

0  47.2 

20 

8    4.8 

20 

4  42.9 

40 

2  50.8 

20 

1  43.4 

52  00 

0  46.5 

25 

7  59.3 

25 

4  40.9 

50 

2  49.2 

40 

1  42.0 

53  00 

0  43.9 

6  30 

7  53.9 

11  30 

4  38.9 

19  00 

2  47.7 

30  00 

1  40.6 

54  00 

0  42.3 

35 

7  48.7 

35 

4  36.9 

10 

2  46.1 

20 

1  39.3 

66  00 

0  40.8 

40 

7  43.5 

40 

4  35.0 

20 

2  44.6 

40 

1  38.0 

56  00 

0  39.3 

45 

7  38.4 

45 

4  33. 1 

30 

2  43.1 

31  00 

1  36.7 

57  00 

0  37.8 

■   50 

7  33.5 

50 

4  31.2 

40 

2  41.6 

20 

1  35.5 

68  00 

0  36.4 

55 

7  28.6 

55 

4  29.4 

50 

2  40.2 

40 

1  34.2 

59  00 

0  35.0 

7  00 

7  23.8 

12  00 

4  27.5 

20  00 

2  38.8 

32  00 

1  33.0 

60  00 

0  33.6 

05 

7  19.2 

05 

4  25.  7 

10 

2  37.4 

20 

1  31.8 

61  00 

0  32.3 

10 

7  14.6 

10 

4  23.9 

20 

2  36.0 

40 

1  30.7 

62  00 

0  31.0 

15 

7  10.1 

15 

4  22.2 

30 

2  34.6 

33  00 

1  29.5 

63  00 

0  29.7 

20 

7    5.7 

20 

4  20.4 

40 

2  33.  3 

20 

1  28.4 

64  00 

0  28.  4 

25 

7     1.4 

25 

4  18.7 

50 

2  32.0 

40 

1  27.3 

65  00 

0  27.2 

7  30 

6  57.1 

12  30 

4  17.0 

21  00 

2  30.7 

34  00 

1  26.  2 

66  00 

0  25.9 

35 

6  53.  0 

35 

4  15.3 

10 

2  29.4 

20 

1  25. 1 

67  00 

0  24.7 

40 

6  48.9 

40 

4  13.6 

20 

2  28.1 

40 

1  24.1 

68  00 

0  23.6 

45 

6  44.9 

45 

4  12.0 

30 

2  26.9 

35  00 

1  23.1 

69  00 

0  22.4 

50 

6  41.0 

50 

4  10.4 

40 

2  25.7 

20 

1  22.0 

70  00 

0  21.2 

55 

6  37.1 

55 

4     8.8 

50 

2  24.5 
2  23.3 

40 
36  00 

1  21.0 
1  20.1 

71  00 

72  00 

0  20.1 
0  18.9 

8  00 

6  33.3 

13  00 

4    7.2 

22  00 

05 

6  29.6 

05 

4    5.6 

10 

2  22.1 

20 

1  19.1 

73  00 

0  17.8 

10 

6  25.9 

10 

4    4.1 

20 

2  20.9 

40 

1  18.2 

74  00 

0  16.7 

15 

6  22.3 

15 

4    2.6 

30 

2  19.8 

37  00 

1  17.2 

75  00 

0  16.6 

20 

6  18.8 

20 

4    1.0 

40 

2  18.7 

20 

1  16.3 

76  00 

0  14.6 

25 

6  15.3 

25 

3  59.6 

50 

2  17.5 

40 

1  15.4 

77  00 

0  13.5 

8  30 

6  11.9 

13  30 

3  58.1 

23  00 

2  16.4 

38  00 

1  14.5 

78  00 

0  12.4 

35 

6    8.5 

35 

3  56.6 

10 

2  15.4 

20 

1  13.6 

79  00 

0  11.3 

40 

6    5.2 

40 

3  55. 2 

20 

2  14.3 

40 

1  12.7 

80  00 

0  10.3 

45 

6    2.0 

45 

3  53.7 

30 

2  13.3 

39  00 

1  11.9 

81  00 

0    9.2 

50 

5  58.8 

50 

3  52.3 

40 

2  12.2 

20 

1  11.0 

82  00 

0    8.2 

55 

5  55.7 

55 

3  50.9 

50 

2  11.2 

40 

1  10.2 

83  00 

84  00 

0    7.2 
0    6.1 

9  00 

5  52.6 

14  00 

3  49.5 

24  00 

2  10.2 

40  00 

1     9.4 

05 

5  49.6 

10 

3  46.  8 

10 

2    9.2 

20 

1     8.6 

85  00 

0    5.1 

10 

5  46.6 

20 

3  44.2 

20 

2     8.2 

40 

1     7.8 

86  00 

0    4.1 

15 

5  43.6 

30 

3  41.6 

30 

2    7.2 

41  00 

1     7.0 

87  00 

0    3.1 

20 

5  40.7 

40 

3  39.0 

40 

2     6.2 

20 

1     6.2 

88  00 

0    2.0 

25 

5  37.9 

50 

3  36.  5 

50 

2     5.3 

40 

1     5.4 

89  00 

0    1.0 

9  30 

5  35.1 

15  00 

3  34.1 

25  00 

2     4.4 

42  00 

1     4. 7 

90  00 

0    0.0 

Page  526] 

TABLE  20B. 

Correction  of  the  Sun's  Apparent  Altitude  for  Refraction  and  Parallax. 

[Barometer,  30  inches.  Fahrenheit's  Thermometer, 

50°.] 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  ©. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  ©. 

Apparent 
Altitude. 

Mean  Re- 
fraction and 
Parallax  0. 

o   / 

/  // 

O    / 

'  II 

o   / 

/  // 

o    / 

1     II 

0    1 

'  II 

9  30 

5  26 

15  00 

3  25 

25  00 

1  56 

42  00 

0  58 

0  00 

36  20 

35 

5  23 

10 

3  24 

10 

1  55 

20 

0  57 

1  00 

24  45' 

40 

5  21 

20 

3  21 

20 

1  55 

40 

0  56 

2  00 

18  17 

45 

5  18 

30 

3  19 

30 

1  54 

43  00 

0  55 

3  00 

14  16 

50 

5  15 

40 

3  17 

40 

1  53 

20 

0  55 

4  00 

11  35 

55 

5  13 

50 

3  15 

50 

1  52 

40 

0  54 

5  00 

9  43 

10  00 

5  10 

16  00 

3  13 

26  00 

1  51 

44  00 

0  53 

05 

9  35 

05 

5  8 

10 

3  10 

10 

1  50 

20 

0  53 

10 

9  27 

10 

5  5 

20 

3  8 

20 

1  49 

40 

0  52 

15 

9  20 

15 

5  3 

30 

3  6 

80 

1  48 

45  00 

0  52 

20 

9  12 

20 

5  0 

40 

3  4 

40 

1  48 

20 

0  52 

25 

9  5 

25 

4  58 

50 

3  2 

50 

1  47 

40 

0  51 

5  30 

8  58 

10  30 

4  56 

17  00 

3  0 

27  00 

1  46 

46  00 

0  50 

35 

8  51 

35 

4  53 

10 

2  58 

10 

1  45 

20 

0  50 

40 

8  44 

40 

4  51 

20 

2  57 

20 

1  44 

40 

0  49 

45 

8  38 

45 

4  49 

30 

2  55 

30 

1  44 

47  00 

0  48 

50 

8  31 

50 

4  47 

40 

2  53 

40 

1  43 

20 

0  48 

55 

8  25 

55 

4  44 

50 

2  51 

50 

1  42 

40 

0  47 

6  00 

8  19 

11  00 

4  42 

18  00 

2  50 

28  00 

1  41 

48  00 

0  47 

05 

8  13 

05 

4  40 

10 

2  48 

20 

1  40 

49  00 

0  45 

10 

8  7 

10 

4  38 

20 

2  46 

40 

1  38 

50  00 

0  43 

15 

8  2 

15 

4  36 

30 

2  44 

29  00 

1  37 

51  00 

0  41 

20 

7  56 

20 

4  34 

40 

2  43 

20 

1  35 

52  00 

0  40 

25 

7  50 

25 

4  32 

50 

2  41 

40 

1  34 

53  00 

0  39 

6  30 

7  45 

11  30 

4  30 

19  00 

2  40 

30  00 

1  33 

54  00 

0  37 

35 

7  40 

35 

4  28 

10 

2  38 

20 

1  31 

55  00 

0  36 

40 

7  35 

40 

4  26 

20 

2  37 

40 

1  30 

56  00 

0  34 

45 

7  29 

45 

4  24 

30 

2  35 

31  00 

1  29 

57  00 

0  33 

50 

7  25 

50 

4  22 

40 

2  34 

20 

1  28 

58  00 

0  32 

55 

7  20 

55 

4  20 

50 

2  32 

40 

1  26 

59  00 

0  31 

7  00 

7  15 

12  00 

4  19 

20  00 

2  31 

32  00 

1  25 

60  00 

0  30 

05 

7  10 

05 

4  17 

10 

2  29 

20 

1  24 

61  00 

0  28 

10 

7  6 

10 

4  15 

20 

2  28 

40 

1  23 

62  00 

0  27 

15 

7  1 

15 

4  13 

30 

2  27 

33  00 

1  22 

63  00 

0  26 

20 

6  57 

20 

4  11 

40 

2  25 

20 

1  20 

64  00 

0  24 

25 

6  52 

25 

4  10 

50 

2  24 

40 

1  19 

65  00 

0  23 

7  30 

6  48 

12  30 

4  8 

21  00 

2  23 

34  00 

1  18 

66  00 

0  22 

35 

6  44 

35 

4  6 

10 

2  21 

20 

1  17 

67  00 

0  21 

40 

6  40 

40 

4  5 

20 

2  20 

40 

1  16 

68  00 

0  21 

45 

6  36 

45 

4  3 

30 

2  19 

35  00 

1  15 

69  00 

0  19 

50 

6  32 

50 

4  1 

40 

2  18 

20 

1  15 

70  00 

0  18 

55 

6  28 

55 

4  0 

50 

2  17 

40 

1  14 

71  00 

0  17 

8  00 

6  24 

13  00 

3  58 

22  00 

2  15 

36  00 

1  13 

72  00 

0  16 

05 

6  21 

05 

3  57 

10 

2  14 

20 

1  12 

73  00 

0  16 

10 

6  17 

10 

3  55 

20 

2  13 

40 

1  11 

74  00 

0  15 

15 

6  13 

15 

3  54 

30 

2  12 

37  00 

1  10 

75  00 

0  14 

20 

6  10 

20 

3  52 

40 

2  11 

20 

1  9 

76  00 

0  13 

25 

6  6 

25 

3  51 

50 

2  10 

40 

1  8 

77  00 

78  00 

0  12 
0  10 

8  30 

6  3 

13  30 

3  49 

•  23  00 

2  8 

38  00 

1  8 

35 

6  0 

35 

3  48 

10 

2  7 

20 

1  7 

79  00 

0  9 

40 

5  56 

40 

3  46 

20 

2  6 

40 

1  6 

80  00 

0  8 

45 

5  53 

45 

3  45 

30 

2  5 

39  00 

1  5 

81  00 

0  7 

50 

5  50 

50 

3  43 

40 

2  4 

20 

1  4 

82  00 

0  6 

55 

5  47 

55 

3  42 

50 

2  3 

40 

1  3 

83  00 

0  6 

9  00 

5  44 

14  00 

3  41 

24  00 

2  2 

40  00 

1  2 

84  00 

0  5 

05 

5  41 

10 

3  38 

10 

2  1 

20 

1  2 

85  00 

0  4 

10 

5  38 

20 

3  35 

20 

2  0 

40 

1  1 

86  00 

0  3 

15 

5  35 

30 

3  33 

30 

1  59 

41  00 

1  0 

87  00 

0  2 

20 

5  32 

40 

3  30 

40 

1  58 

20 

0  59 

88  00 

0  2 

25 

5  29 

50 

3  28 

50 

1  57 

40 

0  58 

89  00 

0  1 

9  30 

5  26 

15  00 

3  25 

25  00 

1  56 

42  00 

0  58 

90  00 

0  0 

TABLE  21.                                           [Page  527    1 

Correction  of  the  Mean  Refraction  for  the  Height  of  the  Barometer. 

Barom. 

Mean  refraction. 

Barom. 
Add. 

0 

1      1 

' 

2 

8'        j 

A 

'        1       6' 

6' 

1' 

8'        1       9'         |l0' 

Subtract. 

0" 

80"  j  0" 

80" 

0" 

80" 

0"    80" 

0" 

80"    0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

II 

If    1  " 

„ 

„ 

„ 

„ 

II 

II 

„ 

„ 

„ 

„ 

„ 

n 

// 

// 

II 

II 

;; 

27.50 

0 

2 

5 

7 

10 

12 

15 

17 

20 

23 

25 

28 

30 

33 

35 

38 

40 

43 

45 

48 

51 

27.55 

0 

2 

5 

7 

10 

12 

15 

17 

20 

22 

25 

27 

30 

32 

35 

37 

40 

42 

45 

47 

50 

27.60 

0 

2 

5 

7 

10 

12 

14 

17 

19 

22 

24 

27 

29 

31 

34 

36 

39 

41 

44 

46 

49 

27.65 

0 

2 

5 

7 

9 

12 

14 

16 

19 

21 

24 

26 

28 

31 

33 

36 

38 

40 

43 

45 

48 

27.70 

0 
0 

2 
2 

5 
4 

7 
7 

9 
9 

11 
11 

14 

16 

18 

21 

23 

25 

28 

30 

32 

35 

37 

39 

42 

44 

47 

27.75 

13 

16 

18 

20 

23 

25 

27 

29 

32 

34 

36 

39    41 

43 

46 

27.80 

0 

2 

4 

7 

9 

11 

13 

15 

18 

20 

22 

24 

27 

29 

31 

33 

35 

38    40 

42 

45 

27.85 

0 

2 

4 

6 

9 

11 

13 

15 

17 

19 

22 

24 

26 

28 

30 

32 

35 

37    39 

41 

44 

27.90 

0 

2 

4 

6 

8 

10 

13 

15 

17 

19 

21 

23 

25 

27 

30 

32 

34 

36    38 

40 

43 

27.95 
28.  00 

0 
0 

2     4 

6 
6 

8 
8 

10 
10 

12 
12 

14 
14 

16 
16 

18 
18 

21 
20 

23 

22 

25 
24 

27 
26 

29 

28 

31 
30 

33 
32 

35    37 
34  j36 

39 

42 

2 

4 

38 

41 

28.05 

0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

25 

27 

29 

31 

33 

35 

37 

39 

28.10 

0 

2 

4 

6 

8 

9 

11 

13 

15 

17 

19 

21 

23 

25 

27 

29 

31 

33 

34 

36 

38 

28.15 

0 

2 

4 

6 

7 

9 

11 

13 

15 

17 

19 

20 

22 

24 

26 

28 

30 

32 

34 

36 

37 

28.20 

0 

2 

4 

5 

7 

9 

11 

13 

14 

16 

18 

20 

22 

24 

25 

27 

29 

31 

33 

35 

36 

28.25 

0 

2 

3 

5 

7 

9 

10 

12 

14 

16 

18 

19 

21 

23 

25 

26 

28 

30 

32 

34  35 

28.30 

0 

2 

3 

5 

7 

8 

10 

12 

14 

15 

17 

19 

21 

22 

24 

26 

27 

29 

31 

33   34 

28.35 

0 

2 

3 

5 

7 

8 

10 

12 

13 

15 

17 

18 

20 

22 

23 

25 

27 

28 

30 

32  33 

28.40 

0 

2 

3 

5 

6 

8 

10 

11 

13 

14 

16 

18 

19 

21 

23 

24 

26 

27 

29 

31   32 

28.45 

0 
0 

2 

3 
3 

5 

4 

6 
6 

8 
7 

9 
9 

11 
10 

12 
12 

14 
14 

16 
15 

17 
17 

19 
18 

20 
20 

22 

21 

23 
23 

25 

24 

27 
26 

28 
27 

30  31 
29  30 

28.50 

31.50 

28.55 

0 

3 

4 

6 

7 

9 

10 

12 

13 

15 

16 

17 

19 

20 

22 

23 

25 

26 

28129 

31.45 

28.60 

0 

3 

4 

6 

7 

8 

10 

11 

13 

14 

15 

17 

18 

20 

21 

23 

24 

25 

27128 

31.40 

28.65 

0 

3 

4 

5 

7 

8 

9 

11 

12 

14 

15 

16 

18 

19 

20 

22 

23 

25 

26|27 

31.35 

28.70 

0 

3 

4 

5 

6 

8 

9 

10 

12 

13 

14 

16 

17 

18 

20  121 

22 

24 

25126 

31.30 

28.75 

0 

2 

4 

5 

6 

7 

9 

10 

11 

13 

14 

15 

16 

18 

19 

20 

21 

23 

24 

25 

31.25 

28.80 

0 

2 

4 

5 

6 

7 

8 

10 

11 

12 

13 

14 

16 

17 

18 

19 

21 

22 

23 

24 

31.20 

28.  85 

0 

2 

3 

5 

6 

7 

8 

9 

10 

12 

13 

14 

15 

16 

17 

19 

20 

21 

22 

23 

31.15 

28.90 

0 

2 

3 

4 

5 

7 

8 

9 

10 

11 

12 

13 

14 

16 

17 

18 

19 

20 

21 

22 

31.10 

28.95 

0 

2 

3 

4 

5 

6 

7 

8 

9 
9 

11 
10 

12 
11 

13 

14 

15 

16 

17 

18 

19 

20 

21 

31.05 

29.00 

0 

2 

3 

4 

5 

6 

7 

8 

12 

13 

14 

15 

16 

17 

18 

19 

20 

31.00 

29.05 

0 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

11 

12 

13 

14 

15 

16 

17 

18 

19 

30.95 

29.10 

0 

2 

3 

4 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

15 

16 

17 

18 

30.90 

29.15 

0 

2 

3 

3 

4 

5 

6 

7 

8 

9 

9 

10 

11 

12 

13 

14 

15 

15 

16 

17 

30.85 

29.20 

0 

2 

2 

3 

4 

5 

6 

6 

7 

8 

9 

10 

10 

11 

12 

13 

14 

15 

15 

16 

30.80 

29.25 

0 

2 

3 

4 

4 

5 

6 

7 

8 

8 

9 

10 

11 

11 

12 

13 

14 

14 

15 

30.75 

29.30 

0 

2 

3 

3 

4 

5 

6 

6 

7 

8 

8 

9 

10 

11 

11 

12 

13 

13 

14 

30.70 

29.35 

0 

2 

3 

3 

4 

5 

5 

6 

7 

7 

8 

9 

9 

10 

10 

11 

12 

13 

13 

30.65 

29.40 

0 

2 

2 

3 

4 

4 

5 

5 

6 

7 

7 

8 

8 

9 

10 

10 

11 

12 

12 

30.60 

29.45 
29.50 

0 
0 

0 

-Y 

2 

2 
2 

3 

3 

4 

4 

5 

6 

6 

7 

7 

8 

8 

9 

9 

10 

11 

11 

30.55 

2 

3 

3 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

10 

10 

30.50 

29.55 

0 

0 

2 

2 

3 

3 

4 

4 

5 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

30. 45 

29.60 

0 

0 

2 

2 

2 

3 

3 

4 

4 

4 

5 

5 

6 

6 

6 

7 

7 

8 

8 

30.40 

29.65 

0 

0 

2 

2 

2 

3 

3 

4 

4 

4 

5 

5 

5 

6 

6 

6 

7 

7 

30.35 

29.70 

0 

0 

1 

2 

2 

2 

3 

3 

3 

4 

4 

4 

5 

5 

5 

5 

6 

6 

30.30 

29.75 

0 

0 

0 

1 

1 

2 

2 

2 

3 

3 

3 

3 

4 

4 

4 

4 

5 

5 

5 

30.25 

29.80 

0 

0 

0 

1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

4 

4 

4 

30.20 

29.85 

0 

0 

0 

0 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

30.15 

29.90 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

30.10 

29.95 

0 
0 

0 

0 

0 
0 

0 
0 

0 
0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

30.05 

30.00 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0  ;  0    0 

U 

0 

0 

30.00 

Subtract. 

0" 

30" 

0" 

80" 

0" 

80"    0" 

80" 

0" 

80"    0"    83"   0"    80"  1  C"    80"    0"  |  80" 

0" 1 80" 

0" 

A^d. 

0' 

1' 

2'       1        8' 

4'                5'               C        1        V       \        8' 

9' 

10' 

^lean  refraction. 

Page  528J 

TABLE  ^. 

Correct 

ion 

of  tl 

e  Mean  Refraction  for  the  Height  of  the  Thermometer. 

Mean  refraction. 

Ther. 

Ther. 

Add. 

o 

0' 

I' 

1/ 

"' 

4' 

5'   1 

8'   ;   7'      8' 

9' 

10' 

Add. 

0" 

80" 

II 

0" 

II 

80" 

II 

0" 

80" 

II 

0" 

80" 

II 

0" 

II 

80" 

II 

0" 

80" 

II 

0' 

II 

80" 

0" 

80"  j  0" 

80" 

II 

0" 

II 

80" 

0" 

II       II 

II 

II 

o 

—10 

0 

4 

8 

12 

16 

20 

24 

28 

33 

37 

41 

46 

50 

55  60 

65  !  70 

75 

80 

85  90 

-10 

—  8 

0 

4 

8 

•2 

15 

19 

23 

27 

31 

36 

40 

44 

48 

53  :58 

62  \   67 

72 

n 

82  ,  87 

-  8 

—  6 

0 

4 

7 

11 

15 

19 

22 

26 

30 

34 

38 

42 

47 

51  55 

60  64 

69 

74 

79  84 

—  6 

—  4 

0 

4 

7 

11 

14 

18 

22 

25 

29 

33 

37 

41 

45 

49 

53 

57  i  62 

66 

71 

76  80 

—  4 

—  2 

0 

3 
3 

_7_ 
7 

10 

lb 

14 
13 

17 
16 

21 
20" 

24 
23 

28 
27 

31 
30 

35 
34 

39 
37 

43 
41 

47 
45 

51 
49 

55 
53 

59 
57 

64  I  68 
61  65 

72  77 
69  74 

—  2 

0 

0 

0 

2 

0 

3 

6 

9 

12 

16 

19 

22 

25 

29 

32 

36 

39 

43 

47 

50 

54 

58 

62 

66  i  70 

2 

4 

0 

3 

6 

9 

12 

15 

18 

21 

24 

28 

31 

34 

37 

41 

44 

48 

52 

55 

59 

63  '  67 

4 

6 

0 

3 

6 

8 

11 

14 

17 

20 

23 

26 

29 

32 

36 

39 

42 

46 

49 

53 

56 

60  i  64 

6 

8 
10 

0 
0 

3 
3 

5 
5 

8 
8 

11 
10 

14 
13 

16 
15 

19 
18 

22 

21 

25 
24 

28 
26 

31 
29 

34 
32 

37 
35 

40 
38 

43 
41 

47 
44 

50 

48 

54 
51 

57 
54 

61 

58 

8 

10 

11 

0 

2 

5 

7 

10 

13 

15 

18 

20 

23 

26 

28 

31 

34 

37 

40 

43 

46 

49 

53 

56 

11 

12 

0 

2 

5 

7 

10 

12 

15 

17 

20 

22 

25 

28 

30 

33 

36 

39 

42 

45 

48 

51 

54 

12 

13 

0 

2 

5 

7 

9 

12 

14 

17 

19 

22 

24 

27 

30 

32 

35 

38 

41 

44 

47 

50 

53 

13 

14 
15 

0 
0 

2 
2 

5 
4 

7 
7 

9 
9 

11 
11 

14 
13 

16 
16 

19 
18 

21 
20 

24 
23 

26 
25 

29 

28 

31 
30 

34 
33 

37 
36 

40 

38 

42 
41 

45 
44 

48 
47 

51 
50 

14 

15 

16 

0 

2 

4 

6 

9 

11 

13 

15 

18 

20 

22 

25 

27 

29 

32 

35 

37 

40 

43 

45 

48 

16 

17 

0 

2 

4 

6 

8 

10 

13 

15 

17 

19 

21 

24 

26 

29 

31 

33 

36 

39 

41 

44 

47 

17 

18 

0 

2 

4 

6 

8 

10 

12 

14 

16 

19 

21 

23 

25 

28 

30 

32 

35 

37 

40 

43 

45 

18 

19 
20 

0 

0 

2 
2 

4 
4 

6 
6 

8 
8 

10 
9 

12 
11 

14 
13 

16 
15 

18 
17 

20 
19 

22 
22 

24 
24 

27 
26 

29 

28 

31 
30 

34 
33 

36 
35 

39 
37 

41 
40 

44 
42 

19 

20 

21 

0 

2 

4 

5 

7 

9 

11 

13 

15 

17 

19 

21 

23 

25 

27 

29 

31 

34 

36 

38 

41 

21 

22 

0 

2 

3 

5 

7 

9 

11 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

35 

37 

39 

22 

23 

0 

2 

3 

5 

7 

8 

10 

12 

14 

15 

17 

19 

21 

23 

25 

27 

29 

31 

33 

36 

38 

23 

24 

0 

2 

3 

5 

6 

8 

10 

11 

13 

15 

17 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

24 

25 

0 

2 

3 

5 

6 

8 

9 

11 

13 

14 

16 

18 

19 

21 

23 

25 

27 

29 

31 

33 

35 

25 

26 

0 

3 

4 

6 

7 

9 

11 

12 

14 

15 

17 

19 

20 

22 

24 

26 

28 

29 

31 

33 

26 

27 

0 

3 

4 

6 

7 

9 

10 

12 

13 

15 

16 

18 

19 

21 

23 

25 

26 

28 

30 

32 

27 

28 

0 

3 

4 

5 

7 

8 

10 

11 

12 

14 

15 

17 

19 

20 

22 

23 

25 

27 

29 

30 

28 

29 
30 

0 
0 

3 
2 

4 
4 

5 
5 

6 
6 

8 

7 

9 
9 

11 
10 

12 
11 

13 
13 

15 
14 

16 
15 

18 
17 

19 
18 

21 
20 

22 
21 

24 
23 

26 
24 

27 

29 

29 

26 

28 

30 

31 

0 

2 

3 

5 

6 

7 

8 

9 

11 

12 

13 

15 

16 

17 

19 

20 

22 

23 

25 

26 

31 

32 

0 

2 

3 

4 

6 

7 

8 

9 

10 

11 

13 

14 

15 

16 

18 

19 

20 

22 

23 

25 

32 

33 

0 

2 

3 

4 

5 

6 

7 

8 

10 

11 

12 

13 

14 

15 

17 

18 

19 

21 

22 

23 

33 

34 

0 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

16 

17 

18 

19 

21 

22 

34 

35 

0 

2 

3 

4 

5 

6 

6 

7 

8 

9 

10 

11 

13 

14 

15 

16 

17 

18 

19 

20 

35 

36 

0 

2 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

36 

37 

0 

2 

2 

3 

4 

5 

6 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

37 

38 

0 

2 

3 

4 

4 

5 

6 

7 

7 

8 

9 

10 

11 

12 

13 

13 

14 

15 

16 

38 

39 

0 

2 

3 

3 

4 

5 

5 

6 

7 

8 

8 
8 

9 

8 

10 
9 

11 
10 

11 
10 

12 
11 

13 
12 

14 
13 

15 
13 

39 
40 

40 

0 

2 

2 

3 

4 

4 

5 

6 

6 

7 

41 

0 

2 

2 

3 

3 

4 

4 

5 

6 

6 

7 

7 

8 

9 

9 

10 

11 

11 

12 

41 

42 

0 

0 

2 

2 

3 

3 

4 

4 

5 

5 

6 

7 

7 

8 

8 

9 

S 

10 

11 

42 

43 

0 

0 

2 

2 

3 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

43 

44 

0 

0 

^ 

1 

2 

2 

3 

3 

3 

4 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

44 

45 

0 

0 

1 

1 

2 

2 

2 

3 

3 

3 

4 

4 

4 

5 

5 

6 

6 

6 

t 

45 

46 

0 

0 

0 

1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

4 

4 

4 

4 

5 

5 

5 

46 

47 

0 

0 

0 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

3 

3 

3 

3 

4 

4 

4 

47 

48 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

3 

48 

49 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

49 
50 

50 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80"  i  0" 

Add. 

i 

Add. 

c 

V 

1' 

2' 

3' 

4' 

5'   1 

V               7'      8' 

9'     10' 

Ther. 

Ther. 

Mean  refraction. 

TABLE  22.                  [Page  529 

Correction  of  the  Mean  Refraction  for  the  Height  of  the  Thermometer. 

Ther. 
Subt. 

Mean  refraction. 

Ther. 
Subt. 

0' 

V 

2' 

8' 

4' 

6' 

6' 

7' 

8' 

9' 

10' 

0" 

80" 

0" 

30" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

II 

0 

1 

2 

3 

4 

5 

6 

6 

7 

8 

9 

10 

11 

12 

13 

0" 

II 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

80" 

II 

0 

1 

2 

3 

4 

5 

6 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

0" 

80" 

0" 

o 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 

II 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

II 
0 
0 
0 
0 
0 
0 
0 
0 
0 

2 
2 

II 

0 
0 
0 
0 

0_ 

2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
3 

II 
0 
0 
0 

2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
4 
5 
5 
5 

II 

0 
0 
0 

1 
1 
1 
1 

2 
2 
2 
2 
3 
3 
3 
3 
3 
4 
4 
4 
4 
5 
5 
5 
5 
5 
6 
6 
6 
6 
6 

II 
0 
0 

1 
1 
1 

1 

2 
2 
2 
3 
3 
3 
3 
4 
4 
4 
5 
5 
5 
5 
6 
6 
6 
7 
7 
7 
7 
8 
8 
8 

II 

0 

0 

1 

1 

1 

2 

2 

2 

3 

3 

3 

\ 

5 

5 

II 
0 
0 

1 
1 

2 
2 
2 
3 
3 
4 
4 
4 
5 
5 
6 

II 

0 
0 

1 
1 

2 

2 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

7 

8 

8 

9 

9 

10 

10 

11 

11 

11 

12 

12 

13 

13 

II 
0 

1 

1 

2 

2 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

10 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

// 
0 

1 
1 

2 
2 
3 

4 
4 

5 

5 

6 

7 

7 

8 

8 

9 

9 

10 

11 

11 

12 

12 

13 

13 

14 

14 

15 

16 

16 

17 

II 

0 

1 

1 

2 

3 

3 

4 

5 

5 

6 

7 

7 

8 

8 

9 

10 

10 

11 

11 

12 

12 

13 

14 

14 

15 

16 

16 

17 

18 

18 

II 

0 

1 

1 

2 

3 

4 

4 

5 

6 

6 

7 

8 

9 

9 

10 

11 

11 

12 

13 

13 

14 

15 

16 

16 

17 

18 

18 

19 

20 

20 

II 
0 
1 
2 
2 
3 
4 
5 
6 
6 
7 
8 
9 
9 

10 
11 
12 
12 
13 
14 
15 
16 
16 
17 
18 
18 
19 
20 
21 
21 
22 

II 

0 

1 

2 

2 

3 

4 

5 

6 

7 

8 

9 

9 

10 

11 

12 

13 

14 

14 

15 

16 

17 

18 

18 

19 

20 

21 

22 

22 

23 

24 

" 
0 
1 
2 
3 
5 
6 
7 
8 
9 
10 
11 
12 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 

II 
0 
1 
2 
4 
5 
6 
7 
8 

10 
11 
12 
13 
15 
16 
17 
18 
19 
20 
22 
23 
24 
25 
26 
27 
28 
29 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 

II 
0 
1 
3 
4 
5 

o 

50 
51 
52 
53 
54 

6 
8 
9 
10 
12 
13 
14 
15 
17 
18 
19 
20 
22 
23 
24 
25 
27 
28 
29 
30 
31 
32 
34 
35 
36 
37 
38 
40 
41 
42 

55 
56 

57 
58 
59 

60 
61 
62 
63 
64 

60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

5  6 

6  6 
6i  7 
6:  7 

7i  8 

14  |15 

15  il6 

16  117 

16  !18 

17  |l9 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 
75 
76 
77 
78 
79 

7 
7 
8 
8 
8 
8 
9 
9 
9 
10 

8 

8 

9 

9 

10 

10 

10 

11 

11 

11 

18 
19 
20 
21 
22 

20 
20 
21 
22 
23 

70 
71 
72 
73 
74 

22  124 

23  |25 

24  126 

25  127 

26  28 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
92 
93 
94 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 

3 
3 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
5 
5 
5 
5 
5 
5 
5 
5 
5 

5 
5 
5 
5 
6 
6 
6 
6 
6 
6 
7 
7 
7 
7 
7 
7 
7 
8 
8 
8 
.8 

7 

7 

7 

7 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

11 

11 

8 
9 
9 
9 
9 
10 
10 
10 
10 
11 
11 
11 
11 
12 
12 
12 
12 
13 
13 
13 
13 

10 
10 
11 
11 
11 
12 
12 
12 
13 
13 
13 
14 
14 
14 
14 
15 
15 
15 
16 
16 

12 
12 
13 
13 
13 
14 
14 
14 
15 
15 
16 
16 
16 
17 
17 
17 
18 
18 
18 
19 

14 
14 
14 
15 
15 
16 
16 
17 
17 
17 
18 
18 
19 
19 
19 
20 
20 
21 
21 
21 
22 

15 
16 
16 
17 
17 
18 
18 
19 
19 
20 
20 
21 
21 
22 
22 
22 
23 
23 
24 
24 
25 

17 

18 
18 
19 
19 
20 
20 
21 
21 
22 
23 
23 
24 
24 
25 
25 
26 
26 
27 
27 
28 

19 
20 
20 
21 
21 
22 
23 
23 
24 
24 
25 
25 
26 
27 
27 
28 
28 
29 
29 
30 
31 

21 
21 
22 
23 
23 
24 
25 
25 
26 
27 
"27 
28 
29 
29 

m_ 

30 
31 
32 
32 
33 
34 

23 
24 
24 
25 

26 
26 
27 
28 
28 
29 
30 
31 
31 
32 
33 
33 
34 
35 
35 
36 
37 

25 
26 
26 
27 
28 
29 
29 
30 
31 
32 
32 
33 
34 
35 
35 
36 
37 
38 
38 
39 
40 

27  29 

28  130 

28  131 

29  i31 

30  32 

31 
32 
33 
34 
35 
36 
37 
38 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

80 
81 
82 
83 
84 

31 
32 
32 
33 
34 
35 
36 
37 
37 
38 
39 
40 
41 
41 
42 
43 

33 
34 
35 
36 
37 
38 
39 
39 
40 
41 
42 
43 
44 
44 
45 
46 

43 
44 
45 
46 
48 
49 
50 
51 
52 
53 
54 
55 
56 
58 
59 
60 

85 
86 
87 
88 
89 
90 
91 
92 
93 
94 
95 
96 
97 
98 
99 

95 
96 
97 
98 
99 
100 

16  19 

100 

Subt. 
Then 

0" 

80" 

0" 

80" 

0" 

80" 

0"  1  80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

80" 

0" 

Subt. 
Ther. 

0' 

1' 

2' 

8' 

4' 

5' 

6' 

V 

8' 

9' 

10' 

Mean  refraction. 

22489—03- 


-34 


Page  530] 

TABLES  23,  24. 

TABLE  23. 

Correction  of  the  Moon's  Altitude  for  parallax  and  re- 

fraction corresponding  to  a  mean 

value  of  the  hori- 

zontal  parallax,  57^  ?>W. 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

Corr. 

Moon's 
alt. 

Corr. 

Moon's     p 
alt.         C°'^'^- 

»       o 

, 

o 

, 

0 

, 

o 

, 

10 

51 

31 

48 

51 

35 

71 

18 

11 

52 

32 

47 

52 

35 

72 

17 

12 

52 

33 

47 

53 

34 

73 

17 

13 

52 

34 

46 

54 

33 

74 

16 

14 

52 

35 

46 

55 

32 

75 

15 

15 

52 

36 

45 

56 

32 

76 

14 

16 

52 

37 

45 

57 

31 

77 

13 

17 

52 

38 

44 

58 

30 

78 

12 

18 

52 

39 

44 

59 

29 

79 

11 

19 

52 

40 

43 

60 

28 

80 

10 

20 

51 

21 

51 

41         42 

61 

27 

81 

9 

22 

51 

42         42 

62 

26 

82 

8 

23 

51 

43         41 

63 

26 

83 

7 

24 

50 

44 

40 

64 

25 

84 

6 

25 

50 

45 

40 

65 

24 

85 

5 

26 

50 

46 

39 

66 

23 

86 

4 

27 

49 

47 

38 

67 

22 

87 

3 

28 

49 

48 

38 

68 

21 

88 

2 

29 

49 

49 

37 

69 

20 

89 

1 

30 

48 

50 

36 

70 

19 

90 

0 

TABLE  24. 

Correct] 

on  of  tV 

[B£ 

le  Mooi 
irometer 

I's  Apparent  Altitude 

30  inches.— Fahrenheit's  1 

or  Par 

rhermon 

allax  and  Refr 

aeter,  50°.] 

action. 

Moon's 
app.  alt. 

Horizontal  parallax. 

§ 

Correction  for  seconds  of 
parallax.— Add. 

Corr.  for 

minutes 

of  alt. 

54' 

55' 

56' 

57' 

58' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

o      r 

, 

// 

/      II 

'      // 

/      // 

'      II 

/      II 

1      II 

/     // 

// 

II 

II 

II 

II 

„ 

5    0 

43  56 

44  56 

45  56 

46  56 

47  56 

48  55 

49  55 

50  55 

0 

0 

2 

4 

6 

8 

10 

44 

11 

45  11 

46  11 

47  11 

48  11 

49  10 

50  10 

51  10 

10 

10 

12 

14 

16 

18 

20 

25 

25 

25 

25 

25 

24 

24 

24 

20 

20 

22 

24 

26 

28 

30 

89 

39 

38 

38 

38 

38 

37 

37 

30 

30 

32 

34 

86 

38 

40 

52 

51 

51 

51 

51 

51 

51 

51 

40 

40 

42 

44 

46 

48 

50 

45 

4 

46    3 

47    3 

48    3 

49    3 

50    3 

51     3 

52    3 

52  13 

50 
0 

50  1  52 
0       2 

54 
4 

56 
6 

58 
8 

6    0 

45 

15     46  15 

47  14 

48  14 

49  14 

50  13 

51  13 

10 

26  1        26 

25 

25 

25 

25 

25 

25 

10 

10     12 

14 

16 

18 

20 

36          36 

36 

35 

35 

34 

34 

34 

20 

20     22 

24 

26 

28 

30 

46  1        46 

45 

45 

45 

44 

44 

44 

30 

30:   32 

34 

36 

38 

40 

55 

55 

55 

54 

54 

54 

53 

53 

40 

40  1  42 

44 

46 

48 

50 

7    0 

46 
46 

4 
12 

47    3 

48    3 

49    3 

50    3 
50  12 

51     2 

51  11 

52     1 

53    1 

50 

50 
0 

52 
2 

54 
4 

56 
6 

58 
8 

47  12 

48  12 

49  12 

52  11 

53  10 

0 

10 

21 

20 

20 

20 

19 

18 

18 

18 

10 

10 

12 

14 

16 

18 

20 

29 

28 

28 

27 

27 

26 

25 

25 

20 

20 

22 

24 

26 

28 

30 

36 

36 

35 

35 

34 

34 

34 

33 

30 

30     32 

34 

36 

38 

40 

43 

42 

42 

41 

41 

40 

40 

40 

40 

40     42 

44 

46 

48 

50 

50 

49 

48 

48 

48 

47 

46 

46 

50 

50     52 

54 

56 

58 

Add. 

8     0 

46 

56     47  56 

48  55 

49  54 

50  54 

51  54 

52  53 

53  53 

0 

01     2 

4 

6 

8 

V  \" 

10 

47 

2     48    2 

49     1 

50    0 

51     0 

59 

59 

58 

10 

10     12 

14 

16 

18 

2    1 

20 

8'          7 

7 

6 

6 

52    5 

53    4 

54    4 

20 

20  '   22 

24 

26 

28 

8    2 

30 

13          13 

12 

11 

11 

10 

10 

9 

30 

30  i   32 

34 

36 

38 

4    2 

40 

19          18 

17 

17 

16!        16 

15 

•    14 

40 

40 

42 

44 

46 

48 

5    3 

50 
9     0 

24 

23 

22 
49  26 

22 
50  26 

21           20 

19 
53  24 

19 

50 
0 

50 
0 

52 
2 

54 

4 

56 
6 

58 
8 

6  4 

7  4 

47 

28 

48  27 

51  25 

52  24 

54  23 

10 

33 

32 

31 

30 

30 

29 

28 

27 

10 

10 

12 

14 

16 

18 

8    5 

20 

37 

36 

35 

34 

34 

33 

32 

32 

20 

20 

22 

24 

26 

28 

9    5 

30 

41 

41 

40 

39 

38 

37 

37 

36 

30 

30 

32 

34 

36 

38 

40 

45 

44 

43 

43 

42 

41 

40 

39 

40 

40 

42 

44 

46 

48 

50 

49 

48 

47 

46 

46 

45 

44 

44 

50 

49 

51 

53 

55 

57 

TABLE  24.                  [Page  531  1 

Correction  of  the  Moon'tj  Apparent  Altitude  for  Parallax  and  Refraction.          1 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.]                        1 

Moon's 

Horizontal  parallax. 

Correction  for  seconds  of 
parallax. — Add. 

Corr. 
for 

app.  alt. 

minutes 
of  alt. 

54' 

56' 

66' 

67' 

58' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

O     ' 

'   // 

/   // 

/   // 

'   // 

/   // 

/   // 

/   // 

/  II 

II 

// 

II 

II 

II 

,/ 

Add. 

10  0 

47  53 

48  52 

49  51 

50  50  51  50 

52  48 

53  48 

54  47 

0 

0 

2 

4 

6 

8 

V   ^' 

10 

56 

55 

54 

53    52 

51 

50 

50 

10 

10 

12 

14 

16 

18 

2  1 

20 

59 

58 

57 

56    55 

55 

54 

53 

20 

20 

22 

24 

26 

28 

3  1 

30 

48  2 

49  1 

50  0 

59    58 

57 

56 

55 

30 

29 

31 

33 

35 

37 

4  1 

40 

5 

4 

2 

51  2  52  1 

53  0 

59 

58 

40 

39 

41 

43 

45 

47 

5  2 

50 
11  0 

7 
48  10 

6 

5 

4     4 

2 

54  1 

55  0 

50 
0 

49 
0 

51 
2 

53 
4 

55 
6 

57 
8 

6  2 

7  2 

49  9 

50  8 

51  7  52  7 

53  5 

54  4 

55  3 

10 

12 

11 

10 

9  j    9 

7 

6 

5 

10 

10 

12 

14 

16 

18 

8  2 

20 

15 

14 

12 

12  !    11 

9 

8 

7 

20 

20 

22 

24 

26 

28 

9  3 

30 

17 

16 

14 

13    13 

11 

10 

9 

30 

29 

31 

33 

35 

37 

40 

19 

18 

17 

15 

15 

13 

12 

11 

40 

39 

41 

43 

45 

47 

50 

21 

20 
49  21 

18 

17 

17 
52  17 

15 

14 

13 

50 
0 

49 
0 

51 
2 

53 
4 

55 

6" 

57 
8 

12  0 

48  22 

50  19 

51  18 

53  17 

54  15 

55  14 

10 

24 

23 

21 

20 

19 

18 

16 

15 

10 

10 

12 

14 

16 

18 

20 

26 

25 

23 

22 

21 

20 

18 

17 

20 

20 

22 

24 

25 

27 

30 

27 

26 

24 

23 

22 

20 

19 

18 

30 

29 

31 

33 

35 

37 

40 

28 

27 

25 

24 

23 

21 

20 

19 

40 

39 

41 

43 

45 

47 

50 

29 

28 

26 
50  27 

25 

24 

22 

21 

20 

50 

49 
0 

51 
2 

53 
4 

55 

6 

57 

8 

1  0 

13  0 

48  30 

49  29 

51  26 

52  25 

53  23 

54  22 

55  20 

0 

10 

31 

30 

28 

27 

26 

24 

22 

21 

10 

10 

12 

14 

16 

18 

2  0 

20 

32 

31 

29 

27 

26 

24 

23 

21 

20 

19 

21 

23 

25 

27 

3  0 

30 

33 

32 

30 

28 

27 

25 

23 

22 

30 

29 

31 

33 

35 

37 

4  0 

40 

34 

32 

30 

29 

28 

26 

24 

22 

40 

39 

41 

43 

45 

47 

5  0 

50 

35 

33 

31 

30 

28 

26 

25 

23 

50 
0 

49 
0 

51 
2 

53 
4 

55 
6 

57 

8 

6  0 

7  0 

14  0 

48  35 

49  33 

50  31 

51  30 

52  28 

53  26 

54  25 

55  23 

10 

35 

34 

32 

30 

28 

26 

25 

23 

10 

10 

12 

14 

16 

18 

8  0 

20 

36 

34 

32 

30 

29 

27 

25 

24 

20 

19 

21 

23 

25 

27 

9  0 

30 

36 

34 

32 

30 

29 

27 

25 

23 

30 

29 

31 

33 

35 

37 

40 

36 

34 

32 

30 

29 

27 

25 

23 

40 

39 

41 

43 

45 

47 

50 

15  0 

36 

34 

32 

30 

29 

27 

25 
54  25 

23 
55  23 

50 
0 

49 
0 

51 
2 

53 
4 

55 
6 

57 
8 

48  36 

49  35 

50  33 

51  31 

52  29 

53  27 

10 

36 

35 

32 

30 

28 

26 

24 

22 

10 

10 

12 

14 

16 

18 

20 

36 

35 

32 

30 

28 

26 

24 

22 

20 

19 

21 

23 

25 

27 

30 

36 

34 

31 

29 

28 

25 

23 

21 

30 

29 

31 

38 

35 

37 

40 

36 

34 

31 

29 

27 

25 

23 

21 

40 

39 

41 

43 

45 

47 

50 

35 

48  35 

33 

30 

28 

26 

24 

21 

19 

50 

49 
0 

51 
2 

53 
4 

55 
6 

57 
8 

16  0 

49  32 

50  29 

51  27 

52  25 

53  23 

54  20 

55  18 

0 

10 

34 

32 

29 

27 

25 

23 

20 

18 

10 

10 

12 

13 

15 

17 

20 

34 

32 

29 

27 

25 

22 

20 

17 

20 

19 

21 

23 

25 

27 

30 

33 

31 

28 

26 

24 

21 

19 

16 

30 

29 

31 

33 

35 

36 

40 

33 

31 

28 

25 

23 

21 

18 

16 

40 

38 

40 

42 

44 

46 

50 

32 

30 

27 

24 

22 

20 

17 

15 

50 
0 

48 
0 

50 
2 

52 
4 

54 
6 

56 

8 

Sub. 

17  0 

48  31 

49  29 

50  26 

51  23 

52  21 

53  18 

54  16 

55  13 

10 

30 

28 

25 

22 

20 

17 

14 

12 

10 

10 

12 

13 

15 

17 

2  0 

20 

28 

26 

23 

20 

18 

15 

12 

10 

20 

19 

21 

23 

25 

27 

3  0 

30 

27 

25 

22 

19 

17 

14 

11 

9 

30 

29 

31 

33 

34 

36 

4  0 

40 

26 

24 

21 

18 

16 

13 

10 

7 

40 

38 

40 

42 

44 

46 

5  1 

50 

26 
48  24 

23 

20 

17 

15 
52  13 

12 
53  10 

9 

6 

50 

48 
0 

50 
2 

52 
4 

53 
6 

55 

8 

6  1 

7  1 

18  0 

49  21 

50  18 

51  15 

54  7 

55  4 

0 

10 

23 

20 

17 

14 

12 

9 

6 

3 

10 

10 

11 

13 

15 

17 

8  1 

20 

22 

19 

16 

13 

11 

8 

5 

2 

20 

19 

21 

23 

25 

27 

9  1 

30 

21 

18 

15 

12 

10 

6 

3 

0 

30 

29 

30 

32 

34 

36 

40 

20 

17 

14 

10 

8 

4 

1 

54  58 

40 

38 

40 

42 

44 

46 

50 
19  0 

18 

15 

12 

9 

51  7 

6 
52  4 

2 

53  59 

56 

50 

48 
0 

50 
2 

51 
4 

53 
6 

55 

8 

48  16 

49  13 

50  10 

53  0 

53  57 

54  55 

0 

10 

15 

12 

8 

5 

2 

52  59 

55 

53 

10 

10 

11 

13 

15 

17 

20 

13 

10 

6 

3 

0 

57 

53 

51 

20 

19 

21 

23 

25 

27 

30 

12 

8 

5 

2 

51  58 

55 

51 

49 

30 

29 

30 

32 

34 

36 

40 

10 

6 

3 

0 

56 

53 

49 

47 

40 

38 

40 

42 

44 

46 

50 

9 

5 

2 

50  58 

55 

51 

48 

45 

50 

48 

50 

51 

53 

55 

Page  532]                  TABLE  21. 

1 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction.           | 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

1 

Moon's 

Horizontal  parallax. 

"f  d 

Correction  for  seconds  of 
.  parallax.— Add. 

Corr. 
for 

app.  alt. 

C  c 

1^ 

minutes 
of  alt. 

Sub 

64' 

66' 

56' 

57' 

58' 

69' 

60' 

61' 

0" 

II 

2" 

II 

4" 

II 

6" 

II 

8" 

o   / 

1      II 

1      11^ 

/  II 

/   // 

/  II 

/   // 

/   // 

'  II 

II 

20  0 

48  6 

49  3 

49  59 

50  56 

51  52 

52  49 

53  45 

54  42 

0 

0 

2 

4 

6 

8 

V   ^' 

10 

5 

2 

58 

55 

51 

47 

43 

40 

10 

9 

11 

13 

15 

17 

2  0 

20 

3 

0 

56 

52 

49 

45 

41 

37 

20 

19 

21 

23 

24 

26 

3  1 

30 

1 

48  58 

53 

50 

46 

42 

38 

35 

30 

28 

30 

32 

34 

36 

4  1 

40 

59 

56 

52 

48 

44 

40. 

36 

33 

40 

38 

39 

41 

43 

45 

5  1 

50 

57 
47  55 

54 

50 

46 

42 
51  39 

38 

34 
53  31 

30 

50 

47 
0 

49 
2 

51 
4 

53 
6 

54 

7 

6  1 

7  1 

21  0 

48  51 

49  47 

50  43 

52  35 

54  28 

0 

10 

53 

49 

45 

41 

37 

33 

29 

26 

10 

9 

11 

13 

15 

17 

8  1 

20 

51 

47 

43 

39 

35 

31 

27 

23 

20 

19 

21 

22 

24 

26 

9  2 

30 

48 

44 

40 

36 

32 

28 

24 

20 

30 

28 

30 

32 

34 

35 

40 

46 

42 

38 

33 

29 

25 

21 

17 

40 

37 

39 

41 

43 

45 

50 

43 

39 

35 

31 

27 

22 

18 

14 

50 

47 

49 

50 

52 

54 

22  0 

47  42 

48  37 

49  33 

50  29 

51  25 

52  20 

53  16 

54  11 

0 

0 

2 

4 

6 

7 

10 

40 

35 

30 

26 

22 

17 

13 

8 

10 

9 

11 

13 

15 

17 

20 

37 

32  I   27 

23 

19 

14 

10 

5 

20 

19 

20 

22 

24 

26 

30 

34 

30  i   25 

20 

16 

11 

7 

3 

30 

28 

30 

31 

33 

35 

40 

32 

27    22 

18 

13 

9 

4 

0 

40 

37 

39 

41 

43 

45 

50 

29 

25  ,   20 

48  22  !  49  17 

15 

11 

6 
52  3 

1 

53  57 

50 

46 
0 

48 
2 

50 
4 

52 
6 

54 

7 

23  0 

47  27 

50  13 

51  8 

52  58 

53  54 

0 

10 

25 

20  1   15 

10 

5 

0 

55 

51 

10 

9 

11 

13 

15 

17 

20 

22 

17 

12 

7 

2 

51  57 

52 

48 

20 

18 

20 

22 

24 

26 

30 

19 

14 

9 

4 

0 

54 

49 

45 

30 

28 

29 

31 

33 

35 

40 

16 

11 

6 

1 

50  57 

51 

46 

42 

40 

37 

39 

40 

42 

44 

50 

13 

8 

3 
49  0 

49  58 
49  55 

54 
50  50 

48 

43 

38 

50 
0 

46 
0 

48 
2 

50 
4 

51 
5 

53 

7 

1  0 

24  0 

47  10 

48  5 

51  45 

52  40 

53  35 

10 

8 

3 

48  57 

52 

47 

42 

37 

32 

10 

9 

11 

13 

15 

16 

2  1 

20 

5 

0 

54 

49 

44 

39 

33 

28 

20 

18 

20 

22 

24 

26 

3  1 

30 

2 

47  57 

51 

46 

41 

35 

30 

24 

30 

27 

29 

30 

32 

34 

4  1 

40 

46  59 

54 

48 

43 

38 

32 

27 

21 

40 

36 

38 

40 

42 

44 

5  2 

50 
25  0 

56 

51 

47  48 

45 

40 
49  37 

35 
50  31 

29 
51  26 

23 

52  20 

18 

50 

46 
0 

47 
2 

49 
4 

51 
5 

53 

7 

6  2 

7  2 

46  58 

48  42 

53  14 

0 

10 

50 

45 

39 

33 

28 

22 

16 

10 

10 

9 

11 

13 

14 

16 

8  2 

20 

46 

41 

35 

29 

24 

18 

12 

6 

20 

18 

20 

22 

24 

25 

9  3 

30 

43 

38 

32 

26 

20 

14 

8 

3 

30 

27 

29 

31 

33 

34 

40 

40 

34 

28 

23 

17 

11 

5 

52  59 

40 

36 

38 

40 

42 

43 

50 

37 
46  34 

31  i   25 

19 
49  16 

14 

7 

1 

56 

50 

45 

47 

49 

51 

52 

26  0 

47  28 

48  22 

50  10 

51  4 

51  58 

52  52 

0 

0 

2 

4 

5 

7 

10 

31 

25 

19 

13 

7 

1 

54 

48 

10 

9 

11 

13 

14 

16 

20 

27 

21 

15 

9 

3 

50  57 

50 

44 

20 

18 

20 

22 

23 

25 

30 

24 

18 

12 

6 

49  59 

53 

46 

40 

30 

27 

29 

31 

32 

34 

40 

20 

14 

8 

,2 

55 

49 

42 

36 

40 

36 

38 

39 

41 

43 

50 

17 

11 

47  7 

4 

48  58 

51 

49  48 

45 

38 

32 

52"28 

50 
0 

45 
0 

47 
2 

48 
4 

50 
5 

52 

7 

1  0 

27  0 

46  14 

48  1 

48  54 

50  41 

51  35 

10 

11 

4 

47  58 

51 

44 

37 

31 

24 

10 

9 

11 

12 

14 

16 

2  1 

20 

7 

1 

54 

r   47 

40 

33 

27 

20 

20 

18 

20 

21 

23 

25 

3  1 

30 

3 

46  57 

50 

43 

36 

29 

23 

16 

30 

27 

28 

30 

32 

34 

4  1 

40 

45  59 

53 

46 

39 

32 

25 

19 

12 

40 

36 

37 

39 

41 

43 

5  2 

50 

56 
45  53" 

49 
46  46 

42 
47  38 

35 
48  31 

28 

21 

15 

8 

50 

44 

46 

48 

50 

52 

6  2 

7  3 

28  0 

49  24 

50  17 

51  11 

52  4 

0 

0 

2 

4 

5 

7 

10 

49 

42 

34 

27 

20 

13 

6 

5159 

10 

9 

11 

12 

14 

16 

8  3 

20 

45 

38 

30 

23 

16 

9 

2 

55 

20 

18 

19 

21 

23 

25 

9  3 

30 

41 

34 

26 

19 

12 

5 

50  57 

50 

30 

26 

28 

30 

32 

33 

40 

37 

30    23 

15 

8 

1 

54 

46 

40 

35 

37 

39 

41 

42 

50 

34 

26 
46  22 

19 
47  15 

11 

4 
49  0 

49  57 
49  53 

49 

42 

50 

44 

46 
2 

48 
4 

49 
5 

51 

7 

29  0 

45  30 

48  7 

50  45 

5138 

0 

0 

10 

26 

18 

11 

3 

48  56 

49 

40 

34 

10 

9 

10 

12 

14 

16 

20 

22 

14 

7 

47  59 

52 

44 

36 

29 

20 

17 

19 

21 

23 

24 

30 

18 

10 

2 

55 

47 

39 

31 

24 

30 

26 

28 

30 

31 

33 

40 

14 

6 

46  58 

51 

43 

35 

27 

20 

40 

35 

37 

38 

40 

42 

50 

11 

3 

55 

47 

39 

31 

23 

15 

50 

44 

45 

47 

49 

51 

TABLE  24. 

[Page  533  1 

Correction  of  the  Moon 

's  Apparent  Altitude  for  Parallax  and  Refraction.          1 

[Barometer 

30  inches 

.—Fahrenheit's  Thermometer  50°.]                       1 

Moon's 

Horizontal  parallax 

-5^ 

Correction  for  seconds  of 
paraillax.— Add. 

Corr. 
for 

app.  alt. 

is 

minutes 
of  alt. 

54' 

66' 

56' 

57' 

58' 

69' 

60' 

61' 

0" 

2" 

4" 
II 

6" 
II 

8" 

o   / 

/  // 

/  II 

/   // 

/   // 

/   // 

/   // 

/  II 

/  // 

„ 

// 

II 

II 

Sub. 

30  0 

45  6 

45  57 

46  50 

47  42 

48  34 

49  26 

50  18 

51  10 

0 

0 

2 

3 

5 

7 

V  0'' 

10 

2 

54 

46 

38 

30 

22 

13 

6 

10 

9 

10 

12 

14 

16 

2     1 

20 

44  58 

50 

42 

34 

26 

18 

9 

1 

20 

17 

19 

21 

23 

24 

3  1 

30 

54 

46 

37 

29 

21 

13 

4 

50  56 

30 

26 

28 

29 

31 

33 

4  2 

40 

50 

42 

33 

25 

17 

8 

0 

52 

40 

35 

36 

38 

40 

42 

5  2 

50 
31  0 

45 
44  41 

38 

29 

21 

12 

4 

49  55 

47 
50  42 

50 
0 

43 
0 

45 
2 

47 
3 

49 
5 

50 

7 

6  3 

7  3 

45  33 

46  24 

47  16 

48  7 

48  59 

49  50 

10 

37 

29 

20 

12 

2 

54 

45 

37 

10 

9 

10 

12 

14 

15 

8  4 

20 

33 

24 

15 

7 

47  58 

49 

40 

32 

20 

17 

19 

21 

22 

24 

9  4 

30 

28 

20 

11 

2 

54 

45 

36 

27 

30 

26 

27 

29 

31 

32 

40 

24 

16 

7 

46  58 

49 

40 

31 

22 

40 

34 

36 

38 

39 

41 

50 

20 

.  11 

2 

53 

44 

35 

26 
49  22 

17 
50  13 

50 
0 

43 
0 

44 
2 

46 
3 

48 
5 

50 

7 

32  0 

44  15 

45  7 

45  58 

46  49 

47  40 

48  31 

10 

11 

3 

53 

44 

35 

26 

17 

8 

10 

8 

10 

12 

14 

15 

20 

7 

44  58 

48 

39 

30 

21 

11 

2 

20 

17 

19 

20 

22 

24 

30 

3 

53 

44 

34 

25 

16 

6 

49  57 

30 

25 

27 

29 

30 

32 

40 

43  58 

48 

39 

29 

20 

11 

1 

52 

40 

34 

35 

37 

39 

41 

50 

54 

44 

34 

24 

15 

6 

48  56 

47 

50 

42 
0 

44 
2 

46 
3 

47 

5 

49 

7 

1  0 

33  0 

43  48 

44  39 

45  29 

46  19 

47  10 

48  0 

48  50 

49  41 

0 

10 

44 

34 

25 

15 

5 

47  55 

45 

36 

10 

8 

10 

12 

13 

15 

2  1 

20 

40 

30 

20 

10 

0 

50 

40 

31 

20 

17 

18 

20 

22 

23 

3  1 

30 

35 

25 

15 

5 

46  55 

45 

35 

25 

30 

25 

27 

28 

30 

32 

4  2 

40 

30 

20 

10 

0 

50 

40 

30 

20 

40 

33 

35 

37 

38 

40 

5  2 

50 
34  0 

25 

15 

5 

45  55 

45 

35 

24 

14 

50 

42 

43 

45 

47 

48 

6  3 

7  3 

43  21 

44  11 

45  0 

45  50 

46  40 

47  30 

48  19 

49  9 

0 

0 

2 

3 

5 

7 

10 

16 

6 

44  55 

45 

34 

24 

14 

3 

10 

8 

10 

12 

13 

15 

8  4 

20 

11 

1 

50 

40 

29 

19 

9 

48  58 

20 

17 

18 

20 

21 

23 

9  4 

30 

6 

43  56 

45 

35 

24 

13 

3 

52 

30 

25 

26 

28 

30 

31 

40 

1 

51 

40 

30 

19 

8 

47  58 

47 

40 

33 

35 

36 

38 

40 

50 

42  56 

46 

35 

24 

14 

3 

46  58 

52 

42 

50 
0 

41 
0 

43 
2 

44 
3 

46 
5 

48 

7 

35  0 

42  52 

43  41 

44  30 

45  19 

46  9 

47  47 

48  36 

10 

47 

36 

25 

14 

3 

52 

41 

30 

10 

8 

10 

11 

13 

15 

20 

42 

31 

20 

9 

45  58 

47 

•  36 

25 

20 

16 

18 

20 

21 

23 

30 

37 

26 

15 

3 

52 

41 

30 

19 

30 

24 

26 

28 

29 

31 

40 

32 

21 

10 

44  58 

47 

36 

25 

14 

40 

33 

34 

36 

38 

39 

50 

27 

16 

4 

53 

42 

30 
46  25 

19 

8 
48  2 

50 
0 

41 
0 

42 
2 

44 
3 

46 
5 

47 
6 

36  0 

42  22 

43  11 

43  59 

44  48 

45  37 

47  14 

10 

17 

5 

54 

42 

31 

19 

8 

47  56 

10 

8 

10 

11 

13 

14 

1  1 

20 

12 

0 

48 

37 

25 

14 

2 

50 

20 

16 

18 

19 

21 

23 

2  1 

30 

7 

42  55 

43 

31 

20 

8 

46  56 

44 

30 

24 

26 

27 

29 

31 

3  2 

40 

1 

50 

38 

26 

14 

2 

50 

39 

40 

32 

34 

35 

37 

39 

4  2 

50 

41  56 

44 

32 

20 

8 

45  56 
45  51 

44 

33 

50 

40 
0 

42 
2 

43 
3 

45 
5 

47 
6 

5  3 

6  3 

37  0 

41  51 

42  39 

43  27 

44  15 

45  3 

46  39 

47  27 

0 

10 

46 

34 

21 

9 

44  57 

45 

33 

21 

10 

8 

10 

11 

13 

14 

7  4 

20 

41 

29 

16 

4 

52 

40 

27 

15 

20 

16 

17 

19 

21 

22 

8  4 

30 

35 

23 

11 

43  58 

46 

34 

21 

9 

30 

24 

25 

27 

29 

30 

9  5 

40 

30 

18 

5 

53 

40 

28 

15 

3 

40 

32 

33 

35 

37 

38 

50 

25 
41  19 

12 

42  59 

47 

34 
44  29 

22 
45  16 

9 
46  3 

46  57 
46  51 

50 
0 

40 
0 

41 
2 

43 
3 

45 
5 

46 
6 

38  0 

42  7 

42  54 

43  41 

10 

14 

2 

49 

36 

23 

10 

45  57 

45 

10 

8 

9 

11 

13 

14 

20 

8 

41  56 

43 

30 

17 

4 

51 

38 

20 

16 

17 

19 

20 

22 

30 

3 

51 

38 

24 

12 

44  58 

45 

32 

30 

23 

25 

27 

28 

30 

40 

40  58 

45 

32 

18 

6 

52 

39 

26 

40 

31 

33 

35 

36 

38 

50 

52 

39 

26 
42  20 

13 

43  7 

0 
43  54 

46 
44  40 

33 

20 

50 

39 
0 

41 
2 

42 
3 

44 
5 

46 
6 

39  0 

40  47 

41  33 

45  27 

46  13 

0 

10 

42 

28 

15 

1 

48 

34 

21 

7 

10 

8 

9 

11 

12 

14 

1  1 

20 

36 

23 

9 

42  55 

42 

28 

15 

1 

20 

15 

17 

19 

20 

22 

2  1 

30 

30 

17 

3 

49 

36 

22 

8 

45  54 

30 

23 

25 

26 

28 

29 

3  2 

40 

25 

11 

41  57 

43 

30 

16 

2 

48 

40 

31 

32 

34 

36 

37 

4  2 

50 

19 

5 

51 

37 

23 

9 

44  55 

42 

50 

39 

40 

42 

43 

45 

5  3 

Page  534] 

TABLE  24. 

1 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Eefraction.          | 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
app.  alt. 

Horizontal  parallax. 

- 

Correction  for  .seconds  of 
parallax. — Add. 

Corr. 

for 

minutes 

of  alt. 

54' 

56' 

56' 

57' 

58' 

59' 

60' 

61' 

0" 

// 

2" 

II 

4" 

II 

6" 

II 

8" 
II 

0     / 

/   // 

1      II 

/   // 

1      II 

/  // 

/  II 

'  II 

/  II 

Sub. 

40  0 

40  14 

41  9 

41  46 

42  32 

43  18 

44  4 

44  60 

45  36 

0 

0 

2 

3 

6 

6 

6'  W 

10 

8 

40  54 

39 

26 

11 

43  57 

43 

29 

10 

8 

9 

11 

12 

14 

7  4 

20 

2 

48 

33 

19 

6 

50 

36 

22 

20 

15 

17 

18 

20 

21 

8  5 

30 

39  66 

42 

28 

13 

42  59 

44 

30 

16 

30 

23 

24 

26 

27 

29 

9  6 

40 

50 

36 

22 

7, 

53 

38 

24 

9 

40 

30 

32 

34 

35 

37 

50 

45 

30 

16 

1 

47 

32 

18 
44  11 

3 

60 

38 
0 

40 
2 

41 
3 

43 
5 

44 
6 

41  0 

39  39 

40  24 

41  10 

41  55 

42  41 

43  26 

44  56 

0 

10 

33 

18 

4 

49 

34 

19 

4 

49 

10 

8 

9 

11 

12 

14 

20 

27 

12 

40  58 

43 

28 

13 

43  58 

43 

20 

16 

17 

18 

20 

21 

30 

21 

6 

51 

36 

22 

7 

51 

37 

30 

23 

24 

26 

27 

29 

40 

16 

0 

45 

30 

16 

0 

46 

30 

40 

30 

32 

33 

35 

36 

50 

10 

39  54 

39 

24 

9 

42  63 

38 
43  31 

23 

50 

38 
0 

39 

1 

41 
3 

42 
4 

44 
6 

42  0 

39  4 

39  48 

40  33 

41  17 

42  2 

42  47 

44  16 

0 

10 

38  58 

42 

27 

11 

41  66 

41 

25 

10 

10 

7 

9 

10 

12 

13 

1  1 

20 

52 

36 

21 

6 

60 

34 

18 

3 

20 

16 

16 

18 

19 

21 

2  1 

30 

46 

30 

14 

40  68 

43 

27 

11 

43  56 

30 

22 

24 

25 

27 

28 

3  2 

40 

40 

24 

8 

52 

36 

21 

6 

49 

40 

30 

31 

33 

34 

36 

4  2 

50 

34 

18 

2 

46 

30 

14 

42  68 

42 

50 

37 
0 

38 

1 

40 
3 

41 
4 

43 
6 

5  3 

6  4 

43  0 

38  28 

39  12 

39  56 

40  40 

41  24 

42  8 

42  52 

43  36 

0 

10 

22 

6 

50 

34 

18 

1 

45 

29 

10 

7 

9 

10 

12 

13 

7  4 

20 

16 

38  59 

43 

27 

11 

41  64 

38 

22 

20 

15 

16 

18 

19 

20 

8  5 

30 

10 

53 

37 

20 

5 

48 

31 

15 

30 

22 

23 

25 

26 

28 

9  6 

40 

4 

47 

30 

14 

40  58 

41 

24 

8 

•40 

29 

31 

32 

34 

36 

50 

37  57 
37  51 

41 
38  35 

24 

7 

51 

34 

17 
42  10 

1 

50 
0 

37 
0 

38 
1 

39 
3 

41 
4 

42 
6 

44  0 

39  18 

40  1 

40  44 

41  27 

42  54 

10 

45 

28 

11 

39  54 

37 

20 

3 

46 

10 

7 

9 

10 

11 

13 

20 

38 

21 

4 

47 

30 

13 

41  56 

39 

20 

14 

16 

17 

19 

20 

30 

32 

15 

38  58 

41 

24 

7 

49 

32 

30 

21 

23 

24 

26 

27 

40 

26 

9 

51 

34 

17 

0 

42 

25 

40 

29 

30 

31 

33  34 

50 

20 

2 

44 

27 

10 

40  63 

35 

41  28 

18 
42  11 

60 
0" 

36 
0 

37 
1 

39 
3 

40  i  41 

1  1 

45  0 

37  14 

37  56 

38  38 

39  21 

40  3 

40  46 

4 

6 

10 

7 

49 

31 

14 

39  66 

39 

21 

3 

10 

7 

8 

10 

11 

13 

2  1 

20 

0 

43 

25 

7 

49 

32 

14 

41  56 

20 

14 

15 

17 

18 

20 

3  2 

30 

36  54 

37 

18 

1 

43 

26 

7 

49 

30 

21 

23 

24 

25 

27 

4  3 

40 

48 

30 

11 

38  64 

36 

18 

0 

42 

40 

28 

30 

31 

32 

34 

5  3 

50 
4(5  0 

41 

23 

4 

47 

29 

11 

40  52 

34 

50 

35 
0 

37 

1 

38 
3 

39 

4 

41 
6 

6  4 

7  5 

36  35 

37  17 

37  58 

38  40 

39  22 

40  4 

40  45 

41  27 

0 

10 

29 

10 

51 

33 

16 

39  67 

38 

20 

10 

7 

8 

10 

11 

12 

8  6 

20 

22 

3 

44 

26 

8 

49 

31 

12 

20 

14 

15 

17 

18 

19 

9  6 

30 

16 

36  57 

38 

20 

1 

42 

24 

6 

30 

21 

22 

23 

25 

26 

40 

9 

50 

32 

13 

38  54 

36 

17 

40  58 

40 

28 

29 

30 

32 

33 

50 
47  0 

2 
35  56 

43 
36  37 

25 
37  18 

6 

47 

28 

9 

50 

50 

35 

36 

1 

37 
3 

39 
4 

40 
6 

37  59 

38  40 

39  21 

40  2 

40  43 

0 

0 

10 

49 

30 

11 

52 

34 

14 

39  66 

36 

10 

7 

8 

10 

11 

12 

20 

42 

23 

4 

45 

26 

6 

47 

28 

20 

14 

15 

16 

18 

19 

30 

36 

17 

36  57 

38 

19 

38  69 

40 

21 

30 

20 

22 

23 

24 

26 

40 

30 

10 

50 

31 

12 

62 

32 

13 

40 

27 

29 

30 

31 

33 

50 

23 
35  16 

3 
35  56 

43 
36  36 

24 

5 

46 

26 
39  17 

5 
39  58 

60 
0 

34 
0 

35 
1 

37 
3 

38 
4 

39 
5 

1  1 

48  0 

37  17 

37  57 

38  37 

10 

10 

50 

30 

10 

50 

30 

10 

60 

10 

7 

8 

9 

11 

12 

2  1 

20 

3 

43 

23 

2 

43 

22 

2 

42 

20 

13 

15 

16 

17 

19 

3  2 

30 

34  56 

36 

16 

36  55 

35 

15 

38  66 

34 

30 

20 

21 

23 

24 

26 

4  3 

40 

49 

29 

9 

48 

28 

8 

48 

27 

40 

27 

28 

29 

31 

32 

5  3 

50 
49  0 

42 
34  35 

22 
35  15 

1 

41 

21 

0 

40 

19 

50 
0 

33 
0 

35 
1 

36 
3 

37  39 

6  4 

7  6 

35  64 

36  34 

37  13 

37  53 

38  32 

39  11 

4 

5 

10 

29 

8 

47 

27 

6 

46 

25 

4 

10 

7 

8 

9 

10 

12 

8  5 

20 

22 

1 

40 

20 

36  59 

38 

17 

38  56 

20 

13 

14 

16 

17 

18 

9  6 

30 

15 

34  54 

33 

12 

51 

30 

9 

48 

30 

20 

21 

22 

23 

25 

40 

8 

47 

26 

6 

44 

23 

2 

41 

40 

26 

27 

29 

30 

31 

50 

1 

40 

19 

35  58 

36 

15 

37  54 

33 

50 

33 

34 

35 

36 

38 

TABLE  24. 

[Page  635 

Correction  of  the  Moon's  Apparent  Altitude 

for  Parallax  and  Refraction.           1 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
app.  alt. 

Horizontal  parallax. 

o  2 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 

for 

minutes 

of  alt. 

54' 

55' 

56' 

57' 

68' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

o   » 

'   // 

'  It 

'   // 

'  II 

/  II 

'  II 

'   // 

'  // 

II 

// 

II 

II 

II 

II 

50  0 

33  54 

34  33 

35  11 

35  50 

36  29 

37  8 

37  46 

38  25 

0 

0 

1 

3 

4 

5 

10 

47 

26 

4 

43 

21 

0 

38 

17 

10 

6 

8 

9 

10 

12 

20 

40 

19 

34  57 

36 

14 

36  53 

31 

9 

20 

13 

14 

15 

17 

18 

30 

33 

11 

49 

28 

6 

45 

23 

1 

30 

19 

20 

22 

23 

24 

40 

26 

4 

42 

20 

35  58 

37 

15 

37  53 

40 

26 

27 

28 

29 

31 

50 

19 

33  57 

35 

34  28 

13 

51 

29 

7 

45 

50 
0 

32 
0 

33 
1 

35 
3 

36 
4 

37 
5 

Sub. 

51  0 

33  12 

33  50 

35  6 

35  44 

36  22 

36  59 

37  37 

10 

5 

43 

21 

34  58 

36 

14 

51 

29 

10 

6 

8 

9 

10 

11 

2  1 

20 

32  58 

36 

13 

50 

28 

6 

43 

21 

20 

13 

14 

15 

16 

18 

3  2 

30 

51 

29 

6 

43 

21 

35  58 

36 

13 

30 

19 

20 

21 

23 

24 

4  3 

40 

44 

22 

33  59 

36 

14 

50 

28 

5 

40 

25 

26 

28 

29 

30 

5  4 

50 

37 

14 

51 
33  44 

28 

6 
34  58 

42 

20 
36  12 

36  57 
36  49 

50 
0 

31 
0 

33 
1 

34 

2 

35 
4 

36 
5 

6  4 

7  5 

52  0 

32  30 

33  7 

34  21 

35  35 

10 

23 

0 

36 

13 

50 

27 

4 

41 

10 

6 

7 

9 

10 

11 

8  6 

20 

15 

32  52 

29 

6 

43 

19 

35  56 

33 

20 

12 

13 

15 

16 

17 

9  6 

30 

8 

45 

21 

33  58 

35 

11 

48 

24 

30 

18 

20 

21 

22 

23 

40 

1 

38 

14 

50 

27 

3 

40 

16 

40 

24 

26 

27 

28 

29 

50 

31  54 
31  47 

31 

7 

43 

19 
34  11 

34  55 

32 

8 

50 

31 

32 
1 

33 
2 

34 
4 

35 

5 

53  0 

32  23 

32  59 

33  35 

34  47 

35  24 

36  0 

0 

0 

10 

39 

15 

51 

27 

3 

39 

15 

35  51 

10 

6 

7 

8 

10 

11 

20 

32 

8 

44 

20 

33  56 

31 

7 

43 

20 

12 

13 

14 

16 

17 

30 

25 

0 

36 

12 

48 

23 

34  59 

35 

30 

18 

19 

20 

22 

23 

40 

17 

31  53 

28 

4 

40 

15 

51 

27 

40 

24 

25 

26 

28 

29 

50 

10 

46 
31  38 

21 

32  57 

32 

7 

43 
34  35 

19 

50 
0 

30 
0 

31 

1 

32 
2 

34 
4 

35 
5 

54  0 

31  3 

32  13 

32  49 

33  24 

33  59 

35  10 

10 

30  55 

30 

5 

41 

16 

51 

26 

1 

10 

6 

7 

8 

9 

11 

20 

48 

22 

31  57 

33 

8 

43 

18 

34  53 

20 

12 

13 

14 

15 

16 

30 

40 

15 

49 

25 

0 

35 

10 

45 

30 

18 

19 

20 

21 

22 

40 

33 

8 

42 

17 

32  52 

27 

1 

37 

40 

23 

25 

26 

27 

28 

50 

26 

0 

35 

9 

44 

19 

33  53 
33  45 

28 
34  19 

50 
0 

29 
0 

30 

1 

32 
2 

33 
3 

34 
5 

55  0 

30  18 

30  52 

31  27 

32  1 

32  36 

33  10 

10 

10 

45 

19 

31  53 

28 

2 

36 

11 

10 

6 

7 

8 

9 

10 

20 

3 

38 

12 

46 

20 

32  54 

28 

3 

20 

11 

13 

14 

15 

16 

30 

29  55 

30 

4 

38 

12 

46 

20 

33  54 

30 

17 

18 

19 

20 

22 

40 

48  . 

22 

30  56 

30 

4 

37 

11 

45 

40 

23 

24 

25 

26 

27 

50 
56  0 

40 

14 

48 
30  40 

22 

31  14 

31  55 

29 

3 
32  55 

37 

50 

28 

30 
1 

31 
2 

32 
3 

33 

4 

29  33 

30  7 

31  47 

32  21 

33  28 

0 

0 

10 

25 

29  59 

32 

6 

39 

13 

46 

20 

10 

6 

7 

8 

9 

10 

20 

18 

51 

24 

30  58 

31 

4 

37 

11 

20 

11 

12 

13 

14 

16 

30 

10 

43 

16 

50 

23 

31  56 

29 

2 

30 

17 

18 

19 

20 

21 

1  1 

40 

3 

36 

9 

42 

15 

48 

21 

32  54 

40 

22 

23 

24 

25 

27 

2  2 

50 

28  55 

28 

1 

34» 

7 

40 

12 

45 

50 

28 
0 

29 

1 

30 
2 

31 
3 

32 

4 

3  2 

4  3 

57  0 

28  47 

29  20 

29  53 

30  25 

30  58 

31  31 

32  3 

32  36 

0 

10 

39 

12 

45 

17 

50 

22 

31  55 

27 

10 

5 

6 

7 

9 

10 

5  4 

20 

32 

5 

37 

9 

42 

14 

47 

19 

20 

11 

12 

13 

14 

15 

6  5 

30 

24 

28  57 

29 

1 

33 

6 

38 

10 

30 

16 

17 

18 

19 

21 

7  5 

40 

17 

49 

21 

29  53 

25 

30  57 

29 

1 

40 

22 

23 

24 

25 

26 

8  6 

50 

58  0 

9 

41 

13 

45 

17 

49 

21 

3152 

50 

27 
0 

28 
1 

29 
2 

30 
3 

31 
4 

9  7 

28  1 

28  33 

29  5 

29  37 

30  9 

30  41 

31  12 

3144 

0 

10 

27  53 

25 

28  57 

28 

0 

32 

4 

35 

10 

5 

6 

7 

8 

9 

20 

45 

17 

49 

•  20 

29  52 

23 

30  55 

26 

20 

10 

12 

13 

14 

15 

30 

38 

9 

41 

12 

44 

15 

46 

17 

30 

16 

17 

18 

19 

20 

40 

30 

1 

33 

4 

35 

6 

38 

9 

40 

21 

22 

23 

24 

25 

50 

22 

27  14 

27  53 
27  45 

24 

28  55 

27 

29  58 
29  49 

29 
30  20 

0 

50 

26 
0 

27 
1 

28 
2 

29 
3 

30 
4 

59  0 

28  16 

28  47 

29  18 

30  51 

0 

10 

6 

37 

7 

38 

9 

40 

11 

42 

10 

5 

6 

7 

8 

9 

20 

26  58 

29 

27  59 

30 

1 

31 

2 

33 

20 

10 

11 

12 

13 

14 

30 

51 

21 

51 

22 

28  53 

23 

29  54 

24 

30 

15 

16 

17 

18 

19 

40 

43 

13 

43 

14 

44 

14 

45 

15 

40 

20 

21 

22 

23 

24 

50 

35 

5 

35 

5 

36 

6 

36 

A 

50 

25 

26 

27 

29 

30 

Page  536] 

TABLE  24. 

Dorrection  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
app.  alt. 

Horizontal  parallax. 

§2 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 

for 

minutes 

64' 

55' 

56' 

57' 

58' 

59' 

60' 

61' 

IS 

0" 

2" 
II 

4" 

II 

6" 

II 

8" 
II 

of  alt. 

o    / 

/  It 

/  // 

'  II 

'  II 

/   // 

'   // 

'  II 

'  II 

II 

// 

60  0 

26  26 

26  67 

*^7  27 

27  57 

28  27 

28  57 

29  27 

29  67 

0 

0 

1 

2 

3 

4 

10 

19 

49 

19 

49 

19 

49 

18 

48 

10 

6 

6 

7 

8 

9 

20 

11 

41 

11 

40 

10 

40 

9 

39 

20 

10 

11 

12 

13 

14 

30 

3 

32 

2 

31 

1 

31 

0 

30 

30 

16 

16 

17 

18 

19 

40 

25  55 

24 

26  63 

23 

27  63 

22 

28  61 

21 

40 

20 

21 

22 

23 

24 

50 

47 

16 

46 

14 

44 

13 

42 

12 

50 

26 
0 

26 

1 

27 
2 

28 
3 

29 
4 

61  0 

25  39 

26  8 

26  37 

27  6 

27  36 

28  5 

28  34 

29  3 

0 

10 

31 

0 

29 

26  58 

27 

27  56 

26 

28  54 

10 

5 

6 

7 

8 

9 

20 

23 

26  62 

20 

49 

18 

47 

16 

45 

20 

10 

11 

12 

12 

13 

30 

16 

43 

12 

40 

10 

38 

7 

35 

30 

14 

16 

16 

17 

18 

40 

7 

36 

4 

32 

1 

29 

27  58 

26 

40 

19 

20 

21 

22 

23 

50 

24  59 

27 

25  65 

24 

26  62 

20 

49 

17 

50 
0 

24 
0 

25 
1 

26 

2 

27 
3 

28 
4 

62  0 

24  50 

25  19 

25  47 

26  15 

26  43 

27  11 

27  40 

28  8 

10 

42 

10 

38 

6 

34 

2 

30 

27  68 

10 

5 

6 

6 

7 

8 

20 

34 

2 

29 

25  57 

25 

26  53 

21 

49 

20 

9 

10 

11 

12 

12 

30 

26 

24  54 

21 

49 

17 

45 

12 

40 

30 

14 

15 

16 

17 

18 

40 

18 

46 

13 

41 

8 

36 

3 

31 

40 

19 

19 

20 

21 

22 

50 

10 

37 

4 

32 

25  59 

27 

26  54 

21 

50 

23 

24 

26 

26 

27 

63  0 

24  2 

24  29 

24  56 

26  23 

25  51 

26  18 

26  45 

27  12 

0 

0 

1 

2 

3 

4 

10 

23  54 

21 

48 

15 

42 

9 

36 

3 

10 

4 

5 

6 

7 

8 

20 

46 

13 

39 

6 

33 

0 

27 

26  64 

20 

9 

10 

11 

12 

13 

30 

37 

4 

31 

24  68 

24 

25  51 

18 

45 

30 

13 

14 

15 

16 

17 

40 

29 

23  55 

22 

49 

15 

42 

8 

35 

40 

18 

19 

20 

21 

22 

50 

20 

47 

13 

40 

6 

33 

25  59 

26 

50 

22 
0 

23 
1 

24 
2 

26 
3 

26 
3 

64  0 

23  12 

23  39 

24  6 

24  32 

24  58 

26  24 

25  50 

26  17 

0 

10 

4 

31 

23  67 

23 

49 

16 

41 

8 

10 

4 

6 

6 

7 

8 

20 

22  56 

22 

48 

14 

40 

6 

32 

26  58 

20 

9 

10 

10 

11 

12 

30 

47 

13 

39 

5 

31 

24  57 

22 

48 

30 

13 

14 

16 

16 

16 

40 

39 

5 

30 

23  56 

22 

48 

13 

39 

40 

17 

18 

19 

20 

21 

50 

31 

22  67 

22 

48 

13 

39 

4 
24  55 

30 
25  21 

60 
0 

22 
0 

23 
1 

23 
2 

24 
2 

25 
3 

Sub. 

65  0 

22  23 

22  48 

23  13 

23  39 

24  4 

24  30 

10 

14 

40 

5 

30 

23  56 

20 

46 

11 

10 

4 

6 

6 

7 

7 

V  V 

20 

6 

31 

22  56 

21 

46 

11 

36 

1 

20 

8 

9 

10 

11 

12 

2  2 

30 

21  58 

23 

48 

13 

37 

2 

27 

24  52 

30 

13 

13 

14 

16 

16 

3  3 

40 

49 

14 

39 

4 

28 

23  63 

18 

43 

40 

17 

18 

18 

19 

20 

4  4 

50 

41 

6 

30 

22  55 

19 

44 

8 

33 

60 
0 

21 
0 

22 
1 

23 
2 

23 
2 

24 
3 

5  5 

6  5 

66  0 

21  32 

21  57 

22  21 

22  46 

23  10 

23  35 

23  59 

24  23 

10 

24 

48 

12 

37 

1 

25 

49 

14 

10 

4 

6 

6 

7 

7 

7  6 

20 

15 

39 

3 

28 

22  52 

16 

40 

4 

20 

8 

9 

10 

11 

11 

8  7 

30 

7 

31 

21  55 

19 

43 

6 

31 

23  55 

30 

12 

13 

14 

15 

16 

9  8 

40 

20  59 

22 

46 

10 

34 

22  67 

21 

45 

40 

16 

17 

18 

19 

20 

50 

50 
20  41 

14 

21  5 

37 

1 

25 
22  15 

48 
22  39 

12 
23  2 

36 

50 

20 
0 

21 

1 

22 

2 

23 
2 

24 
3 

67  0 

21  28 

21  52 

23  26 

0 

10 

33 

20  56 

19 

43 

6 

29 

22  52 

16 

10 

4 

5 

5 

6 

7 

20 

25 

48 

11 

34 

21  57 

20 

43 

7 

20 

8 

8 

9 

10 

11 

30 

16 

39 

2 

25 

48 

11 

34 

22  57 

30 

12 

12 

13 

14 

15 

40 

8 

30 

20  63 

16 

39 

2 

24 

47 

40 

16 

16 

17 

18 

18 

50 

19  59 

21 

44 

7 
20  68 

30 
21  21 

21  52 

15 

37 

50 

19 
0 

20 
1 

21 
1 

22 
2 

22 
3 

68  0 

19  50 

20  13 

20  36 

21  43 

22  6 

22  28 

0 

10 

42 

4 

27 

49 

12 

34 

21  66 

19 

10 

4 

4 

5 

6 

7 

20 

33 

19  56 

18 

40 

2 

24 

47 

9 

20 

7 

8 

9 

9 

10 

30 

25 

47 

9 

31 

20  53 

16 

37 

21  59 

30 

11 

12 

13 

13 

14 

40 

16 

38 

0 

22 

44 

5 

27 

49 

40 

16 

16 

16 

17 

18 

50 

7 

29 
19  21 

19  51 
19  42 

13 
20  4 

34 
20  25 

20  56 

17 
21  8 

39 
21  30 

60 
0 

18 
0 

19 
1 

20 
1 

21 
2 

21 
3 

69  0 

18  59 

20  47 

10 

50 

12 

33 

19  65 

16 

37 

20  59 

20 

10 

4 

4 

5 

6 

6 

20 

42 

3 

24 

45 

7 

28 

49 

10 

20 

7 

8 

8 

9 

10 

30 

33 

18  64 

15 

36 

19  57 

18 

39 

0 

30 

11 

11 

12 

13 

13 

40 

24 

45 

6 

27 

48 

9 

29 

20  50 

40 

14 

16 

16 

16 

17 

50 

16 

37 

18  67 

18 

39 

0 

20 

41 

50 

18 

18 

19 

20 

20 

TABLE  24. 

[Page  537  1 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer  30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 

Horizontal  parallax. 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 
for 

app.  alt. 

minutes 
of  alt. 

64' 

55' 

56' 

57' 

58' 

59' 

60' 

61' 

0" 

2" 

4" 

6" 

8" 

o   / 

1      II 

/  II 

'    H 

/  // 

'  II 

/  // 

/  II 

/   // 

II 

// 

II 

// 

II 

II 

70  0 

18  7 

18  28 

18  48 

19  9 

19  30 

19  50 

20  11 

20  31 

0 

0 

1 

1 

2 

3 

10 

17  58 

19 

39 

0 

20 

41 

1 

21 

10 

3 

4 

5 

5 

6 

20 

50 

10 

30 

18  50 

11 

31 

19  51 

11 

20 

7 

7 

8 

9 

9 

30 

41 

1 

21 

41 

1 

21 

41 

1 

30 

10 

11 

11 

12 

13 

40 

32 

17  53 

12 

32 

18  52 

12 

32 

19  52 

40 

13 

14 

15 

15 

16 

50 

24 

44 
17  35 

3 

23 
18  14 

43 

3 
18  53 

22 

42 

50 

17 
0 

17 
1 

18 
1 

19 
2 

19 
3 

71  0 

17  15 

17  54 

18  34 

19  12 

19  32 

0 

10 

6 

26 

45 

5 

24 

43 

3 

22 

10 

3 

4 

4 

5 

6 

20 

16  57 

17 

36 

17  55 

14 

33 

18  53 

12 

20 

6 

7 

8 

8 

9 

30 

48 

8 

27 

46 

5 

24 

43 

2 

30 

10 

10 

11 

12 

12 

40 

40 

16  59 

18 

37 

17  56 

15 

34 

18  52 

40 

13 

13 

14 

15 

15 

50 

31 

50 

9 

28 

47 
17  37 

5 

24 

42 

50 

16 
0 

17 
1 

17 

1 

18 
2 

19 
2 

72  0 

16  22 

16  41 

17  0 

17  18 

17  55 

18  14 

18  32 

0 

10 

13 

32 

16  50 

9 

27 

46 

4 

22 

10 

3 

4 

4 

5 

5 

20 

5 

23 

41 

16  59 

18 

36 

17  54 

12 

20 

6 

7 

7 

8 

8 

30 

15  57 

14 

32 

50 

9 

27 

45 

3 

30 

9 

10 

10 

11 

11 

40 

48 

5 

23 

41 

16  59 

17 

35 

17  53 

40 

12 

13 

13 

14 

14 

50 

39 

15  56 

14 

32 

16  22 

50 
16  40 

7 

25 

43 
17  33 

50 
0 

15 
0 

16 

1 

16 
1 

17 
2 

18 

2 

73  0 

15  30 

15  47 

16  5 

16  58 

17  15 

10 

21 

38 

15  56 

13 

30 

48 

5 

23 

10 

3 

3 

4 

5 

5 

20 

12 

29 

47 

4 

21 

39 

16  56 

13 

20 

6 

6 

7 

7 

8 

30 

3 

20 

37 

15  55 

12 

29 

46 

3 

30 

9 

9 

10 

10 

11 

40 

14  54 

11 

28 

45 

2 

19 

36 

16  53 

40 

11 

12 

13 

13 

14 

50 

45 

2 
14  53 

19 

35 

15  52 
15  42 

9 

26 

42 

50 

14 

15 

15 

16 
2 

17 
2 

Sub. 

74  0 

14  36 

15  9 

15  26 

15  59 

16  16 

16  32 

0 

0 

1 

1 

10 

28 

44 

0 

17 

33 

49 

6 

22 

10 

3 

3 

4 

4 

5 

Y  1// 

20 

19 

35 

14  51 

8 

24 

40 

15  56 

12 

20 

0 

6 

6 

7 

8 

2  2 

30 

10 

26 

42 

14  58 

14 

30 

46 

2 

30 

8 

9 

9 

10 

11 

3  3 

40 

1 

17 

33 

49 

5 

20 

36 

15  52 

40 

11 

11 

12 

12 

13 

4  4 

50 
75  0 

13  52 

8 

23 

39 

14  55 

10 

26 

42 

50 

13 

14 
1 

14 
1 

15 

16 

5  5 

6  6 

13.43 

13  59 

14  14 

14  29 

14  45 

15  1 

15  16 

15  32 

0 

0 

2 

2 

10 

34 

50 

5 

20 

36 

14  52 

7 

22 

10 

3 

3 

4 

4 

5 

7  7 

20 

25 

41 

13  56 

11 

27 

42 

14  57 

12 

20 

5 

6 

6 

7 

7 

8  8 

30 

16 

32 

46 

1 

17 

32 

47 

2 

30 

8 

8 

9 

9 

10 

9  9 

40 

7 

22 

37 

13  52 

7 

22 

37 

14  51 

40 

10 

11 

11 

12 

12 

50 

12  58 

13 

28 

42 

13  57 
13  47 

12 

27 

41 

50 

13 
0 

13 
0 

14 
1 

14 
1 

15 
2 

76  0 

12  49 

13  4 

13  18 

13  33 

14  2 

14  17 

14  31 

0 

10 

41 

12  55 

9 

24 

38 

13  53 

7 

21 

10 

2 

3 

3 

4 

4 

20 

32 

46 

0 

14 

28 

43 

13  57 

11 

20 

5 

5 

6 

6 

7 

30 

23 

37 

12  51 

5 

19 

33 

47 

1 

30 

7 

8 

8 

8 

9 

40 

14 

27 

41 

12  55 

9 

23 

36 

13  50 

40 

9 

10 

10 

11 

11 

50 

5 

18 

32 

45 

12  59 

13 

26 

40 

50 

12 

12 

13 

13 

14 

77  0 

11  56 

12  9 

12  22 

12  36 

12  49 

13  3 

13  16 

13  30 

0 

0 

0 

1 

1 

2 

10 

47 

0 

13 

27 

40 

12  53 

7 

20 

10 

2 

3 

3 

4 

4 

20 

38 

11  51 

4 

17 

30 

43 

12  57 

10 

20 

4 

5 

5 

6 

6 

30 

29 

42 

11  55 

8 

21 

33 

47 

0 

30 

7 

7 

7 

8 

8 

40 

19 

32 

45 

11  58 

11 

23 

36 

12  49 

40 

9 

9 

9 

10 

10 

50 

10 

23 

35 

48 

1 

13 
12  4 

26 
12  16 

39 

50 

11 
0 

11 
0 

12 
1 

12 

1 

13 

2 

78  0 

11  1 

11  14 

11  26 

11  39 

11  52 

12  29 

0 

10 

10  52 

5 

17 

30 

42 

11  54 

6 

19 

10 

2 

2 

3 

3 

4 

20 

43 

10  55 

8 

20 

32 

44 

11  56 

8 

20 

4 

4 

5 

5 

6 

30 

34 

46 

10  58 

10 

22 

34 

46 

11  58 

30 

6 

6 

7 

7 

8 

40 

25 

37 

48 

0 

12 

24 

36 

48 

40 

8 

8 

9 

9 

10 

50 
79  0 

16 

28 

39 

10  51 

3 

15 

26 

38 

50 

10 
0 

10 
0 

11 

1 

11 

1 

12 
1 

10  7 

10  19 

10  30 

10  42 

10  53 

11  5 

11  16 

11  28 

0 

10 

9  58 

9 

21 

32 

43 

10  55 

6 

17 

10 

2 

2 

3 

3 

3 

20 

49 

0 

11 

22 

33 

44 

10  56 

7 

20 

4 

4 

4 

5 

5 

30 

40 

9  50 

1 

12 

23 

34 

45 

10  56 

30 

6 

6 

6 

7 

7 

40 

31 

41 

9  52 

3 

13 

24 

35 

46 

40 

7 

8 

8 

8 

9 

50 

22 

32 

43 

9  54 

4 

15 

25 

36 

50 

9 

10 

10 

10 

11 

Page  538] 

TABLE  24. 

Correction  of  the  Moon's  Apparent  Altitude  for  Parallax  and  Refraction. 

[Barometer 

30  inches.— Fahrenheit's  Thermometer  50°.] 

Moon's 
app.  alt. 

Horizontal  parallax. 

•a  .2 
5g 

Correction  for  seconds  of 
parallax.— Add. 

Corr. 

for 

minutes 

54' 

55' 

66' 

57' 

58' 

69' 

60' 

61' 

■ji  "^ 

0" 

2" 

4" 

6" 

8" 

of  alt. 

o         / 

'      n 

'     "•! 

'     II 

/     // 

/     // 

/     // 

/      // 

/      // 

II 

II 

II 

II 

II 

II 

80    0 

9  13 

9  23 

9  34 

9  44 

9  55 

10    5 

10  15 

10  26 

0 

0 

0 

1 

1 

1 

10 

3 

14 

24 

34 

45 

9  55 

5 

15 

10 

2 

2 

2 

3 

3 

20 

8  54 

4 

14 

24 

35 

45 

9  55 

5 

20 

3 

4 

4 

4 

5 

30 

45 

8  55 

5 

15 

25 

35 

45 

9  54 

30 

5 

5 

6 

6 

6 

40 

36 

46 

8  55 

5 

15 

25 

35 

44 

40 

/ 

7 

7 

8 

8 

50 

27 

37 

46 
8  37 

8  56 

6 

15 

25 
9  14 

34 

50 

8 
0 

9 
0 

9 
1 

9 
1 

10 
1 

81     0 

8  18 

8  27 

8  46 

8  56 

9    5 

9  24 

0 

10 

9 

18 

27 

36 

46 

8  55 

4 

13 

10 

1 

2 

2 

2 

3 

20 

7  59 

8 

17 

26 

36 

45 

8  54 

3 

20 

3 

3 

4 

4 

4 

30 

50 

7  59 

8 

17 

26 

35 

44 

8  52 

30 

4 

5 

5 

5 

6 

40 

41 

50 

7  59 

8 

17 

25 

34 

42 

40 

6 

6 

6 

7 

7 

50 

32 

41 

49 

7  58 

7 

15 

24 
8  13 

32 

50 
0 

7 
0 

8 
0 

8 

1 

8 
1 

9 
1 

82     0 

7  23 

7  31 

7  40 

7  48 

7  57 

8    5 

8  22 

10 

14 

22 

30 

38 

47 

7  55 

3 

11 

10 

1 

2 

2 

2 

2 

20 

4 

12 

20 

28 

37 

45 

7  52 

0 

20 

3 

3 

3 

3 

4 

30 

6  55 

3 

11 

19 

27 

35 

42 

7  50 

30 

4 

4 

5 

5 

5 

40 

46 

6  54 

2 

10 

17 

25 

32 

40 

40 

5 

6 

6 

6 

6 

50 

37 

45 

6  52 

0 
6  50 

1 

15 

7    5 

22 

7  12 

30 

50 

7 

7 
0 

7 
0 

7 
1 

8 

1 

Sub. 

83    0 

6  28 

6  35 

6  43 

6  57 

7  20 

0 

0 

10 

19 

26 

33 

40 

47 

6  54 

2 

9 

10 

1 

1 

2 

2 

2 

V  V 

20 

9 

16 

23 

30 

37 

44 

6  51 

6  58 

20 

2 

3 

3 

3 

3 

2    2 

30 

0 

1 

13 

20 

27 

34 

41 

48 

.30 

3 

4 

4 

4 

4 

3    3 

40 

5  51 

5  58 

4 

11 

18 

24 

31 

38 

40 

5 

5 

5 

5 

6 

4    4 

50 

42 

49 
5  39 

5  55 

1 

8 

14 

21 

27 

50 

6 

6 

6 
0 

6 
1 

7 
1 

5  5 

6  6 

84    0 

5  33 

5  45 

5  52 

5  58 

6    4 

6  10 

6  17 

0 

0 

0 

10 

23 

30 

36 

42 

48 

5  54 

0 

6 

10 

1 

1 

1 

2 

2 

7     7 

20 

14 

20 

26 

32 

38 

44 

5  50 

5  55 

20 

2 

2 

2 

3 

3 

8    8 

30 

5 

10 

16 

22 

28 

34 

39 

45 

30 

3 

3 

3 

3 

4 

9    9 

40 

4  56 

1 

1 

13 

18 

24 

29 

35 

40 

4 

4 

4 

4 

5 

50 
85    0 

47 

4  52 

4  58 
4  48 

3 
4  53 

8 

14 

19 

25 

50 

5 
0 

5 
0 

5 
0 

5 
0 

6 

1 

4  37 

4  43 

4  58 

5    4 

5    9 

5  14 

0 

10 

28 

33 

38 

43 

48 

4  53 

4  58 

3 

10 

1 

1 

1 

1 

1 

20 

18 

24 

28 

33 

38 

43 

48 

4  53 

20 

2 

2 

2 

2 

2 

30 

9 

14 

19 

23 

28 

33 

38 

43 

30 

2 

3 

3 

3 

3 

40 

0 

5 

10 

14 

19 

23 

28 

33 

40 

3 

3 

4 

4 

4 

50 
86    0 

3  51 

3  56 

0 

5 

9 
3  59 

13 

18 

22 

50 

4 
0 

4 
0 

4 
0 

5 
0 

5 

1 

3  42 

3  46 

3  50 

3  55 

4    3 

4    7 

4  11 

0 

10 

33 

37 

41 

45 

49 

3  53 

3  57 

1 

10 

1 

1 

1 

1 

1 

20 

23 

27 

31 

35 

39 

43 

46 

3  50 

20 

1 

1 

2 

2 

2 

30 

14 

18 

21 

25 

29 

33 

36 

40 

30 

2 

2 

2 

2 

2 

40 

5 

9 

12 

16 

19 

23 

26 

30 

40 

3 

3 

3 

3 

3 

50 

2  56 

2  59 

3 
2  53 

6 

9 

13 

16 

19 

50 
0 

3 
0 

3 

0 

3 

0 

4 
0 

4 
0 

87    0 

2  47 

2  50 

2  56 

2  59 

3    2 

3    5 

3    9 

10 

37 

40 

43 

46 

49 

2  52 

2  55 

2  58 

10 

0 

1 

1 

1 

1 

20 

28 

31 

33 

36 

39 

42 

45 

47 

20 

1 

1 

1 

1 

1 

30 

19 

21 

24 

26 

29 

32 

34 

37 

30 

1 

1 

2 

2 

2 

40 

10 

12 

15 

17 

19 

22 

24 

27 

40 

2 

2 

2 

2 

2 

50 

1 

3 

5 

7 

9 

12 

14 

16 

50 

2 

2 
0 

2 
0 

3 
0 

3 
0 

88    0 

1  51 

1  53 

1  55 

1  57 

1  59 

2     2 

2    4 

2    6 

0 

0 

10 

42 

43 

45 

47 

49 

1  51 

1  53 

1  55 

10 

0 

0 

0 

0 

0 

20 

32 

34 

36 

38 

39 

41 

43 

44 

20 

1 

1 

1 

1 

1 

30 

23 

25 

26 

28 

29 

31 

32 

34 

30 

1 

1 

1 

1 

] 

40 

14 

15 

16 

19 

20 

21 

22 

24 

40 

1 

1 

1 

1 

1 

50 

5 

6 

7 

9 

10 

11 

12 

13 
1     3 

50 
0" 

1 
0 

1 
0 

1 
0 

2 
0 

2 
0 

89     0 

0  56 

0  57 

0  58 

0  59 

1    0 

1     1 

1     2 

10 

46 

47 

48 

49 

0  50 

0  51 

0  51 

0  52 

10 

0 

0 

0 

0 

0 

20 

37 

37 

38 

39 

40 

40 

41 

42 

20 

0 

0 

0 

0 

0 

30 

28 

28 

28 

29 

30 

30 

31 

31 

30 

0 

0 

0 

0 

0 

40 

19 

19 

19 

19 

20 

20 

21 

21 

40 

0 

0 

0 

0 

0 

50 

9 

10 

■      10 

10 

10 

10 

10 

10 

50 

1 

1 

1 

1 

1 

TABLE  25 

[Page  539 

Table  showing  the  variation  of  the  altitude  of  an  object  arising  from  a  change  of  100  seconds  in  the  | 

declination. 

Unmarked  quantities  in  the  Table  are  positive.     It  the  change  move  the  body  toward  1 

the  elevated  pole,  apply  the  correction 

L  to  the  altitude  with  the  signs  m  the  Table;  otherwise,  | 

change  the 

signs. 

a 
o 

"S 
a 

1 
Q 

o 

o 
o 

0 

Latitude  of  same  name  as  declination. 

Latitude  of  different  name  from  declination. 

< 

d 
.2 
% 

c 

1 

70° 

60° 

60° 

40° 

80° 

20° 

10° 

0° 
0 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

94 

87 

76 

64 

50 

34 

17 

17 

It 
34 

50 

64 

76 

II 
87 

94 

o 

0 

o 

10 

95 

88 

78 

65 

51 

35 

18 

0 

18 

35 

51 

65 

78 

88 

95 

10 

?.o 

100 

92 

82 

68 

53 

36 

18 

0 

18 

36 

53 

68 

82 

92 

100 

20 

30 

100 

88 

74 

57 

39 

20 

0 

20 

39 

57 

74 

88 

100 

30 

0 

40 

100 

84  i  65 

45 

22 

0 

22 

45 

65 

84 

100 

40 

0 

fSO 

100 

78 

53 

27 

0 

27 

53 

78 

100 

50 

60 

100 

68 

35 

0 

35 

68 

100 

60 

70 

50 

100 
34 

51 
17 

0 

51 

100 

70 
0 

0 

94 

87 

77 

64 

0 

17 

34 

50 

64 

77 

87 

94 

10 

95 

87 

77 

65 

50 

34 

17 

-  1 

18 

35 

51 

66 

78 

88 

96 

10 

20 

99 

91 

81 

67 

52 

35 

17 

-  1 

19 

37 

54 

69 

83 

93 

101 

20 

30 

107 

98 

87 

73 

56 

38 

18 

-  2 

22 

41 

59 

76 

90 

102 

30 

?, 

40 

111 

98 

82 

63 

42 

20 

-  2 

25 

47 

68 

86 

102 

40 

2 

50 

116 

97 

74 

50 

24 

-  3 

30 

57 

81 

103 

50 

60 

124 

95 

64 

30 

-  5 

40 

73 

103 

60 

70 

139 

92 

43 

-  8 

59 

108 

64 

70 

0 

94 

87 

77 

64 

50 

34 

17 

0 

17       34 

50 

77 

87 

94 

0 

10 

94 

87 

77 

64 

50 

34 

16 

—  1 

19       36 

52 

67 

79 

89 

97 

10 

20 

98 

90 

79 

66 

51 

34 

16 

-  3 

21 

39 

56 

71 

84 

95 

103 

20 

;  30 

105 

96 

85 

70 

54 

36 

16 

-  4 

24' 

44 

62 

78 

93 

104 

30 

4     40 

107 

94 

78 

59 

39 

17 

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29 

51 

71 

90 

106 

40 

4 

50 

111 

92 

70 

45 

19 

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35 

62 

86 

109 

50 

60 

117 

88 

56 

23 

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47 

81 

112 

60 

70 

127 

81 

32 

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0 

70 

119 

70 

0 

94 

87 

77 

65 

50 

34 

17 

17 

34 

50 

65 

77 

87 

94 

0 

10 

94 

87 

76 

64 

49 

33 

16 

-  2 

20 

37 

53 

67 

80 

90 

98 

10 

20 

97 

89 

78 

65 

50 

33 

15 

-  4 

22 

40 

57 

73 

86 

96 

104 

20  1        1 

30 

103 

94 

83 

69 

52 

34 

14 

-  6 

26 

46 

64 

81 

95 

107 

30  1        1 

6 

40 

105 

92 

76 

57 

36 

14 

-  9 

32 

54 

74 

93 

109 

40 

6 

50 

107 

88 

66 

41 

15 

-13 

40 

66 

91 

113 

50 

60 

111 

82 

51 

17 

-18 

53 

87 

119 

60 

70 
0 

95 

65 

118 

72 

22 
18 

-29 

80 

129 

70 

87 

77 

50 

35 

0 

18 

35 

50 

65 

,   77 

87 

95 

0 

10 

94 

86 

76 

63 

49 

33 

15 

-  3 

20 

38 

54 

68 

81 

91 

99 

10 

20 

96 

88 

77 

64 

49 

32 

14 

-  5 

24 

40 

59 

74 

87 

98 

106 

20          1 

30 

101 

93 

81 

67 

50 

32 

12 

-  8 

28 

48 

66 

83 

97 

109 

30 

8 

40 

102 

89 

73 

54 

33 

11 

-12 

35 

57 

78 

97 

113 

40 

8 

50 

104 

84 

62 

37 

11 

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44 

70 

95 

118 

50 

60 

105 

77 

45 

11 

-24 

59 

93 

125 

60 

70 

» 

109 

62 

13 

-39 

90 

140 

70 

0 

95 

88 

78 

6^ 

51 

35 

18 

0 

18 

35 

51 

65 

78 

88 

95 

0 

10 

94 

86 

75 

63 

48 

32 

15 

-  3 

21 

38 

55 

69 

82 

92 

100 

10 

20 

95 

87 

76 

63 

48 

31 

12 

-  6 

25 

43 

60 

76 

89 

100 

20  1        1 

30 

100 

91 

80 

65 

49 

30 

10 

-10 

30 

50 

69 

86 

100 

30 

10 

40 

100 

87 

70 

51 

31 

8 

-15 

38 

60 

81 

100 

40 

10 

50 

100 

81 

58 

33 

6 

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48 

75 

100 

50 

60 

100 

71' 

39 

5 

-31 

66 

100 

60 

70 

100 

53 

3 

-48 

100 

70 

0 

96 

89 

78 

66 

51 

35 

18 

0 

18 

35 

51 

66 

78 

89 

96 

0 

10 

94 

86 

76 

63 

48 

32 

14 

—  4 

22 

39 

56 

70 

83 

94 

101 

10 

20 

94 

86 

76 

62 

47 

29 

11 

-  8 

27 

45 

62 

78 

91 

102 

20 

30 

99 

90 

78 

64 

47 

28 

8 

-12 

33 

53 

71 

88 

103 

30 

12 

40 

108 

98 

84 

68 

49 

28 

5 

-18 

41 

63 

85 

104 

40 

12 

50 

112 

97 

77 

54 

29 

2 

-25 

53 

80 

105 

50 

60 

120 

95 

65 

33 

-1 

-37 

72 

107 

60 

1 

a 

70 

134 

91 

44 

-6 

-58 

110 

70 

1 

B 

6 

70° 

60° 

60° 

40° 

80° 

20° 

10° 

0° 

10° 

20° 

80° 

40° 

50° 

60° 

70° 

0) 

3 

I 

latitude  of  same  name  as  6 

eclinat 

tion. 

Latitude  of  different  name  from  declination. 

O        < 

< 

Q 

Page  640]                                           TABLE  25. 

Table  showing  the  variation  of  the  altitude  of  an  object  arising  from  a  change  of  100  seconds  in  the 
declination.     Unmarked  quantities  in  the  Table  are  positive.     If  the  change  move  the  body  toward 
the  elevated  pole,  apply  the  correction  to  the  altitude  with  the  signs  m  the  Table;  otherwise, 
change  the  signs. 

Declination. 



Altitude. 

Latitude  of  same  name  as  declination. 

Latitude  of  different  name  from  declination. 

< 

c 

1 

70° 

60° 

^o 

40° 

80° 

20° 

10° 

0° 

10° 

20° 

80° 

40° 

60° 

60° 

70° 

0 

14 

o 

0 
10 
20 
30 
40 
50 
60 
70 

// 

97 
94 
94 
97 
106 

n 

89 
86 
86 
89 
96 
109 

II 

79 
76 
75 
77 
82 
93 
115 

II 

66 
63 
61 
62 
66 
73 
89 
125 

II 

52 
48 
46 
45 
46 
50 
60 
82 

II 

35 

31 

27 

26 

25 

25 

27 

35 

II 

18 

14 

10 

6 

2 

-  2 

-  7 
-16 

II 

0 

-  4 

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-  14 

-  21 

-  30 

-  43 

-  69 

II 

18 
23 
28 
35 
44 
58 
79 
121 

II 

35 
40 
45 
55 

67 

85 

114 

// 

52 
57 
64 
74 
88 
110 

II 

66 
72 
80 
91 
107 

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79 

85 

93 

106 

II 

89 

95 

104 

II 

97 
103 

o 

0 
10 
20 
30 
40 
50 
60 
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0 
10 
20 
30 
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50 
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o 

14 

16 



18 
20 
22 
24 

26 

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0 
10 
20 
30 
40 
50 
60 
70 

98 
94 
94 
96 
104 

90 

86 
85 
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94 
106 

80 
76 
74 
75 
80 
90 
110 

67 
63 
61 
61 
63 
70 
84 
117 

52 
48 
45 
44 
44 
47 
54 
73 
53 
48 
44 
42 
41 
43 
49 
64 

36 
31 
27 
25 
22 
21 
21 
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18 

13 

9 

4 

0 

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0 

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18 
23 
30 
37 
48 
62 
86 
132 

36 
41 

48 
58 
70 
90 
121 

52 

58 
66 
77 
92 
115 

67 
73 

82 

94 

111 

80 

86 

95 

109 

90 

97 

106 

98 
104 

18 
20 

0 
10 
20 
30 
40 
50 
60 
70 

0 
10 
20 
30 
40 
50 
60 
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99 
95 
93 
95 
102 

100 
95 
93 
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100 

91 

87 
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92 
103 

81 
76 

74 
74 
78 
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68 
63 
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36 
31 
26 
23 
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16 
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31 
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36 
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53 
59 
68 
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96 
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68 
74 
84 
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81 

88 

98 

112 

91 

98 

109 

99 
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0 
10 
20 
30 
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92 

87 
85 
85 
90 
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82 
76 
74 
73 
76 
83 
100 

68 
63 
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58 
59 
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74 
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53 

48 
43 
40 
39 
39 
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56 

18 

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6 

0 

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54 
62 
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104. 

69 

78 

88 

103 

83 

91 

103 

93 
102 

101 

0 
10 
20 
30 
40 
50 
60 
70 

24 

0 
10 
20 
30 
40 
50 
60 
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97 
93 
93 
97 
107 

95 
88 
85 
84 
86 
93 
112 

84 
77 
73 
71 
72 
77 
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123 

70 
64 
59 
56 
54 
56 
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55 
48 
42 
38 
34 
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32 
38 

37 

30 

24 

18 

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5 

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19 
11 
4 
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0 

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19 
27 
36 
48 
62 
83 
115 

37 
46 
56 
69 
86 
111 

55 
63 
74 
89 
109 

70 

79 

91 

107 

84 

93 

105 

95 
104 

103 

0 
10 
20 
30 
40 
50 
60 
70 

0" 
10 
20 
30 
40 
50 
60 
70 

26 

0 
10 
20 

30 
40 
50 
60 
70 

98 
95 
93 
96 
105 

96 
89 
85 
83 
85 
92 
108 

85 
78 
73 
70 
70 
74 
86 
115 

72 
64 
59 
54 
52 
53 
58 
75 

56 
48 
41 
36 
32 
28 
27 
29 

38 

30 

23 

16 

9 

1 

-  8 

-23 

19 

11 

3 

-  6 
-16 

-28 
-46 

-78 

0 

-  9 

-  18 

-  28 

-  41 

-  58 

-  84 
-134 

19 
28 
38 
50 
66 
88 
123 

38 
47 
58 
72 
91 
117 

56 
65 

77 

92 

114 

72 

81 

94 

111 

85 

95 

108 

96 
106 

105 

© 

c 
"3 

OJ 

1 

< 

70° 

60° 

50° 

40° 

80° 

20° 

10° 

0° 

10° 

20° 

80° 

40° 

50° 

60° 

70° 

6 

Latitude  of  same  name  as  declination. 

L 

atitud 

eof  d 

iflerent  name  from  declination. 

TABLE  26. 

[Page  641 

Variation  of  Altitude  in  one  minute  from  meridian 

passage 

Declination  of  the 

same  name  a.s  the  latitude; 

npper  transit;  reduction  additive. 

Lati- 
tude. 

0° 

Lati- 
tude. 

1° 

.2° 

3° 

40 

5° 

6° 

70 

8° 

9° 

10° 

11° 

o 

II 

II 

II 

II 

// 

II 

II 

// 

II 

II 

II 

II 

0 

0 

28.1 

22.4 

18.7 

16.0 

14.0 

12.4 

11.1 

10.1 

0 

1 

28.0 

22.4 

18.6 

16.0 

13.9 

12.4 

11.1 

1 

2 

28.0 

22.3 

18.6 

15.9 

13.9 

12.3 

2 

3 

27.9 

22.3 

18.5 

15.8 

13.8 

3 

4 
5 

28.1 
22.  4^ 

27.8 

22.2 

18.5 

15.8 

4 

28.0 

27.7 

22.1 

18.4 

5 

6 

18.7 

22.4 

28.0 

27.6 

22.0 

6 

7 

16.0 

18.6 

22.3 

27.9 

27.4 

7 

8 

14.0 

16.0 

18.6 

22.3 

27.8 

8 

9 

12.4 
11.1 

13.9 
12.  4 

15.9 

18.5 

22.2 
18.5 

27.7 
22.1 

9 
10 

10 

13.9 

15.8 

27.6 

11 

10.1 

11.1 

12.3 

13.8 

15.8 

18.4 

22.0 

27.4 

11 

12 

9.2 

10.1 

11.1 

12.3 

13.8 

15.7 

18.3 

21.9 

27.3 

12 

13 

8,5 

9.2 

10.0 

11.0 

12.2' 

13.7 

15.6 

18.2 

21.7 

27.1 

13 

14 

15 

7.9 

8.5 

9.2 

10.0 

10.9 

12.1 
10.9 

13.6 
12.1 

15.5 

18.0 

21.6 

26.9 

14 

15 

7.3 

7.8 

8.4 

9.1 

9.9 

13.5 

15.4 

17.9 

21.4 

26.7 

16 

6.8 

7.3 

7.8 

8.4 

9.1 

9.8 

10.8 

12.0 

13.4 

15.3 

17.8 

21.3 

16 

17 

6.4 

6.8 

7.2 

7.8 

8.3 

9.0 

9.8 

10.7 

11.9 

13.3 

15.2 

17.6 

17 

18 

6.0 

6.4 

6.8 

7.2 

7.  7 

8.3 

8.9 

9.7 

10.6 

11.8 

13.2 

15.0 

18 

19 

5.7 

6.0 

6.3 

6.7 
6.3 

7.2 

7.6 

8.2 

8.9 

9.6 

10.6 
9.5 

11.7 

13.1 

19 
20 

20 

5.4 

5.7 

6.0 

6.7 

7.1 

7.6 

8.1 

8.8 

10.5 

11.6 

21 

5.1 

5.4 

5.6 

5.9 

6.3 

6.6 

7.0 

7.5 

8.1 

8.7 

9.5 

10.4 

21 

22 

4.9 

5.1 

5.3 

5.6 

5.9 

6.2 

6.6 

7.0 

7.5 

8.0 

8.6 

9.4 

22 

23 

4.6 

4.8 

5.0 

5.3 

5.5 

5.8 

6.1 

6.5 

6.9 

7.4 

7.9 

8.5 

23 

24 

4.4 

4.6 

4.8 

5.0 

5.2 

5.5 

5.8 

6.1 

6.4 

6.8 

7.3 

7.8 

24 
25 

25 

4.2 

4.4 

4.6 

4.7 

5.0 

5.2 

5.4 

5.7 

6.0 

6.4 

6.8 

7.2 

26 

4.0 

4.2 

4.3 

4.5 

4.7 

4.9 

5.1 

5.4 

5.7 

6.0 

6.3 

6.7 

26 

27 

3.9 

4.0 

4.1 

4.3 

4.5 

4.7 

4.9 

5.1 

5.3 

5.6 

5.9 

6.2 

27 

28 

3.7 

3.8 

4.0 

4.1 

4.3 

4.4 

4.6 

4.8 

5.0 

5.3 

5.5 

5.8 

28 

29 

3.5 

3.7 

3.8 

3.9 

4.1 

4.2 

4,4 

4.6 

4.7 

5.0 

5.2 

5.5 
5.1 

29 
30 

80 

3.4 

3.5 

3.6 

3.7 

3.9 

4.0 

4.2 

4.3 

4.5 

4.7 

4.9 

31 

3.3 

3.4 

3.5 

3.6 

3.7 

3.8 

4.0 

4.1 

4.3 

4.4 

4.6 

4.8 

31 

32 

3.1 

3.2 

3.3 

3.4 

3.5 

3.7 

3.8 

3.9 

4.1 

4.2 

4.4 

4.6 

32 

33 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

3.9 

4.0 

4.2 

4.3 

33 

34 

2.9 

3.0 

3.1 

3.2 

3.2 

3.3 

3.4 

3.6 

3.7 

3.8 

3.9 

4.1 

34 

35 

2.8 

2.9 

3.0 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

3.9 

35 

36 

2.7 

2.8 

2.8 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3.7 

36 

37 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

37 

38 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

3.0 

3.0 

3.2 

3.2 

3.3 

38 

39 

2.4 

2.5 

2.5 

2.6 

2.7 

2.7 

2.8 

2.9 

2.9 

3.0 

3.1 

3.2 

39 
40 

40 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.7 

2.8 

2.9 

3.0 

3.0 

41 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.6 

2.7 

2.8 

2.8 

2.9 

41 

42 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.6 

2.7 

2.8 

42 

43 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

2.6 

2.7 

43 

44 

2.0 
2.0 

2.1 

2.1 

2.1 

2.2 
2.1 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.5 

44 

45 

2.0 

2.0 

2.1 

2.2 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

45 

46 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.2 

2.3 

2.3 

46 

47 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.1 

2.2 

2.2 

47 

48 

1.8 

1.8 

1.8 

1.9 

1.-9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.1 

48 

49 
50 

1.7 
1.6 

1.7 

1.8 

1.8 

1.8 

1.8 

1.9 
1.8 

1.9 

1.9 

2.0 
1.9 

2.0 

2.1 

49 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

2.0 

50 

51 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

51 

52 

1.5 

1.6 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

52 

53 

1.5 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1.7 

1.7 

53 

54 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 
1.5 

1.5 

1.6 

1.6 

1.6 

1.6 

1.7 

54 

55 

1.4 

1.4 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

1.6 

1.6 

1.6 

55 

56 

1.3 

1.3 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

56 

57 

1.3 

1.3 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.5 

57 

58 

1.2 

1.2 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

58 

59 

1.2 

1.2 

1.2 

1.2 

1.2 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

59 

60 

1.1 

1.1 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.3 

1.3 

60 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

70 

8° 

90 

10° 

11° 

De 

elinatio 

n  of  the 

same  name  as  the 

latitude; 

upper  tra 

nsit;  red) 

etion  add 

Itire. 

Page  542J 

TABL?: 

26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  the 

same  name  as  the  latitude;  upper  transit 

reduction  addltlre. 

Lati- 
tude. 

12° 

18° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

28° 

24° 

c 

0 

9.2 

8.5 

7.9 

II 
7.3 

6.8 

6.4 

II 
6.0 

5.7 

II 
5,4 

II 

5.1 

4.9 

II 
4.6 

4.4 

0 

0 

1 

10.1 

9.2 

8.5 

7.8 

7.3 

6.8 

6.4 

6.0 

5.7 

5.4 

5.1 

4.8 

4.6 

1 

2 

11.1 

10.0 

«.2 

8.4 

7.8 

7.2 

6.8 

6.3 

6.0 

5.6 

5.3 

5.0 

4.8 

9 

3 

12.3 

11.0 

10.0 

9.1 

8.4 

7.8 

7.2 

6.7 

6.3 

5.9 

5.6 

5.3 

5.0 

3 

4 

13.8 
15.7 

12.2 
13.7 

10.9 

9.9 

9.1 

8.3 

7.7 

7,2 

6.7 

6.3 

5,9 

5.5 

5.2 

4 

5 

12.1 

10.9 

9.8 

9.0 

8.3 

7,6 

7.1 

6.6 

6.2 

5.8 

5.5 

5 

6 

18.3 

15.6 

13.6 

12.1 

10.8 

9.8 

8.9 

8,2 

7.6 

7.0 

6.6 

6.1 

5.8 

6 

/ 

21.9 

18.2 

15.5 

13.5 

12.0 

10.7 

9.7 

8,9 

8.1 

7.5 

7.0 

6.5 

6.1 

7 

8 

27.3 

21.7 

18.0 

15.4 

13.4 

11.9 

10.6 

9,6 

8.8 

8.1 

7.5 

6.9 

6.4 

8 

9 

27.1 

21.6 

17.9 

15.3 

13.3 

11.8 

10.6 

9.5 

8.7 

8.0 

7.4 

6.8 

9 
10 

10 

26.9 

21.4 

17.8 

15.2 

13.2 

11.7 

10,5 

9.5 

8.6 

7.9 

7.3 

11 

26.7 

21.3 

17.6 

15.0 

13.1 

11,6 

10.4 

9.4 

8,5 

7.8 

11 

12 

26.5 

21.1 

17.5 

14,9 

13,0 

11.5 

10.3 

9,3 

8.4 

12 

13 

26.2 

20.9 

17,3 

14.8 

12.8 

11.3 

10,1 

9.2 

13 

14 

26.0 

20.7 

17.1 

14.6 

12.7 

11,2 

10.0 

14 

15 

25.7 

20.4 

16.9 

14,4 

12.5 

11.1 

15 

16 

26.5 

25.4 

20.2 

16,7 

14,3 

12.4 

16 

17 

21.1 

26.2 

25.1 

20.0 

16.5 

14,1 

17 

18 

17.5 

20.9 

26.0 

24.8 

19.7 

16.3 

18 

19 

14.9 

17.3 

20.7 

25.7 

24.5 

19,5 

19 

20 

13.0 

14.8 

17.1 

20.4 

25.4 

24.2 

20 

21 

11.5 

12.8 

14.6 

16.9 

20.2 

25.1 

21 

22 

10.3 

11.3 

12.7 

14.4 

16.7 

20.0 

24.8 

22 

23 

9.3 

10.1 

11.2 

12.5 

14.3 

16.5 

19.7 

24,5 

23 

24 

8.4 

9.2 

10.0 
9.0 

11.1 

12.4 

14.1 

16.3 

19,5 

24.2 

24 

25 

7.7 

8.3 

9.9 

10.9 

12.2 

13.9 

16,1 

19.2 

23.8 

25 

26 

7.1 

7.6 

8.2 

8.9 

9.8 

10.8 

12.1 

13,7 

15,9 

18.9 

23,5 

26 

27 

6.6 

7.0 

7,5 

8.1 

8.8 

9.6 

10.6 

11.9 

13,5 

15.6 

18.6 

23.1 

27 

28 

6.2 

6.5 

7.0 

7.4 

8.0 

8.7 

9.5 

10,5 

11,7 

13.3 

15,4 

18.3 

22,7 

28 

29 

5.7 

6.1 

6.4 

6.9 

7.3 

7.9 

8.6 

9,4 

10,3 

11.5 

13.1 

15.1 
12.8 

18.0 

29 

30 

5.4 

5.7 

6.0 

6.4 

6.8 

7.2 

7,8 

8,4 

9,2 

10.1 

11.3 

14.9 

30 

31 

5.1 

5.3 

6.6 

5.9 

6.3 

6.7 

7,1 

7.7 

8,3 

9.0 

10.0 

11.1 

12.6 

31 

32 

4.8 

5.0 

5.2 

5.5 

5.8 

6.2 

6,5 

7.0 

7,5 

8.1 

8.9 

9.8 

10,9 

32 

33 

4.5 

4.7 

4.9 

5.1 

5.4 

5.7 

6,1 

6,4 

6,9 

7.4 

8.0 

8.7 

9,6 

33 

34 

4.3 

4.4 

4.6 

4.8 

5.1 

5.3 

5,6 

5.9 

6,3 

6.8 

7.3 

7.8 

8.6 

34 

35 

4.0 

4.2 

4.4 

4.5 

4.7 

5.0 

5,2 

5.5 

5,8 

6.2 

6.6 

7.1 

7,  7 

35 

36 

3.8 

4.0 

4.1 

4.3 

4.5 

4.7 

4.9 

5.1 

5,4 

5.7 

6.1 

6.5 

7.0 

36 

37 

3.6 

3.8 

3.9 

4.0 

4.2 

4.4 

4,6 

4.8 

5.0 

5.3 

5.6 

6.0 

6,4 

37 

38 

3.4' 

3.6 

3.7 

3.8 

4.0 

4.1 

4.3 

4,5 

4.7 

4.9 

5.2 

5.5 

5.8 

38 

39 

3.3 

3.4 

3.5 

3.6 

3.8 

3.9 

4.0 

4,2 

4.4 

4.6 

4.8 

5.1 

5,4 

39 

40 

3.1 

3.2 

3.3 

3.4 

3.6 

3.7 

3.8 

4,0 

4.1 

4.3 

4.5 

4.7 

5.0 

40 

41 

3.0 

3.1 

3.2 

3.3 

3.4 

3.5 

3.6 

3,7 

3.9 

4.0 

4.2 

4.4 

4.6 

41 

42 

2.9 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3,5 

3.7 

3.8 

4.0 

4.1 

4.3 

42 

43 

2.7 

2.8 

2.9 

3.0 

3.0 

3.1 

3.2 

3,3 

3.5 

3.6 

3.7 

3.9 

4.0 

43 

44 

2.6 

2.7 

2.7 

2.8 

2.9 

3.0 

3,1 

3,2 

3.3 

3.4 

3.5 

3.6 

3.8 

44 

45 

2.5 

2.6 

2.6 

2.7 

2.8 

2,8 

2,9 

3.0 

3.1 

3,2 

3.3 

3.4 

3,5 

45 

46 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2,8 

2.8 

2.9 

3,0 

3.1 

3.2 

3.3 

46 

47 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2,9 

2.9 

3.0 

3.1 

47 

48 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2,6 

2.6 

2,7 

2.8 

2.9 

3.0 

48 

49 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

49 

50 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2,4 

2.5 

2.6 

2.6 

50 

51 

1.9 

2.0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.3 

2,3 

2.4 

2.4 

2.5 

51 

52 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.1 

2.1 

2.1 

2.2 

2.2 

2.3 

2:4 

52 

53 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2,0 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

.53 

54 

1.7 

1.7 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

1.9 

2,0 

2.0 

2.1 

2.1 
2,0 

54 
55 

55 

1.6 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1,8 

1.9 

1.9 

1.9 

2.0 

56 

1.5 

1.6 

1.6 

1.6 

1.6 

1.7 

1.7 

1,7 

1.8 

1,8 

1.8 

1.9 

1,9 

56 

57 

1.5 

1.5 

1.5 

1.5 

1.6 

1,6 

1.6 

1,6 

1.7 

1.7 

1.7 

1.8 

1,8 

57 

58 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

1.5 

1,6 

1.6 

1.6 

1.6 

1.7 

1.7 

58 

59 

1.4 

1.4 

1.4 

1.4 

1.4 

1.5 

1.5 

1.5 

1.5 

1,5 

1.6 

1.6 

1.6 

59 

60 

1.3 

1.3 

1.3 

1.3 

1.4 

1.4 

1.4 

1,4 

1.4 

1.5 

1.5 

1.5 

1.5 

60 

12° 

18° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

De< 

jlinatior 

I  of  the  t 

ame  nai 

ne  as  th 

3  latitud 

e;  uppei 

transit; 

reducti 

on  addit 

l¥e. 

TABLE 

26. 

[Page  543 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Declination  of  the 

same  name  as  the  latitude;  upper  transit 

reduction  additive. 

Lati- 
tude. 

Lati- 
tude. 

26° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

83° 

34° 

35° 

36° 

37° 

o 

0 

4.2 

4.0 

3.9 

3.7 

3.5 

3.4 

3.3 

3.1 

3.0 

2.9 

2.8 

2.7 

2.6 

o 

0 

1 

4.4 

4.2 

4.0 

3.8 

3.7 

3.5 

3.4 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

1 

2 

4.6 

4.3 

4.1 

4.0 

3.8 

3.6 

3.5 

3.3 

3.2 

3.1 

3.0 

2.8 

2.7 

2 

3 

4.7 

4.5 

4.3 

4.1 

3.9 

3.7 

3.6 

3.4 

3.3 

3.2 

3.0 

2.9 

2.8 

3 

4 
5 

5.0 

4.7 

4.5 

4.3 

4.1 

3.9 

3.7 

3.5 

3.4 

3.3 

3.1 

3.0 
3.1 

2.9 

4 

5.2 

4.9 

4.7 

4.4 

4.2 

4.0 

3.8 

3.7 

3.5 

3.3 

3.2 

3.0 

5 

6 

5.4 

6.1 

4.9 

4.6 

4.4 

4.2 

4.0 

3.8 

3.6 

3.5 

3.3 

3.2 

3.0 

6 

7 

5.7 

5.4 

5.1 

4.8 

4.6 

4.3 

4.1 

3.9 

3.7 

3.6 

3.4 

3.3 

3.1 

7 

8 

6.0 

5.  7 

5.3 

5.0 

4.8 

4.5 

4.3 

4.1 

3.9 

3.7 

3.5 

3.4 

3.2 

8 

9 

6.4 

6.0 

5.6 

5.3 

5.0 

4.7 

4.4 

4.2 

4.0 

3.8 

3.6 

3.5 

3.3 

9 

10 

6.8 

6.3 

5.9 

5.5 

5.2 

4.9 

4.6 

4.4 

4.2 

3.9 

3.8 

3.6 

3.4 

10 

11 

7.2 

6.7 

6.2 

5.8 

5.5 

5.1 

4.8 

4.6 

4.3 

4.1 

3.9 

3.7 

3.5 

11 

12 

7.7 

7.1 

6.6 

6.2 

5.8 

5.4 

5.1 

4.8 

4.5 

4.3 

4.0 

3.8 

3.6 

12 

13 

8.3 

7.6 

7.1 

6.5 

6.1 

5.7 

5.3 

5.0 

4.7 

4.4 

4.2 

4.0 

3.8 

13 

14 
15 

9.1 
9.  9 

8.2 

7.6 

7.0 

6.4 

6.0 

5.6 

5.2 

4.9 

4.6 

4.4 

4.1 

3.9 
4.0 

14 

8.9 

8.1 

7.4 

6.9 

6.4 

5.9 

5.5 

5.2 

4.8 

4.5 

4.3 

15 

16 

10.9 

9.8 

8.8 

8.0 

7.3 

6.8 

6.3 

5.8 

5.4 

5.1 

4.8 

4.5 

4.2 

16 

17 

12.2 

10.8 

9.6 

8.7 

7.9 

7.2 

6.7 

6.2 

5.7 

5.3 

5.0 

4.7 

4.4 

17 

18 

13.9 

12.1 

10.6 

9.5 

8.6 

7.8 

7.1 

6.6 

6.1 

5.6 

5.2 

4.9 

4.6 

18 

19 

16.1 

13.7 

11.9 

10.5 

9.4 

8.4 

7.7 

7.0 

6.4 

6.0 

5.5 

5.1 

4.8 

19 

20 

19.2 

15.9 

13.5 

11.7 

10.3 

9.2 

8.3 

7.5 

6.9 

6.3 

5.8 

5.4 

5.0 

20 

21 

23.8 

18.9 

15.6 

13.3 

11.5 

10.2 

9.1 

8.2 

7.4 

6.8 

6.2 

5.7 

5.3 

21 

22 

23. 5 

18.6 

15.4 

13.1 

11.3 

10.0 

8.9 

8.0 

7.3 

6.6 

6.1 

5.6 

22 

23 

23.1 

18.3 

15.1 

12.8 

11.1 

9.8 

8.7 

7.9 

7.1 

6.5 

6.0 

23 

24 

22.7 

18.0 

14.9 

12.6 

10.9 

9.6 

8.6 

7.7 

7.0 

6.4 

24 

25 

22.3 

17.7 

14.6 

12.4 

10.7 

9.4 

8.4 

7.5 

6.8 

25 

26 

21.9 

17.4 

14.3 

12.1 

10.5 

9.2 

8.2 

7.4 

26 

27 

21.5 

17.0 

14.0 

11.9 

10.3 

9.1 

8.1 

27 

28 

. 

21.1 

16.7 

13.8 

11.7 

10.1 

8.9 

28 

29 

22.3 

20.6 

16.3 

13.5 

11.4 

9.9 

29 

30 

17.7 

21.9 

20.2 

16.0 

13.2 

11.1 

30 

31 

14.6 

17.4 

21.5 

19.8 

15.6 

12.9 

31 

32 

12.4 

14.3 

17.0 

21.1 

19.3 

15.3 

32 

33 

10.7 

12.1 

14.0 

16.7 

20.6 

18.9 

33 

34 

9.4 

10.5 

11.9 

13.8 

16.3 

20.2 

34 

35 

8.4 

9.2 

10.3 

11.7 

13.5 

16.0 

19.8 

35 

36 

7.5 

8.2 

9.1 

10.1 

11.4 

13.2 

15.6 

19.3 

36 

37 

6.8 

7.4 

8.1 

8.9 

9.9 

11.1 

12.9 

15.3 

18.9 

37 

38 

6.2 

6.7 

7.2 

7.9 

8.7 

9.6 

10.9 

12.6 

14.9 

18.4 

38 

39 

5.7 
5.3 

6.1 

6.5 

7.1 

7.7 

8.5 

9.4 

10.6 
9.2 

12.2 

14.5 

17.9 

39 

40 

5.6 

6.0 

6.4 

6.9 

7.5 

8.2 

10.4 

11.9 

14.1 

17.4 

40 

41 

4.9 

5.2 

5.5 

5.8 

6.2 

6.7 

7.3 

8.0 

8.9 

10.1 

11.6 

13.8 

17.0 

41 

42 

4.5 

4.8 

5.0 

5.3 

5.7 

6.1 

6.6 

7.1 

7.8 

8.7 

9.8 

11.3 

13.4 

42 

43 

4.2 

4.4 

4.6 

4.9 

5.2 

5.5 

5.9 

6.4 

6.9 

7.6 

8.5 

9.5 

11.0 

43 

44 

3.9 

4.1 

4.3 

4.5 

4.8 

5.1 

5.4 

5.8 

6.2 

6.7 

7.4 

8.2 

9.3 

44 

45 

3.7 

3.8 

4.0 

4.2 

4.4 

4.7 

4.9 

5.2 

5.6 

6.0 

6.6 

7.2 

8.0 

45 

46 

3.5 

3.6 

3.7 

3.9 

4.1 

4.3 

4.5 

4.8 

5.1 

5.4 

5.9 

6.4 

7.0 

46 

47 

3.3 

3.4 

3.5 

3.6 

3.8 

4.0 

4.2 

4.4 

4.6 

4.9 

5.3 

5.7 

6.2 

47 

48 

3.1 

3.2 

3.3 

3.4 

3.5- 

3.7 

3.9 

4.0 

4.3 

4.5 

4.8 

5.1 

5.5 

48 

49 
50 

2.9 

3.0 

3.1 

3.2 

3.3 

3.4 

3.6 

3.7 

3.9 

4.1 

4.4 

4.6 

5.0 

49 

2.7 

2.8 

2.9 

3.0 

3.1 

3.2 

3.3 

3.5 

3.6 

3.8 

4.0 

4.2 

4.5 

50 

51 

2.6 

2.6 

2.7 

2.8 

2.9 

3.0 

3.1 

3.2 

3.4 

3.5 

3.7 

3.9 

4.1 

51 

52 

2.4 

2.5 

2.6 

2.6 

2.7 

2.8 

2.9 

3.0 

3.1 

3.2 

3.4 

3.6 

3.7 

52 

53 

2.3 

2.3 

2.4 

2.5 

2.5 

2.6 

2.7 

2.8 

2.9 

3.0 

3.1 

3.3 

3.4 

53 

54 

2.2 

2.2 

2.3 

2.3 

2.4 

2.5 

2.5 

2.6 

2.7 

2.8 

2.9 

3.0 

3.2 

54 

55 

2.0 

2.1 

2.1 

2.2 

2.3 

2.3 

2.4 

2.4 

2.5 

2.6 

2.7 

2.8 

2.9 

55 

56 

1.9 

2.0 

2.0 

2.1 

2.1 

2.2 

2.2 

2.3 

2.4 

2.4 

2.5 

2.6 

2.7 

56 

57 

1.8 

1.9 

1.9 

2.0 

2.0 

2.0 

2.1 

2.2 

2.2 

2.3 

2.3 

2.4 

2.5 

57 

58 

1.7 

1.8 

1.8 

1.8 

1.9 

1.9 

2.0 

2.0 

2.1 

2.1 

2.2 

2.3 

2.3 

58 

59 

1.6 

1.7 

1.7 

1.7 

1.8 

1.8 

1.9 

1.9 

1.9 

2.0 

2.0 

2.1 

2.2 

59 

60 

1.6 

1.6 

1.6 

1.6- 

1.7 

1.7 

1.7 

1.8 

1.8 

1.9 

1.9 

2.0 

2.0 

60 

25° 

26° 

27° 

28° 

29° 

80° 

31° 

32° 

88° 

34° 

85°| 

86° 

87° 

De 

3linatlor 

1  of  the 

same  na 

me  as  th 

e  latltuc 

le;  uppe 

r  transit 

reduct 

on  addl 

tlve. 

Page  544 

TABLE 

26. 

Variation  of  Altitude  in  one  minute  from  meridian  past^age. 



Declination  of  the 

same  name  a«  the  latitude;  upper  transit 

reduction  additive. 

Lati- 
tude. 

Lati- 
tude. 

o 

0 

88° 

89° 

40° 

41° 

42° 

48° 

44° 

46° 

46° 

47° 

48° 

49° 

60° 

o 

0 

2.5 

2.4 

2.3 

2.3 

2.2 

2.1 

2.0 

It 
2.0 

1.9 

1.8 

1.8 

II 

1.  7 

1.7 

1 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

1.7 

1 

2 

2.6 

2.5 

•  2.4 

2.4 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

2 

3 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

3 

4 

5 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

4 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.8 

5 

6 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

6 

7 

3.0 

2.9 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

1.8 

7 

8 

3.1 

2.9 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

1.9 

1.9 

8 

9 

3.2 

3.0 

2.9 

2.8 

2.7 

2.5 

2.4 

2.3 

2.2 

2.2 

2.1 

2.0 

1.9 

9 

10 

3.3 

3.1 

3.0 

2.8 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

1.9 

10 

11 

3.4 

3.2 

3.1 

2.9 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

2.1 

2.1 

2.0 

11 

12 

3.5 

3.3 

3.1 

3.0 

2.9 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 

2.0 

12 

13 

3.6 

3.4 

3.2 

3.1 

2.9 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

2.1 

2.0 

13 

14 

3.7 

3.5 

3.3 

3.2 

3.0 

2.9 

2.7 

2.6 

2.5 

2.4 

2.3 

2.2 

2.1 
2.1 

14 
15 

15 

3.8 

3.6 

3.4 

3.3 

3.1 

3.0 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

16 

4.0 

3.8 

3.6 

3.4 

3.2 

3.0 

2.9 

2.8 

2.6 

2.5 

2.4 

2.3 

2.2 

16 

17 

4.1 

3.9 

3.7 

3.5 

3.3 

3.1 

3.0 

2.8 

2.7 

2.6 

2.4 

2.3 

2.2 

17 

18 

4.3 

4.1 

3.8 

3.6 

3.4 

3.2 

3.1 

2.9 

2.8 

2.6 

2.5 

2.4 

2.3 

18 

19 

4.5 

4.2 

4.0 

3.7 

3.5 

3.3 

3.2 

3.0 

2.8 

2.7 

2.6 

2.4 

2.3 

19 
20 

20 

4.7 

4.4 

4.1 

3.9 

3.7 

3.5 

3.3 

3.1 

2.9 

2.8 

2.6 

2.5 

2.4 

21 

4.9 

4.6 

4.3 

4.0 

3.8 

3.6 

3.4 

3.2 

3.0 

2.9 

2.7 

2.6 

2.4 

21 

22 

5.2 

4.8 

4.5 

4.2 

4.0 

3.7 

3.5 

3.3 

3.1 

2.9 

2.8 

2.6 

2.5 

22 

23 

5.5 

5.1 

4.7 

4.4 

4.1 

3.9 

3.6 

3.4 

3.2 

3.0 

2.9 

2.7 

2.6 

23 

24 
25 

5.8 

5.4 

5.0 

4.6 

4.3 

4.0 

3.8 

3.5 

3.3- 

3.1 

3.0 

2.8 

2.6 
2.7 

24 
25 

6.2 

5.7 

5.3 

4.9 

4.5 

4.2 

3.9 

3.7 

3.5 

3.3 

3.1 

2.9 

26 

6.7 

6.1 

5.6 

5.2 

4.8 

4.4 

4.1 

3.8 

3.6 

3.4 

3.2 

3.0 

2.8 

26 

27 

7.2 

6.5 

6.0 

5.5 

5.0 

4.6 

4.3 

4.0 

3.7 

3.5 

3.3 

3.1 

2.9 

27 

28 

7.9 

7.1 

6.4 

5.8 

.    5.3 

4.9 

4.5 

4.2 

3.9 

3.6 

3.4 

3.2 

3.0 

28 

29 

8.7 

7.7 

6.9 

6.2 

5.7 

5.2 

4.8 

4.4 

4.1 

3.8 

3.5 

3.3 

3.1 

29 

30 

9.6 

8.5 

7.5 

6.7 

6.1 

5.5 

5.1 

4.7 

4.3 

4.0 

3.7 

3.4 

3.2 

30 

31 

10.9 

9.4 

8.2 

7.3 

6.6 

5.9 

5.4 

4.9 

4.5 

4.2 

3.9 

3.6 

3.3 

31 

32 

12.6 

10.6 

9.2 

8.0 

7.1 

6.4 

5.8 

5.2 

4.8 

4.4 

4.0 

3.7 

3.5 

32 

33 

14.9 

12.2 

10.4 

8.9 

7.8 

6.9 

6.2 

5.6 

5.1 

4.6 

4.3 

3.9 

3.6 

33 

34 
35 

18.4 

14.5 

11.9 

10.1 

8.7 

7.6 

6.7 

6.0 

5.4 

4.9 

4.5 

4.1 

3.8 

34 

17.9 

14.1 

11.6 

9.8 

8.5 

7.4 

6.6 

5.9 

5.3 

4.8 

4.4 

4.0 

35 

36 

17.4 

13.8 

11.3 

9.5 

8.2 

7.2 

6.4 

5.7 

5.1 

4.6 

4.2 

36 

37 

17.0 

13.4 

11.0 

9.3 

8.0 

7.0 

6.2 

5.5 

5.0 

4.5 

37 

38 

16.5 

13.0 

10.7 

9.0 

7.7 

6.8 

6.0 

5.3 

4.8 

38 

39 

16.0 

12.6 

10.3 

8.7 

7.5 

6.5 

5.8 

5.1 

39 

40 

15.5 

12.2 

10.0 

8.4 

7.2 

6.3 

5.6 

40 

41 

15.0 

11.8 

9.7 

8.1 

7.0 

6.1 

41 

42 

16.5 

14.5 

11.4 

9.3 

7.9 

6.7 

42 

43 

13.0 

16.0 

14.0 

11.0 

9.0 

7.6 

43 

44 

10.7 

12.6 

15.5 

13.6 

10.6 

8.7 

44 

45 

9.0 

10.3 

12.2 

15.0 

13.1 

10.2 

45 

46 

7.7 

8.7 

10.0 

11.8 

14.5 

12.6 

46 

47 

6.8 

7.5 

8.4 

9.7 

11.4 

14.0 

47 

48 

6.0 

6.5 

7.2 

8.1 

9.3 

11.0 

13.6 

48 

49 

5.3 

5.8 

6.3 

7.0 

7.9 

9.0 

10.6 

13.1 

49 

50 

4.8 

5.1 

5.6 

6.1 

6.7 

7.6 

8.7 

10.2 

12.6 

50 

51 

4.3 

4.6 

5.0 

5.4 

5.9 

6.5 

7.3 

8.4 

9.9 

12.1 

51 

52 

3.9 

4.2 

4.5 

4.8 

5.2 

5.7 

6.3 

7.0 

8.0 

9.5 

11.6 

52 

53 

3.6 

3.8 

4.0 

4.3 

4.6 

5.0 

5.4 

6.0 

6.7 

7.  7 

9.1 

11.1 

53 

54 
55 

3.3 

3.5 

3.7 

3.9 
3.5 

4.1 
3.7 

4.4 

4.8 

5.2 

5.8 

6.5 

7.4 

8.7 
7.1 

10.6 

54 
55" 

3.0 

3.2 

3.3 

4.0 

4.3 

4.6 

5.0 

5.5 

6.2 

8.3 

56 

2.8 

2.9 

3.1 

3.2 

3.4 

3.6 

3.8 

4.1 

4.4 

4.8 

5.3 

5.9 

6.8 

56 

57 

2.6 

2.7 

2.8 

2.9 

3.1 

3.2 

3.4 

3.6 

3.9 

4.2 

4.6 

5.0 

5.6 

o/ 

58 

2.4 

2.5 

2.6 

2.7 

2.8 

2.9 

3.1 

3.3 

3.5 

3.7 

4.0 

4.4 

4.8 

58 

59 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

3.0 

3.1 

3.3 

3.6 

3.8 

4.2 

59 

60 

2.1 

2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

3.0 

3.2 

3.4 

3.6 

60 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

De 

.'linatior 

1  of  the 

«anie  nai 

Tie  as  th 

e  latitiid 

c;  uppei 

transit 

red  net  i 

on  addit 

hi'. 

TABLE 

26. 

[Page 

545 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Declination  of  the 

same  name  as  the  latitude;  upper  transit 

reduction  additive. 

Lati- 
tude. 

Lati- 
tude. 

51° 

52° 

oS° 

54° 

55° 

56° 

67° 

58° 

69° 

60° 

61° 

62° 

68° 

n 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

0 

0 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

0 

1 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1 

2 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

2 

3 

L7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

3 

4 

1.7 

1.6 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

4 

5 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

1.1 

1.1 

5 

6 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

6 

7 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

7 

8 

1,8 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.2 

1.2 

1.1 

1.1 

8 

9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

1.1 

9 

10 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

10 

11 

1.9 

1.8 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

11 

12 

1.9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

1.2 

1.1 

12 

13 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

13 

14 

2.0 

1.9 

1.8 

1.7 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

14 

15 

2.0 

1.9 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.2 

15 

16 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

1.2 

16 

17 

2.1 

2.0 

1.9 

1.8 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

17 

18 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

18 

19 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

19 

20 

2.3 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.4 

1.3 

1.2 

20 

21 

2.3 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

1.2 

21 

22 

2.4 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.3 

1.3 

22 

23 

2.4 

2.3 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.4 

1.3 

23 

24 

2.5 

2.4 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

1.3 

24 

25 

2.6 

2.4 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

1.6 

1.5 

1.4 

1.3 

25 

26 

2.6 

2.5 

2.3 

2.2 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.3 

26 

27 

2.7 

2.6 

2.4 

2.3 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.4 

27 

28 

2.8 

2.6 

2.5 

2.3 

2.2 

2.1 

2.0 

1.8 

1.7 

1.6 

1.5 

1.5 

1.4 

28 

29 

2.9 

2.7 

2.5 

2.4 

2.3 

2.1 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

29 

30 

3.0 

2.8 

2.6 

2.5 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

30 

31 

3.1 

2.9 

2.7 

2.5 

2.4 

2.2 

2.1 

2.0 

1.9 

1.7 

1.6 

1.5 

1.4 

31 

32 

3.2 

3.0 

2.8 

2.6 

2.4 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

1.5 

32 

33 

3.4 

3.1 

2.9 

2.7 

2.5 

2.4 

2.2 

2.1 

1.9 

1.8 

1.7 

1.6 

1.5 

33 

34 
35 

3.5 

3.2 

3.0 

2.8 

2.6 

2.4 

2.3 

2.1 

2.0 

1.9 

1.7 

1.6 

1.5 

34 

3.7 

3.4 

3.1 

2.9 

2.7 

2.5 

2.3 

2.2 

2.0 

1.9 

1.8 

1.7 

1.6 

35 

36 

3.9 

3.6 

3.3 

3.0 

2.8 

2.6 

2.4 

2.3 

2.1 

2.0 

1.8 

1.7 

1.6 

36 

37 

4.1 

3.7 

3.4 

3.2 

2.9 

2.7 

2.5 

2.3 

2.2 

2.0 

1.9 

1.7 

1.6 

37 

38 

4.3 

3.9 

3.6 

3.3 

,3.0 

2.8 

2.6 

2.4 

2.2 

2.1 

1.9 

1.8 

1.7 

38 

39 
40 

4.6 

4.2 

3.8 

3.5 

'3.2 

2.9 

2.7 

2.5 

2.3 

2.1 

2.0 

1.8 

1.7 

39 

5.0 

4.5 

4.0 

3.7 

3.3 

3.1 

2.8 

2.6 

2.4 

2.2 

2.0 

1.9 

1.8 

40 

41 

5.4 

4.8 

4.3 

3.9 

3.5 

3.2 

2.9 

2.7 

2.5 

2.3 

2.1 

1.9 

1.8 

41 

42 

5.9 

5.2 

4.6 

4.1 

3.7 

3.4 

3.1 

2.8 

2.6 

2.4 

2.2 

2.0 

1.9 

42 

43 

6.5 

5.7 

5.0 

4.4 

4.0 

3.6 

3.2 

2.9 

2.7 

2.5 

2.3 

2.1 

1.9 

43 

44 

7.3 

6.3 

5.4 

4.8 

4.3 

3.8 

3.4 

3.1 

2.8 

2.6 

2.3 

2.2 

2.0 

44 

45 

8.4 

7.0 

6.0 

5.2 

4.6 

4.1 

3.6 

3.3 

3.0 

2.7 

2.4 

2.2 

2.0 

45 

46 

9.9 

8.0 

6.7 

5.8 

5.0 

4.4 

3.9 

3.5 

3.1 

2.8 

2.6 

2.3 

2.1 

46 

47 

12.1 

9.5 

7.7 

6.5 

5.5 

4.8 

4.2 

3.7 

3.3 

3.0 

2.7 

2.4 

2.2 

47 

48 

11.6 

9.1 

7.4 

6.2 

5.3 

4.6 

4.0 

3.6 

3.2 

2.8 

2.6 

2.3 

48 

49 

11.1 

8.7 

7.1 

5.9 

5.0 

4.4 

3.8 

3.4 

3.0 

2.7 

2.4 

49 

50 

10.6 

8.3 

6.8 

5.6 

4.8 

4.2 

3.6 

3.2 

2.9 

2.6 

50 

51 

10.2 

.    7.9 

6.4 

5.4 

4.6 

4.0 

3.5 

3.0 

2.7 

51 

52 

9.7 

7.6 

6.1 

5.1 

4.3 

3.8 

3.3 

2.9 

52 

53 

9.2 

7.2 

5.9 

4.9 

4.1 

3.6 

3.1 

53 

54 

8.8 

6.8 

5.5 

4.6 

3.9 

3.4 

54 

55 

10.2 

8.3 

6.5 

5.3 

4.3 

3.7 

55 

56 

7.9 

9.7 

7.9 

6.1 

5.0 

4.1 

56 

57 

6.4 

7.6 

9.2 

7.4 

5.8 

4.7 

57 

58 

5.4 

6.1 

7.2 

8.8 

7.0 

5.4 

58 

59 

4.6 

5.1 

5.9 

6.8 

8.3 

6.6 

59 

60 

4.0 

4.3 

4.9 

5.5 

6.5 

7.9 

60 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

69° 

60° 

61° 

62° 

68° 

De 

^linatioi 

1  of  the 

liame  nai 

ne  as  th 

e  latitat 

e;  uppe 

r  transit 

reduct 

on  addll 

Ive. 

22480—03- 


Page  546] 

TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian 

passage 

Lati- 
tnde. 

Declination  of  a  different  name  from  the  latitude 

;  upper  transit;  reduction  additive. 

Lati- 
tude. 

0° 

1° 

go 

8° 

4° 

5° 

6° 

70 

8° 

9° 

10° 

11° 

o 

II 

// 

II 

II 

// 

II 

II 

II 

II 

II 

II 

II 

0 

0 

28.1 

22.4 

18.7 

16.0 

14,0 

12.4 

11.1 

10.1 

0 

1 

28.1 

22.4 

18.7 

16.0 

14.0 

12.4 

11.2 

10.1 

9.3 

1 

2 

22]  4 

22.4 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

2 

3 

28.1 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

3 

4 

28.1 

22.4 

18.7 

16.0 

14.0 

12.5 
11.2 

11.2 

10.2 

9.3 

8.6 

8.0 

7.4 

4 

5 

22.4 

18.7 

16.0 

14.0 

12.5 

10.2 

9.3 

8.6 

8.0 

7.4 

7.0 

5 

6 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 

6 

7 

16.0 

14.0 

12.4 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 

6.2 

7 

8 

14.0 

12.4 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 

6.2 

5.9 

8 

9 

12.4 

11.2 

10.2 

9.3 

8.6 

8.0 
7.4 

7.5 

7.0 

6.6 

6.2 

5.9 

5.6 
5.3 

9 
10 

10 

11.1 

10.1 

9.3 

8.6 

8.0 

7.0 

6.6 

6.2 

5.9 

5.6 

11 

10.1 

9.3 

8.6 

8.0 

7.4 

7.0 

6.6 

6.2 

5.9 

5.6 

5.3 

5.1 

11 

12 

9.2 

8.5 

7.9 

7.4 

7.0 

6.5 

6.2 

5.9 

5.6 

5.3 

5.0 

4.8 

12 

13 

8.5 

7.9 

7.4 

6.9 

6.5 

6.2 

5.8 

5.6 

5.3 

5.0 

4.8 

4.6 

13 

14 

7.9 

7.4 

6.9 

6.5 

6.2 

5.8 

5.5 

5.3 

5.0 

4.8 

4.6 

4.4 

14 
15 

15 

7.3 

6.9 

6.5 

6.1 

5.8 

5.5 

5.3 

5.0 

4.8 

4.6 

4.4 

4.2 

16 

6.8 

6.5 

6.1 

5.8 

5.5 

5.2 

5.0 

4.8 

4.6 

4.4 

4.2 

4.1 

16 

17 

6.4 

6.1 

5.8 

5.5 

5.  2        5. 0 

4.8 

4.6 

4.4 

4.2 

4.1 

3.9 

17 

18 

6.0 

5.7 

5.5 

5.2 

5. 0        4. 8 

4.0 

4.4 

4.2 

4.1 

3.9 

3.8 

18 

19 

5.7 

5.4 

5.2 

4.9 

4.7 

4.5 

4.4 

4.2 

4.0 

3.9 

3.8 

3.6 

19 

20 

5.4 

5.1 

4.9 

4.7 

4.5 

4.3 

4.2 

4.0 

3.9 

3.8 

3.6 

3.5 

20 

21 

5.1 

4.9 

4.7 

4.5 

4.3 

4.2 

4.0 

3.0 

3.7 

3.6 

3.5 

3.4 

21 

22 

4.9 

4.7 

4.5 

4.3 

4.1 

4.0 

3.9 

3.7 

3.6 

3.5 

3.4 

3.3 

22 

23 

4.6 

4.4 

4.3 

4.1 

4.0 

3.8 

3.7 

3.6 

3.5 

3.4 

3.3 

3.2 

23 

24 

4.4 

4.2 

4.1 

3.9 

3.8 

3.7 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

24 

25 

4.2 

4.1 

3.9 

3.8 

3.7 

3.5 

3.4 

3.3 

3.2 

3.1 

3.1 

3.0 

25 

26 

4.0 

3.9 

3.8 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

3.0 

2.9 

26 

27 

3.9 

3.7 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

27 

28 

3.7 

3.6 

3.5 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

28 

29 

3.5 

3.4 

3.3 

3.2 

3.1 

3.1 
3.0 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

29 

30 

3.4 

3.3 

3.2 

3.1 

3.0 

2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

30 

31 

3.3 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

2.7 

2.6 

2.6 

2.5 

2.5 

31 

32 

3.2 

3.1 

3.0 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.5 

2.4 

32 

33 

3.0 

2.9 

2.9 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

33 

34 

2.9 

2.8 

2.8 

2.7 

2.6 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

34 

35 

2.8 

2.7 

2.7 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

35 

36 

2.7 

2.6 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

36 

37 

2.6 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.2 

2.1 

2.1 

37 

38 

2.5 

2.5 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

38 

39 

2.4 

2.4 

2.3 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 
2.0 

2.0 

2.0 

2.0 

39 

40 

2.3 

2.3 

2.2 

2.2 

2.2 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

40 

41 

2.3 

2.2 

2.2 

2.1 

2.1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

41 

42 

2.2 

2.1 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

42 

43 

2.1 

2.1 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

43 

44 
45 

2.0 

2.0 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

44 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

45 

46 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

46 

47 

1.8 

1.8 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.6 

47 

48 

1.8 

1.7 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

48 

49 

1.7 

1.7 

1.7 

1.6 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.5 

49 

50 

1.6 

1.6 

1.6 

1.6 

1.6 

,  1.5 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

50 

51 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

51 

52 

1.5 

1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

52 

53 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

53 

54 

1.4 

1.4 

1.4 

1.4 

1.4 
1.3 

,    1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

54 

55 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

55 

56 

1.3 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

56 

57 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

57 

58 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

58 

59 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

59 

50 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1  0 

1.0 

1.0 

60 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

70 

8° 

9° 

10° 

11° 

Declir 

lation  0: 

a  differ 

ent  name  from  th 

s  latitude 

;  upper  tr 

ansit;  rer 

luction  a( 

Iditire. 

TABLE  26.                                            [Page  547 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  a  different  name  from  the  latitude;  upper  transit;  reduction  additive. 

Lati- 
tude. 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20°          21° 

22° 

23° 

24° 

o 

0 
1 
2 
3 
4 

9.2 

8.5 
7.9 
7.4 
7.0 

8.5 
7.9 
7.4 
6.9 
6.5 

II 

7.9 
7.4 
•6.9 
6.5 
6.2 
5.8 
5.5 
5.3 
5.0 
4.8 

II 

7.3 
6.9 
6.5 
6.1 
5.8 
5.5 
5.3 
5.0 
4.8 
4.6 

II 

6.8 
6.5 
6.1 
5.8 
5.5 
5.2 
5.0 
4.8 
4.6 
4.4 

II 

6.4 
6.1 
5.8 
5.5 
5.2 

II 

6.0 
5.7 
5.5 
5.2 
5.0 

II 

5.7 
5.4 
5.2 
4.9 
4.7 

II 

5.4 
5.1 
4.9 
4.7 
4.5 

II 

5.1 
4.9 
4.7 
4.5 
4.3 

II 

4.9 
4.7 
4.5 
4.3 
4.1 

II 

4.6 
4.4 
4.3 
4.1 
4.0 

II 
4.4 
4.2 
4.1 
3.9 
3.8 

0 
0 
1 
2 
3 
4 

5 
6 

7 
8 
9 

6.5 
6.2 
5.9 
5.6 
5.3 

6.2 

5.8 
5.6 
5.3 
5.0 

5.0 
4.8 
4.6 
4.4 
4.2 

4.8 
4.6 
4.4 
4.2 
4.1 

4.5 
4.4 
4.2 
4.0 
3.9 

4.3 
4.2 
4.0 
3.9 
3.8 

4.2 
4.0 
3.9 
3.7 
3.6 

4.0 
3.9 
3.7 
3.6 
3.5 

3.8 
3.7 
3.6 
3.5 
3.4 

3.7 
3.6 
3.5 
3.4 
3.3 

5 

6 
7 
8 
9 

10 

11 
12 
13 
14 

5.0 
4.8 
4.6 
4.4 
4.2 

4.8 
4.6 
4.4 
4.3 
4.1 

4.6 
4.4 
4.3 
4.1 
3.9 

4.4 
4.2 
4.1 
3.9 

3.8 

4.2 

4.1 
3.9 
3.8 
3.7 

4.1 
3.9 
3.8 
3.7 
3.5 

3.9 
3.8 
3.7 
3.5 
3.4 

3.8 
3.6 
3.5 
3.4 
3.3 

3.6 
3.5 
3.4 
3.3 
3.2 

3.5 
3.4 
3.3 
3.2 
3.1 

3.4 
3.3 
3.2 
3.1 
3.0 

3.3 
3.2 
3.1 
3.0 
2.9 

3.2 
3.1 
3.0 
2.9 

2.8 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

4.1 
3.9 
3.8 
3.7 
3.5 

3.9 
3.8 
3.7 
3.5 
3.4 

3.8 
3.7 
3.5 
3.4 
3.3 

3.7 
3.5 
3.4 
3.3 
3.2 

3.5 
3.4 
3.3 
3.2 
3.1 

3.4 
3.3 
3.2 
3.1 
3.0 

3.3 
3.2 
3.1 
3.0 
2.9 

3.2 
3.1 
3.0 
2.9 
2.9 

3.1 
3.0 
2.9 
2.9 
2.8 

3.0 

2.9 
2.8 
2.8 
2.7 

2.9 
2.8 
2.8 
2.7 
2.6 

2.8 
2.8 
2.7 
2.6 
2.6 

2.8 
2.7 
2.6 
2.5 
2.5 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

3.4 
3.3 
3.2 
3.1 
3.0 

3.3 
3.2 
3.1 
3.0 
2.9 

3.2 
3.1 
3.0 
2.9 

2,8 

3.1 
3.0 
2.9 

2.8 
2.8 

3.0 
2.9 

2.8 
2.8 
2.7 

2.9 
2.8 
2.8 
2.7 
2.6 

2.9 
2.8 
2.7 
2.6 
2.5 

2.8 
2.7 
2.6 
2.6 
2.5 

2.7 
2.6 
2.6 
2.5 
2.4 

2.6 
2.6 
2.5 
2.4 
2.4 

2.6 
2.5 
2.4 
2.4 
2.3 

2.5 
2.4 
2.4 
2.3 
2.3 

2.4 
2.4 
2.3 
2.3 
2.2 

20 
21 
22 
23 
24 

2.9 
2.8 
2.7 
2.6 
2.6 

2.8 
2.7 
2.7 
2.6 
2.5 

2.7 
2.7 
2.6 
2.5 
2.4 
2.4 
2.3 
2.2 
2.2 
2.1 
2.1 
2.0 
2.0 
1.9 
1.9 

2.7 
2.6 
2.5 
2.5 
2.4 

2.6 
2.5 
2.5 
2.4 
2.3 

2.5 
2.5 
2.4 
2.3 
2.3 

2.5 
2.4 
2.4 
2.3 
2.2 

2.4 
2.4 
2.3 
2.2 
2.2 

2.4 
2.3 
2.2 
2.2 
2.1 

2.3 
2.3 
2.2 
2.1 
2.1 

2.3 
2.2 
2.1 
2.1 
2.0 

2.2 
2.1 
2.1 
2.1 
2.0 

2.2 
2.1 
2.1 
2.0 
2.0 

25 
26 

27 
28 
29 

30 
31 
32 
33 
34 

2.5 
2.4 
2.3 
2.3 
2.2 

2.4 
2.4 
2.3 
2.2 
2.2 

2.3 
2.3 
2.2 
2.1 
2.1 

2.3 
2.2 
2.2 
2.1 
2.0 

2.2 
2.2 
2.1 
2.1 
2.0 
2.0 
1.9 
1.9 
1.8 
1.8 

2.2 
2.1 
2.1 
2.0 
2.0 

2.1 
2.1 
2.0 
2.0 
1.9 

2.1 
2.0 
2.0 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.8 

2.0 
1.9 
1.9 
1.8 
1.8 

1.9 
1.9 
1.8 
1.8 
1.8 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

35 
36 
37 
38 
39 
40 
41 
42 
43 
44 

2.2 
2.1 
2.0 
2.0 
1.9 

2.1 
2.1 
2.0 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.8 

2.0 
1.9 
1.9 
1.8 
1.8 

1.9 
1.9 

1.8 
1.8 
1.7 

1.9 
1.8 
1.8 
1.8 
1.7 

1.8 
1.8 
1.8 
1,7 
1.7 

1.8 
1.8 
1.7 
1.7 
1.6 

1.8 

1.7 
1.7 
1.7 
1.6 

1.7 
1.7 
1.7 
1.6 
1.6 

1.7 
1.7 
1.6 
1.6 
1.6 

1.9 
1.8 
1.8 
1.7 
1.7 

1.8 
1.8 
1.7 
1.7 
1.6 

1.8 
1.8 
1.7 
1.7 
1.6 

1.8 
1.7 
1.7 
1.6 
1.6 

1.7 
1.7 
1.7 
1.6 
1.6 

1.7 
1.7 
1.6 
1.6 
1.5 

1.7 
1.6 
1.6 
1.6 
1.5 

1.7 
1.6 
1.6 
1.5 
1.5 

1.6 
1.6 
1.6 
1.5 
1.5 

1.6 
1.6 
1.5 
1.5 
1.5 

1.6 
1.5 
1.5 
1.5 

1.4 

1.6 
1.5 
1.5 
1.4 
1.4 

1.5 
1.5 
1.5 
1.4 
1.4 
1.4 
1.3 
1.3 
1.3 
1.2 

40 
41 
42 
43 
44 

45 
46 

47 
48 
49 

1.6 
1.6 
1.5 
1.5 
1.4 

1.6 
1.6 
1.5 
1.5 
1.4 

1.6 
1.5 
1.5 
1.4 
1.4 

1.5 
1.5 
1.5 
1.4 
■   1.4 

1.5 
1.5 
1.4 
1.4 
1.4 

1.5 
1.5 
1.4 
1.4 
1.3 

1.5 
1.4 
1.4 
1.4 
1.3 

1.5 
1.4 
1.4 
1.4 
1.3 

1.4 
1.4 
1.4 
1.3 
1.3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.4 
1.3 
1.3 
1.3 
1.2 

45 
46 
47 
48 
49 

50 
51 
52 
53 

54 
55 
56 

57 
58 
59 
60 

1.4 
1.4 
1.3 
1.3 

1.2 

1.4 
1.3 
1.3 
1.3 
1.2 

1.4 
1.3 
1.3 
1.3 
1.2 

1.3 
1.3 
1.3 
1.2 
1.2 

1.3 
1.3 
1.3 
1.2 
1.2 

1.3 
1.3 
1.3 
1.2 
1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

1.3 

1.2 
1.2 
1.2 
1.1 

1.3 
1.2 

1.2 
1.2 
1.1 

1.3 

1:2 
1.2 
1.2 
1.1 

1.2 
1.2 
1.2 
1.1 
1.1 

1.2 
1.2 
1.1 
1.1 
1.1 

1.2 

1.2 
1.1 
1.1 
1.1 
1.1 
1.0 
1.0 
1.0 
0.9 
0.9 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

1.2 
1.2 
1.1 
1.1 
1.1 
1.0 

1.2 
1.1 
1.1 
1.1 
1.0 
1.0 

13° 

1.2 
1.1 
1.1 
1.1 
1.0 
1.0 

1.2 
1.1 
1.1 
1.1 
1.0 
1.0 

1.1 
1.1 
1.1 
1.0 
1.0 
1.0 

1.1 
1.1 

Ivl 

1.0 
1.0 
1.0 

1.1 
1.1 
1.1 
1.0 
1.0 
1.0 

1.1 
1.1 
1.0 
1.0 
1.0 
0.9 

1.1 
1.1 
1.0 
1.0 
1.0 
0.9 

1.1 
1.1 
1.0 
1.0 
1.0 
0.9 

1.1 
1.0 
1.0 
1.0 
1.0 
0.9 

1.1 
1.0 
1.0 
1.0 
0.9 
0.9 

12° 

14° 

16° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

Declination  of  a  different  name  from  the  latitude:  upper  transit;  reduction  additive. 

Page  548]                                           TABLE  26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Lati- 
tude. 

Declination  of  a  different  name  from  the  latitude;  upper  transit;  reduction  addltlre.                    1 

Lati- 
tude. 

26° 

26° 

27° 

28° 

29° 

80° 

81° 

820 

88° 

84° 

85° 

86° 

87° 

o 

0 
1 
2 
3 

4 

4.2 
4.1 
3.9 
3.8 
3.7 

II 

4.0 
3.9 
3.8 
3.6 
3.5 

II 

3.9 
3.7 

3.5 
3.4 

II 

3.7 
3.6 
3.5 
3.4 
3.3 

II 

3.5 
3.4 
3.3 
3.2 
3.2 

II 

3.4 
3.3 
3.2 
3.1 
3.0 

II 

3.3 
3.2 
3.1 
3.0 
2.9 

II 

3.1 
3.1 
3.0 
2.9 
2.8 

n 
■  3.0 
2.9 
2.9 
2.8 
2.7 

II 

2.9 
2,8 
2,8 
2,7 
2.6 

II 

2.8 
2.7 
2.7 
2.6 
2.6 

II 

2.7 
2.6 
2.6 
2.5 
2.5 

II 
2,6 
2,6 
2.5 
2.4 
2.4 

o 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

5 
6 
7 
8 
9 

3.6 
3.4 
3.3 
3.2 
3.1 

3.4 
3.3 
3.2 
3.1 
3.0 

3.3 
3.2 
3.1 
3.0 
2.9 

3.2 
3.1 
3.0 
2.9 
2.9 

3.1 
3.0 
2.9 

2.8 
2.8 

3.0 
2.9 
2.8 
2.7 
2.7 

2.9 
2.8 
2.7 
2.7 
2.6 

2.8 
2.7 
2.6 
2.6 
2.5 

2.7 
2.6 
2,5 
2.5 
2.4 

2.6 
2,5 
2.6 
2,4 

2,4 

2.5 
2.4 
2.4 
2.3 
2.3 

2.4 
2.4 
2.3 
2.3 
2.2 

2.3 
2.3 
2.2 
2,2 
2,2 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

3.1 
3.0 
2.9 
2.8 
2.7 

3.0 

2.9 
2.8 
2.7 
2.7 

2.9 

2.8 
2.7 
2.7 
2.6 

2.8 
2.7 
2.6 
2.6 
2.5 

2.7 
2.6 
2.6 
2.5 
2.4 

2.6 
2.5 
2.5 
2.4 
2.4 

2.5 
2.5 
2.4 
2.4 
2.3 

2.5 
2.4 
2-.  3 
2.3 
2.3 

2.4 
2.3 
2.3 
2.2 
2.2 

2,3 
2,3 
2,2 
2,2 
2,1 

2.2 
2.2 
2,2 
2,1 
2.1 

2.2 
2,1 
2,1 
2.1 
2.0 

2,1 
2,1 
2.0 
2.0 
2.0 

10 
11 
12 
13 
14 

2.7 
2.6 
2.5 
2.5 
2.4 

2.6 
2.5 
2.5 
2.4 
2.4 

2.5 
2.5 
2.4 
2.4 
2.3 

2.5 
2.4 
2.3 
2.3 
2.2 

2.4 
2.3 
2.3 
2.2 
2.2 

2.3 
2.3 
2.2 
2.2 
2.1 

2.3 
2.2 
2.2 
2.1 
2.1 

2.2 
2.2 
2.1 
2.1 
2.0 

2.1 
2.1 
2.1 
2.0 
2.0 

2.1 
2.0 
2.0 
2.0 
1.9 

2,0 
2,0 
2,0 
1,9 
1.9 

2.0 
1.9 
1.9 
1.9 

1.8 

1.9 
1.9 
1.9 
1.8 
1.8 

15 
16 
17 
18 
19 

2.4 
2.3 
2.3 
2.2 
2.2 

2.3 
2.3 
2.2 
2.2 
2.1 

2.3 
2.2 
2.2 
2.1 
2.1 

2.2 
2.1 
2.1 
2.1 
2.0 

2.1 
2.1 
2.1 
2.0 
2.0 

2.1 
2.0 
2.0 
2.0 
1.9 

2.0 
2.0 
2.0 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.8 

1.9 
1.9 
1.9 
1.8 
1.8 

1.9 

1.9 

1.8 

1,8 

.1,8 

1.9 
1.8 
1.8 
1.8 
1.7 

1,8 
1,8 
1,7 
1,7 
1.7 

1.8 
1.7 
1.7 
1.7 
1.6 

20 
21 
22 
23 
24 

25 
26 

27 
28 
29 

2.1 
2.1 
2.0 
2.0 
1.9 

2.1 
2.0 
2.0 
1.9 
1.9 

2.0 
2.0 
1.9 
1.9 
1.9 

2.0 
1.9 
1.9 
1.9 

1.8 

1.9 
1.9 
1.9 
1.8 

1.8 

1.9 
1.9 
1.8 
1.8 
1.7 

1.8 
1.8 
1.8 
1.7 
1.7 

1.8 
1.8 
1.7 
1.7 
1.7 

1.8 
1.7 
1.7 
1.7 
1.6 

1.7 
1.7 
1.7 
1.6 
1.6 

1,7 
1.7 
1.6 
1.6 
1,6 

1.6 
1.6 
1,6 
1,6 
1,5 

1.6 
1.6 
1.6 
1.5 
1.5 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 

30 
31 
32 
33 
34 

1.9 

1.8 
1.8 
1.8 
1.7 

1.8 
1.8 
1.8 
1.7 
1.7 

1.8 
1.8 
1.7 
1.7 
1.7 

1.8 
1.7 
1.7 
1.7 
1.6 

1.7 
1.7 
1.7 
1.6 
1.6 

1.7 
1.7 
1.6 
1.6 
1.6 

1.7 
1.6 
1.6 
1.6 
1.5 

1.6 
1.6 
1.6 
1.5 
1.5 

1.6 
1.6 
1.5 
1.5 
1.5 

1.6 
1.5 
1.5 
1.5 
1.5 

1,5 
1,5 
1.5 
1.5 
1,4 

1,5 
1,5 
1,5 
1,4 
1,4 

1.5 
1.5 
1.4 
1.4 
1.4 

35 
36 
37 

38 
39 

1.7 
1.6 
1.6 
1.6 
1.5 

1.7 
1.6 
1.6 
1.5 
1.5 

1.6 
1.6 
1.6 
1.5 
1.5 

1.6 
1.6 
1.5 
1.5 
1.5 

1.6 
1.5 
1.5 
1.5 
1.4 

1.5 
1.5 
1.5 
1.5 
1.4 

1.5 
1.5 
1.5 
1.4 
1.4 

1.5 
1.5 
1.4 
1.4 
1.4 

1.5 
1.4 
1.4 
1.4 
1.4 

1.4 
1,4 
1,4 
1,4 
1,3 

1,4 
1,4 
1,4 
1,3 
1,3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.4 
1.3 
1.3 
1.3 
1.3 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

1.5 
1.5 
1.4 
1.4 
1.4 

1.5 
1.4 
1.4 
1.4 
1.4 

1.5 
1.4 
1.4 
1.4 
1.3 

1.4 
1.4 
1.4 
1.3 
1.3 

1.4 
1.4 
1.4 
1.3 
1.3 

1.4 
1.4 
1.3 
1.3 
1.3 

1.4 
1.3 
1.3 
1.3 
1.3 

1.3 
1.3 
1,3 
1.3 
1.2 

1.3 
1.3 
1.3 
1.2 
1.2 

1,3 
1,3 
1.2 
1,2 
1,2 

1,3 
1.3 
1.2 
1.2 
1.2 

1.3 
1.2 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.2 
1.2 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

1.3 
1.3 
1.3 
1.2 
1.2 

1.3 
1.3 
1.3 
1.2 
1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

1.3 
1.3 
1.2 
1.2 
1.2 

1.3 
1.2 
1.2 
1.2 
1.2 

1.2 
1.2 
1.2 
1.2 
1.1 

1.2 

1.2 
1.2 
1.1 
1.1 

1.2 
1.2 
1.2 
1.1 
1.1 

1.2 
1.2 
1.1 
1.1 
1.1 

1,2 
1.2 
1.1 
1.1 
1.1 

1.2 
1.1 
1.1 
1.1 
1.1 

1.1 
1,1 
1,1 
1,1 

1.1 
1.1 
1.1 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

1.2 
1.2 
1.1 
1.1 
1.1 

1.2 
1.1 
1.1 
1.1 
1.0 

1.2 
1.1 
1.1 
1.1 
1.0 

1.1 
1.1 
1.1 
1.1 
1.0 

1.1 
1.1 
1.1 
1.0 
1,0 

1.1 
1.1 
1.1 
1.0 
1.0 

1.1 
1.1 
1.0 
1.0 

1.1 
1.1 

1.0 

1,1 
1,0 

1.1 

50 
51 
52 
53 
54 

55 

56 

57 
58 
59 
60 

1.0 
1.0 
1.0 
1.0 
0.9 

1.0 
1.0 
1.0 
0.9 

1.0 
1.0 
1.0 

1.0 
1.0 

1.0 

55 
56 
57 
58 
59 
60 

0.8 
0.8 

0,8 

25° 

2G° 

27° 

28° 

29° 

80° 

31° 

82° 

88° 

84° 

85° 

86° 

87° 

Declination  of  the  Hanie  name  as  the  latitude;  lower  transit;  reduction  subtraotlve. 

TABLE 

26. 

[Page  549 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Declination  of  a  different  name  from  the  latitude;  upper  transit;  reduction  additive. 

Lati- 
tude. 

o 

Lati- 
tude. 

88° 

89° 

40° 

41° 

42° 

48° 

44° 

45° 

46° 

47° 

48° 

49° 

60° 

II 

II 

"       1 

II 

II 

II 

II 

II 

II 

II 

II 

II 

II 

o 

0 

2.5 

2.4 

2.3 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

1.7 

0 

1 

2.5 

2.4 

2.3 

2.2 

2.1 

2.1 

2.0 

1.9 

1.9 

1.8 

1.7 

1.7 

1.6 

1 

2 

2.4 

2.3 

2.3 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

2 

3 

2.4 

2.3 

2.2 

2.1 

2.1 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.6 

1.6 

3 

4 

2.3 

2.2 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

4 
5 

5 

2.3 

2.2 

2.1 

2.1 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.5 

6 

2.2 

2.2 

2.1 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

6 

7 

2.2 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.5 

1.5 

7 

8 

2.1 

2.1 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

8 

9 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

9 

10 

2.1 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

1.4 

10 

11 

2.0 

2.0 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

11 

12 

2.0 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

12 

13 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

13 

14 

1.9 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

14 

15 

1.9 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

15 

16 

1.8 

1.8 

1.7 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

16 

17 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

17 

18 

1.8 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

18 

19 

1.7 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

19 

20 

1.7 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

20 

21 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1,3 

21 

22 

1.7 

1.6 

1.6 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

22 

23' 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.2 

23 

24 

1.6 

1.6 
1.5 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

24 

25 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

25 

26 

1.6 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

26 

27 

1.5 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

27 

28 

1.5 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

28 

29 

1.5 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

29 

30 

1.5 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

30 

31 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

31 

32 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

32 

33 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

33 

34 

1.4 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

34 

35 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

35 

36 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

36 

37 

1.3 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

37 

38 

1.3 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

38 

39 

1.2 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

39 

40 

1.2 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

40 

41 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

. 

41 

42 

1.2 

1.2 

1.1 

1.1 

1.1 

42 

43 

1.2 

1.1 

1.1 

1.1 

43 

44 

1.1 

1.1 

1.1 

44 

45 
46 
47 
48 
49 

1.1 
1.1 

1.1 

45 
46 

47 
48 
49 

0.9 
0.9 
0.9 
0.8 

0.9 
0.9 
0.9 

0.9 
0.9 

0.9 

50 
51 
52 
53 
54 
55 
56 
57 
58 

0.9 
0.9 
0.9 
0.8 
0.8 

0.9 
0.9 
0.8 
0.8 
0.8 

0.9 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

50 
51 
52 
53 
54 

0.9 
0.9 
0.8 
0.8 

0.9 
0.9 
0.8 

0.9 
0.9 

0.9 

0~9' 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.7 

0.8 
0.8 
0.7 
0.7 

0.8 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 

55 
56 

57 
58 

0.8 
0.8 
0.8 

0.8 
0.8 

0.8 

59 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

59 

60 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

60 

38° 

89° 

40° 

41° 

42° 

48° 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

Dec 

lination 

of  the  N 

ime  nan 

16  as  the 

latitude 

;  lower 

transit; 

reductio 

n  Hnbtrii 

ctlve. 

Page  550] 

TABLE 

26. 

Variation  of  Altitude  in  one  minute  from  meridian  passage. 

Declination  of  a  different  name  from  the  latitude:  uuner  transit:  reduction  additlre. 

Lati- 
tude. 

o 

0 

Lati- 
tude. 

0 

0 

61° 

62° 

58° 

64°. 

66° 

56° 

57° 

68° 

59° 

60° 

61° 

62° 

68° 

1.6 

1.5 

1.5 

II 
1.4 

II 
1.4 

II 
1.3 

II 
1.3 

\%^ 

II 
1.2 

! 
1.1 

II 
1.1 

1.0 

1.0 

1 

1.6 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

1.1 

1.0 

1.0 

1 

2 

1.5 

1.5 

f.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

2 

3 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

3 

4 

1.5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

4 

5 

1.5 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

5 

6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

6 

7 

1.4 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

0.9 

7 

8 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

0.9 

8 

9 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

9 

10 

1.4 

1.4 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

10 

11 

1.4 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

11 

12 

1.4 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

0.9 

0.9 

12 

13 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

13 

14 

1.3 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

14 

15 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

15 

16 

1.3 

1.3 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

16 

17 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

17 

18 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

18 

19 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

19 

20 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

0.8 

20 

21 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

0.8 

21 

22 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

22 

23 

1.2 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

0.9 

0.9 

23 

24 

1.2 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

"0.9 

24 

25 

1.2 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

0.9 

25 

26 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

0.9 

26 

27 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

27 

28 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

28 

29 

1.1 

1.1 

1.0 

1.0 

1.0 

29 
30 

30 

1.1 

1.1 

1.0 

1.0 

31 

1.1 

1.0 

1.0 

31 

32 
33 
34 

1.1 
1.1 

1.0 

32 
33 
34 

0.8 
0.7 

0.8 

35 
36 
37 
38 
39 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 

35 
36 
37 
38 
39 

0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 

0.8 
0.8 

0.8 

40 
41 
42 
43 
44 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.8 
0.8 

0.8 
0.8 
0.8 
0.7 
0.7 

0.8 
0.7 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 

0.7 
0.7 
0.7 
0.7 
0.7 

40 
41 
42 
43 
44 
45 

0.9 
0.8 
0.8 
0.8 

0.9 
0.9 
0.8 

0.9 
0.9 

0.9 

45 

0.9 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

46 

0.9 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

46 

47 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

47 

48 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

48 

49 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

49 

50 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

50 

51 

0.8 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

51 

52 

0.8 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

52 

53 

0.8 

0.8 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

53 

54 

0.8 

0.7 

1    0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

54 
55 

55 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

56 

0.7 

0.7 

!    0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

56 

57 

0.7 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

57 

58 

0.7 

0.7 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

58 

59 

0.7 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.5 

59 

60 
1 

0.7 

0.7 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.5 

60 

51° 

52° 

58° 

64° 

55° 

56° 

67° 

58° 

59° 

60° 

61° 

62° 

68° 

D 

eclinatl( 

)n  of  the 

same  nc 

ime  as  t 

be  latitu 

de;  low€ 

r  transi 

I  reduc 

ion  subt 

ractlre. 

TABLE 

27. 

■ 

[Page 

551 

Reduction  to  be  a 

pplied 

to  Altitudes  near  the  Meridian. 

Var. 

Time  from  meridian  passage. 

Var. 
1  min. 
(Table 

(Table 

TO.   S. 

TO.  8. 

TO.   S. 

TO.  8. 

TO.  8. 

TO.  8. 

TO.  8. 

TO.  8. 

TO.   8. 

TO.  8. 

TO.   8. 

TO.  8. 

TO.   8. 

26.) 

0  30 

1  0 

1  30 

2  0 

2  30 

3  0 

3  30 

4  0 

4  30 

5  0 

o  30 

6  0 

6  30 

26.) 

II 

/    II 

/     II 

/     // 

/     // 

/     // 

1    II 

/    // 

1     II 

'     II 

/    II 

'     II 

'     // 

'     II 

II 

0.1 

0  0 

0    0 

0    0 

0    0 

0    1 

0    1 

0    1 

0     2 

0     2 

0     2 

0    3 

0    4 

0     4 

0.1 

0.2 

0  0 

0    0 

0    0 

0    1 

0    1 

0    2 

0    3 

0    3 

0    4 

0    5 

0    6 

0    7 

0     8 

0.2 

0.3 

0  0 

0    0 

0    1 

0    1 

0    2 

0    3 

0    4 

0    5 

0    6 

0    7 

0    9 

0  11 

0  13 

0.3 

0.4 

00 

0    0 

0    1 

0    2 

0    2 

0    4 

0    5 

0    6 

0    8 

0  10 

0  12 

0  14 

0  17 

0.4 

0.5 

0  0 

0    0 

0     1 

0    2 

0    3 

0    4 

0    6 

0    8 

0  10 

0  12 

0  15 

0  18 

0  21 

0.5 

0.6 

0  0 

0     1 

0    1 

0    2 

0    4 

0    5 

0    7 

0  10 

0  12 

0  15 

0  18 

0  22 

0  25 

0.6 

0.7 

0  0 

0    1 

0    2 

0    3 

0    4 

0    6 

0    9 

0  11 

0  14 

0  17 

0  21 

0  25 

0  30 

0.7 

0.8 

0  0 

0    1 

0    2 

0    3 

0    5 

0    7 

0  10 

0  13 

0  16 

0  20 

0  24 

0  29 

0  34 

0.8 

0.9 

0  0 

0     1 

0    2 

0    4 

0    6 

0    8 

0  11 

0  14 

0  18 

0  22 

0  27 

0  32 

0  38 

0.9 

1.0 

0  0 

0     1 

0    2 

0    4 

0    6 

0    9 

0  12 

0  16 

0  20 

0  25 

0  30 

0  36 

0  42 

1.0 

2.0 

0  0 

0    2 

0    4 

0    8 

0  12 

0  18 

0  24 

0  32 

0  41 

0  50 

1    0 

1  12 

1  24 

2.0 

3.0 

0  1 

0    3 

0    7 

0  12 

0  19 

0  27 

0  37 

0  48 

1     1 

1  15 

1  31 

1  48 

2     6 

3.0 

4.0 

0  1 

0    4 

0    9 

0  16 

0  25 

0  36 

0  49 

1    4 

1  21 

1  40 

2    1 

2  24 

2  49 

4.0 

5.0 

0  1 

0    5 

0  11 

0  20 

0  31 

0  45 

1     1 

1  20 
1  36 

1  41 

2    5 

2  31 

3    0 

3  31 

5.0 
6.0 

6.0 

0  1 

0    6 

0  13 

0  24 

0  37 

0  54 

1  13 

2     1 

2  30 

3    1 

3  36 

4  13 

7.0 

0  2 

0    7 

0  16 

0  28 

0  44 

1     3 

1  26 

1  52 

2  22 

2  55 

3  32 

4  12 

4  56 

7.0 

8.0 

0  2 

0    8 

0  18 

0  32 

0  50 

1  12 

1  38 

2    8 

2  42 

3  20 

4    2 

4  48 

5  38 

8.0 

9.0 

0  2 

0    9 

0  20 

0  36 

0  56 

1  21 

1  50 

2  24 

3    2 

3  45 

4  32 

5  24 

6  20 

9.0 

10.0 

0  2 

0  10 

0  22 

0  40 
0  44 

1     2 

1  30 

2    3 

2  40 
2  56 

3  23 

4  10 

5    2 

6    0 

7    2 

10.0 

11.0 

0  3 

0  11 

0  25 

1    9 

1  39 

2  15 

3  43 

4  35 

5  32 

6  36 

7  45 

11.0 

12.0 

0  3 

0  12 

0  27 

0  48 

1  15 

1  48 

2  27 

3  12 

4    3 

5    0 

6    3 

7  12 

8  27 

12.0 

1.3.0 

0  3 

0  13 

0  29 

0  52 

1  21 

1  57 

2  39 

3  28 

4  23 

5  25 

6  33 

7  48 

9    9 

13.0 

14.0 

0  3 

0  14 

0  31 

0  56 

1  27 

2    6 

2  51 

3  44 

4  43 

5  50 

7    4 

8  24 

9  51 

14.0 

15.0 

0  4 

0  15 

0  34 

1     0 
1    4 

1  34 

2  15 

3    4 

4    0 

5    3 

6  15 

7  34 

9    0 

10  34 

15.0 
16.0 

16.0 

0  4 

0  16 

0  36 

1  40 

2  24 

3  16 

4  16 

5  24 

6  40 

8    4 

9  36 

11  16 

17.0 

0  4 

0  17 

0  38 

1     8 

1  46 

2  33 

3  28 

4  32 

5  44 

7    5 

8  34 

10  12 

11  58 

17.0 

18.0 

0  4 

0  18 

0  40 

1  12 

1  52 

2  42 

3  40 

4  48 

6    4 

7  30 

9    4 

10  48 

12  40 

18.0 

19.0 

0  5 

0  19 

0  43 

1  16 

1  59 

2  51 

3  53 

5    4 

6  25 

7  55 

9  35 

11  24 

13  23 

19.0 

20.0 

0  5 

0  20 

0  45 

1  20 

2    5 

3    0 

4    5 

5  20 

6  45 

8  20 

10    5 

12    0 

14    5 
14  47 

20.0 
21.0 

21.0 

0  5 

0  21 

0  47 

1  24 

2  11 

3    9 

4  17 

5  36 

7    5 

8  45 

10  35 

12  36 

22.0 

0  5 

0  22 

0  49 

1  28 

2  17 

3  18 

4  30 

5  52 

7  25 

9  10 

11     5 

13  12 

15  29 

22.0 

23.0 

0  6 

0  23 

0  52 

1  32 

2  24 

3  27 

4  42 

6    8 

7  46 

9  35 

11  36 

13  48 

16  12 

23.0 

24.0 

0  6 

0  24 

0  54 

1  36 

2  30 

3  36 

4  54 

6  24 

8    6 

10    0 

12    6 

14  24 

16  54 

24.0 

25.0 

0  6 

0  25 

0  56 

1  40 

2  36 

3  45 

5    6 

6  40 

8  26 

10  25 

12  36 

15    0 

25.0 

26.0 

0  6 

0  26 

0  58 

1  44 

2  42 

3  54 

5  18 

6  56 

8  46 

10  50 

13    6 

26.0 

27.0 

0  7 

0  27 

1     1 

1  48 

2  49 

4    3 

5  30 

7  12 

9    7 

11  15 

27.0 

28.0 

0  7 

0  28 

1     3 

1  52 

2  55 

4  12 

5  43 

7  28 

9  27 

11  40 

28.0 

Page  662] 

TABLE  27. 

Reduction  to  be  applied  to  Altitudes  near  the  Meridian. 

Var. 
1  min. 

Time  from  meridian  passage. 

Var. 

(Table 

m.  8. 

m.  s. 

m.  s. 

m.  g. 

m.  s. 

m.  s. 

m.  s. 

m.   «. 

m.  8. 

m.   ». 

m.  s. 

m.  s. 

m.  K. 

(Table 

26.) 

7  0 

7  SO 

8  0 

H  SO 

»  0 

9  30 

10  0 

10  30 

11  0 

11  30 

12  0 

12  30 

13  0 

26.) 

0.1 

0    5 

0  6 

0  6 

0  7 

0  8 

'  " 

0  9 

0  10 

0  11 

/  II 

0  12 

0  13 

0  14 

1     II 
0  16 

1     II 

0  17 

0.1 

0.2 

0  10 

0  11 

g  13 
0  19 

0  14 

0  16 

0  18 

0  20 

0  22 

0  24 

0  26 

0  29 

0  31 

0  34 

0.2 

0.3 

0  15 

0  17 

0  22 

0  24 

0  27 

0  30 

0  33 

0  36 

0  40 

0  43 

0  47 

0  51 

0.3 

0.4 
0.5 

0  20 
0  24 

0  23 
0  28 

0  26 
0  32 

0  29 

0  32 

0  36 

0  40 

0  44 

0  48 

0  53 

0  58 

1  12 

1  2 

1  18 

1  8 

0.4 

0  36 

0  40 

0  45 

0  50 

0  55 

1  0 

1  6 

1  24 

0.5 

0.6 

0  29 

0  34 

0  38 

0  43 

0  49 

0  54 

1  0 

1  6 

1  13 

1  19 

1  26 

1  34 

1  41 

0.6 

0.7 

0  34 

0  39 

0  45 

0  51 

0  57 

1  3 

1  10 

1  17 

1  25 

1  33 

1  41 

1  49 

1  58 

0.7 

0.8 

0  39 

0  45 

0  51 

0  58 

1  5 

1  12 

1  20 

1  28 

1  37 

1  46 

1  55 

2  5 

2  15 

0.8 

0.9 

0  44 

0  51 

0  57 

1  5 

1  13 

1  21 

1  30 

1  39 

1  49 

1  59 

2  10 

2  21 

2  32 

0.9 

1.0 

0  49 

0  56 

1  4 

1  12 

1  21 

1  30 

1  40 

1  50 

2  1 

2  12 

2  24 

2  36 

2  49 

1.0 

2.0 

1  38 

1  52 

2  8 

2  24 

2  42 

3  0 

3  20 

3  40 

4  2 

4  24 

4  48 

5  12 

5  38 

2.0 

3.0 

2  27 

2  49 

3  12 

3  37 

4  3 

4  30 

5  0 

5  31 

6  3 

6  37 

7  12 

7  49 

8  27 

3.0 

4.0 

3  16 

3  45 

4  16 

4  49 

5  24 

6  1 

6  40 

7  21 

8  4 

8  49 

9  36 

10  25 

11  16 

4.0 

5.0 

4  5 

4  41 

5  20 

6  1 

6  45 

7  31 

8  20 

9  11 

10  5 

11  1 

12  0 

13  1 

14  5 

5.0 

6.0 

4  54 

5  37 

6  24 

7  14 

8  6 

9  1 

10  0 

11  1 

12  6 

13  13 

14  24 

15  37 

16  54 

6.0 

7.0 

5  43 

6  34 

7  28 

8  26 

9  27 

10  32 

11  40 

12  52 

14  7 

15  26 

16  48 

18  14 

19  43 

7.0 

8.0 

6  32 

7  30 

8  32 

9  38 

10  48 

12  2 

13  20 

14  42 

16  8 

17  38 

19  12 

20  50 

22  32 

8.0 

9.0 

7  21 

8  26 

9  36 

10  50 

12  9 

13  32 

15  0 

16  32 

18  9 

19  50 

21  36 

23  26 

25  21 

9.0 

10.0 

8  10 
8  59 

9  22 
10  19 

10  40 

11  44 

12  2 

13  30 

14  51 

15  2 

16  33 

16  40 

18  22 

20  10 

22  2 

24  0 

26  2 

28  10 

10.0 
11.0 

11.0 

13  15 

18  20 

20  13 

22  11 

24  15 

26  24 

28  39 

12.0 

9  48 

11  15 

12  48 

14  27 

16  12 

18  3 

20  0 

22  3 

24  12 

26  27 

28  48 

12.0 

13.0 

10  37 

12  11 

13  52 

15  39 

17  33 

19  33 

21  40 

23  53 

26  13 

28  39 

13.0 

14.0 

11  26 

13  7 

14  56 

16  51 

18  54 

21  3 

23  20 

25  43 

28  l4 

14.0 

15.0 

12  15 

14  4 

16  0 

18  14 

20  15 

22  34 

25  0 

27  34 

15.0 

16.0 

13  4 

15  0 

17  4 

19  16 

21  36 

24  4 

26  40 

16.0 

17.0 

13  53 

15  56 

18  8 

20  28 

22  57 

25  34 

17.0 

18.0 

14  42 

16  52 

19  12 

21  40 

24  18 

18.0 

19.0 

15  31 

17  49 

20  16 

19.0 

20.0 

16  20 

18  45 

20.0 

21.0 

17  9 

21.0 

TABLE 

27. 

[Page  553 

Reduction  to  be  applied  to  Altitudes  near  the  Meridian 

Var. 

Time  from  meridian  passage. 

Var. 
1  mln. 
(Table 

(Table 

m.  «. 

m.  8. 

TO.    S. 

m.  8. 

TO.    8. 

m.  8. 

TO.    «. 

TO.  8. 

TO.    8. 

m.  8. 

TO.    8. 

m.  s. 

TO.    8. 

26.) 

18  30 

14  0 

14  30 

15  0 

15  80 

16  0 

16  80 

17  0 

17  30 

18  0 

18  80 

19  0 

19  30 

26.) 

„ 

/    II 

/    II 

/    II 

/    II 

/    // 

/    II 

/    // 

/    // 

1    II 

/    II 

/    II 

/    II 

'     II 

„ 

0.1 

0  18 

0  20 

0  21 

0  22 

0  24 

0  26 

0  27 

0  29 

0  31 

0  32 

0  34 

0  36 

0  38 

0.1 

0.2 

0  36 

0  39 

0  42 

0  45 

0  48 

0  51 

0  54 

0  58 

1    1 

1    5 

1    8 

1  12 

1  16 

0.2 

0.3 

0  55 

0  59 

1    3 

1    7 

112 

117 

122 

127 

132 

137 

143 

148 

154 

0.3 

0.4 

1  13 

1  18 

124 

130 

136 

1  42 

149 

156 

2    2 

2  10 

2  17 

2  24 

2  32 

0.4 

0.5 

131 

138 

145 

152 

2    0 

2    8 

2  16 

2  24 

2  33 

2  42 

2  51 

3    1 

3  10 

0.5 

0.6 

149 

158 

2    6 

2  15 

2  24 

2  34 

2  43 

2  53 

3    4 

3  14 

3  25 

3  37 

3  48 

0.6 

0.7 

2    8      2  17 

2  27 

2  37 

2  48 

2  59 

3  11 

3  22 

3  34 

3  47 

4    0 

4  13 

4  26 

0.7 

0.8 

2  26|    2  37 

2  48 

3    0 

312 

3  25 

3  38 

3  51 

4    5 

4  19 

4  34 

4  49 

5    4 

0.8 

0.9 

2  44      2  56 

3    9 

3  22 

3  36 

3  50 

4    5 

4  20 

4  36 

4  52 

5    8 

5  25 

5  42 

0.9 
1.0 

1.0 

3    2  i    3  16 

3  30 

3  45 

4    0 

4  16 

4  32 

4  49 

5    6 

5  24|    5  42 

6    1 

6  20 

2.0 

6    4  1    6  32 

7    0 

7  30 

8    0 

8  32 

9    4 

9  38 

10  12 

10  48    11  24 

12    2 

12  40 

2.0 

3.0 

9    7 

9  48 

10  30 

1115 

12    1 

12  48 

13  38 

14  27 

15  19 

16  12    17    7 

18    3 

19    1 

3.0 

4.0 

12    9 

13  14 

14    1 

15    0 

16    1 

17    4 

18    9 

19  16 

20  25 

2136 

22  49 

24    4 

25  21 

4.0 

5.0 

15  11 

16  20 

17  31 

18  45 

20    1 

2120 

22  41 

24    5 

25  31 

27    0 

28  31 

5.0 

6.0 

18  13 

19  36 

21    2 

22  30 

24    1 

25  36 

27  13 

6.0 

7.0 

21  16 

22  52 

24  32 

26  15 

28    1 

7.0 

8.0 

24  18 

26    8 

28    2 

8.0 

9.0 

27  20 

9.0 

Var. 

T 

ime  fror 

a  meridi 

anpasss 

ge. 

Var. 
1  mill. 

(Table 

m.  s. 

m.  «. 

m.  s. 

m.  8. 

TO.  8. 

TO.    8. 

TO.  8. 

TO.    8. 

TO.  8. 

TO.    8. 

TO.  8. 

TO.    8. 

TO.   8. 

(Table 

26.) 

20  0 

20  80 

21  0 

21  80 

22  0 

22  30 

23  0 

23  30 

24  0 

24  30 

25  0 

25  80 

26  0 

26.) 

II 

/    II 

'    // 

'      H 

'    II 

'    n 

/    n 

/    // 

/    II 

/    II 

/    II 

'    // 

/    // 

/     // 

II 

0.1 

0  40 

0  42 

0  44 

0  46 

0  48 

0  51 

0  53 

0  55 

0  58 

1    0 

1    2 

1    6 

1    8 

0.1 

0.2 

120 

124 

128 

132 

137 

141 

146 

150 

155 

2    0 

2    5 

2  10 

2  15 

0.2 

0.3 

2    0 

2    6 

2  12 

219 

2  25 

2  32 

2  39 

2  46 

2  53 

3    0 

3    7 

3  15 

3  23 

0.3 

0.4 

2  40 

2  48 

2  56 

3    5 

3  14 

3  22 

3  32 

3  41 

350 

4    0 

4  10 

4  20 

4  30 

0.4 

0.5 

3  20 

3  30 

3  41 

3  51 

4    2 

4  13 

4  24 

4  36 

4  48 

5    0 

5  12 

5  25 

5  38 

0.5 

0.6 

4    0 

4  12 

4  25 

4  37 

4  50 

5    4 

5  17 

5  31 

5  46 

6    0 

615 

6  30 

6  46 

0.6 

0.7 

4  40 

4  54 

5    9 

5  24 

5  39 

5  54 

6  10 

6  27 

6  43 

7    0 

7  17 

7  35 

7  53 

0.7 

0.8 

5  20 

5  36 

5  53 

6  10 

6  27 

6  45 

7    3 

7  22 

7  41 

8    0 

8  20 

8  40 

9    1 

0.8 

0.9 

6    0 

6  18 

6  37 

6  56 

7  16 

7  36 

7  56 

8  17 

8  38 

9    0 

9  22 

9  45 

10    8 

0.9 
1.0 

1.0 

6  40 

7    0 

7  21 

7  42 

8    4 

8  26 

8  49 

9  12 

9  36 

10    0 

10  25 

10  50 

1116 

2.0 

13  20 

14    0 

14  42 

15  24 

16    8 

16  52 

17  38 

18  24 

19  12 

20    0 

20  50 

2140 

22  32 

2.0 

3.0 

20    0 

21    0 

22    3 

23    7 

24  12 

25  19 

26  27 

27  37 

28  48 

30    0 

3.0 

4.0 

26  40 

28    1 

29  24 

4.0 

Page  554]  TABLE  28A. 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 
[A=l8t  correction.    Argument,  the  star's  hour  angle  (or  24i>— the  star's  hour  angle).] 

Qh  ih  2h  j  3h  1  41.  5h 


12  00.0 
11  59.9 
11  59.8 
11  59.6 
11  59.3 
11  58.9 
11  58.5 
11  58.0 
11  57.4 
11  56.7 


10 
11 
12 
13 
14 
15 
16 
17 
18 
19 


-1  11  55.9 

'  11  55.0 

11  54.1 

11  53.1 

11  52.0 

-1  11  50.8 
11  49.5 
1148.1 
11  46.7 
11  45.2 


20 
21 
22 
23 

24 
25 
26 

27 
28 
29 


11  43.6 
11  41.9 
11  40.1 
11  38.3 
11  36.3 
11  34.3 
11  32.2 
11  30.0 
11  27.8 
11  25.5 


30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 


-1  11  23.1 
11  20.6 
11  18.0 
11  15.3 
11  12.6 

-1  11  09.7 
11  06.8 
11  03.8 
11  00.8 

^057^ 

-1  10  54.4 
10  51.1 
10  47.7 
10  44.2 
10  40.7 

-1  10  37.0 
10  33.3 
10  29.5 
10  25.6 
10  21.7 

-1  10  17.6 
10  13.5 
10  09.3 
10  05.0 
10  00.7 

-1  09  56.2 
09  51.7 
09  47.1 
09  42.4 
09  37.7 

-1  09  32.8 


.0 
.1 
.1* 

.3 
.4 


-1 


-1 


-1 


09  32.8 
09  27.9 
09  22.9 
09  17.9 
09  12.7 
09  07.4 
09  02.1 
08  56.7 
08  51.3 
08  45.8 
08  40.2 
08  34.4 
08  28.6 
08  22.7 
08  16.8 
08  10.8 
08  04.7 
07  58.5 
07  52.3 
07  46.0 
07  39.6 
07  33.1 
07  26.5 
07  19.9 
07  13.1 
07  06.3 
06  59.5 
06  52.5 
06  45.5 
06  38.4 
06  31.2 
06  24.0 
06  16.7 
06  09.3 
06  01.8 
05  54.2 
05  46.6 
05  38.9 
05  31.1 
05  23.3 
05  15.3 
05  07.3 
04  59.3 
04  51.1 
04  42.9 
04  34.6 
04  26.2 
04  17.8 
04  09.3 
04  00.7 


— 1 


llh 


03  52.0 
03  43.3 
03  34.5 
03  25.6 
03  16.6 
03  07.6 
02  58.6 
02  49.4 
02  40.2 
02  30.8 
02  21.4 


4.9, 
5.0 
5.0; 

5.2, 
5.3 
5.3 

m; 

5.4' 

5.5| 
5.6, 
5.8 

5.8| 

5.9; 

5.9 
6.0 
6.1; 
6.2' 
6.2, 
6.3, 
G.4 
G.5 

6.6; 

6.6 

6.8 

6.8 

6.8 

7.0' 

7.0' 

7.1' 

7.2 

7.2 

7.3! 

7.4' 

7.5' 

7.6' 

7.6 

7.7^ 

7.8! 

7.8 

8.0 

8.0' 

8.0! 

8.2' 

8.31 
8.4|- 
8.4, 
8.5 

8.6; 

8.7;- 
8.7:  ■ 


9.0 

9.0; 
9.0: 

9.2 
9.2| 

9.4 
9.4 


-1  02  21 

02  11. 

02  02. 

0152. 

0143. 
-1  01  33. 

0123. 

0113. 

0103. 

00  53. 


4    — ' 
^  9.5 

9.5 

9.6 

9.7^ 


-1  00  43. 
00  33. 
00  23. 
00  12. 
00  02. 

-0  59  52, 
59  41 
59  31. 
59  20. 
59  09. 

-0  58  58, 
58  48, 
58  37, 
58  26 
58  15, 

-0  58  04 
57  52 
57  41 
57  30 
57  18 


-0  57  0 
56  56 
56  44 
56  32. 
56  21. 

-0  56  09. 
55  57. 
55  45. 
55  33. 
55  21. 

-0  55  09. 
54  57. 
54  45. 
54  32. 
54  20. 

-0  54  08. 
53  55. 
53  43. 
53  30. 
53  18. 

-0  53  05 
52  52 
52  39 
52  26 
52  13 

-0  52  00 
5147 
5134 
5121 
5108, 

-0  50  54, 


9.8: 
9.9; 

10.0' 

I 

10.1 

10.2 

10.21 

IO.3I 

10.3: 

10.5| 

10.5 

10.6 

10.6; 

10.7; 

10.8 

10.9' 

10.9! 

10.9 

11.1 

ll.l| 

11.2' 

11.2; 

11.3 

11.4' 

I 

11.4 

11.6 

11.6 

11.6 

11.7' 

11.8 

11.8: 

11.9 

12.0' 

12.0 

12.1 

12.1 

12.2 

12.3| 

12.3 

12.4! 

12.5j 

12.5, 

12.6 

12.6 

12.7 

12.8 

12.8; 

12.9 

13.0 

13.0 

13.0 

13.1 

13.2 

13.3 

13.3 


-0  50  54. 
50  41. 
50  28. 
50  14. 
50  01. 

-0  49  47. 
49  33. 
49  20. 
49  06. 
48  52. 

-0  48  38. 
48  24. 
48  10. 
47  56. 
47  42. 

-0  47  28. 
47  14, 
47  00. 
46  45. 
46  31, 

-0  46  17 
46  02 
45  48 
45  33 
45  18 

-0  45  04 
44  49 
44  34 
44  19 
44  04 

-0  43  50 
43  35 
43  20 
43  05 
42  49 

-0  42  34 
42  19 
42  04 
4148 
4133 


-0  41  18 
4102 
40  47 
40  31 
4016 

-0  40  00, 
39  44 
39  28 
39  13 
38  57 


-0  38  41 
38  25 
38  09 
37  53 
37  37 

-0  37  21 
37  05 
36  48 
36  32 
36  16 

-0  36  00 


13.3 
13.4; 
13..5 
13.5 
13.6; 
13.7, 
13.71 
13.7 

13.8: 
13.9, 
14.0 
14.0 
14.0 
14.1 
14.1 
14.2 
14.2 
14.3; 
14.4, 
•14.4 
14.5 
14.5; 
14.6] 
14.6 
14.7| 
14.8 
14.8! 

14.8; 

14.9 

i 
14.9 

15.0 

15.0! 

15.0' 

15.1! 

15.2; 

15.2J 

15.3 

15.3; 

15.3: 

15.4 

15.5; 

15.5 

15.6' 

15.6| 

15.71 

15.7 

15.7; 

15.8; 

15.8 

15.9 

15.9 

16.0 

16.0 

16.1 

16.1 

16.2 

16.2 

16.3 

16.3 

I6.3! 


-0  36  00 

35  43 
35  27 
35  10. 
34  54. 

-0  34  38. 
34  21. 
34  05. 
33  48. 
33  31. 

-0  33  15^ 
32  58. 
32  41, 
32  24. 
32  07, 

-0  31  50, 
31  34, 
31  27, 
31  10, 
30  53, 

-0  30  36, 
30  18, 
30  01, 
29  44, 
29  17, 

-0  29  00, 
28  42, 
28  25 
28  08 
27  50 


-0  27  33 
27  16 
26  58 
26  41 
26  23 

-0  26  05 
25  48 
25  30 
25  13 
24  55 


-0  24  37 
24  20 
24  02 
23  44 
23  26 

-0  23  08 
22  50 
22  33 
22  15 
2157 

-0  21  39 
2121 
2103 
20  45 
20  27 

-0  20  09 
19  50 
19  32 
19  14 
18  56 

-0  18  38 


16.3 
16.4 
16.4 
16.4 
16.4 
16.5 
16.6; 
16.6 
16.7 
16.7 
16.8 
16.8 
16.8 
16.8 
16.9 
I6.9; 
16.9 
17.0 
17.1; 

17.0 
17.1 
17.2 
17.2 
17.2 
17.2 
17.3j 

17.3; 

17.4; 

17.4 

17.4 

17.5 

17.5: 

17.5; 

17.6 

17.6 

17.6 

17.6 

17.7 

17. 

17.7 

17.8 

17.8! 

17.8 

17.8' 

17.9 

17.9 

17.9 

17.9 

18.0 

18.0 

18.0 

18.0, 

18.1 

18.1 

18.1 

18.1 

18.2 

I8.2' 

18.2 


4 
.0 
.5 
0 
5 
9 
3 
.7 
.1 
A 
.7  ,--  — 


-0  18  38. 
18  20. 
18  01. 
17  43. 
17  25. 

-0  17  06. 
16  48. 
16  30. 
16  11. 
15  53. 

-0  15  35 
15  16. 
14  58. 
14  39 
14  21, 

-0  14  03 
13  44 
13  26, 
13  07 
12  48 

-0  12  30. 
12  11, 
1153. 
1134. 
1115. 

-0  10  57 
10  38 
10  20 
10  01 
09  42 

-0  09  24 
09  05 
08  46 
08  27 
08  09 


-0  07  50 
07  31 
07  12, 
06  54 
06  35 


lOh 


9h 


Sh 


Ih 


0  06  16 
05  57 
05  39 
05  20 
05  01 

-0  04  42 
04  23 
04  05 
03  46 
03  27 

-0  03  08 
02  49 
02  30 
02  12 
01  53 

-0  01  34 
0115 
00  56 
00  37 
00  18 

-0  00  00, 

01' 


18.2 

18.2 

18.3 

18.3 

18.3 

18.3 

18.3 

18.4 

18.4 

18.4' 

18.4! 

I8.4! 

18.4' 

18.4J 

18.5! 

I8.5; 

18.5 

18.5 

18.6; 

18.6- 

18.6| 

18.6 

18.6 

18.6 

18.7 

18.6 

18.6 

18.6 

I8.7' 

18.7- 

18.7| 

18.71 

I8.7' 

18.7 

18.7; 

18.71 

18.7; 

18.8! 
18.8 
18.7 

18.8' 
18.8; 
18.8, 

18.8; 

18.8' 
18.8! 
18.8 
18.8 
18.8 
18.9 

18.8; 

18.8 
18.9 
18.8 
18.8 
18.9 
18.8 
18.9 
18.9 
18.9 


60 
59 
58 
57 
5<> 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 
44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
18 
17 
16 
15 
14 
13 
12 
Jl_ 
10 


Change  the  sign  to  +  when  the  argument  is  found  at  tlie  bottom. 


TABLE  28B. 

[Page  555 

For  finding  the  Latitude  of  a 

L  place  by  Altitudes  of  Polaris. 

[B=the  2d  correction.    This  correction  is  always  additive.] 

Star's 

Star's  altitude.                                                                             1 

star's 
hour 
angle. 

hour 
angle. 

10° 

15° 

16° 

17° 

18° 

^  19° 

20° 

21° 

22° 

23° 

h.  m. 

// 

// 

II 

II 

II 

// 

// 

II 

II 

//      ' 

h.    m. 

0  00 

0.0   0 

0.0   0 

0.0   0 

0.0    n 

0.0   0 

0-0.0 

0-0.0 

0-0.0 

0.0.0 

0-0.0 

12  00 

10 

0.0 ', 

0.0? 

0.0 ', 

0.0 

1 

0.0   1 

0.0  " 

0.0   1 

0.0   " 

0.0  1 

0.0  1 

11  50 

20 

0.1- 

0.1- 

0.1- 

0.1 

\ 

0.1  •; 

0.1  •; 

0.1     0 

0.1  \ 

0-1  \ 

0.1  \ 

40 

30 

0.2  \ 

0.2' 

0.2' 

0.2 

0 

0.2  \ 

0.2 1 

0.3-2 

0.3-5 

0.3-3 

0.3-3 

30 

40 

0.3- 

0.3   2 

0.4" 

0.4 

0 

0.4'^ 

0.5-3 

0.5-3 

0.5-3 

0-63 

0-6-3 

20 

50 

0.4- 

0.5    t, 

0.6' 

0.6 

3 

0.7 -J 

0.8-3 

0.8   3 

0.8-3 

0-9-3 

0.9 -, 

10 

1  00 

0.5- 

0._8- 

1.1  ! 

0.9- 

0.9 

3 

1.0- 

1-1  ■, 

1-1 

1-1  ■ 

1.2' 

1.3' 

00 

10 

0.7-; 

1.2-3 

1-8  1 
2.3-5 
2.8- 

3- 2' 

1.2 

1.3-4 

1.4-^ 

1-45 

1.5-5 

1.6 -J 

1-75 

10  50 

20 

1.1 'll  1.8  •: 

1.4 -'l     2.2-! 

1.6 

1.7-1 

2.6 -J 

3-1  1 
3.6- 

1-8-6 

1-9  1 

2-0 -J 

2-1  1 

2-7- 

2-2-6 

40 

30 

2.0 

i 

2.3-, 

2-4 -5 

2-5-6 

2-8-6 

30 

40 

2.4 

2-8  1 

2-9-6 

3-1  1 

3.7- 

4.4-^ 

3-2  •« 

3.8-; 

4.5-^ 

a 

3-4-6 

20 

50 

1.7- 

2.0"' 

2.3-^ 

2.6-4 

3.5 -J 

2.9 

3-3 -fi 
3.9- 

3-5-6 

4.0-5 

10 

2  00 

3.4 

ts 

4.1- 

4.7- 

00 

10 

3.7 -fi 
4.3- 
4.8 -J 
5.3-! 
5-9 -« 

7-0  1 
8.7-, 

3.9 

6 
6 
6 

4.9 -J 
5.5 -J 

6.7-; 
7.4-^ 

4-5    fi 
5.1- 
5.8-' 
6.4- 

7.1-; 

8.4-? 
9.1- 
9.8  •' 

10.4 -; 

4.8-; 

5.4- 

6.1 -; 

6.8-, 

7.5-; 
8.3-^ 

5.0-5 

5.7-; 
6.4-; 

8.7-^ 

9.4 -J 
10.2  -, 
10.9  -, 
11.6 -, 

5.3-5 
6-0  •; 

6.8-5 

8.3 -J 
9.1  •* 

5.6-" 

7-1    8 
7-9-8 
8-7-8 

9  50 

20 

2.6-: 

4.0  •; 

4.5 

40 

30 

2.9'^ 

4.5-^ 

5.1 

30 

40 

3.3   t 

5.0-:^ 

5.7 

20 

50 

3.6'^ 

5.5 -J 

6.3 

10 

3  00 

4.0-'' 

6.0-^ 

6.9 

6 
6 
5 
6 
6 

00 

10 

4.3 -J 

6.6-^ 

7.5 

8-0  •« 

8.9-2 

9-6 -« 

10.4-^ 

9.9 -J 
10.  7 -J 

10.4 -' 
11-3-8 

12-1-8 
12.9-^ 

8  50 

20 

4.7-^ 

7.1 -J 

8.1 

8.6-' 

40 

30 

5.0-^ 

7.6-; 

8.6 

9.2-5 

11.5  -, 

30 

40 

5.3 -J 

8.1  •; 

9.2 

9-9   I 

11.0  •? 

12.2 -J 

20 

50 

5.7-^ 

8.6-^ 

9.2-^ 

9.8 

10.5-^ 

11.1  •! 

11.  7-' 

12.3  •; 

13.0-5 

13.  7-! 

10 

4  00 

6.0-^ 

9.1-^ 

9.7-^ 

10.4 

h 

11.0-^ 

11.7-'^ 

12.3-" 

13.0-^ 

13.7-^ 

14.4-^ 

00 

10 

6.3-^ 

9.6-;; 

10.2-^ 

10.9 

11.6-^ 

12.2-^ 

13.0-^ 

13.6-^ 

14-3 -' 

15.0-5 

7  50 

20 

6.6, 

10.0'^ 

10.7-^ 

11.3 

12.1  1 

12.8  ■. 

13.6-° 

14.3-^ 

14.9-^ 

15-7 -„ 

40 

30 

6.8-^ 

10.4-^ 

11. 1-! 

11.7 

12:5 -f 

13.3-^ 

14.  0-* 

14.8  -, 

15.6  •! 

16.3-^ 

30 

40 

7.0- 

10.8 -J 

11.4^ 

12.1 

13.0 -, 

13.8  -, 

14.5-^ 

15.3-^ 

16.1  -l 

16.9-° 

20 

50 

7.3-^ 

11.1  -l 

11.8 -J 

12.5 

4 

13.4 -J 

14.2   J 

15.0-^ 

15.8    , 

16.6-^ 

17.5-^ 

10 

5  00 

7.5-^ 

11.4-^ 

12.1  -^ 

12.9 

13.7  -^ 

14.5  -^ 

15.4-^ 

16.2-^ 

17.1  -^ 

17.9-^ 

00 

10 

7.6-; 

11.6-^ 

12.4 -J 

13.2 

14.0 -J 

14.8-^ 

15.7-^ 

16.5-^ 

17.4-3 

18.3-^ 

6  50 

20 

7.8 -f 

11.7-^ 

12.6   , 

13.4 

2 

14.2  ■; 

15.1  -l 

16.0-^ 

16.8-^ 

17.7-^ 

18.6-^ 

40 

30 

7.9-, 

11.9    f 

12.7  ■, 

13.6 

14.4-2 

15.3-2 

16.2  -; 

17.1-.' 

18.0  -^ 

18.9  -f 

30 

40 

7.9-^ 

12.0  "I 

12.9  -f 

13.7 

14.6  -^ 

15.5-2 

16.4-2 

17.3-2 

18.1  -^ 

19.0 -, 

20 

50 

7.9-^ 

12.1  -^ 

13.0 -^ 

13.8 

14.  7 -^ 

15.6 -^ 

16.5-^ 

17.3  •« 

18.2-1 

19.1  ■] 

10 

6  00 

7.9-^ 

12.2-^ 

13.0  •" 

13.9-^ 

14.7-° 

15.6-0 

16.5  •" 

17.3-0 

18.3  -1 

19.2-1 

6  00 

TABI 

.E  28C. 

[C=the  3d  correction. 

Hor.  Arg. 

the  star's 

declination.    Vert.  Arg.,  B=the 

2d  correct 

ion.] 

B. 

88°  47' 

88°  48' 

88°  49'               1 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

80" 

40" 

50" 

0" 

10" 

20" 

// 

// 

« 

II 

II 

II 

1          " 

II 

II 

II 

II 

II 

II 

II 

0 

0.0 

0.0 

0.0 

0.0 

o.c 

)         0.0 

0.0 

0.0 

0.0 

0.0 

0 

.0 

0.0 

0.0 

10 

+0.2 

+0.1 

+0.1 

+ 

0.0 

0.( 

)     -0.0 

-0.1 

-0.1 

-0.2 

- 

-0.2 

-0 

.3 

—0.4 

-0.4 

20 

0.4 

0.3 

0.2 

0. 1     0.  ( 

)         0.1 

t      0.2  ;      0.3 

0.4 

0.5 

0 

.6 

0.7 

0.8 

30 

0.6 

0.5 

0.3 

0.1 

o.c 

)         0.1 

0.  3         0.  5 

0.6 

0.7 

0 

.8 

1.1 

1.2 

40 

0.8 

0.6 

0.4 

0.2 

o.c 

)         0.2 

0.4 

0.6 

0.8 

1.0 

1 

.2 

1.5 

1.6 

50 

+1.0 

4-0.7 

+0.5 

+ 

0.2 

o.c 

)      -0.2 

0.5 

-0.9 

-1.0 

- 

-1.2 

-1 

.5 

-1.7 

-2.1 

Note. — Below  15°  B  is  nearly  proportional  to  the  altitude. 


Page  656] 

TABLE  28B 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

[B=the  2d  correction.    This  correction 

is  always  additive.] 

Star's 
hour 

Star's  altitude.                                                                         1 

SUir's 
hour 

angle. 

24° 

26° 

26° 

27° 

28° 

28° 

80° 

31° 

82° 

Z9fi 

angle. 

h.   m. 

»  II 

II 

// 

II 

// 

// 

// 

II 

II 

II 

h.    in. 

0  00 

0.0    „ 

0-0.0 

0.0    . 
0.0   l 

0.2  •; 
0.4  l 
0.7  l 

1-1  1 
1.5  •" 

0.0    ^ 
0.0  -l 
0.2  -i 

0.4    l 
0.7  -^ 

1.1    4 

1.5  -^ 

0.0    „ 
0.0  •° 
0.2  -i 

0.4  'l 
0.7    l 

1-1 1 

1.6  -^ 

0.0    „ 
0.0  •° 
0.2  -t 
0.4  'l 
0.7    l 
1.1   -J 
1.7  ■' 
2.3  -^ 

2.9  ■; 

3.6  •; 

0.0    ^ 
0.0  •° 
0.2  -t 
0.4  'l 
0.8    , 
1.2  -J 
1.7  -^ 

0.0    ^ 
0.0  •" 

0.0    „ 

0.0    ,, 

12  00 

10 

0.0  -J 

0.  o*-? 

0.0  •; 

0.0  -° 

11  50 

20 

0.1  • 

0.1  i 

0.2  •; 
0.5  5 

0.2  -2 

0.2  -2 

40 

80 

0.3  •: 

0.3   -^ 

0.5  \ 

0.5  -, 

30 

40 

0.6   ■, 

0.6    . 

0.8  ■: 
1.3  -^ 

0.8  z 

1.3  -l 

0.9  -. 

20 

50 

1.0  ■' 

1.0    J 

1.4  'X 

10 

1  00 

1.4   ■' 

1.4  •' 

1.9  •; 

1.8  •' 

1.9  •'^ 

1.9  -' 

00 

10 

1.8   ■' 

2.0  i 

2.1  -^ 

2.2  -J 
2.8  •; 
3.5  l 

4.3  -^ 
5.1  -l 

2.3  ■; 

3.0  -J 
3.8  -l 
4.7  -^ 
5.6  'l 
6.5  -^ 
7.51-° 

2.4  -^ 

2.5  -^ 

2.6  -: 

10  50 

20 

2.3  ■: 

2.4  -l 

2.5  , 

2.7  -^ 

3.2  -J 

3.3  'l 

3.4  'l 

40 

30 

2.9    ! 

3.1  ■; 

3.8  •; 

3.2  ■; 

3.4    ! 

4.0  -l 

4.1  -^ 

4-3/0 

30 

40 

3.6  •: 

4.0  -i 
4.7  •! 

4-1  ■« 

4.5  -l 

5.3  ■; 

4.9  •; 

S-Oi'o 

5.31-° 

20 

5f) 

4.3  •: 

4.5   -l 

4.9  -^ 

5.8 -J 

6.0  -J 

6.2,-; 

10 

2  00 

5.0  ■' 

5.3  -^ 

5.5  ■« 

5.8  -^ 

6.0  -^ 

6.2  -^ 

6.8l-° 

7.0i-° 

7.  3  1-1 

00 

10 

5.8  -J 

6.1  •; 

6.4  -^ 

6.7  'l 

7.0l-° 

7.2i-° 

7.91-1 

8.  2 1-2 

8.51-2 

9  50 

20 

6.6  'l 

7.0  -^ 

7.3  -l 

7.6  -^ 

7-9,n 

8.3-1 

8.61-; 

8.9  -J 

9.31-1 

9.6-1 

40 

30 

i.b 

7.9  -l 

8.2  -^ 

8-5/n 

8.9  ■; 

9.3  -J 

9.6  •° 

10.0 1-1 

10.4  - 

10.81-2 

30 

40 

8.  3-  'l 

8.7  -^ 

9.1   'l 

9.51-° 

10.0 11 

10.4    1 

10.8  -J 

11.21-2 

11.6-2 

12.0 1-2 

20 

50 

9.2   'l 

9.6  'l 

10.0  •„ 

10.51° 

ii.oi° 

11.41° 

11. 9 1- 

12.4!-^ 

12.  9  i-„ 

13.  3 1-^ 

10 

3  00 

10.0  -^ 

10.5  -^ 

11.01° 

11. 5 1-° 

12.0l° 

12.  5 11 

13.0 1-1 

13.61-2 

14.11-2 

14.  6 1-** 

00 

10 

10.9  'l 

11-4/2 

12.0;° 

12.51° 

i3.di° 

13.611 

T4.2i-'f 

14.  7 1-1 

I5.4I-5 

16.  oj-; 

8  50 

20 

11.8   'l 

12.41° 

13.0i° 

13.5    O 

14. 1 11 

14.7  ■ 

15.3  • 

15.9-2 

16.61-2 

17.3  -^ 

40 

30 

12.6  'l 

13.3  -l 

13.9  -l 

14.5  -J 

15.ll° 

15.8-1 

16.4  ■ 

17.1 1-2 

17.8-2 

18.5-2 

30 

40 

13.5  •; 

14.2    J 

14.8  -^ 

15.51° 

16-1    n 

16.  8 1-° 

17.5-1 

18.  2 1-1 

19.  0  1-2 

19.7-2 

20 

50 

14.3  'l 

15.0  'l 

15.7  -l 

16.4  -l 

17.1    ^ 

17.8  •" 

18.5  -^ 

19.4-2 

20. 1 1-1 

20. 9 1-2 

10 

4  00 
10 

15.1  •*' 
15.9  -t 

15.8  •'^ 
16.6  -^ 

16.5  -^ 
17.3  •« 

17.3  -^ 
18.1  •* 

18. 1 1-° 

18. 8 1-° 
19.7  -l 

19.61-1 

20.41° 
21.41-° 

21.  2 1-1 

22.  3 1-1 

22.0  1-1 

00 

19.0  'l 

20. 6 1-° 

23. 1 1-1 

7  50 

20 

16.6  •; 

17.3    ! 

18.1   -Z 

19.0  •; 

19.8  •« 

20.6  'l 

21.5  -l 

22.41-° 

23.2  -„ 

24.1    -° 

40 

30 

17.2    J 

18.0  -J 

18.8  -^ 

19.7    ! 

20.5  -l 

21.4  •" 

22.3  -Z 

23.2  'l 

24.1  \ 

25.li-° 

30 

40 

17.8  i 

18.6  'l 

19.5  -l 

20.3  -^ 

21.2  •: 

22.1  -l 

23.0  -^ 

24.0  i 

24.9  'l 

25.9  -^ 

20 

50 

18.3  i 

19.2  -^ 

20.1  -^ 

21.0    ! 

21.9  •' 

22.8  -l 

23.7  -' 

24.6  •_ 

Ih.l  -_ 

26.7  -l 

10 

5  00 

18.8  -^ 
19.2  -f 

19.7  -5 

20.6  -^ 

21.1  •; 

21.  { 

22.4  -^ 

23.4  -^ 
23.9  -^ 

24.4  •' 
24.9  -f 

25.3 

.5 

26.4 

.6 

27.4  •' 

28.0  -^ 

00 

10 

20.1   ■] 

22.  ( 

22.9   ••' 

25.8 

27.0 

6  50 

20 

19.5  i 

20.5  -^ 

21.4    l 

22.4  -^ 

23.3  -t 

24.3  -t 

25.4  •; 

26.2   -^ 

27.4  -^ 

28.5  -5 

40 

30 

19.8  -l 

20.7  • 

21.7  -l 

22.6  -l 

23.6  'l 

24.6  -^ 

25.7  -l 

26.6  -J 

27.8  -t 

28.8    l 

30 

40 

20.0  -2 

20.9  f 

21.9  -^ 

22.8  -2 

23.9  -^ 

24.9  -f 

25.9  -2 

26.9  -^ 

28.0  -2 

29.1   -^ 

20 

50 

20.1   -^ 

21.0  -1 

22.0  -1 

23.0  ■] 

24.0    1 

25.0  -1 

26.0  -1 

27.0  -1 

28.2  -2 

29.3  ■; 

10 

6  00 

20.2  -^ 

21.1   -1 

22.0  •" 

23.1    1 

24.1  -1 

25.1   -1 

26.1   -1 

27.1   -1 

28.3    1 

29.4  •' 

6  00 

TABLE  28C 

[C=the  3d  c 

orrection. 

Her.  Arg.,  the  star's  declinatio 

n.    Vert.  Arg.,  B=th€ 

2d  correct 

ion.] 

B. 

88°  4 

V 

88 

°  48' 

88-^  49'                1 

20" 

80" 

40" 

50" 

0" 

10" 

20" 

80" 

40" 

50" 

0" 

10" 

20" 

II 

w 

// 

II 

II 

II 

II 

II 

II 

II 

II 

/ 

1 

II 

ii 

0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0 

.0 

0.0 

0.0 

10 

+0.2 

+0.1 

+0.1 

■+ 

0.0 

0.0 

-0.0 

-0.1 

-0.1 

-0.2 

-0.2 

-0 

.3 

-0.4 

-0.4 

20 

0.4 

0.3 

0.2 

0.1 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

0 

.6 

0.7 

0.8 

30 

0.6 

0.5 

0.3 

0.1 

0.0 

0.1 

0.3 

0.5 

0.6 

0.7 

0 

.8 

1.1 

1.2 

40 

0.8 

0.6 

0.4 

0.2 

0.0 

0.2 

0,4 

0.6 

0.8 

1.0 

1 

.2 

1.5 

1.6 

50 

+1.0 

+0.7 

+0.5 

4 

-0.2 

0.0 

-0.2 

-0:5 

-0.7 

-1.0 

-1.2 

-1 

.5 

-1.7 

-2.1 

TABLE  28B. 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 
[B  =  the  2d  correction.    This  correction  is  always  additive.] 


[Page  557 


star's 
hour 
angle. 


h.  in. 

0  00 
10 
20 
30 
40 
50 

1  00 


10 
20 
30 
40 
50 
00 


10 
20 
30 
40 
50 
3  00 


10 
20 
30 
40 
50 
4  00 


10 
20 
30 
40 
50 
5  00 


10 
20 
30 
40 
50 
6  00 


Star's  altitude. 


0.0 
0.1 
0.2 
0.5 
0.9 
1.5 
2.0 


S.8 
10.0 
11.3 
12.6 
13.9 
15.2 


16,6 
17.9 
2 
20.5 

21.7 
22.8 


24.0 
25.0 
26.1 
27.0 
27.8 
28.4 
29.1 
29.6 
30.0 
30.3 
30.5 
30.5 


24.9 
26.0 
27.1 
27.9 
28.8 
29.6 
30.2 
30.7 
31.1 
31.4 
31.6 
31.7 


38° 


89° 


0.0 
0.1 
0.3 
0.6 
1. 1 
1.7 
2.4 


3.3 
4.3 
5.3 
6.6 
7.8 
9.2 


10.6 
12.1 
13.6 
15.1 
16.7 
18.3 


19.9, 
21.5, 
23.1, 
24.6; 
26.1, 


27.5 


28.8 


40° 


0.0 
0.1 
0.3 
0.6 
1.1 
1.8 
2.5 


3.4 
4.5 
5.6 
6.8 
8.1 
9.5 


29.9 
31.2 
32.4 
33.5 
34.4 
35.3 


36.1 
36.8 
37.3 
37.6 
37.8 
37.9 


0.0 
0.1 
0.3 
0.7 
1.2 
1.9 
2.7 


3.6 
4.6 
5.8 
7.0 
8.3 


11.3 
13.0 
14.6 
16.2 
18.0 
19.7 


21.4 
23.1 
24.7 
26.4 
27.9 
29.5 
30.9 
32.3 
33.5 
34.7 
35.8 
36.7 


37.5 
38.2 
38.6 
39.0 
39.3 
39.4 


42° 


11.7: 

13.4 
15.1 
16.8 
18.  5: 
20.3: 


38.8 
39.5 
40.0 
40.4 
40.7 
40.8 


48° 


9.0: 
10.5: 
12.1; 
13.9; 

15.6: 


26.5: 
28.3: 

30.  0: 


Star's 
hour 
angle. 

/(.  ?;(. 

12  00 

11  50 
40 
30 
20 
10 
00^ 

10  50 
40 
30 
20 
10 
00 


6  50 
40 
30 
20 
10 

6  00 


TABLE  28C. 

[C  =  the  3d  correction.    Hor.  Arg.,  the  star's  declination.    Vert.  Arg.j  B  =  the  2d  correction.] 


B. 


0 
10 
20 
30 
40 
50 


20' 


0.0 
+0.2 
0.4 
0.6 
0.8 
+1.0 


88°  47' 


80' 


0.0 
+0.1 
0.3 
0.5 
0.6 
+0.7 


40' 


0.0 
+0.1 
0.2 
0.3 
0.4 
+0.5 


60' 


0.0 
+0.0 
0.1 
0.1 
0.2 
+0.2 


88°  48' 


0.0 
0.0 
0.0 
0.0 
0.0 
0.0 


10' 


0.0 
-0.0 
0.1 
0.1 
0.2 
-0.2 


20" 


0.0 


80' 


0.0 
-0.1 
0.3 
0.5 
0.6 
-0.7 


40' 


0.0 
-0.2 
0.4 
0.6 
0.8 
-1.0 


50' 


0.0 
-0.2 
0.5 
0.7 
1.0 
-1.2 


0.0 
-0.3 
0.6 
0.8 
1.2 
-1.5 


88°  49' 


10" 


0.0 
-0.4 
0.7 
1.1 
1.5 
-1.7 


20' 


0.0 
-0.4 
0.8 
1.2 
1.6 
-2.1 


Page  558] 

TABLE  28B. 

For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

[B=the  2d  correction.    This  correction  is  always  additive.] 

star's 
hour 

Star's  altitude.                                                                             1 

star's 
liour 

angle. 

44° 

45° 

46° 

47° 

48° 

49° 

50° 

51° 

52° 

angle. 

h.    m. 

„ 

// 

„ 

II 

// 

„ 

„ 

„ 

„ 

//.    m. 

0  00 

0.0    1 

0.0    , 

0.0    , 

0.0    1 

0.0    1 

0.0    1 

0.0    , 

0.0    , 

0.0    , 

12  00 

10 

0.1 

o 

0.1. -2 

0.1      2 

0.1     2 

0.1    .3 

0-1 :3 

0.1 :3 

0.1  -3 

0.1  i 

11  50 

20 

0.3 

1 

0.3    4 

0.3-5 

0.3    5 

0.4   .5 

0.4  5 

0.4  5 

0.4    6 

0.4  i 

.]     40 

30 

0.7 

(i 

0.7  \ 

0.8  % 

0.8  ; 

0.9    6 

0.9  ; 

0.9  7 

1.0    7 

1.0    8 

30 

40 

1.3 

7 

1.4  •; 

1.4  % 

1.5  \ 

1-5    8 

1.6    8 

1-6 :9 

1.7    9 

1.  8  i-,3 

20 

50 

2.0 

9 

2-1 :9 

2.2i: 

2.3    9 

2.3i 

2.  4  1.1 

2.  5  1.1 

2.61: 

2.8    • 

10 

1  00 

2.9 

3.0^^ 

^•2io 

3.2^„ 

^•^1 

3.5,. 

•^•^3 

3-7i3 

3.9    • 

00 

10 

4.0 

1 

4.iil.2 

4.2 :3 

4.4 :3 

4.5 : 

4.7 :4 

4.9  4 

5.0 1:6 

5.3    • 

10  50 

20 

5.1 

^ 

^'  ^  1.3 

5. 5 1.4 

5- 7  1.4 

5. 9 1.5 

6.1 1.5 

6.  3  1.6 

6.  6  1.6 

6.  8  ;•- 

40 

30 

6.4 

4 

6.61.5 

6.9i4 

'  •  1 1.6 

7. 4  1.0 

7.61.7 

7.  9  1.7 

8.  2  1.8 

8.5  •; 

30 

40 

7.8, 

8-1 1.5 

8.  3  1.7 

8.  7  1.7 

H-2l-7 

9.  3  1.8 

9. 6 1.9 

10.0 1.9 

10-3  20 

20 

50 

9.3t 

f) 

9.61.7 

10.  0 1  7 

10- 4 1.8 

10.  7  1.9 

11.1  1.9 

11.5  2.0 

11.9  2.0 

12.  3  22 

10 

2  00 
10 

10.9 
12.  6  T 

7 

11.3 

13. 0^:; 

11.' 

U.8 

>iq 

12-2is 

12.6 

1.9 

13-0  2.0 
I5.O21 

13-5  2.1 
15.621 

13.9, 

2 

a 

14-5'- 

00 

13.  J 

14.0 : 

14.5 

16.1  2 

16.7^2 
19-0  25 

9  50 

20 

14.3, 

q 

14.  9  1.9 

15.4i:9 

16.0  2.0 

16.5  2.1 

17.1  2.2 

17.7  2.3 

18.42:3 

40 

30 

16.2, 

^ 

16.  8 1.9 

17.3  2.1 

18.0  2.0 

18.  621 

ly.  *j  2  2 

20.0  2.3 

20.  7  2  4 

21.5;' 
23.9^' 

30 

40 

18.1, 

8 

18.7  2.0 

19.4  2.0 

20.0,, 

20.  7 20 

Zl,  t)  2  2 

22.3  2.3 

23.12:4 

20 

50 

19.9^ 

n 

20.  7 1.9 

21.4  2.0 

22.12:1 

22. 9  22 

23,  7  2.3 

24.62.4 

25.524 

26.4  2 
28. 9  ^-"^ 

31-5  25 
34.  0  ,- 

36.  5  ^J 

10 

3  00 

21.9 

22.6,^ 

23-4„o 

24.2_ 

25-122 

26.0,3 

27-023 

27- 9 06 

00 

10 

23.  7  1 

<» 

24.62:0 

25.4;:; 

26.  4  21 

97  3 
■^'.  •'2.2 

^o*  ^00 

.^y.  *^  2  4 

30.4  24 

8  50 

20 

25.  6 , 

q 

26.  61  9 

27. 5  2.0 

28.  5  2  0 

29.52  1 

30. 5  2  2 

31.7  22 

32.  8  "4 

40 

80 

27.  5  1 

8 

28.  5 1.9 

29.  5  1.9 

30.  5  2  1 

31.621 

32.  7  22 

00,  y  2  3 

35.22:3 

30 

40 

29.3, 

8 

30.  4 1.8 

31.  4 1.9 

32.61:9 

33.  7  20 

34.9  2.1 

36.  2  2 1 

37.  5  2.3 

38.9  2, 
41.  2 

20 

50 

31.1, 

6 

32.2i7 

33.  3 19 

34.5,0 

35.  7  20 

37.0  2.0 

38.  3  2.1 

OU,  ^01 

10 

4  00 

32.7 

6 

33.9/^ 

35.2  • 

36.  4  ^-g 

37.7^3 

39.0,^ 

40.4,, 

41.9,-, 

00 

10 

34.3, 

35.  6 1  g 

36.  9 1:6 

38.2,'7 

39. 5 18 

41.  0^8 

42.5^:8 

44.01:9 

45-5  2-; 

47.5;-; 

49.4     ! 

51. 1  ;■! 

52.7    • 
54.  0  ^-^ 

7  50 

20 

35.  9 , 

1 

37.  2 1.4 

38.  5 1.5 

39.  9 1:5 

41- 3 1.5 

42.81.6 

44.  3 1.7 

45.  9 1.8 

40 

30 

37.  3 , 

S 

38. 6 1  3 

4o.o;-4 

41.4;.4 

42.81.6 

44.  4  1.5 

46.0 1.6 

47.  7  1.6 

30 

40 

38.6, 

'> 

oy.  y  1  0 

41.4 

42.81.3 

44.41.3 

45.  9  1.4 

47.61.4 

49.  3 1.5 

20 

50 

39.8 

q 

4i.ii:i 

42.61.1 

44.1 1.2 

45.  7 1.2 

47.  3 1.3 

49.0 1.3 

50.  8 1  0 

10 

5  00 

40.7 

9 

e 

42.2  •„ 

43.7  • 

45-3io 

46-9io 

48-6ii 

50.3,, 

52.1,-, 

00 

10 

41.6 

43.1    8 

44.6  \ 

46.3'-° 

47. 9 'g 

49.7  . 

51.5  .9 

53. 2 1 Q 

55.2  1-2 

6  50 

20 

42.4 

" 

43.9   \ 

45.4    7 

47.1    6 

48.7    7 

50.5    7 

52.4    7 

54. 2    7 

56.1    'l 

40 

30 

42.9 

1 

44.5    4 

46.1   "4 

47.7  \ 

49.4  -5 

51.2  \ 

53.1   -5 

54.9  'e 

56.9    'l 

30 

40 

43.3 

3 

44.9    2 

46.5  \ 

48.1    3 

49.9  "2 

51.7  ■; 

53.6    0 

55.5    2 

57.5    'l 

20 

50 

43.6 

45.1    0 

46.7  ■, 

48.4    1 

50.1   ■, 

51.9  '0 

53.9  ■-, 

55.7  \ 

57.8    -f 

10 

6  00 

43.7  "^ 

45.3  ■ 

46.8  ■ 

48.5  ■ 

50.2  ■ 

52.1   ■ 

54.0  ■ 

55.9  ■ 

57.9    -1 

6  00 

TABLE  28C. 

[C 

=the  3d  correction.    Hor.  Arg.,  the  star's  declination.    Vert.  Arg.,  B=t 

he  2d  corre( 

Jtion.] 

B. 

88°  47' 

88°  48' 

88°  49'                1 

20" 

80" 

40" 

50" 

0" 

10" 

20" 

80" 

40" 

60" 

0" 

10" 

20" 

30 

+0.6 

+0.5 

II 
+0.3 

II 
+0.1 

0.0 

-0.1 

II 

-0.3 

-0.5 

II 

-0.6 

II 
-0.7 

II 
0.8 

II 
-1.1 

-1.2 

40 

0.9 

0.6 

0. 4  1    0.  2 

0.0 

0.2 

0.4 

0.6 

0.9 

1.0 

1.2 

1.4 

1.6 

50 

1.0 

0.7 

0.5 

0.2 

0.0 

0.2 

0.5 

0.7 

1.0 

1.2 

1.5 

1.7 

i     2.0 

60 

1.2 

0.9 

0.6 

0.2 

0.0 

0.2 

0.6 

0.9 

1.2 

1.5 

1.8 

2.1 

2.5 

70 

1.5 

1      1-1 

0.7 

0.4 

0.0 

0.4 

0.7 

1.1 

1.5 

1.8 

2.1 

2.5 

2.8 

80 

+1.6 

+1.2 

+0.8 

+0.4 

0.0 

-0.4 

-0.8 

-1.2 

-1.6 

-2.1 

■2.5 

-2.8 

-3.3 

TABLE  28B. 

[Page  559 

For  finding  the  Latitude  of  a  place  by  Altitudes  <jf  Polaris. 

LB  =  the  2d  c 

orrecti 

on.    This 
star's  a 

correction  is  always  additive.] 

star's 

Ititude. 

Star's 

hour 

hour 

angle. 

58° 

54° 

55° 

56° 

57° 

58° 

59° 

60° 

angle. 

//.  m. 

/       ,> 

/      /' 

/       n 

/ 

„ 

/     ,, 

,     ,/ 

/    // 

h.    m. 

0  00 

0    0.0  0.1 

0    0.0  0.1 

0     0.0  0.1 

0 

0.0  0.2 

0    0. 0  0  2 

0    O.Ooo 

0    0.  0  0  0 

0    0.  0  0  2 

12  00 

10 

0.  1  0.4 

0-1  0.4 

0-1  0.4 

0.2o3 

0.2  0:3 

0.2  0:4 

0-2  0:4 

0.2o4 

11  .50 

20 

0-'^0.6 

0-5  0.5 

0-5  0.6 

0.5o6 

0.0  0.7 

0-60.6 

0.60.7 

0.60.7 

40 

30 

1-0  0.8 

1-0  0.8 

1-1  0.8 

I-I09 

1-2  0.9 

1-2 1.0 

1-3  0.9 

1-3  1.0 

30 

40 

1-8  1.0 

1-«1.1 

1-9 1.1 

2.O11 

2.1 1.1 

2- 2  1.2 

2.  2 1.3 

2.3i3 

20 

50 

2.81.2 

2.  9  1.3 

3.0 1.3 

3.1i4 

3.  2  1.5 

3- 4 1.5 

3.  5 1.5 

3.617 

10 

1  00 

4.0-  . 

4.2,  , 

4.3,^ 

4.5,, 

4.7 

4.  9 

5.0 

5.3 

00 

1.4 

1  fi 

0  5.8;-7 

T 

6.1-^8 

0    6.  3 1:9 

0  6.61:8 

0    6.8  2'o 

0    7.1^:2 

10 

0    5.4 

0    5.6/7 

10  50 

20 

7.0 1.8 

7.  3  1:8 

7.  5  2.0 

7.^19 

8-2  2.0 

8.4  2.2 

0.  0  0  0 

9.1  24 

40 

30 

^-  ^  1.9 

^- 1  2.0 

9.  5  20 

9.  8  2.1 

10.22.3 

10.624 

11.02:4 

11-5  2.5 

30 

40 

10.7  2.1 

11-12.2 

11.5  2.3 

11.9.4 

12.5  2.3 

13.02:5 

13.4  2.6 

14.02? 

20 

50 

12.  8  2.2 

13.  3  2.3 

13.  8  2.3 

14.3,., 

14.82.6 

15.  5  2  6 

16.0  2.8 

16.  7  2  9 

10 

2  00 

15.0.,, 

15.  6„, 

16. 1  „ . 

16.  8„, 

17. 4„, 

18. 1    „ 

18.8    ° 

19.6 

00 

0  22.632 

10 

0  17.324 

0  18.  0  2  5 

0  18.6" 

0 

19.  3  2  8 

0  20. 1  28 

020.830 

0  21.7 

9  50 

20 

19.7  2.5 

20.52:6 

21.32:7 

22.1,8 

22.  9  2.9 

23.  8 go 

24.83 

25.  8  33 

40 

30 

ZZ,  '^2  6 

23.1  2.6 

^!-^-7 

24.9, « 

25.  8  3  0 

26.83.1 

27.93.2 

29.1  33 

30 

40 

24.  8  2.C 

25.7  2.7 

26.7  2.8 

27.  V,, 

28.  8  3  0 

29.93.1 

31.1  3.2 

32.434 

20 

50 

27.4  2.7 

28.4  2.7 

29.  5  2.8 

30.  6  2  q 

31.  8  3  0 

33.0  32 

34.  3  33 

35.  834 

10 

'  3  00 

30. 1  „  ^ 

31.1„., 

32.  3„, 

33.  5  ■„ 

34.  8    " 

36.  2 

37.  6    „ 

39.  2 

00 

0  42.6^J 

10 

0  32.626 

0  33.  8 27 

0  35. 1  2  8 

0  36. 5  ;■; 

037.93:0 

0  39.4^7 

0  40.9  3.3 

8  50 

20 

35.  2  2.6 

36.  5  2*7 

37.9  2.8 

39.428 

40.9  2.9 

42.53 

44.232 

46.0  33 

40 

30 

37.82.5 

39. 2  2  6 

40.7  2.6 

42.2,, 

43.  8  2.9 

45.63:0 

47.43:1 

49.  3  3  3 

30 

40 

40.3  2.4 

41-82.5 

43.  3  2.6 

45.0,7 

46.  7  2  9 

48.629 

50.  5  3  0 

52.631 

20 

50 

42.7  2.3 

44.3  2.4 

45.9  2.5 

47.  V,  6 

49.62:6 

51.5  28 

53.  5  2.9 

55.  7  3  1 

10 

'  4  00 

-    45.0^2 

46.7^,3 

^A4  2  4 

50.3.,, 

52.2 

54.3^" 
0  56.  9  \\ 

56. 4 
0  59.2,7 

1     1.6  • 

00 

10 

0  47.2  21 

0  49.  0  "\ 

0  50. 8 ;l 

0  52. 8  ;■, 

0  54.824 

7  50 

20 

49.32:0 

51.12:0 

53. 1  21 

55.  loo 

57.22:3 

59.4  24 

1     1.9.^-J 

1     4.4^^ 

40 

30 

51.  3 1.8 

53.1 1.9 

55.  2 1:9 

57.  3,9 

59.52  1 

1     \.%^\ 

1     4.3  •* 

1     6.92:3 

30 

40 

53.1 1.5 

o5.0i6 

^Hl-7 

5y-2i8 

1     1-6 1.8 

1     3.9  2.0 

1     6.52:0 

1     9.2  2^ 

20 

50 

54.61.5 

56-61.5 

.  ^^•^•5 

l-Oifi 

^     ^-^-6 

1     5.9i7 

1     8.5i^^ 

lll-3i8 

10 

5  00 

56.1^., 

^^•^3 

1    ^-^3 

^•So 

1      ^-014 
1     6.4i2 

1     7.6 

110.3  •; 

1  11.8ii 

113.1   -^ 

00 

10 

0  57.  3  0.9 

0  59.4^:0 

1  1-6 : 

3.9- 

1  9.0 :2 

114.7  • 

6  50 

20 

5|^-  2  0.8 

1     0-4  0.8 

}    f-Io-8 

5-O09 

1     7.60.9 

110.2  ^ 

1  13.1  0:9 

1  16.1  0:9 

40 

30 

59.0  0.6 

}  }-h-^ 

1     3.  5  0.7 

5-^07 

1     8- 5  0.7 

1  11- 2  0.6 

114.0^8 

1  17.  Oj-^ 

30 

40 

59.60.3 

1     1-80.3 

1     4.  2  0.3 

6-604 

1     9.  2  0.4 

1  11.80.4 

1  14.8j° 

117.804 

20 

50 

59.9oi 

1     2.I02 

1     4.5oo 

7.001 

1     9.601 

1  12.  2  02 
1  12.4"- 

1  15.  2  J-^ 
1  15.4  • 

118.  2 02 
1  18.4 

10 

6  00 

1   0.0°-^ 

1     2.3 

1    4.7°- 

7.1°-^ 

1     9.7°-^ 

6  00 

TABLE  28C. 

[C  =  the  3d  correction.    Hor.  Arg.,  the  star's  declination. 

Vert.  Arg.,  B  =  the  2d  corr 

ection.] 

B. 

88°  47' 

88°  48' 

88°  49'                1 

20" 

80" 

40" 

50" 

0" 

10" 

20"           8 

tO" 

40" 

50" 

0"          10" 

20" 

„ 

„ 

„ 

„ 

„ 

„ 

II 

// 

„ 

„ 

„ 

„ 

II 

„ 

30 

-rO.6 

+0.5 

+0.3 

+0.1 

0.0 

-0.1 

-0.3     - 

0.5 

-0.6 

-0.7 

-0.8 

-1.1 

-1.2 

40 

0.9 

0.6 

0.4 

0.2 

0.0 

0.2 

0.4 

0.6 

0.9 

1.0 

1.2 

1.4 

1.6 

50 

1.0 

0.7 

0.5 

0.2 

0.0 

0.2 

0.5 

0.7 

1.0 

1.2 

1.5 

1.7 

2.0 

60 

1.2 

0.9 

0.6 

0.2 

0.0 

0.2 

0.6 

0.9 

1.2 

1.5 

1.8 

2.1 

2.5 

70 

1.5 

1.1 

0.7 

0.4 

0.0 

0.4 

0.7 

1.1 

1.5 

1.8 

2.1 

2.5 

2.8 

80 

+1.6 

+1.2 

+0.8 

+0.4 

0.0 

-0.4 

-0.8 

— 

1.2 

-1.6 

-2.1 

-2.5   -2.8 

-3.3 

Page  660] 


TABLE  28D. 


For  finding  the  Latitude  of  a  place  by  Altitudes  of  Polaris. 

[D=the  4th  correction.     (D  has  the  same  sign  as  A  when  the  Dec.  <88°48',  the  oppo.^ite  sign  when  the  Dec.  >88°  48'.)] 
[Vertical  Argument,  A  =  the  1st  correction.    Horizontal  Argument,  the  star's  declination.] 


A. 


10 
12 
14 
16 
18 
20 
22 
24 


68 
70 
72 


0  20 

0  40 

1  00 
1  20 

1  40 

2  00 


Declination,  88°  47' 


20"      25 


0.0 

1.1 

2.2 

3.3 

4.4 

5.6 

6.7 

7.8 

8.9 

10.0 

11.1 

12.2 

13.3 


27.8 
28.9 
30.0 
31.1 
32.  2 
33.3 
34.4 
35.6 


36.7 
37.8 
38.9 
40.0 


0.0 
1.0 
1.9 
2.9 
3.9 


4.9 

5.8 
6.8 
7.8 
8.8 
9.7 
10.7 
11.7 


12.7 
13.6 
14.6 
15.6 


16.6 
17.5 
18.4 
19.4 
20.4 
21.4 
22.3 
23.3 


24.3 
25.3 
26.2 
27.2 
28.2 
29.2 
30.1 
31^1 
32. 1 
33.0 
34.0 
35.0 


«0" 


o.t 

0.8 
1.7 
2.5 
3.3 
4.2 
5.0 
5.8 

^•1 

7.5 

8.3 

9.2 

10^ 

10.8 

11.7 

12.5 

13.3 


14.2 
15.0 
15.8 
16^7 
"17.  6 
18.3 
19.2 
20.0 


20.8 
21.7 
22.5 
23.3 


24.2 
25.0 
25.8 
26.7 
27.5 
28.3 
29.2 


30.0 


85' 


0.0 
0.7 
1.4 
2.1 

2.8 


11.8 
12.5 
13.2 
13.9 


14.6 
15.3 
16.0 
16.7 
17.3" 
18.0 
18.8 
19.4 


20.1 
20.8 
21.5 
22.2 
"22.9 
23.6 
24.3 
25.0 


40" 


0.0 
0.6 
1.1 
1.7 
2.2 


2.8 
3.3 
3.9 
4.4 


6.0 
5.5 
6.1 
6.7 
7.2 
7.8 
8.3 
8.9 


9.4 
10.0 
10.6 
11.1 


11.7 
12.2 
12.8 
13.3 
13. 9" 
14.4 
15.0 
15.6 


16.1 
16.7 
17.2 
17.8 


18.3 
18.9 
19.4 
20.0 


45' 


0.0 
0.4 
0.8 
1.2 
1.7 


2.1 
2.5 
2.9 
3.3 


3.8 
4.2 
4.6 

AO 
5.4 
5.8 
6.2 


7.9 
8.3 


8.8 

9.2 

9.6 

10.0 


10.4 
10.8 
11.2 
11.7 


12.1 
12.5 
12.9 
13.3 


13.8 
14.2 
14.6 
15.0 


2.5 
2.8 
3.0 
3.3 
3.6 
3.9 
4.2 
4.4 
4.7 
5.0 
5.3 
5.6 


5.8 
6.1 
6.4 
6.7 
6.9 
7.2 
7.5 
7.8 


8.0 
8.3 
8.6 

_8^9 
9.2 
9.4 
9.7 

10.0 


0.0 
0.1 
0.3 
0.4 
06 
0.7 
0.8 
1.0 
1.1 
1.2 
1.4 
1.6 
1.7 


1.8 
1.9 
2.1 
2^2 
"2.3 
2.5 
2.7 
2.8 


2.9 
3.0 
3.2 
3.3 


3.4 
3.6 
3.8 
3.9 


4.0 
4.2 
4.3 
4.4 
4.6 
4.7 
4.9 
5,0 


88°  48' 


0.0 

1.2 

0.0 

1.4 

0.0 

1.6 

0.0 

1.7 

0.0 

1.8 

0.0 

1.9 

0.0 

2.1 

0.0 

2.2 

0.0 
0.0 
0.0 
0^0 
0.0 
0.0 
0.0 
OJ) 
0.0" 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 


0.0 
0.0 
0.0 
0.0 


0.0 
0.1 
0.3 
0.4 
0^ 
0.7 
0.8 
1.0 

1.1 


2.3 
2.5 
2.7 

2.8 


2.9 
3.0 
3.2 
3.3 


3.4 
3.6 
3.8 
3.9 


4.0 
4.2 
4.3 
4.4 


4.6 
4.7 
4.9 
5.0 


10"      15 


4.7 
5.0 
5.3 
5.6 


5.8 
6.1 
6.4 
6.7 


6.9 

7.2 
7.5 
7.8 


8.0 
8.3 
8.6 
8.9 


9. 


2 
4 
9.7 
10.0 


0.0 
0.4 
0.8 
1.2 
1.7 
2.1 
2.5 
2.9 
3.3 


3.8 
4.2 
4.6 
5.0 


5.4 
5.8 
6.2 
6.7 
7.1 
7.5 
7.9 
8.3 


9.2 

9.6 

10.0 


10.4 
10.8 
11.2 
11.7 
12.1 
12.5 
12.9 
13.3 


13.8 
14.2 
14.6 
X5.0 


20' 


0.0 
0.6 
1.1 
1.7 
2.2 
2.8" 
3.3 
3.9 
4.4 


25" 


0.0 
0.7 
1.4 
2.1 
2.8 


5.0 
5.5 
6.1 
6.7 


3.4 
4.1 
4.9 
5.5 


7.2 

7.8 
8.3 


9.4 
10.0 
10.6 
11.1 


11.7 
12.2 
12.8 
13.3 


13.9 
14.4 
15.0 
15.6 


16.1 
16.7 
17.2 
17.8 


18.3 
18.9 
19.4 
20.0 


6.2 
6.9 

7.7 
8.3 


9.0 

9.7 

10.4 

11.1 


Proportional  parts. 


0.0 
0.0 
0.1 
0.1 
0.1 


0.1 
0.2 
0.2 
0.2 


0.2 
0.3 
0.3 
0.3 


11.8 
12.5 
13.2 
13.9 


14.6 
15.3 
16.0 
16.7 


0.4 
0.4 
0.4 
0.4 
0.5 
0.5 
0.5 
0.6 


0.6 
0.6 
0.6 
0.7 


17.3  0.7 
18.0  0.7 
18.810.7 
19.410.8 


20.1 
20.8 
21.5 
22.2 


0.8 
0.8 
0.9 
0.9 


0.0 
0.0 
0.1 
0.2 
0.2 


0.3 
0.3 
0.4 
0.4 


0.5 
0.6 
0.6 
0.7 
0.7 
0.8 
0.8 
0^ 
"0.9 
1.0 
1.1 
1.1 


22.9  0.9 
23.6  0.9 
24.3  1.0 
25.0  1.0 


1.2 
1.2 
1.3 
1^3 
1.4 
1.4 
1.5 
jL6 
1.6 
1.7 
1.7 
L_8 
1.8 
1.9 
1.9 
2.0 


0.0 
0.1 
0.2 
0.2 
0.3 
0.4 
0.5 
0.6 

0.7 
0.8 
0.9 
1.0 


1.1 
1.1 
1.3 
1.3 
1.4 
1.5 
1.6 
1^ 
1.7 
1.8 
1.9 
2^^ 
'2.1 
2.2 
2.2 
2.^ 
2.4 
2.5 
2.6 
2^ 
"2.8 
2.8 
2.9 
3.0 


4' 


0.0 
0.1 
0.2 
0,3 
0.4 


0.6 
0.6 
0.8 
0.9 


1.0 
1.1 
1.3 
1.4 


2.3 
2.4 
2.6 
2.6 


2.8 
2.9 
3.0 
3.1 


Proportional  parts. 


0.2 
0.4 
0.6 
0.7 
0.9 
1.1 


„ 

„ 

„ 

„ 

„ 

„ 

„ 

„ 

n 

„ 

II 

II 

0.2 

0.1 

0.1 

0.1 

0.1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.1 

0.1 

0.3 

0.3 

0.2 

0.2 

0.1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.1 

0.2 

0.5 

0.4 

0.4 

0.3 

0.2 

0.1 

0.1 

0.0 

0.1 

0.1 

0.2 

0.3 

0.7 

0.5 

0.5 

0.4 

0.2 

0.1 

0.1 

0.0 

0.1 

0.1 

0.2 

0.4 

0.8 

0.7 

0.6 

0.5 

0.3 

0.2 

0.1 

0.0 

0.1 

0.2 

0.3 

0.5 

1.0 

0.8 

0.7 

0.6 

0.4 

0.2 

0.1 

0.0 

0.1 

0.2 

0.4 

0.6 

0.1 
0.2 
0.4 
0.5 
0.6 
0.7 


TABLE 

28D. 

[Page  561    | 

For 

finding  the  Latitude  of  a  place  by 

Altitudes  of  Polaris. 

[D= 

the  4th  correction.    (D  has  the  same  sign 

as  A  when  the  Dec.  <88°  48',  the  oppo.site  sign  when  the  Dec 

>88°48'.)] 

[Vertical  Argument  A=the  1st  correction.    Horizontal  Argument,  the  star's  declination.] 

A. 

Declination,  88°  48' 

88°  49'                              1 

Proportional  parts.       1 

80" 

36" 

40" 

45" 

60" 

65" 

0" 

5" 

10" 

16" 

20" 

1" 

2" 

8" 

4" 

0 

0.0 

0.0 

0.0 

II 
0.0 

II 
0.0 

0.0 

II 
0.0 

II 
0.0 

0.0 

0.0 

II 

0.0 

II 
0.0 

0.0 

0.0 

0.0 

2 

0.8 

1.0 

1.1 

1.2 

1.4 

1.6 

1.7 

1.8 

1.9 

2.1 

2.2 

0.0 

0.1 

0.1 

0.1 

4 

1.7 

1.9 

2.2 

2.5 

2.8 

3.1 

3.3 

8.6 

8.9 

4.2 

4.4 

0.1 

0.1 

0.1 

0.2 

6 

2.5 

2.9 

3.3 

3.8 

4.2 

4.6 

5.0 

5.3 

5.8 

6.2 

6.7 

0.1 

0.2 

0.2 

0.8 

8 

8.3 

3.9 

4.4 

5.0 

5.6 

6.1 

6.7 

7.2 

7.8 

8.3 

8.9 

0.1 

0.2 

0.3 

0.4 

10 

4.2 

4.9 

5.6 

6.2 

6.9 

7.6 

8.3 

9.0 

9.7 

10.4 

11.1 

0.1 

0.3 

0.4 

0.6 

12 

5.0 

5.8 

6.7 

7.5 

8.3 

9.2 

10.0 

10.8 

11.7 

12.5 

13.3 

0.2 

0.3 

0.5 

0.7 

14 

5.8 

6.8 

7.8 

8.8 

9.8 

10.8 

11.8 

12.7 

13.7 

14.6 

15.6 

0.2 

0.4 

0.6 

0.8 

16 
18 

6.7 

7.8 

8.9 

10.0 

11.1 

12.2 

13.3 

14.4 

15.6 

16.7 

17.8 

0.2 
0.2 

0.4 

0.7 

0.9 

7.5 

8.8 

10.0 

11.2 

12.5 

13.8 

15.0 

16.2 

17.5 

18.8 

20.0 

0.5 

0.7 

1.0 

20 

8.3 

9.7 

11.1 

12.5 

13.9 

15.3 

16.7 

18.1 

19.4 

20.9 

22.2 

0.3 

0.6 

0.8 

1.1 

22 

9.2 

10.7 

12.2 

13.8 

15.3 

16.8 

18.3 

19.8 

21.4 

22.9 

24.4 

0.3 

0.6 

1.0 

1.3 

24 

10.0 

11.7 

13.3 

15.0 

16.7 

18.4 

20.0 

21.7 

23.8 

25.0 

26.7 

0.3 
0.4 

0.7 

1.0 

1.4 

26 

10.8 

12.7 

14.4 

16.2 

18.0 

19.9 

21.7 

23.5 

25.3 

27.1 

28.9 

0.7 

1.1 

1.4 

28 

11.7 

13.6 

15.6 

17.5 

19.4 

21.4 

23.3 

25.3 

27.2 

29.2 

31.1 

0.4 

0.8 

1.2 

1.6 

80 

12.5 

14.6 

16.7 

18.8 

20.8 

22.9 

25.0 

27.1 

29.2 

31.2 

38.3 

0.4 

0.8 

1.2 

1.6 

32 

13.3 

15.6 

17.8 

20.0 

22.2 

24.4 
26.0 

26.7 

28.4 

28.9 

31.1 

83.8 

35.5 

0.4 

0.9 

1.3 

1.8 

84 

14.2 

16.6 

18.9 

21.2 

23.6 

30.7 

33.1 

35.4 

37.8 

0.5 

0.9 

1.4 

1.9 

86 

15.0 

17.5 

20.0 

22.5 

25.0 

27.5 

30.0 

32.5 

35.0 

37.5 

40.0 

0.5 

1.0 

1.5 

2.0 

88 

15.8 

18.4 

21.1 

23.8 

26.4 

29.0 

81.6 

34.2 

87.0 

39.6 

42.2 

0.5 

1.1 

1.6 

2.2 

40 
42 

16.7 

19.4 

22.2 

25.0 

27.8 

30.6 

83.3 

36.1 

88.9 

41.7 

44.4 

0.6 

1.1 

1.7 

2.2 

17.6 

20.4 

23.3 

26.2 

29.2 

32.1 

85.0 

37.9 

40.8 

48.8 

46.7 

0.6 

1.2 

1.8 

2.4 

44 

18.3 

21.4 

24.4 

27.5 

30.6 

33.7 

36.8 

39.8 

42.8 

45.9 

48.9 

0.6 

1.2 

1.8 

2.4 

46 

19.2 

22.3 

25.6 

28.8 

32.0 

35.1 

38.3 

41.5 

44.8 

47.9 

51.1 

0.6 

1.3 

1.9 

2.6 

48 
50 

20.0 

23.3 

26.7 

30.0 

33.3 

36.7 
88.2 

40.0 

43.8 
45.1 

46.7 

50.0 

58.3 

0.7 

1.3 

2.0 

2.7 

20.8 

24.3 

27.8 

31.2 

34.7 

41.7 

48.6 

52.1 

55.5 

0.7 

1.4 

2.1 

2.8 

52 

21.7 

25.3 

28.9 

32.5 

36.1 

39.7 

43.3 

46.9 

50.5 

54.2 

57.8 

0.7 

1.4 

2.2 

2.9 

54 

22.5 

26.2 

30.0 

33.8 

37.5 

41.2 

45.0 

48.7 

52.5 

56.2 

60.0 

0.7 

1.5 

2.2 

8.0 

56 

58 

23.3 

27.2 

31.1 

35.0 

88.9 

42.8 

46.7 

50.5 
52.  3 

54.4 

58.8 

62.2 

0.8 

1.6 

2.3 

3.1 

24.2 

28.2 

32.2 

36.2 

40.3 

44.3 

48.8 

56.4 

60.4 

64.4 

0.8 

1.6 

2.4 

3.2 

60 

25.0 

29.2 

33.3 

37.5 

41.7 

45.9 

50.0 

54.2 

58.3 

62.5 

66.7 

0.8 

1.7 

2.5 

3.8 

62 

25.8 

30.1 

34.4 

38.8 

43.0 

47.3 

51.7 

56.0 

60.3 

64.6 

68.9 

0.9 

1.7 

2.6 

3.4 

64 
66 

26.7 

31.1 

35.6 

40.0 

44.4 

48.9 

53.3 

57.8 

62.2 

66.7 

71.1 

0.9 

1.8 

2.7 
2.7 

3.6 

27.5 

32.1 

36.7 

41.2 

45.8 

50.4 

55.0 

59.6 

64.2 

68.8 

73.3 

0.9 

1.8 

3.6 

68 

28.3 

33.0 

37.8 

42.5 

47.2 

52.0 

56.7 

61.3 

66.1 

70.9 

75.5 

0.9 

1.9 

2.8 

3.8 

70 

29.2 

34.0 

38.9 

43.8 

48.6 

53.5 

58.3 

63.1 

68.0 

72.9 

77.7 

1.0 

1.9 

2.9 

3.9 

72 
0  20 

30.0 

35.0 

40.0 

45.0 

50.0 

55.0 

60.0 

65.0 

70.0 

75.0 

80.0 

1.0 

2.0 

3.0 

4.0 

Proportional  parts. 

0.1 

0.1 

0.1 

II 
0.2 

0.2 

0.3 

0.3 

0.3 

0.3 

0.3 

0.4 

0  40 

0.2 

0.3 

0.4 

0.4 

0.5 

0.5 

0.6 

0.6 

0.6 

0.7 

0.7 

100 

0.4 

0.5 

0.6 

0.6 

0.7 

0.8 

0.8 

0.9 

0.9 

1.0 

1.1 

120 

0.5 

0.7 

0.7 

0.8 

0.9 

1.1 

1.1 

1.2 

1.3 

1.4 

1.5 

140 

0.6 

0.8 

0.9 

1.0 

1.1 

1.3 

1.4 

1.5 

1.6 

1.7 

1.8 

2  00 

0.8 

1.0 

1.1 

1.2 

1.4 

1.6 

1.7 

1.8 

1.9 

2.1 

2.2 

22489—03- 


-36 


Page  562] 

TABLE  29. 

Conversion  Tables  for  Nautical  and  Statute  Miles. 

XmUical  miles  into  statute  miles. 

Statute  miles  into  naiUical  miles. 

1  nautical  mile  or  knot  =  6,080  feet. 

1  statute  mile 

=  5,280  feet. 

1  statute  mile 

=6,280  feet. 

1  nautical  mile  or  knot  =  6,080  feet. 

' 

Nautical 

Statute 

Nautical 

Statute 

Nautical 

statute 

Statute 

Nautical 

Statute 

Nautical 

Statute 

Nautical 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

miles. 

1.00 

1.151 

8.75 

10. 075 

16.50 

18.  999 

1.00 

0.868 

^00 

7.815 

17.00 

14. 763 

1.25 

1.439 

9.00 

10.  363 

16.75 

19. 287 

1.25 

1.085 

9.25 

8.032 

17.25 

14.980 

1.50 

1.727 

9.25 

10.651 

17.00 

19.  575 

1.50 

1.302 

9.50 

8.249 

17.50 

15.  197 

1.75 

2.015 

9.50 

10. 939 

17.25 

19. 863 

1.75 

1.519 

9.75 

8.467 

17.75 

15.414 

2.00 

2.303 

9.75 

11.227 

17.50 

20. 151 

2.00 

1.736 

10.00 

8.684 

18.00 

15. 632 

2.25 

2.590 

10.00 

11.515 

17.75 

20.  439 

2.25 

1.953 

10.25 

8.901 

18.  25 

15. 849 

2.50 

2.878 

10.25 

11.803 

18.00 

20.  727 

2.50 

2.170 

10.50 

9.118 

18.50 

16.  066 

2.75 

3.166 

10.50 

12. 090 

18.25 

21.015 

2.75 

2.387 

10.75 

9.335 

18.75 

16.  283 

3.00 

3.454 

10.75 

12.  378 

18.50 

21. 303 

3.00 

2.604 

11.00 

9.552 

19.00 

16.500 

3.25 

3.742 

11.00 

12. 666 

18.75 

21. 590 

3.25 

2.821 

11.25 

9.769 

19.25 

16.717 

3.50 

4.030 

11.25 

12. 954 

19.00 

21.878 

3.50 

3.038 

11.50 

9.986 

19.50 

16. 934 

3.75 

4.318 

11.50 

13. 242 

19.25 

22. 166 

3.75 

3.256 

11.75 

10. 203 

19.75 

17.151 

4.00 

4.606 

11.75 

13. 530 

19.50 

22.  454 

4.00 

3.473 

12.00 

10.  420 

20.00 

17.  369 

4.25 

4.893 

12.00 

13. 818 

19.75 

22.  742 

4.25 

3.690 

12.25 

10. 638 

20.25 

17.  586 

4.50 

5.181 

12.25 

14. 106 

20.00 

23. 030 

4.50 

3.907 

12.50 

10.  855 

20.50 

17.  803 

4.75 

5.469 

12.50 

14.  393 

20.25 

23. 318 

4.75 

4.124 

12.75 

11. 072 

20.75 

18. 020 

5.00 

5.757 

12.75 

14.  681 

20.50 

23.  606 

5.00 

4.341 

13.00 

11.  289 

21.00 

18. 237 

5.25 

6.045 

13.00 

14. 969 

20.75 

23. 893 

5.25 

4.559 

13.25 

11.  507 

21.25 

18. 454 

5.50 

6.333 

13.25 

15. 257 

21.00 

24. 181 

5.50 

4.776 

13.  50 

11. 724 

21.50 

18.  671 

5.75 

6.621 

13.50 

15. 545 

21.25 

24.  469 

5.75 

4.994 

13.75 

11. 941 

21.75 

18.888 

6.00 

6.909 

13.75 

15. 833 

21.50 

24. 757 

6.00 

5.211 

14.00 

12. 158 

22.00 

19. 105 

6.25 

7.196 

14.00 

16. 121 

21.75 

25.045 

6.25 

5.428 

14.25 

12. 376 

22.25 

19. 322 

6.50 

7.484 

14.25 

16.409 

22.00 

25.  333 

6.50 

5.645 

14.50 

12. 593 

22.50 

19. 539 

6.75 

7.772 

14.50 

16. 696 

22.25 

25. 621 

6.75 

5.862 

14.75 

12. 810 

22.75 

19. 756 

7.00 

8.060 

14.75 

16.984 

22.50 

25. 909 

7.00 

6.079 

15.00 

13. 027 

23.00 

19. 973 

7.25 

8.348 

15.00 

17. 272 

22.75 

26. 196 

7.25 

6.296 

15.25 

13.244 

23.25 

20. 191 

7.50 

8.636 

15.25 

17. 560 

23.00 

26. 484 

7.50 

6.513 

15.50 

13. 461 

23.50 

20. 408 

7.75 

8.924 

15.50 

17.  848 

23.50 

27.  060 

7.75 

6.730 

15.75 

13.  678 

23.75 

20. 625 

8.00 

9.212 

15.75 

18. 136 

24.00 

27. 636 

8.00 

6.947 

16.00 

13.  895 

24.00 

20.842 

8.25 

9.500 

16.00 

18. 424 

24.50 

28.  212 

8.25 

7.164 

16.25 

14. 112 

24.25 

21. 060 

8.50 

9.787 

16.25 

18.712 

25.00 

28. 787 

8.50 

7.381 

16.50 

14.  329 

24.50 

21.  277 

8.75 

7.598 

16.75 

14. 546 

25.00 

21.711 

TABLE  30.                                          [Page  563 

Conversion  Tables  for  Metric  and  English  Linear  Measure. 
Metric  to  Eiiglwi. 

Meters. 

Feet. 

Yards. 

Statute  miles. 

Nautical  miles. 

1 
2 
3 
4 

3. 280     833     3 

6. 561    666     7 

9.842    500    0 

13.123    333    3 

1.093    611     1 
2.187     222     2 
3.280    833    3 
4.374    444    4 

0.000    621     369 
.001     242    738 
.001    864    106 
.002    485    475 
.003    106    844 
.003    728    213 
.004    349    582 
.004    970    950 
.005    592    319 

0. 000    539    593 
.001    079    185 
.001    618    778 
.002    158    370 

5 
6 

7 
8 
9 

16.404    166     7 
19.685    000    0 
22.965    833    3 
26.246    666     7 
29.527    500    0 

5. 468    055    6 
6.561    666    7 
7.655    277     8 
8.748    888    9 
9. 842    500    0 

.002    697    963 
.003    237    556 
.003    777     148 
.004    316    741 
.004    856    333 

English  to  metric. 

No. 

Feet  to  meters. 

Yards  to  meters. 

Statute  miles  to  meters. 

Nautical  miles  to  meters. 

1 
2 
3 

4 

0.304    800    6 
0.609    601     2 
0.914    401     8 
1.219    202    4 

0.914    401     8 
1.828    803     7 
2.743    205    5 
3.657    607    3 

1,609.35 
3,  218.  70 
4, 828. 05 
6, 437. 40 

1,  853. 25 
3,  706. 50 
5, 559.  75 
7, 413. 00 

5 
6 

7 
8 
9 

1.524    003    0 
1.828    803     7 
2.133    604    3 
2.438    404    9 
2.743    205    5 

4. 572    009     1 
5.486    411     0 
6.400     812     8 
7.315     214    6 
8.229    616    5 

8, 046.  75 

9, 656. 10 

11,265.45 

12, 874. 80 

14,484.15 

9, 266.  25 
11, 119. 50 
12, 972.  75 
14, 826. 00 
16, 679.  25 

Page  564] 

TABLE  31. 

Conversion  Tables  for  Thermometer  Scales. 

[F°=Fahrenheit  temperature;  C°=Centigrade  temperature;  R°=R6aumur  temperature.] 

Equivalent  temperatures— Fahr.,  Cent., 

Mail 

R°=*  C°=i  (F°- 

-32°). 

C 

3=JRO  =  g  (F°- 

-32°). 

S 

F°. 

C°. 

R°. 

r 

C°. 

R°. 

1 

-17.2 

-13.8 

51 

+10.6 

+  8.4 

2 

16.7 

13.3 

52 

11.1 

8.9 

Equivalent  temperatures— Centigrade  and  Fahrenheit. 

3 
4 

16.1 
15.6 

12.9 
12.4 

53 
54 

11.7 
12.2 

9.3 

9.8 

F°=  1  C°-h32°. 

5 
6 

7 

15.0 
14.4 
13.9 

12.0 
11.6 
11.1 

55 
56 

57 

12.8 
13.3 
13.9 

10.2 
10.7 
11.1 

C°. 

pa 

C°. 

F°. 

c° 

F°. 

c°. 

F°. 

C°. 

F°. 

8 

13.3 

10.7 

58 

14.4 

11.6 

-10 

14.0 

0 

32.0 

10 

50.0 

20 

68.0 

30 

86.0 

9 

12.8 

10.2 

59 

15.0 

12.0 

—  9 

15.8 

1 

33.8 

11 

51.8 

21 

69.8 

31 

87.8 

10 

12.2 

9.8 

60 

15.6 

12.4 

-  8 

17.6 

2 

35.6 

12 

53.6 

22 

71.6 

32 

89.6 

11 

11.7 

9.3 

61 

16.1 

12.9 

—  7 

19.4 

3 

37.4 

13 

55.4 

23 

73.4 

33 

91.4 

12 

11.1 

8.9 

62 

16.7 

13.3 

—  6 

21.2 

4 

39.2 

14 

57.2 

24 

75.2 

34 

93.2 

13 

10.6 

8.4 

63 

17.2 

13.8 

—  5 

23.0 

5 

41.0 

15 

59.0 

25 

77.0 

35 

95.0 

14 

10.0 

8.0 

64 

17.8 

14.2 

-  4 

24.8 

6 

42.8 

16 

60.8 

26 

78.8 

36 

96.8 

15 

9.4 

7.6 

65 

18.3 

14.7 

-  3 

26.6 

7 

44.6 

17 

62.6 

27 

80.6 

37 

98.6 

16 

8.9 

7.1 

66 

18.9 

15.1 

_  2 

28.4 

8 

46.4 

18 

64.4 

28 

82.4 

38 

100.4 

17 

8.3 

6.7 

67 

19.4 

15.6 

—  1 

30.2 

9 

48.2 

19 

66.2 

29 

84.2 

39 

102.2 

18 
19 

7.8 
7.2 

6.2 

5.8 

68 
69 

20.0 
20.6 

16.0 
16.4 

1 

20 

6.7 

5.3 

70 

21.1 

16.9 

21 

6.1 

4.9 

71 

21.7 

17.3 

22 

5.6 

4.4 

72 

22.2 

17.8 

23 

5.0 

4.0 

73 

22.8 

18.2 

24 

4.4 

3.6 

74 

23.3 

18.7 

25 

3.9 

3.1 

75 

23.9 

19.1 

26 

3.3 

2.7 

76 

24.4 

19.6 

27 

2.8 

2.2 

77 

25.0 

20.0 

Equivalent  temperatures— Riaumitr  and  Fahrenheit. 

28 

2.2 

1.8 

78 

2.5.6 

20.4 

•    •                                     F°=|  R°-|-32°. 

29 
30 

1.7 
1.1 

1.3 
0.9 

79 
80 

26.1 
26.7 

20.9 
21.3 

R°. 

F°. 

R°. 

F°. 

R°. 

F°. 

R°. 

F°. 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41. 

42 

-0.6 
0.0 

+  0.6 
1.1 
1.7 
2.2 
2.8 
3.3 
3.9 
4.4 
5.0 
5.6 

-0.4 
0.0 

+  0.4 
0.9 
1.3 
1.8 
2.2 
2.7 
3.1 
3.6 
4.0 
4.4 

81 
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
92 

27.2 
27.8 
28.3 
28.9 
29.4 
30.0 
30.6 
31.1 
31.7 
32.2 
32.8 
33.3 

21.8 
22.2 
22.7 
23.1 
23.6 
24.0 
24.4 
24.9 
25.3 
25.8 
26.2 
26.7 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

-10 

-  9 

-  8 

-  7 

-  6 

-  5 

-  4 

-  3 

-  2 

-  1 

9.5 
11.8 
14.0 
16.2 
18.5 
20.8 
23.0 
25.2 
27.5 
29.8 

32.0 
34.2 
36.5 
38.8 
41.0 
43.2 
45.5 
47.8 
50.0 
52.2 

10 
11 
12 
13 
14 
15 
16 
17 
18 
19 

54.5 
56.8 
59.0 
61.2 
63.5 
65.8 
68.0 
70.2 
72.5 
74.8 

20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

77.0 
79.2 
81.5 
83.8 
86.0 
88.2 
90.5 
92.8 
95.0 
97.2 

43 

6. 1 

4.9 

93 

33.9 

27. 1 

44 

6!  7 

5!  3 

94 

34^4 

27!  6 

45 

7.2 

5.8 

95 

35.0 

28.0 

46 

7.8 

6.2 

96 

35.6 

28.4 

47 

8.3 

,  6.7 

97 

36.1 

28.9 

48 

8.9 

7.1 

98 

36.7 

29.3 

49 

9.4 

7.6 

99 

37.2 

29.8 

50 

+10.0 

+  8.0 

100 

+37.8 

+  30.2 

TABLE  32. 


[Page  565 


To  obtain  the  True  Force  and  Direction  of  the  Wind  from  its  Apparent  Force  and  Direction  on  a 

Moving  Vessel. 


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N«iOmTf<iO'^iOtOintOt-!Ol^Q0C~a000000001000>OOO^Oi-(rHi-li-lc^iMC^C^~104C^ 


■Moq  aqi  J90  s^uiod  'uoijoajip  atux 


CO<lOtOtD<OOiO«OCOlC»C?OiCiC^iCiOidC»OiOlft>'5iCi^i/2iCiO»Cif5Uci05DiOiClOtCiCiO 


■81B08  :)jojnB8a  'aajoj  atux 


C^CCOCO-^iO-^iCOiOOt^^t^oDt^OOOOQOODOsaOCSOOSOOOr-li-iUHT-lc^C^C^C^KMC^C^ 


•Moq  aqj  yo  sjuiod  'uoijaaiip  arux 


iOOCOii^iCiOiCiOi^iCiOiC»C»0»CiCiCiC"^iC'^-^idO"^iCiC'^-^»C   •^TT'iC'^'^-f-^-^T^ 


•ajBas  :)jojn'Baa  'aaaoj  atux 


c^cciocO'^iC'^icto»ceot^«ot^oot*t^cct*ooa^oO'35ascsoooi-*i-iU-ii-(c^c^e^c^(NMej 


■Aioq  aqi  jjo  s^uiod  'uojiaajip  arux 


iootoidninTjiiom"»''*iO'*'*-*Tf9<r)<i)<'^T(<T(<->jiTj<..ji.^ij< «-»<■<>'  cc^'«<cotj"'^ MM-* 


•aiBOS  jjojtiBaa  'aajoj  arux 


(NM'«J<MTjllOr}imtO>/5t0t~«Or"t^t»t»00t~0Ca000  050>05OOOOr-tr-li-mC^e^C^C^C^C^ 


'Aioq  aqi  yo  s^ujod  'uopoajip  arux 


li^iOtO-^iOiC't'^iO^'^-^M'^'V   M-^-^MM-^MMMMMMMMM   MMMC<IMMC^MM 


•axuas  ■jjojnBaa  'aaaoj  arux 


(^^M'9lM-*l0^lCtOlOtotOlra^oc~!0^»■ooc~oooooooDOiO»o^oooo^-l.-l1-lr-lm^c^(^^c^ 


•Moq  aq;  jjo  sjuiod  'uorioajip  arux 


lOlOlC■*■^lreM-*■*MM-*MM"*c>)MMe^MMI^lc^Mc^lMMc^IMc^INN(^J^^l^^c^<^^M^^ 


•aiBas  jjojn'Baa;  'aajoj  arux 


INMTt<M'S<i'2M'*iO-*idOU5«3t-«5t~t-t~t>0D0000ai0>0»OOOOr-li-li-li-liMC^iM(N:^ 


•Avoq  aqj  BO  sjaiod  'uoijoajjp  arux 


lOmiO'"»"fl<>OMM-*<«MMe^C4MC^e^Mr-ie>«C^rHe^drHi-IC<r-li-l(Nl-(i-li-Hi-(r-lr-lrti-Ci-l 


•aXBas  ^jojnBaa  'aojoj  arux 


e^MT»ie<M'^eO"«'iO'*iO<om<o<okoot~t~t-t~i>ooooooo>o>o»oooi-<>-i!-ii-i(N<NNc^ 


•Aioq  aqi  BO  s^urod  'uoipajip  arux 


lCiniCM-^'<J<C<M-*01HM^«C^li-IIN<NrJi-IC^O"-l>-IOT-l.-IOO'-liOOi-lOOOOOO 


•aXBOS  '4J0jnBaa  'aoJOj  arux 


CJM'^C^M'<1*M'^iC'^-^iC-^iCtOu050«OtOt*l:^t^t^00000005C>CiOSOOOt-lT--rHC^C^M 


•  Avoq  aqj  BO  sjurod  'uoi:>aajrp  arux 


miOiOM-^-^e-lMMi-HMMOfHC^l    Or-IC^OO^mO-HOJOOO>00   OS0500>OSOO>C50> 


'ai^Ds  ^jojnBaa  'aajoj  arux 


C4o9^e<M^eo«o^e<9vm^i(5iou5io«o«D<or~t»r-t»»ooaoe»05oooooi-ir-ir-(c^Nc^ 


•Moq  aq:)  bo  8:}rrrod  'uorjaaarp  arux 


lOiOiCMf-^i-tC^MOf-'C^O^C^    asOV-IOiOOOOOaOCOOiO>OOOaOi   0000O>0000OS«GC00 


•axBos  laojnBaa  'aojoj  arux 


c<M'^NW*Nm'^weiS'*'^'^-^io>OiOtD«o«oi~«ct»ooooooo»aooooo>a>r-(^0(NC<ie<i 


•Moq  aq?  BO  s^uiod  'uorjoajrp  anix 


ioicmc^'*'*oe^MO»i-ic^o»o>-i!ooosoooo>ot-.ooo>t~ooo»t~xoot»t~aot-t»oot~t>-t» 


•a[BOs  iiojn'Bag  'aajoj  arux 


4C^-»1<i-IMMC^C^MC^MMMM-*'^-*MiOiOiO<00'Ot»t~t^CCOOaOO»0>01000?^r-'r-l 


•AVoq  aqi  bo  s-juiod  'uorjoaarp  arux 


io>nme^"»'"*oc^MaoorJooo»oi-~-ooot~ooo>tot»aotot»ootDtoi»totot-«i;ct-;ctoto 


•aiBDS  jjojnBag  'aojoj  arux 


i-(iMTtir-ic^MiHe^MNC<we<9eOOT'*e<5MiO'*^toiomt~c~eoaDoot~o>o>ooooOr-ir-i-H 


•M.oq  aqj  bo  sjniod  'uoijaaarp  arux 


iOiCiCC^-1''^P>C^M30OC^t-CCO   50t^05  0t>-OOiCOt>»C!OCOidC«OidC«OiCiCiO-V»CiO 


•aiBos  jjojnBag  'aojoj  arux 


l-IC^'<)<r-IC<MiH.HNC<rHNC^Ne<e0MM'*-<>"M«>lO"9<t~!OtO00t^t^0»a000OO01i^--<.-( 


•  Moq  aqi  bo  s^nrod  'uorjoaarp  arux 


K3icnoc^'«»">coo<NM<eo»Ntot»o  in!3ao'^iot~^io<e'*^iO'«j"<»'ift  ■^■^^^^tjimtji'v 


•aiBos  jjojriBaa  'aojoj  arux 


rHC^MOC^MOr-iC^iHrHi-l!NrHr-l,e>5C^C^-<«"MC^lO-<)<-<(<t>tOlO»t~tDOSOOOOOO>3S-H  — O 


•Aioq  aqj  go  sjutod  'uoijoaJlp  arux 


lO'^OM-^iCt-C^-^iOOOC^-^^Oa 


MlOt~M'^iCMM^MM'^CMMMCMMMC^MMC^e^M 


•aXBDs  iJojUBag  'aajoj  arux 


r-ie^MOrHC^OOe^rlOrHC^rHO 


MPjTH'*MC^iO-*MtD<OmXlt»50»COt»00»0>r-lr-IO 


•Avoq  aq:>  bo  sjurod  'uor^aajrp  arux 


«ototOT)<ic>ntoM>oweceocjr(<o> 


NMUtC^C4Mrt(NINrtC^C^r-(rHC^ 


•aiBos  ^jojnBag  aojoj  arux 


iHC^MOr-IC^OOrtr-IOOC^rHO 


MCJO-»J<MC^iO-rl<M«OiO'<»'OOt^«> 


OiOOt>OOiOir-'t— 'O 


Moqaq^  Bosjnrod  'uopoai}p  arux 


cooec^o^otooooooo 


ooooooooooooooo 


ooooooooo 


•s^ouj[  'xassaA  jo  paadg 


OiOOOiCOOiCOOiOOOiOO 

r-li-l(NrH^!NiHT-IC^i-(i-ie^i-(r-lC^ 


oireoo>oooioooiooo>oo 

rHi-lC^i-lrH(Ni-li-IOJi-lT-l(NrtrH(M 


oioooinooiao 


O  rH  C^  M 


00  o> 


Page  566] 


TABLE  33. 

Distance  by  Vertical  Angle. 


05 


Q    CC  t^  ^  Vi 


N  e^  M  T--  r-l 


^    iOeO(NrH 


OCPJMOOQ 


I-Hr-IOIOT 
OlOOOlN 


■Ir-lrtr-l    00000 


^  ^  CC  CQ  CC 
00000 


00000 


i-lrHSc 


■^t^  i-Ht^  CC 
i-I>-ItHOO 


3  tir~ooo 

^.-lOOO 


OkOiC-^ -^ 

r-(0000 


~    (MT)'0(NiOCC(Nr-IO 

o  OTjiece^ 


.     CCOOOl-* 
^    li5<MlOr-l 

O    00-<J'(MCJ 


.     -  -(  t^-^o 
lO  >o  -^  "^  "^ 

00000 


>  t^t^o 

SrHOO 


■.^  ■f54Tj<CC 

00000 


CSrHTfO 
O    00-*(NC^ 


c^Jioec^i  t^ 
— irtOlO 

H,-I.HO 


~  >cS-<}<o 


"    M-.J'CcS 
O    t~CCINrH 


QiO>2t~0 
CCtHOiO  in 

1-lr-IOO 


occc>iT)> 

O    r-CCO)rH 


iCt-H  rH  CCI> 
Mi-lOiO-* 

tHi-Ii-HOO 


O    OCCI^i-l 


.     00O5  CCiO 

CC  ■'T  »r5  c^ 


»  oxj-r  » 

r-lCC'^.-l 
O    iONtHiH 


Til  (N  CC  tH 
O    ■<)<  cq  r-l  rH 


O    •<9' (M  r-(  r-l 


^  cocci/sr* 

*■    T)<lflr-im 
O    CCi-Hi-IO 


O-^"^  CC  CC 
00000 


lO'^Tf.J^'^hj'CCCCCCCC 

0000000000 


CC    CC  CC  CC  CC  CC 

00000  00000 


lOiNOOCS 
^  ^  ■^  CC  CC 

00000 


.-loit^iocc 

Tf  CC  CC  CC  CC 

00000 


CC  CC  CC  CC  C4 

ooooo 


ccccfSo)  (N 
ooooo 


ooooo 


ccccecccM 
ooooo 


■*  <N  O  00  l- 

CCCCCCCNC-^ 

ooooo 


ooooo 


00  !•»  lO  ■^  M 

ooooo 


CCCC64fSM 

ooooo 


^  00  t^  O  iC 

ooooo 


-     JiQ'^CC 

ojmSic^(N 
ooooo 


ooooo 


-  <  o  a>  00  00 1^ 

O)  (N  tH  tH  .H  r-l 

ocoooo 


•O  v(5  CC  51  r-( 

ooooo 


ooQor*  co^ 


lO  CC  C-1  p  o> 

ooooo 


OCt^l^tOiftiO 


000000 


ooooo 


t>- CO  iCiC  ■*** -^ 


000000 


i-HOOOl-tD 


«0  lO  ■* '<' CC  c^ 


ooooo 


000000 


ec?i>Hoo 
ooooo 


ooooo 


rH  rH  001  Oi 


lO-q'CClN^lOOOlOOOO 


>o»occaOT)iot~-*  jJOoot^iC'^ccoii-io 

>eq00>0    'J' Tfi  TT  CC  CC    CCCC(N04lN  'C^M!N<m55 
4rHrHr-IO    OOOOO    OOOOO    OOOOO 


OS  to  I^  CI  -^ 
rHOOO 


■^■-HCCtOrH 
rHOift  ■*■* 

i-hOOO 


gt^oOC^QO 
inT)<Ti!cc 

0000 


m-^cccc 

i-HOOOO 


t^t^OlOf-H 
UD  ^  ^  CC  CC 

OOOOO 


lOiHOOlO  C^ 
T}*-^CCCC  CC 

OOOOO 


cj  OS  i<5  CC  o 

■•  -5C<iCCCC 

ooooo 


CC?S  MC<IIM 

ooooo 


CCC^f-tOa>QDt^t^«<C' 


ooooo  ooooo 


ooooo 


CCCCCCOl 

ooooo 


r*  ccr-t  000 


T*  1-H  00  «5  ■"»< 

ccccc5c^c^ 
ooooo 


to  iQ  CC  C-)  .H 
CM  C<l  C^  (N  C^ 

ooooo 


iCCC<M  005 


ooooo 


ooooo 


i-H  00  O  -^  C-1  It-h  (3i  OC'  l^  to 


cccm^mM 

ooooo  ooooo 


COtO'*C^O 

ooooo 


rHCqOC^lOOlCCCrHOOO 


lO'^CCCCO) 

ooooo 


iCl  00  <N  00  IQ 
•<*<  CC  CC  fl  C<l 

ooooo 

iO5Ot~-00O5 


ooooo 


3>00  t^tOlO 


ooooo 


t^toic  -^cc 


ooooo 


ooooo 


OrHCqCC^ 


lO-^CCCCO) 
OOOOO 


10  or*  00  OS 


OSOOOD  t^t^ 

ooooo 


T-IOOOOOO 


OOOOO 


OOOOO 


o  a>oo  t>-i^ 


OOOOO 


00  X  t^  to  in 
ooooo 


I^  tOiO-^  -^ 


ooooo 


to  »o  '^  -^  CC 

ooooo 


■*Tf  CClMffJ 


ooooo 


CCCCOIOt-I 

ooooo 


i-<-HOOO 

ooooo 


Or-lC^CC* 


to  iCiC  ■'I*  ■^ 


OOOOO 


a>oo  t^toio 

OOOOO 


Tj*  ^  CC  CC  C^  r^ 


000000 


CO  t^  tO>OTj< 

ooooo 


t- to  lO  ■«<"  CC 


ooooo 


to  10  "*  CC  CC 

ooooo 


in-^cocc^j 
ooooo 


^CCC^Ni-l 

ooooo 


CCC4C^r-IO 


ooooo 


iC-^  ^  cccc  c^ 

ooooo  o 


CCCCOCJi-H 


ooooo 


ooooo 


.-I  rHOOO 

ooooo 


1-1  000105 

ooooo 


0>0>0>0000 

0000© 


iCCOI~*00O> 


ONtJIOOO 


CC  CC  C^  C<  i-H  r-l 

000000 


CC  CJ  C^  rH  1-1  O 

000000 


C^rH— 1000 

000000 


ON'*  to  000 


TABLE  33. 

Distance  bv  Vertical  Angle. 


[Page  567 


CO  O 

55 


-  r-i  C^  O 


00  =0000  CO 
O  t0  51000 


rHC05irHT-t|C^CClO(NiO 


0»T»((NQO 
OiOCOINrH 


OOiCOOC^ 
rl  0)10  0110 

,-(005  OS  00 


tOi-ltOMOO    lOt^Olt^O^ 

t^COOOOtOi-*050Ii-<0 
01c3c4rHrH,i-lTHiHr-li-l 


0  -T^QcccOT-txaiOicco 

lO   Tj<0r-I001i0  1'i0001 

01  -^rHOOOf'oi^-lOOOJ 


C-leCiOOKM 

COr-ITl<lOC^ 

rloOiCMOl 


OOOOO^ 
i-Hi-IOloSO 

i-ioa>ooao 


■^  .-*  Ice  O  CC  l^  r-l 
•^  (M  ^>-l  Ol  i-H  M  O) 

00  Ol  lOOlOCOr-IO 
55  Ol  |iH  r-l  rH  i-H  rH 


0  05  0 
lOC^OJ 

_  OOTt-IOO> 

01(?J    .-(rHiHr-l 


lOOlOlOOi 
■*lMC001i-l 

(NOOiOO 


lOOirHrl 
OlOOiOOt^ 


tH  rt  lO 

OOOM 


o>oot-t-«> 


lO  O  Ol  O  Ol 
OJ'^OCOO 

00t>t-«O5O 


OOrHOJin 
rH<NOOi-l 


OOOOIIMCO 
Ol  '^  -^lO  i-H 

OS  t*  OiOiC 


O  WJ  Ol 


C3010:OiOO)(Ni-l 
1-(01M    «.-(OlTJ>r-< 

ooojo>  r»^iO'*»j' 


CO  -^  O  cc  O 
iO'^T)<eoco 


rHOtrH'^ 
O    00  OitO-^ 


.     i-H  M  1-  00 
^    OJiOiO  O) 

o  r^ooiOT^ 


C^COOiCiO 


*1*  05  O*  '^  c^ 

coiooio'* 
Oio  loirs'^ 


0-*(M0 


-     _500Oa-Ji 
lO  Ol*^  i-H  lO 

O>CJ>O0O0t~ 


■*i-ICOt^iO 

TJi  rH  -^  ^  lO 

00  GC  t^  t^  CO 


rHlOC0»-llO 
?0  lO  lO  lO  "^ 


00  t^  OiOl  t^ 

C0i-li0'*0» 

lO  lO  -^  -^  -^ 


0-^<N  i-HiO 
IC  T)l  Tl<  TJI  CO 


Q  CO  1^  Ol  00 

«  rHiO  '^  Ol 

t~  r-  o  -o  o 


iC-HOi-iOjiiOOiOOIQ 
OJO-VlNOjTfcOiHOio 

oooor-t^t--toototOiO 


lO  Ol  O)  CO  l^ 


-  _5  I--.  iO  lO  CO 

■*  (M  I—  C3  lO  ■.»< 

f*  ^  Tf  CO  CO 


00 1^  OS  n  i^ 


lO  lO  ^  ^  ^ 


OOCOSOliO-JI^-fOlrH 


-)■  lo  OS  "i<  o> 

CO  Tl  lO  ■>J<  ?l 
*-0  O  lO  iC  iC 


iOlOiO"iJ<')'Ujc.JiTjiT>iC0 


■J5  -*  CO  0>  OJ 

i-fOiOT»<cO 

lO  lO  T)<  ■.p  Tjl 


ojosr-ioio 
— -^i-cOiO 

Tj<  ^  ^  •<}<  CO 


•^COCMOlrl 

CO  CO  CO  CO  CO 


-^  Ol  »-l  rH  Ol 

i-H  OlO  -^t*  CO 

^  ^  CO  CO  CO 


CO  CO  X  ^1  lO 
O)  rH  OOiO 

CO  COCO  CO  (N 


-O  lO  lO  CO  00 
TCCOOlrt  o 

CO  CO  CO  CO  CO 


CO  t~  O)  O  00 

oioiO'j'oi 

1<-^  CO  CO  CO 


OOOOOIMlO 
T-lOOlO-* 

CO  CO  cooler 


i-t  Ol  CO  ,H  00 


cot^oiooo 

OlOiO'^O) 

tT'^COCOCO 


r><COr-IOiO 
CO  CO  CO  CO  CI 


lOI^^OCO 


CO  IC  lO  CO  GC'  ,-t 
■*  C0  0)i-(00 

coco  CO  CO  CO  CO 


30  «  O  O  lO  00 
iHOOiO'^CO 

CO  CO  cool  (MO) 


OS  ^  -^  t^i-H  CO 
^  ■*  CO  Ol  Ol  rH 

0)0)010)010) 


1-1  lO  00  CO  00  CO 
OlrHOOiCiO 

COOIOIOIO)   0)010)01>-i>H 


OS  OS  O  1-1  -r    t^  r-(  CO  ^^  CO  c 
TCOCOOIr-liOOlOiO'^' 

0)0101010)    O)  O)  1-1  r-(  .H  r 


.^^1^,-tCO    r-*^C0COOS 
OiO-*'>1<CO   COO)i-lOiO 

C0  0)0)010)010)0101i-I 


COCOOlOlrH 
010)01010) 


^ooco  oo'fl'o 
J -^  -.a*  CO  CO  CO 


oi3|coQ:g"Os-^Qcoo)os 
i-iOiSio-^  cocoeoo)0)iH 

OlOlf-lT- 


COOlOSOOCCOSr-lTj'f.i-l'COOCOiHt^ 
■TCOi-IOiOTfi-^COOlOli-d-IOOiO 

COCOCOCOOl   Ol  Ol  Ol  Ol  Ol   OI  Ol  Ol  Ol  T-l 


O)  (■-  lO  t^  O) 

•cCrHlOCOO) 

Tj*  T^  CO  CO  CO 


t^coi^  gs 

lO  -tiCOOl 
COOIOIOIOI 


COiOOp-^iH 
■^  Ol  OiO  -^ 

CO  CO  cool  01 


1-t  ^  coco  OS 

COOlrHOlO 
01010)0)  iH 


Osfi-IOt-i 

■*eoo)T-io 

0)0)0)0)01 


Scoo3;os 
■^'S'COOl 


CQCCr-lr-ICO    CO  CO  •*  t^  >-l 
^©■"tOlO   lOrfcOOlOl 

eocoo)oioi 


iC  »-(t^cOO 
1-1  iH  o  o  o 


lO  OS  CO  -*  OS 
CO  iC  CO  1— I  lO 

COOIO)  Olr-I 


r-QOOco  t^ 

TTCOCOOlr-l 


^    OSiOOO-^   COOsiOt^ 
^     OlOlCOrH    -'  —  -•  — 

O    COOOiO'* 


^  r*  CO  OS  o 

^    COiOiH  O 

Q    lO  t^  lO  ■^ 


COOsiO  t^  CO 

oS-^oioio 

COO)0101rH 


0)Qt~Ot~ 

1-1^1-1  0-* 

COOlOlOlrH 


»  lOOi-icg 
•cP  CO  o  ^ 

Q  ^  t*  us  CO 


SeoQ 

COOJOliHrH 


lOCOt^OOOs 


leoioooc 

>C0Oli-lr 


CO  0)0)1-10 


Oi-IOlCO'* 


Olt^COQt 

r-tO  OOi 


1-liHOO 


SOt^COiH 
O  iCiO  to 

HOOO 


St^COQOO 
SiOiOiO^ 

HOOOO 


lO  i-IJ^ -nj"  rH  5C 
ol  O)  rt  iH  1-1  S 


i-liOOOCOQC'jCOOSiOi-II^I'I'OOCOOS-.^f 

"i-iooioiif'^' — ^^' — " 

Ol  OIOIO 


"'J"'^CO:COO)01rHi-( 


010)i-li-liH 


r»^i-iosr- 

-  lOlOTjlTjl 

OOOOO 


■^  1-1  OSI>iO 
lO  lO  ij'  'J' ■«< 

OOOOO 


1-1 00  CO  31  o) 

OOOOO 


3D  CO-*  0)0 


COO)0)0)i-i 


S;^SSS 


OOiOCOi-IQO   t-*C0Ot^iO 
OOOOiOjiOiOiO'^Tji 

Hr-(i-lO    OOOOO 


-     I<0)Q0S 
OOOOO 


-*  CO  CO  CO  w 

OOOOO 


r-l  t^  -r  1-1  0>  !■- 

i-IOOOiOiO 

T-li-lr-lrtOO 


t^ -*  1-1  OS  r^  »o 

lO  lO  lO  ^  *1i  * 
OOOOOO 


O)00st-i0'* 

■*  'J' CO  95  CO  CO 

OOOOOO 


ociocoi-iooQr-coio-*co 
eocOeococop)oiO)0«o)o5 

OOOOO OOOOOO 


C0'*0)000    t^CO-«iC0O)i-c 
COCOCOCOOl   010101010)C< 

OOOOO   OOOOOO 


■^  0)000  1> 

CO  CO  CO  O)  O) 

OOOOO 


aot~co-<t|co  o)OoQ«^io 

COCOCOCOCO    COCOOiO)OI 
OOOOO   OOOOO 


lOCOi-fOSOQ    cpiO'^Oli-H 
^  1J1  ^  CO  CO    CO  CO  CO  CO  CO 

OOOOO  OOOOO 


lO  ■*  cool  1-1  o 
0)0)0)0)0101 

OOOOOO 


■*C0  01i-<  OOs 

0)05  0)01  O)  rH 

OOOOOO 


ooor^iOTjicooii-iposoo 
cooioioioiiNoiois5i-ii-i 

OOOOOOOOOOO 


iOC0t^000SOrH01C0'.^i0C0t^000SO0)-^O«O0)'*C000O 


Page  568]                                             TABLE  34. 

For  finding  the  distance  of  an  object  by  an  angle,  measured  from  an  elevated  position,  between  the 

object  and  the  horizon  beyond. 

Dlst., 
yards. 

Height  of  the  Eye  Above  the  Level  of  the  Sea,  In  Feet. 

Dist, 
yards. 

20 

30 

40 

50 

60 

TO 

80 

»o 

lOO 

no 

ISO 

100 
200 
300 
400 
500 

0  / 

3  44 

1  50 
1  12 

52 
41 

0  1 

5  37 
2  46 

1  4% 
1  21 
1  03 

0  ( 

7  29 
3  43 
2  26 

1  48 
1  25 

0  / 

9  21 
4  39 
3  04 
2  16 

1  48 

0     r 
11  11 
5  35 
3  41 
2  44 
2  10 

o       / 

13  00 
6  31 
4  19 
3  12 
2  32 

o      / 

14  47 
7  27 
4  56 
3  40 
2  54 

o       / 

16  34 
8  23 
5  33 
4  08 
3  17 

o      / 

18  16 
9  18 
6  11 
4  36 
3  39 

O         1 

19  58 

10  13 

6  48 

5  04 

4  01 

o       / 

21  37 

11  08 

7  25 

5  32 

4  24 

100 
200 
300 
400 
500 

600 
700 
800 
900 
1,000 

34 
28 
24 
21 
18 

52 
44 
38 
33 
29 

1  10 

1  01 

51 

45 

40 

1  29 

1  15 

1  05 

57 

50 

1  47 
1  31 
1  18 
1  09 
1  01 

2  05 
1  46 
1  32 
1  22 
1  12 

2  24 
2  01 
1  46 
1  33 
1  23 
1  15 
1  08 
1  02 
57 
52 

2  42 
2  18 
2  00 
1  45 
1  34 

3  01 
2  34 
2  13 

1  57 
1  45 

3  20 
2  50 
2  27 
2  10 
1  56 

3  38 
3  05 
2  41 
2  22 
2  07 

600 
700 
800 
900 
1,000 

1,100 
1,200 
1,300 
1,400 
1,500 
1,600 
1,700 
1,800 
1,900 
2,000 

16 
15 
13 
12 
11 

26 
23 
21 
19 
18 

35 
32 
29 

27 
24 

45 
41 
37 
34 
31 

55 
50 

45 
41 
38 

1  05 
59 
53 
49 
45 

1  24 
1  17 
1  10 
1  04 
59 

1  34 
1  26 
1  18 
1  12 
1  07 

1  44 
1  35 
1  27 
1  20 
1  14 

1  54 
1  44 
1  35 
1  27 
1  21 

1,100 
1,200 
1,300 
1,400 
1,500 

10 

16 
15 
14 
13 
12 

22 
21 
19 
18 
17 

29 
27 
25 
23 
22 

35 
33 
31 
29 
27 

42 
39 
36 
34 
32 

48 
45 
42 
39 
37 

55 
51 
48 
45 
42 

1  02 
58 
54 
50 
47 

1  08 

1  04 

1  00 

56 

53 

1  15 
1  10 
1  06 
1  02 

58 

1,600 
1,700 
1,800 
1,900 
2,000 

2,100 
2,200 
2,300 
2,400 
2,500 

11 
10 

16 
15 
14 
13 

12 

20 
19 
18 
17 
16 

25 
24 
22 
21 
20 

30 
28 
27 
25 
24 

35 
33 
31 
29 

28 

40 
38 
36 
34 
32- 

45 
42 
40 
38 
36 

50 
47 
45 
42 
40 

55 

52 
49 
47 
44 

2,100 
2,200 
2,300 
2,400 
2, 500 

2,600 
2,700 
2,800 
2,900 
3,000 

11 
11 
10 

15 
14 
14 
13 

12 

19 
18 
17 
16 
15 

23 
22 
20 
19 
19 

26 
25 
24 
23 
22 

30 
29 
28 
26 
25 

34 
33 
31 
30 

28 

38 
36 
35 
33 
32 

42 
40 
38 
37 
35 

2,600 
2,700 
2,800 
2,900 
3,  000 

3,100 
3,200 
3,300 
3, 400 
3,500 

12 
11 
10 

15 
14 
13 
13 
12 

18 
17 
16 
15 
15 

21 
20 
19 
18 

17 

24 
23 
22 
21 
20 

27 
26 
25 
24 
23 

30 
29 
28 
27 
26 

34 
32 
31 
30 
29 

3,100 
3,200 
3,300 
3,400 
3,500 

3,600 
3,700 
3,800 
3,900 
4,000 

12 
11 
11 
10 

14 
13 
13 
12 
12 

17 
16 
15 
15 
14 

19 
19 
18 
17 
16 

22 
21 
20 
20 
19 

25 
24 
23 
22 
21 

27 
26 
25 
25 
24 

3,600 
3,700 
3,800 
3,900 
4,000 

4,100 
4,200 
4,300 
4,400 
4,500 

11 
11 
10 

14 
13 
13 
12 
12 

16 
15 
15 
14 
14 

18 
17 
17 
16 
16 

20 
20 
19 
18 
18 

23 
22 
21 
21 
20 

4,100 
4,200 
4,300 
4,400 
4,500 

4,600 
4,700 
4,800 
4,900 
5,000 

11 
11 
10 

13 
13 
12 
12 
11 

15 
15 
14 
14 
13 

17 
17 
16 
15 
15 

19 
19 
18 
17 
17 

4,600 
4,700 
4,800 
4,900 
5,000 

TABLE  35. 

[Page  569 

Speed  in  knots  per  hour  developed  by  a 

vessel  traversing  a  measured  nautical  mile  in  any  given  1 

number  of  minutes  and  seconds. 

1 

Number  of  minutes. 

1 

2 

8 

4 

5 

6                7 

8 

9 

10 

11 

12 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

Knots. 

0 

60.000 

30.  000 

20. 000 

15. 000 

12. 000 

10.  000 

8.571 

7.500 

6.666 

6.000 

5.455 

5.000 

0 

1 

59.  016 

29. 752 

19.  890 

14. 938 

11.960 

9.972 

8.551 

7.484 

6.654 

5.990 

5.446 

4.993 

1 

2 

58. 065 

29.  508 

19. 780 

14.  876 

11.920 

9.944 

8.530 

7.468 

6.642 

5.980 

5.438 

4.986 

2 

8 

57. 143 

29. 268 

19.  672 

14.  815 

11.880 

9.917 

8.510 

7.453 

6.629 

5.970 

5.429 

4.979 

3 

4 
5 

56. 250 
55. 385 

29. 032 

28. 800 

19. 565 

14.  754 

11. 841 
11. 803 

9.890 

8.490 

7.438 

6.617 

5.960 

5.421 

4.972 
4.965 

4 
5 

19. 460 

14. 694 

9.863 

8.470 

7.422 

6.605 

5.950 

5.413 

6 

54. 545 

28. 571 

19. 355 

14.  634 

11.764 

9.836 

8.450 

7.407 

6.593 

5.940 

5.405 

4.958 

6 

7 

53. 731 

28.346 

19. 251 

14. 575 

11. 726 

9.809 

8.430 

7.392 

6.581 

5.930 

5.397 

4.951 

7 

8 

52.  941 

28. 125 

19. 149 

14, 516 

11. 688 

9.783 

8.411 

7.377 

6.569 

5.921 

5.389 

4.945 

8 

9 

10 

52. 174 

27. 907 
27.  692 

19.  048 
"18:947 

14. 458 

11.650 

9.756 

8.392 

7.362 
7.346 

6.557 

5.911 

5.381 

4.938 

9 

51.429 

14. 400 

"11.613 

9.729 

8.372 

6.545 

5.902 

5.373 

4.932 

10 

11 

50.  704 

27. 481 

18. 848 

14. 342 

11.575 

9.703 

8.  353 

7.331 

6.533 

5.892 

5.365 

4.924 

11 

12 

50. 000 

27.  273 

18. 750 

14. 286 

11.538 

9.677 

8.334 

7.317 

6.521 

5.882 

5.357 

4.918 

12 

13 

49. 315 

27. 068 

18. 652 

14. 229 

11.501 

9.651 

8.315 

7.302 

6.509 

5.872 

5.349 

4.911 

13 

14 
15 

48. 649 

48. 000 

26. 866 

18. 556 
18. 461 

14. 173 
l4ril8 

11.465 

9.625 

8.295 

7.287 

6.498 
6.486 

5.863 
5.  853 

5.341 

4.904 

14 
15 

26.  667 

11.428 

9.600 

8.276 

7.272 

5.333 

4.897 

16 

47.  368 

26. 471 

18. 367 

14. 063 

11.392 

9.574 

8.257  !  7.258 

6.474 

5.844 

5.325 

4.891 

16 

17 

46. 753 

26.  277 

18. 274 

14. 008 

11.356 

9.549 

8.238  1  7.243 

6.463 

5.834 

5.317 

4.884 

17 

18 

46. 154 

26. 087 

18. 182 

13. 953 

11.321 

9.524 

8.219     7.229 

6.451 

5.825 

5.309 

4.878 

18 

19 
20 

45. 570 

25. 899 

18. 090 
18.000 

13. 900 
13.  846 

11.285 
11. 250 

9.499 

8.200  i  7.214 

6.440 
6.428 

5.815 

5.301 

4.871 

19 

45. 000 

25. 714 

9. 473  !  8.  181      7.  200 

5.806 

5.294 

4.865 

20 

21 

44. 444 

25. 532 

17.910 

13.  793 

11.214 

9. 448    8. 163     7. 185 

6.417 

5.797 

5.286 

4.858 

21 

22 

43.  902 

25.  352 

17.  822 

13.  740 

11. 180 

9.424    8.144      7.171 

6.405 

5.787 

5.278 

4.851 

22 

23 

43. 373 

25. 175 

17.734 

13. 688 

11.146 

9.  399    8. 126     7. 157 

6.394 

5.778 

5.270 

4.845 

23 

1 

42.  857 

25.000 

17.647 
17:560 

13.  636 
13.584 

11.111 
"11.077 

9.375    8.108  :  7.142 
9.350    8.090     7.128 

6.383 
6.371 

5.769 

5.263 

4.838 

24 
25 

42. 353 

24.  828 

5.760 

5. 255 

4.832 

26 

41. 860 

24. 658 

17.475 

13. 533 

11.043 

9.  326    8. 071  !  7. 114 

6.360 

5.750 

5.247 

4.825 

26 

27 

41.379 

24. 490 

17.  391 

13. 483 

11.009 

9.302:  8.053 

7.100 

6.349 

5.741 

5.240 

4.819 

27 

28 

40. 909 

24. 324 

17.  307 

13. 433  1 10. 975 

9.  278  1  8. 035 

7.086 

6.338 

5.732 

5.232 

4.812 

28 

29 
30 

40. 449 
40. 000 

24. 161 
24. 000 

17. 225 

13. 383 1 10. 942 

9.254 
9.230 

8.017 

7.072 

6.  327 

5.  723 
5.  714 

5.224 

4.806 

29 

17. 143 

13. 333 

10. 909 

8.000 

7.059 

6.315 

5.217 

4.800 

30 

31 

39. 560 

23.  841 

17.061 

13. 284 

10. 876 

9.207 

7.982 

7.045 

6.304 

5.705 

5.210 

4.793 

31 

32 

39. 130 

23.  684 

16. 981 

13.  235 

10.  843 

9. 183 

7.964  i  7.031 

6.293 

5.696 

5.202 

4.787 

32 

33 

38.  710 

23. 529 

16.  901 

13. 186 

10.810 

9.160 

7.947 

7.017 

6.282 

5.687 

5.195 

4.780 

33 

34 
35 

38.  298 

23. 377 
23.  226 

16. 822 
16.  744 

13. 138 

10.  778 

9.137 

7.929 
7.912 

7.004 
6.990 

6.  271     5.  678 
6.260  1  5.669 

5.187 
5.179 

4.774 
"4.  768 

34 
35 

37.  895 

13. 091 

10.  746 

9.113 

36 

37.  500 

23. 077 

16. 667 

13. 043 

10.  714 

9.090 

7.895 

6.977 

6.250 

5.660 

5.172 

4.761 

36 

37 

37. 113 

22. 930 

16.  590 

12. 996 

10. 682 

9.068    7.877 

6.963 

6.239  1  5.651 

5.164 

4.  755 

37 

38 

36.  735 

22. 785 

16.514 

12.  950 

10.  651 

9.045 

7.860 

6.950 

6.228 

5.642 

5.157 

4.749 

38 

39 
40 

36.  364 
36.  000' 

22.642 

16. 438 

12.  903 

10.619 

9.022 

7.843 

6.936     6.217 

5.633 

5. 150    4.  743  1 

39 
40 

22. 500 

16.  363 

12. 857 

10. 588 

9.000    7.826 

6.923 

6.207 

5.625 

5.143 

4.737 

41 

35.644 

22. 360 

16. 289 

12.811 

10. 557 

8.9771  7.809 

6.909 

6.196 

5.616 

5.135 

4.731 

41 

42 

35. 294 

22. 222 

16.216 

12.  766 

10. 526 

8.955    7.792 

6.896 

6.185 

5.607 

5.128 

4.724 

42 

43 

34. 951 

22. 086 

16. 143 

12. 721 

10. 495 

8.933    7.775 

6.883 

6.174 

5.598 

5.121 

4.718 

43 

44 
45 

34. 615 

21.  951 

16. 071 

12.  676 

10. 465 

8.911     7.758 

6.870 

6.164 

5.590 

5.114 

4.712 

44 
45 

34.  286 

21.818 

16.000 

12. 631 

10.434 

8.889 

7.741 

6.857 

6.153 

5.581 

5.106 

4.706 

46 

33.  962 

21. 687 

15. 929 

12.  587 

10.404 

8.867 

7.725 

6.844 

6.143 

6.572 

5.099 

4.700 

46 

47 

33.645 

21.557 

15. 859 

12.  543 

10.  375 

8. 845 

7.708 

6.831 

6.132 

5.564 

5.091 

4.693 

47 

48 

33.  333 

21.429 

15. 789 

12.500 

10. 345 

8.823 

7.692 

6.818 

6.122 

5.555 

5.084 

4.687 

48 

49 
50 

33.  028 

21.  302 

15. 721 
15.652 

12. 456 

10.  315 

8.801 

7.675 
7.659 

6.805 
6.792 

6.112 
6.101 

5.547 

5.077 

4.681 

49 
50 

32.  727 

21. 176 

12.413 

10.  286 

8.780 

5.538 

5.070 

4.675 

51 

32. 432 

21.053 

15. 584 

12.  371 

10.  256 

8.759 

7.643 

6.779 

6.091 

5. 530 

5.063 

4.669 

51 

52 

32. 143 

20.  930 

15.517 

12. 329 

10. 227 

8.737 

7.627 

6.766 

6.081 

5.521 

5.056 

4.663 

52 

53 

31.858 

20. 809 

15. 450 

12.  287 

10. 198 

8.716 

7.611 

6.754 

6.071 

5.  513 

5.049 

4.657 

53 

54 
55 

31.579 

20.  690 
20.  571 

15. 384 

12. 245 
12.  203" 

10. 169 

8.695 
8.675 

7.595 
7.579 

6.741 
6.739 

6.060 
6.050 

5.504 
5.496 

5.042 

4.651 

54 
55 

31.  304 

15.319 

10. 140 

5.  035 

4.  645 

56 

31.  034 

20. 455 

15. 254 

12. 162 

10. 112 

8.654 

7.563 

6.716 

6.040 

5.487 

5.028 

4.639 

56 

57 

30.  769 

20. 339 

15. 190 

12. 121 

10.  084 

8.633 

7.547 

6.704 

6.030 

5.479 

5.020 

4.633 

57 

58 

30.  508 

20. 225 

15. 126 

12.  080 

10. 055 

8.612 

7.531 

6.691 

6.020 

5.471 

5.013 

4.627 

58 

59 

30.  252 

20. 112 

15. 062 

12.  040 

10. 027 

8.591 

7.515 

6.679 

6.010 

5.463 

5.006 

4.621 

59 

Sec. 

Sec. 

1 

2 

3 

4 

5 

6 

7 

8 

« 

10 

11 

12 

Page  670]                                            TABLE  36. 

Eeduction  of  Local  Mean  Time  to  Standard  Meridian  Time,  and  the  reverse. 

[If  local  meridian  is  east  of  standard  meridian,  subtract  from  local  mean  time,  or  add  to  standard  meridian  time.    If  local 

meridian  is  west  of  standard  meridian,  add  to  local  mean  time,  or  subtract  from  standard  meridian  time.] 

Difference  of  longitude  be- 

Reduction to 

be  applied 

to  local  mean 

time. 

Difference  of   longitude  be- 

Reduction to 

tween  local  meridian  and 
standard  meridian. 

tween  local  meridian  and 
standard  meridian. 

De  appiieci 

to  local  mean 

time. 

o      /             o      / 

^f^7mtes. 

O        '                   0        ' 

Minutes. 

0  oft  to  0  07 

0 

7  23  to    7  37 

30 

0  08  to  0  22 

1 

7  38  to    7  52 

31 

0  23  to  0  37 

2 

7  53  to    8  07 

32 

0  38  to  0  52 

3 

8  08  to    8  22 

33 

0  53  to  1  07 

4 

8  23  to    8  37 

34 

1  08  to  1  22 

5 

8  38  to    8  52 

35 

1  23  to  1  37 

6 

8  53  to    9  07 

36 

1  38  to  1  52 

7 

9  08  to    9  22 

37 

1  53  to  2  07 

8 

9  23  to    9  37 

38 

2  08  to  2  22 

9 

9  38  to    9  52 

39 

2  23  to  2  37 

10 

9  53  to  10  07 

40 

2  38  to  2  52 

11 

10  08  to  10  22 

41 

2  53  to  3  07 

12 

10  23  to  10  37 

42 

3  08  to  3  22 

13 

10  38  to  10  52 

43 

3  23  to  3  37 

14 

10  53  to  11  07 

44 

3  38  to  3  52 

15 

11  08  to  11  22 

45 

3  53  to  4  07 

16 

11  23  to  11  37 

46 

4  08  to  4  22 

17 

11  38  to  11  52 

47 

4  23  to  4  37 

18 

11  53  to  12  07 

48 

4  38  to  4  52 

19 

12  08  to  12  22 

49 

4  53  to  5  07 

20 

12  23  to  12  37 

50 

5  08  to  5  22 

21 

12  38  to  12  52 

51 

5  23  to  5  37 

22 

12  53  to  13  07 

52 

5  38  to  5  52 

23 

13  08  to  13  22 

53 

5  53  to  6  07 

24 

13  23  to  13  37 

54 

6  08  to  6  22 

25 

13  38  to  13  52 

55 

6  23  to  6  37 

26 

13  53  to  14  07 

56 

6  38  to  6  52 

27 

14  08  to  14  22 

57 

6  53  to  7  07 

28 

14  23  to  14  37 

58 

7  08  to  7  22 

29 

14  38  to  14  52 

59 

TABLE  37. 

[Page  571 

Log.  A  and  Log.  B. 

For  Computing  the  Equation  of  Equal  Altitudes.  For  Noon,  A-; 

for  Midnight,  A+; 

for  Noon  or  Midnight,  B+.    | 

Argument=Elapsed  Time.] 

05 -^ 

Oh 

1 

h 

2h 

gh 

4h 

5)>       1 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

m. 
0 

9. 4059 

9. 4059 

9. 4072 

9. 4034 

9.  4109 

9.  3959 

9. 4172 

9. 3828 

9.4260 

9.  3635 

9. 4374 

9.  3369 

1 

.4059 

.4059 

.4072 

.4034 

.4110 

.3957 

.4173 

.  3825 

.4261 

.3631 

.  4376 

.3364 

2 

.4059 

.4059 

.4073 

.4033 

.4111 

.3955 

.4174 

.3822 

.4263 

.3627 

.4378 

.  3358 

3 

.  4059 

.4059 

.4073 

.4032 

.4112 

.3953 

.4175 

.3820 

.4265 

.3624 

.4380 

.3353 

4 

.4059 

.4059 
9. 4059 

.4074 

.4031 

.4113 

.3952 

.4177 

.3817 
9.  3814 

.4266 

.3620 

.4383 

.3348 

5 

9. 4059 

9. 4074 

9. 4030 

9.4113 

9.  3950 

9. 4178 

9. 4268 

9.  3616 

9. 4385 

9.  3343 

6 

.4060 

.4059 

.4074 

.4029 

.4114 

.3948 

.4179 

.3811 

.4270 

.3612 

.4387 

.3337 

7 

.4060 

.4059 

.4075 

.4028 

.4115 

.3946 

.4181 

.  3809 

.4272 

.3608 

.4389 

.3332 

8 

.4060 

.4059 

.  4075 

.4027 

.4116 

.3944 

.4182 

.3806 

.4273 

.3604 

.4391 

.3327 

9 
10' 

.4060 
9. 4060 

.4059 
9.  4059 

.4076 
9. 4076 

.4026 
"9.  4025 

.4117 

.3943 

.4183 

.3803 
9.  3800 

.4275 
9. 4277 

.3600 

.4393 
9. 4396 

.3221 
9. 3316 

9.  4118 

9. 3941 

9.  4184 

9. 3596 

11 

.4060 

.4059 

.4077 

.4024 

.4119 

.3939 

.4186 

.3797 

.4279 

.3592 

.4398 

.3311 

12 

.4060 

.  4058 

.4077 

.  4023 

.4120 

.3937 

.4187 

.3794 

.4280 

.3588 

.4400 

.3305 

13 

.4060 

.  4058 

.4078 

.4022 

.4121 

.3935 

.4188 

.  3792 

.4282 

.3584 

.4402 

.3300 

14 
15 

.4060 

.4058 

.4078 

.4021 

.4121 

.3933 

.4190 

.3789 
9.  3786' 

.4284 
9.  4'286 

.3580 

.4405 

.3294 

9. 4060 

9. 4058 

9. 4079 

9. 4020 

9.  4122 

9. 3931 

9. 4191 

9.  3576 

9. 4407 

9.  3289 

16 

.4060 

.4058 

.4079 

.4019 

.4123 

.3929 

.4193 

.3783 

.4288 

.3572 

.4409 

.3283 

17 

.4060 

.4057 

.4080 

.4018 

.4124 

.3927 

.4194 

.3780 

.4289 

.  3568 

.4411 

.3278 

18 

.4061 

.4057 

.4080 

.4017 

.4125 

.3925 

.4195 

.  3777 

.4291 

.3564 

.4414 

.3272 

19 
20 

.4061 

.4057 

.4081 

.4016 
9.  4015 

.4126 

.3923 

.4197 

.3774 

.4293 
9. 4295 

.3559 

.4416 

.3266 

9. 4061 

9. 4057 

9. 4081 

9. 4127 

9.  3921 

9.  4198 

9. 3771 

9.  3555 

9.4418 

9.  3261 

21 

.4061 

.4056 

.4082 

.4014 

.4128 

.3919 

.4199 

.  3768 

.4297 

.3551 

.4420 

.3255 

22 

.4061 

.4056 

.4083 

.4013 

.4129 

.3917 

.4201 

.3765 

.  4299 

.3547 

.4423 

.3249 

23 

.4061 

.4056 

.  4083 

.4012 

.4130 

.3915 

.4202 

.3762 

.4300 

.3542 

.4425 

.3244 

24 
25 

.4061 

.4055 

.4084 
9. 4084 

.4010 
9.4009 

.4131 

.3913 

.4204 

.3759 

.4302 

.  3538 

.4427 

.3238 

9. 4062 

9. 4055 

9. 4132 

9.  3911 

9.  4205 

9. 3756 

9. 4304 

9.3534 

9.4430 

9. 3232 

26 

.4062 

.4055 

.4085 

.4008 

.4133 

.3909 

.4207 

.3752 

.4306 

.  3530 

.4432 

.3226 

27 

.4062 

.4054 

.4086 

.4007 

.4134 

.3907 

.4208 

.3749 

.4308 

.3525 

.4434 

.  3220 

28 

.4062 

.4054 

.4086 

.4006 

.4135 

.3905 

.4209 

.3746 

.4310 

.3521 

.4437 

.3214 

29 
30 

.4062 
9. 4062 

.4054 
9. 4053 

.4087 

.4004 
9.4003 

.4136 

.3903 

.4211 

.3743 

.4312 

.3516 

.4439 

.3208 

9. 4087 

9.  4137 

9.3900 

9. 4212 

9.3740 

9. 4314 

9. 3512 

9.4441 

9.  3203 

31 

.  4063 

.4053 

.4088 

.4002 

.  4138 

.3898 

.4214 

.3737 

.4315 

.3508 

.4444 

.3197 

32 

.4063 

.4052 

.4089 

.4001 

.4139 

.  3896 

.4215 

.3733 

.4317 

.  3503 

.4446 

.3191 

33 

.4063 

.4052 

.4089 

.  3999 

.4140 

.3894 

.4217 

.3730 

.4319 

.3499 

.4448 

.3185 

34 

.  4063 

.4051 

.4090 
9. 4091 

.  3998 
9. 3997 

.4141 

.3892 

.4218 
9. 4220 

.3727 

.4321 

.  3494 

.4451 

.3178 

35 

9. 4064 

9. 4051 

9.  4142 

9.  3889 

9.  3723 

9. 4323 

9.3490 

9.4453 

9. 3172 

36 

.4064 

.4050 

.  4091 

.  3995 

.4144 

.3887 

.4221 

.3720 

.4325 

.3485 

.4456 

.3166 

37 

.4064 

.  4050 

.4092 

.  3994 

.4145 

.3885 

.4223 

.3717 

.4327 

.3480 

.4458 

.3160 

38 

.4064 

.4049 

.4093 

.3993 

.4146 

.3882 

.4224 

.3713 

.4329 

.3476 

.4460 

.3154 

39 

.  4065 

.4049 

.4093 

.  3991 

.4147 
9.  4148 

.3880 
9.  3878 

.4226 
9. 4227 

.3710 
9.  3707 

.4331 
9. 4333 

.3471 

.4463 

.3148 

40 

9. 4065 

9. 4048 

9. 4094 

9. 3990 

9. 3467 

9.4465 

9.  3142 

41 

.4065 

.4048 

.  4095 

.3988 

.4149 

.3875 

.4229 

.3703 

.4335 

.3462 

.4468 

.3135 

42 

.4065 

.4047 

.4095 

.3987 

.4150 

.3873 

.4231 

.3700 

.4337 

.3457 

.4470 

.3129 

43 

.4066 

.4047 

.4096 

.3985 

.4151 

.3871 

.4232 

.3696 

.4339 

.3453 

.4473 

.3123 

44 
45 

.4066 

.4046 
9. 4045 

.4097 

.3984 

.4152 

.3868 

.4234 

.3693 
9. 3690 

.4341 
9. 4343 

.3448 

.4475 

.3116 

9. 4066 

9. 4097 

9. 3982 

9. 4154 

9. 3866 

9. 4235 

9. 3443 

9. 4477 

9.3110 

46 

.4067 

.4045 

.4098 

.3981 

.4155 

.3863 

.4237 

.3686 

.4345 

.  3438 

.4480 

.  3103 

47 

.4067 

.4044 

.4099 

.3979 

.  4156 

.3861 

.4238 

.3683 

.4347 

.3433 

.4482 

.3097 

48 

.4067 

.4043 

.4100 

.3978 

.4157 

.3859 

.4240 

.  3679 

.4349 

.3429 

.4485 

.  3091 

49 
50 

.4068 

.4043 

.4100 
9.  4101 

.3976 
9."3975 

.4158 
9.  4159 

.3856 
9. 3854 

.4242 

.  3675 
9.  3672 

.4351 
"9.  4353' 

.3424 

.4487 

.3084 

9. 4068 

9. 4042 

9. 4243 

9.  3419 

9. 4490 

9.  3078 

51 

.4068 

.4041 

.4102 

.  3973 

.  4161 

.3851 

.4245 

.3668 

.  4355 

.3414 

.4492 

.3071 

52 

.4069 

.4041 

.4103 

.  3972 

.4162 

.3849 

.4246 

.  3665 

.4357 

.3409 

.4494 

.3064 

53 

.4069 

.4040 

.  4103 

.3970 

.4163 

.3846 

.4248 

.3661 

.  4359 

.3404 

.4497 

.  3058 

54 
55 

.4069 
9.  4070 

.4039 
9. 4038 

.4104 
9. 4105 

.3969 

.4164 
9.4165 

.3843 
9. 3841 

.4250 

.3657 
9.  3654 

.  4361 
9.  4363 

.3399 

.4500 
9. 4503 

.3051 

9. 3967 

9. 4251 

9. 3394 

9.  3044 

56 

.4070 

.4038 

.4106 

.3965 

.4167 

.3838 

.4253 

.3650 

.4366 

.3389 

.4505 

.3038 

57 

.4071 

.4037 

.4107 

.3964 

.4168 

.3836 

.4255 

.3646 

.  4368 

.  3384 

.4508 

.3031 

58 

.4071 

.4036 

.4107 

.3962 

.4169 

.  3833 

.4256 

.3643 

.4370 

.3379 

.4510 

.  3024 

59 
60 

.4071 
9. 4072 

.4035 
9. 4034 

.4108 
9.'4T09 

.3960 
9. 3959 

.4170 

.  3830 

9. 3828 

.4258 

.3639 

.4372 

.3374 

.4513 

.3017 

9.4172 

9. 4260 

9. 3635 

9.  4374 

9. 3369 

9. 4515 

9.  3010 

Page  572] 

TABLE  37. 

Log.  A  and  Log.  B. 

[For  Computing  the  Equation  of  Equal  Altitudes.  For  Noon,  A-;  for  Midnight,  A  +  ;  for  Noon  or  Midnight,  B+.    | 

Argument=Elapsed  Time.] 

0 

h 

7 

h 

-      I 

1 

10^      1 

Ilk     1 

Log.  A. 

Log.B. 

Log.  A. 

Log.B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.B. 

Log.  A. 

Log.B. 

Log.  A. 

Log.B. 

m. 
0 

9.  4515 

9.  3010 

9^4685 

9. 2530 

9. 4884 

9. 1874 

9.5115 

9. 0943 

9. 5379 

8. 9509 

9.  5680 

8. 6837 

1 

.4518 

.3003 

.4688 

.2520 

.4888 

.1861 

.5119 

.0925 

.5384 

.9478 

.5685 

.6770 

2 

.4521 

.2996 

.4691 

.2511 

.4892 

.1848 

.5123 

.0906 

.5389 

.9447 

.5691 

.6701 

3 

.  4523 

.2989 

.4694 

.2502 

.4895 

.1835 

.5127 

.0887 

.5393 

.9416 

.5696 

.6632 

4 
5 

.4526 
9. 4528 

.2982 

.4697 

.2492 

.4899 
9. 4902 

.1822 
9. 1809 

.5132 
9. 5136 

.0867 

.5398 

.9384 

.5701 

.6560 
8.  6488 

9. 2975 

9. 4701 

9. 2483 

9. 0848 

9.5403 

8. 9352 

9. 5707 

6 

.4531 

.2968 

.4704 

.2473 

.4906 

.1796 

.5140 

.0828 

.5408 

.9320 

.  5712 

.6414 

7 

.4534 

.2961 

.4707 

.2463 

.4910 

.1782 

.5144 

.0809 

.5412 

.9287 

.5718 

.6339 

8 

.4536 

.2954 

.4710 

.2454 

.4913 

.1769 

.5148 

.0789 

.5417 

.9254 

.5723 

.6262 

9 
10 

.4539 

.2947 

.4713 

.2444 
9.  2434 

.4917 

.1756 
9. 1742 

.5153 

.0769 

.5422 

.9221 

.5728 

.6183 

9. 4542 

9. 2940 

9. 4716 

9. 4921 

9. 5157 

9. 0749 

9. 5427 

8.9187 

9.5734 

8.  6103 

11 

.4544 

.2932 

.4719 

.  2425 

.4924 

.1728 

.  5161 

.0729 

.5432 

.9153 

.  5739 

.6021 

12 

.4547 

.2925 

.4723 

.2415 

.4928 

.1715 

.  5165 

.0708 

.5436 

.9118 

.5745 

.5937 

13 

.4550 

.2918 

.4726 

.2405 

.4932 

.1701 

.5169 

.0688 

.5441 

.9083 

.5750 

.5852 

14 

.4552 

.2911 
9. 2903 

.4729 

.2395 

.4935 

.1687 

.5174 

.0667 

.5446 

.9048 

.5756 

.5764 

15 

9. 4555 

9. 4732 

9. 2385 

9. 4939 

9. 1673 

9.5178 

9. 0646 

9. 5451 

8. 9013 

9. 5761 

8.  5674 

16 

.4558 

.2896 

.4735 

.2375 

.  4943 

.1659 

.5182 

.0625 

.5456 

.8977 

.5767 

.5583 

17 

.4561 

.2888 

.4738 

.2365 

.4946 

.1645 

.5186 

.0604 

.5461 

.8940 

.5772 

.5488 

18 

.4563 

.2881 

.4742 

.2355 

.4950 

.1630 

.5191 

.0583 

.  5466 

.8903 

.5778 

.5392 

19 
20 

.4566 

.2873 
'9.  28*66 

.4745 

.2344 

.4954 
9. 4958 

.1616 

.  5195 

.0561 

.5470 

.8866 

.5783 

.5293 

9. 4569 

9.  4748 

9.  2334 

9. 1602 

9.5199 

9. 0540 

9. 5475 

8. 8829 

9.  5789 

8.  5192 

21 

.4572 

.  2858 

.4751 

.2324 

.4961 

.1587 

.5204 

.0518 

.5480 

.8791 

.5794 

.5088 

22 

.  4574 

.2850 

.4755 

.2313 

.4965 

.1573 

.  5208 

.0496 

.5485 

.8752 

.5800 

.4981 

23 

.4577 

.2843 

.4758 

.2303 

.4969 

.1558 

.5212 

.0474 

.5490 

.8713 

.5806 

.4871 

24 

.4580 

.2835 

.4761 

.2292 

.4973 

.1543 

.5217 

.0452 

.  5495 
9. 5500 

.8674 

.5811 

.  4758 

25 

9. 4583 

9. 2827 

9. 4764 

9. 2282 

9. 4977 

9. 1528 

9. 5221 

9. 0429 

8.  8634 

9.  5817 

8. 4641 

26 

.4585 

.2819 

.4768 

.  2271 

.4980 

.1513 

.5225 

.0406 

.5505 

.8594 

.5822 

.4521 

27 

.4588 

.2812 

.4771 

.  2261 

.4984 

.1498 

.5230 

.0383 

.5510 

.  8553 

.5828 

.  4397 

28 

.4591 

.2804 

.4774 

.2250 

.4988 

.1483 

.5234 

.0360 

.5515 

.  8512 

.5834 

.4270 

29 
30 

.4594 

.2796 
9.  2788 

.4778 

.2239 

.4992 
9.  4996 

.1468 

.5238 
9. 5243 

.  0337 

.5520 

.8470 

.5839 

.  4138 

9. 4597 

9. 4781 

9.  2228 

9. 1453 

9.  0314 

9. 5525 

8. 8427 

9. 5845 

8. 4001 

31 

.4600 

.2780 

.4784 

.2217 

.5000 

.1437 

.5247 

.0290 

.5530 

.8384 

.5851 

.3860 

32 

.4602 

.2772 

.4788 

.2206 

.5003 

.1422 

.5252 

.0266 

.  5535 

.8341 

.5856 

.3713 

33 

.4605 

.2764 

.4791 

.2195 

.5007 

.1406 

.5256 

.0242 

.  5540 

.8297 

.5862 

.  3561 

34 

.4608 

.  2756 

.4794 

.2184 
9.  2173 

.5011 

.1390 

5261 
9. 5265 

.0218 

.5545 
9. 5550 

.8253 

.5868 

.  3403 
8. 3239 

35 

9. 4611 

9.  2747 

9. 4798 

9. 5015 

9. 1375 

9.  0194 

8. 8208 

9.  5874 

36 

.4614 

.2739 

.4801 

.2162 

.5019 

.1359 

.5269 

.0169 

.5555 

.8162 

.5879 

.3067 

37 

.4617 

.2731 

.4804 

.2151 

.5023 

.1343 

.5274 

.0144 

.5560 

.8115 

.5885 

.2888 

38 

.4620 

.2723 

.4808 

.2140 

.5027 

.1327 

.5278 

.0119 

.5565 

.8068 

.5891 

.2701 

39 
40 

.4622 
9.  4625 

.2714 
9. 2706 

.4811 

.2128 

.5031 

.1310 

.5283 
9.5287 

.0094 

.5570 

.8020 

.5897 

.2505 

9.4815 

9.2117 

9. 5035 

9.1294 

9. 0069 

9. 5576 

8.  7972 

9. 5902 

8. 2299 

41 

.4628 

.2698 

.4818 

.2105 

.5038 

.1278 

.5292 

.0043 

.5581 

.7923 

.5908 

.2082 

42 

.4631 

.2689 

.4821 

.2094 

.5042 

.1261 

.  5296 

.0017 

.5586 

.7873 

.5914 

.1853 

43 

.  4634 

.2681 

.4825 

.2082 

.5046 

.1244 

.5301 

8. 9991 

.5591 

.7823 

.5920 

.1611 

44 
45 

.4637 

.2672 

.4828 

.2070 
9.2059 

.5050 

.1228 

.5305 

.9965 
8. 9938 

.  5596 
9. 5601 

.7772 

.5926 

.1354 

9. 4640 

9.2664 

9.  4832 

9. 5054 

9.1211 

9.  5310 

8.7720 

9.  5931 

8. 1080 

46 

.4643 

.2655 

.4835 

.2047 

.  5058 

.1194 

.5315 

.9911 

.5606 

.7668 

.5937 

.0786 

47 

.4646 

.2646 

.4839 

.2035 

.5062 

.1177 

.  5319 

.9884 

.5612 

.7614 

.5943 

.0470 

48 

.4649 

.2638 

.4842 

.2023 

.5066 

.1159 

.5324 

.9857 

.5617 

.7560 

.5949 

.0128 

49 
50 

.4652 

.2629 
9. 2620 

.4846 

.2011 

.5070 

.1142 
9. 1125 

.5328 

.9830 

8. 9802 

.5622 

.7505 
8. 7449 

.5955 

7. 9756 

9. 4655 

9.4849 

9. 1999 

9. 5074 

9. 5333 

9. 5627 

9. 5961 

7. 9348 

51 

.4658 

.2611 

.4853 

.1987 

.5078 

.1107 

.5337 

.9774 

.5632 

.7392 

.5967 

.8897 

52 

.4661 

.2602 

.4856 

.1974 

.5082 

.1089 

.5342 

.9745 

.5638 

.7335 

.  5973 

.8391 

53 

.4664 

.2593 

.4860 

.1962 

.5086 

.1072 

.5347 

.9717 

.5643 

.7276 

.5979 

.7817 

54 

.4667 

.2584 
9. 2575 

.4863 
9. 4867 

.1950 

.5091 

.1054 

.5351 

.9688 
8. 9659 

.5648 
9.5654 

.7217 
8.  7156 

.5985 

.7154 

55 

9. 4670 

9. 1937 

9.  5095 

9. 1036 

9. 5356 

9. 5991 

7. 6368 

56 

.4673 

.2566 

.4870 

.1925 

.5099 

.1017 

.5361 

.9630 

.5659 

.7094 

.5997 

.5405 

57 

.4676 

.2557 

.4874 

.1912 

.5103 

.0999 

.  5365 

.9600 

.5664 

.7032 

.6003 

.4162 

58 

.4679 

.2548 

.4877 

.1900 

.5107 

.0981 

.5370 

.9570 

.5669 

.6968 

.6009 

.2407 

59 
60 

.4682 

.2539 
9. 2530 

.4881 

.  1887 

.5111 

.0962 
9. 0943 

.5375 
9. 5379 

.9540 
8.9509 

.5675 
9. 5680 

.6903 

.6015 

6. 9591 

9.  4685 

9. 4884 

9. 1874 

9.  5115 

8. 6837 

9.6021 

Inf. 

f  OF  THE     ^  X 


%£^LypnBKa>._^ 

/ 

TABLE  37. 

[Page  573 

Log.  A  and  Log.  B. 

[For  Computing  the  Equation 

of  Equal 

Altitudes.  For  Noon,  A  — ; 

for  Midnight,  A +; 

for  Noon  or  Midnlgh 

t,  B-. 

Argument  =  Elapsed  Time.  1 

■  .  lai" 

18" 

14h 

loh 

itt- 

1 

7" 

Log.  A. 

Log.  B. 
Inf. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

in. 
0 

9. 6021 

9.6406 

8. 7563 

9. 6841 

9. 0971 

9. 7333 

9.  3162 

9. 7895 

9.4884 

9. 8539 

9.  6383 

1 

.6027 

6. 9608 

.6412 

.7641 

.  6848 

.1014 

.7:342 

.  3194 

.7905 

.4911 

.8550 

.6407 

9 

.6038 

7. 2431 

.  6419 

.7718 

.6856 

.  1057 

.  7351 

.  8225 

.7915 

.4937 

.  8562 

.6431 

8 

.6039 

.4198 

.6426 

.7794 

.6864 

.1099 

.7360 

.8256 

.7925 

.4963 

.8573 

.6455 

4 
5 

.6045 

.  5453 

7. 6428 

.  6438 
9.6440 

.7868 

.6872 

.1141 
9. 1183 

.7369 
9.  7378 

.8287 

.7935 

.4990 

.8585 

.6478 

9. 6051 

8. 7942 

9.  6879 

9. 3319 

9. 7945 

9.  5016 

9. 8597 

9. 6502 

B 

.  6057 

.7226 

.6447 

.  8015 

.6887 

.1224 

.  7386 

.3350 

.  7955 

.5042 

.8608 

.6526 

7 

.  6063 

.7902 

.  6454 

.8087 

.  6895 

.  1265 

.7395 

.3880 

.7965 

.  5068 

.8620 

.6550 

8 

.6069 

.8488 

.6461 

.8158 

.6903 

.1806 

.7404 

.8411 

.7975 

.5094 

.  8632 

.  6573 

9 
10 

.  6075 

.9005 

.6467 
9.6474 

.8227 
8. 8296 

.6911 
9.  6919 

.1347 
9. 1887 

.7418 

.3442 
9.  8472 

.7986 
9.  7996' 

.5120 
9.  5146 

.8644 

.6597 

9.  6082 

7. 9469 

9.  7422 

9. 8655 

9. 6621 

n 

.6088 

.9889 

.6481 

.8364 

.6926 

.1428 

.7431 

.  8503 

.8006 

.5171 

.8667 

.6644 

12 

.6094 

8. 0273 

.6488 

.  8482 

.6934 

.1468 

.7440 

.  3533 

.8016 

.5197 

.8679 

.  6668 

18 

.6100 

.0627 

.6495 

.8498 

.6942 

.1507 

.7449 

.3563 

.8027 

.  5223 

.8691 

.6691 

14 

15 

.6106 
9.6112 

.0955 
8. 1260 

.6502 
9.  6509 

.  8564 
8. 8628 

.6950 
9. 6958 

.1547 
9. 1586 

.7458 

.  3593 
9.8628 

.  8037 
9.  8047' 

.5248 

.  8708 

.6715 
9. 6738 

9. 7467 

9. 5274 

9.8715 

16 

.6119 

.  1547 

.6516 

.8692 

.6966 

.1625 

.7476 

.3653 

.8058 

.5800 

.8727 

.6762 

17 

.6125 

.1816 

.  6523 

.8756 

.6974 

.1664 

.  7485 

.  3688 

.8068 

.5325 

.8789 

.6785 

18 

.6131 

.2071 

.6580 

.8818 

.6982 

.1703 

.7494 

.3713 

.8078 

.5851 

.8751 

.6809 

19 

.6137 

.  2312 

.  6538 

.8880 

.6990 
9. 6998 

.1741 

.7503 

.  3742 
9. 3772^ 

.8089 
9. 8099 

.5376 
9. 5401 

.8763 
9. 8775 

.6832 

20 

9.6144 

8. 2541 

9.  6545 

8. 8941 

9. 1779 

9.  7512 

9. 6856 

21 

.6150 

.2759 

.  6552 

.9002 

.7006 

.1817 

.7522 

.3801 

.8110 

.5427 

.8787 

.6879 

22 

.6156 

.2967 

.6559 

.9062 

.7014 

.1855 

.7531 

.3831 

.8120 

.5452 

.8799 

.6903 

28 

.6163 

.3166 

.6566 

.9121 

.7022 

.1893 

.7540 

.8860 

.8131 

.5477 

.8812 

.6926 

24 
25 

.6169 

.8357 

.6573 
9.  6580 

.9180 
8. 9288 

.7030 
9. 7088 

.1930 

.7549 

.  3889 
9.  3918 

.8141 
9. 8152 

.5502 
9. 5528 

.8824 

.6949 
9.  6973 

9.6175 

8.  3540 

9. 1967 

9. 7558 

9. 8836 

26 

.6182 

.3717 

.6588 

.9295 

.7047 

.2004 

.7568 

.3947 

.8162 

.5553 

.8848 

.6996 

27 

.6188 

.3887 

.  6595 

.  9852 

.7055 

.2041 

.7577 

.3976 

.8173 

.  5578 

.8861 

.7019 

28 

.6194 

.  4051 

.6602 

.9408 

.7063 

.2078 

.7586 

.4005 

.8184 

.  5603 

.8873 

.7043 

29 
80 

.6201 
9. 6207 

.4210 
8.  4363 

.6609 

.9464 
8.  9519 

.7071 
9.  7079 

.2114 
9. 2150 

.7595 

.4083 
9. 4062 

.8194 

.  5628 

.8885 

.7066 

9. 6616 

9. 7605 

9. 8205 

9. 5653 

9. 8898 

9. 7089 

81 

.  6214 

.4512 

.6624 

.9573 

.7088 

.2186 

.7614 

.4090 

.8216 

.5677 

.8910 

.7112 

82 

.6220 

.  4657 

.  6631 

.9627 

.7096 

.2222 

.7624 

.4119 

.8227 

.5702 

.8923 

.7186 

88 

.6226 

.4796 

.  6638 

.9681 

.7104 

.2258 

.7638 

.4147 

.8237 

.5727 

.  8935 

.7159 

34 
85 

.6233 
9. 6239 

.  4932 
8. 5064 

.  6645 

.  9734 

8. 9787 

.7112 

.2293 

.7642 

.4175 

.8248 

.5752 

.8948 

.7182 

9. 6653 

9.  7121 

9.  2329 

9.  7652 

9. 4204 

9.  8259 

9. 5777 

9.  8961 

9.  7205 

86 

.6246 

.5192 

.6660 

.  9889 

.7129 

.2364 

.7661 

.4232 

.8270 

.5801 

.8973 

.7228 

87 

.6252 

.5318 

.6667 

.9891 

.7137 

.2399 

.7671 

.4260 

.8281 

.5826 

.8986 

.7251 

88 

.6259 

.5440 

.6675 

.9942 

.7146 

.2434 

.7680 

.4288 

.8292 

.5850 

.8999 

.7275 

39 

40 

.6265 

.  5559 

.6682 
9. 6690 

.  9993 

.7154 

.2468 

.7690 

.4316 

.8803 

.5875 

.9011 

.7298 

9. 6272 

8. 5675 

9. 0043 

9. 7162 

9.  2508 

9. 7699 

9. 4348 

9.  8314 

9. 5900 

9. 9024 

9. 7821 

41 

.6279 

.5788 

.6697 

.0093 

.7171 

.  2587 

.7709 

.4371 

.8325 

.5924 

.  9037 

.7344 

42 

.6285 

.5899 

.6704 

.0142 

.7179 

.2571 

.7718 

.439^ 

.  8336 

.  5948 

.9050 

.7367 

48 

.6292 

.6008 

.6712 

.0191 

.7187 

.2605 

.7728 

.4426 

.8347 

.5973 

.9063 

.7390 

44 
45 

.6298 

.6114 
8.  6218 

.6719 

.0240 

.7196 
9.  7204 

.2639 

.7788 

.4454 

.8358 

.5997 
9.6022 

.9075 

.7413 

9.  6305 

9.  6727 

9. 0288 

9.  2673 

9. 7747 

9.4481 

9. 8369 

9. 9088 

9. 7436 

46 

.6311 

.6320 

.6734 

.0336 

.7213 

.2706 

.  7757 

.4509 

.8380 

.6046 

.9101 

.7459 

47 

.6318 

.6419 

.6742 

.0384 

.7221 

.2740 

.7767 

.4536 

.  8391 

.6070 

.9114 

.7482 

48 

.6325 

.6517 

.6749 

.0431 

.7230 

.  2773 

.7776 

.4563 

.8402 

.6094 

.9127 

.7505 

49 
50 

.6381 
9. 6338 

.6613 
8.  6707 

.6757 
9.  6764 

.0478 
9. 0524 

.7238 

.2806 

.7786 

.4590 

.8414 

.6119 

.9140 

.7529 

9. 7247 

9. 2839 

9. 7796 

9.4617 

9. 8425 

9.  6143 

9. 9154 

9. 7552 

51 

.6345 

.6799 

.6772 

.0570 

.7256 

.2872 

.7806 

.4644 

.8486 

.6167 

.9167 

.7575 

52 

.6351 

.6890 

.6779 

.0616 

.7264 

.2905 

.7815 

.4671 

.8447 

.6191 

.9180 

.7598 

53 

.  6358 

.6979 

.6787 

.0662 

.7273 

.2937 

.7825 

.4698 

.8459 

.6215 

.9193 

.7621 

54 

.6365 

.7067 

.6795 
9.  6802 

.0707 
9.  0752 

.7281 

.2970 
9.  8002 

.  7835 

.4725 
9. 4752 

.8470 
9.8481 

.6239 

.9206 

.7644 

55 

9. 6372 

8.  7153 

9. 7290 

9. 7845 

9. 6263 

9. 9220 

9.  7667 

56 

.6378 

.7237 

.6810 

.0796 

.7299 

.  8034 

.7855 

.  4778 

.8493 

.6287 

.9233 

.7690 

57 

.6385 

.7321 

.6818 

.0840 

.7307 

.3066 

.7865 

.4805 

.8504 

.6311 

.9246 

.7713 

58 

.6392 

.7402 

.6825 

.0884 

.7316 

.3098 

.7875 

.4831 

.8516 

.6335 

.9260 

.7736 

59 

.6399 

.  7483 

.6833 

.0928 

.7324 

.3130 

.7885 

.4858 

.8527 

.6359 

.9273 

.7759 

60 

9.6406 

8. 7568 

9.6841 

9.0971 

9. 7333 

9.  3162 

9.  7895 

9.4884 

9. 8539 

9. 6383 

9. 9287 

9.  7782 

Page  574 

TABLE  37. 

Log.  A  and  Log.  B. 

[For  Computing  the  Equation  of  Equal  Altittide.s 

.  For  Noon,  A  — ;  for  Midnight,  A  +; 

for  Noon  or  Midnight,  B  -.   1 

Argument  =  Elapsed  Time.] 

fa 
l| 

18" 

IS" 

200 

2ih 

221- 

o 

jh 

Ivog.  A. 

Log.B. 

Log.  A. 

Log.B. 

Log.  A. 

Log.B. 

Log.  A. 
0. 2623 

Log.B. 

Log.  A. 

Log.  B. 

Log.  A. 

Log.  B. 

m. 
0 

9. 9287 

9.  7782 

• 
0.  0172 

9. 9167 

0. 1249 

0. 0625 

0.  2279 

0. 4523 

0.  4372 

0.  7689 

0.  7652 

1 

.9300 

.7804 

.  0188 

.9190 

.1269 

.0650 

.2649 

.2309 

.4562 

.4414 

.  7765 

.7729 

2 

.9314 

.7827 

.  0204 

.  9213 

.1290 

.0676 

.2676 

.  2339 

.4601 

.4455 

.7842 

.7807 

3 

.  9327 

.7850 

.0221 

.9237 

.1310 

.0701 

.2702 

.2370 

.4640 

.4497 

.7920 

.7886 

4 
5 

.9341 
9.9355 

.7873 

.0237 

.9260 

.  1330 

.0727 

.2729 

.2401 
0.2431 

.4680 
0. 4720 

.  4540 

.8000 
0.  8081 

.7967 

9.  7896 

0.  0253 

9. 9284 

0.1351 

0. 0753 

0. 2756 

0. 4582 

0.8049 

6 

.9368 

.7919 

.0270 

.9307 

.1371 

.0779 

.  2783 

.2462 

.4761 

.4625 

.8163 

.8133 

7 

.9382 

.7942 

.0286 

.9331 

.1392 

.0805 

.2810 

.2493 

.4801 

.4668 

.8247 

.8218 

8 

.9396 

.7965 

.0303 

.  9355 

.1412 

.0830 

.2838 

.  2524 

.4842 

.4711 

.  8333 

.8305 

9 

.9410 

.7988 

.0319 
0. 0336 

.9378 

.  1433 
0. 1454 

.0856 

.2865 

.  2556 
0.2587 

.4884 
0. 4926 

.4755 

.8420 

.  8393 
0.  8483 

10 

9. 9424 

9.8011 

9. 9402 

0. 0882 

0.  2893 

0.4799 

0. 8508 

11 

.9437 

.8034 

.  0353 

.9426 

.1475 

.0909 

.2921 

.2619 

.4968 

.4844 

.  8599 

.8574 

12 

.9451 

.8057 

.0370 

.9449 

.1496 

.0935 

.2949 

.2650 

.5010 

.4889 

.8691 

.8667 

13 

.9465 

.8080 

.0386 

.9473 

.1517 

.0961 

.2977 

.2682 

.5053 

.4934 

.8786 

.8763 

14 
15 

.9479 

.8103 

.0403 

.9497 

.1538 

.0987 

.3005 

.2714 
0.  2746 

.5097 

.4980 

.8882 

.8860 

9. 9493 

9.  8126 

0. 0420 

9. 9520 

0. 1559 

0. 1013 

0. 3034 

0. 5140 

0. 5026 

0.  8980 

0. 8959 

16 

.9508 

.8149 

.0437 

.9544 

.1581 

.1040 

.3063 

.2778 

.5184 

.5072 

.9080 

.9060 

17 

.9522 

.8172 

.0454 

.9568 

.1602 

.1066 

.  3091 

.2811 

.  5229 

.5118 

.9183 

.9164 

18 

.9536 

.8195 

.0472 

.9592 

.1623 

.1093 

.3120 

.2843 

.5274 

.5165 

.9288 

.9270 

19 
20 

.9550 
9.9564 

.8218 
9. 8241 

.0489 

.9616 

.1645 

.1119 

.  3150 

.2876 
"0.  2909 

.  5319 
0. 5365 

.  5213 
0. 5261 

.  9396 

.9378 

0. 0506 

9.9640 

0. 1667 

0. 1146 

0.  3179 

0. 9506 

0. 9489 

21 

.9579 

.8264 

.0523 

.9664 

.1689 

.1173 

.3208 

.2942 

■ . 5411 

.5309 

.9618 

.9603 

22 

.9593 

.8287 

.0541 

.9687 

.1711 

.1200 

.3238 

.2975 

.  5458 

.5358 

.9734 

.9719 

23 

.9607 

.8310 

.0558 

.9711 

.1733 

.1226 

.3268 

.3008 

.5505 

.5407 

.9853 

.9839 

24 
25 

.9622 
9. 9636 

.8333 

.  0576 

.9735 

.1755 

.1253 
0. 1280 

.3298 

.3041 

.  5553 

.5457 

.9975 

.9961 

9. 8356 

0. 0593 

9. 9760 

0. 1777 

0. 3328 

0.  3075 

0. 5601 

0. 5507 

1.0100 

1.0087 

26 

.9651 

.8379 

.0611 

.9784 

.1799 

.1308 

.3359 

.3109 

.5649 

.5557 

.0228 

.0216 

27 

.9665 

.8402 

.0628 

.9808 

.1821 

.1335 

.3389 

.3143 

.5698 

.5608 

.0361 

.0350 

28 

.9680 

.8425 

.0646 

.9832 

.1844 

.1362 

.3420 

.3177 

.5748 

.5660 

.0497 

.0487 

29 
30 

.9695 
9. 9709 

.8448 

.0664 

.9856 

.1867 

.1389 
0. 1417 

.3451 
0. 3482 

.3211 
0.  3245 

.5798 
0.5848 

.5712 

.0638 

.0628 

9. 8471 

0. 0682 

9. 9880 

0. 1889 

0.5764 

1  1. 0783 

1.  0774 

31 

.9724 

.8494 

.0700 

.9904 

.1912 

.1444 

.3514 

.3280 

.  5899 

.5817 

.0934 

.0925 

32 

.9739 

.  8517 

.0718 

.9929 

.1935 

.1472 

.3545 

.3315 

.  5951 

.5871 

.1089 

.1081 

33 

.9754 

.8540 

.0736 

.9953 

.1958 

.1499 

.3577 

.3350 

.6003 

.5925 

.1250 

.1242 

34 

.9769 

.8563 

.0754 

.9977 

.1981 

.1527 
0. 1555 

.3609 

.3385 
0.  3420' 

.6056 

.5979 

.1416 

.1409 

35 

9.9784 

9. 8586 

0. 0772 

0.0002 

0.  2004 

0. 3641 

0.  6110 

0.6034 

1. 1590 

1. 1583 

36 

.9798 

.8609 

.0790 

.0026 

.2028 

.1582 

.3674 

.3456 

.6164 

.6090 

.1770 

.1764 

37 

.9813 

.8632 

.0809 

.0051 

.2051 

.1610 

.3706 

.3491 

.6218 

.6147 

.1958 

.1952 

38 

.9829 

.8655 

.0827 

.0075 

.2075 

.1638 

.3739 

.3527 

.6273 

.6204 

.2154 

.2149 

39 
40 

.9844 

.8678 

.  0845 

.0100 

.2098 

.1667 

.3772 

.3563 

.6329 

.6261 
0.  6319 

.2359 

.  2354 
1. 2569 

9. 9859 

9.  8701 

0.0864 

0.  0124 

0.  2122 

0. 1695 

0.  3805 

0.  3599 

0. 6386 

1.  2573 

41 

.9874 

.8724 

.0883 

.0149 

.2146 

.1723 

.3839 

.3636 

.6443 

.6378 

.2799 

.2795 

42 

.9889 

.8748 

.0901 

.0173 

.2170 

.1751 

.3873 

.3673 

.6501 

.6438 

.3037 

.3033 

43 

.9904 

.8771 

.0920 

.0198 

.2194 

.1780 

.3907 

.3710 

.6560 

.6498 

.3288 

.3285 

44 

45 

.9920 
9. 9935 

.8794 

.0939 
0. 0958 

.0223 

.2218 

.1808 

.3941 

.3747 
0.  3784 

.6619 
0.6679 

.6559 

.3554 

.3552 

9.  8817 

0. 0248 

0. 2243 

0. 1837 

0.  3975 

0. 6621 

1. 3837 

1.3835 

46 

.9951 

.8840 

.0976 

.0272 

.2267 

.1866 

.4010 

.3822 

.6740 

.6684 

.4140 

.4138 

47 

.9966 

.8863 

.0995 

.0297 

.2292 

.1895 

.4045 

.3859 

.6802 

.6747 

.4465 

.4463 

48 

.9982 

.8887 

.1015 

.0322 

.2316 

.1924 

.4080 

.3897 

.6865 

.6811 

.4815 

.4814 

49 
50 

.9998 

.8910 

.1034 

.0347 

.2341 

.1953 

.4115 

.3936 
0.  3974 

.6928 
0. 6993 

.6876 

.5196 
1.  5613 

.5195 

0.0013 

9.  8933 

0. 1053 

0.  0372 

0. 2366 

0. 1982 

0. 4151 

0. 6942 

1.5612 

51 

.0029 

.8956 

.1072 

.0397 

.2391 

.2011 

.4187 

.4013 

.7058 

.7008 

.6074 

.6073 

52 

.0044 

.8980 

.1092 

.0422 

.2416 

.2040 

.4223 

.  4052 

.7124 

.7076 

.6588 

.6587 

53 

.0060 

.9003 

.1111 

.0447 

.2442 

.2070 

.4260 

.4091 

.7191 

.7144 

.7171 

.7171 

54 

.0076 

.9026 

.1131 

.0473 

.2467 

.2099 

.4297 

.4130 
0. 41 70 

.7259 
0.  7328' 

.7214 

.7844 

.7843 

55 

0.0092 

9. 9050 

0. 1150 

0. 0498 

0. 2493 

0.2129 

0. 4334 

0.  7284 

1. 8638 

1. 8638 

56 

.0108 

.9073 

.1170 

.0523 

.2518 

.2159 

.  4371 

.4210 

.7398 

.  7355 

.9610 

.9610 

57 

.0124 

.9096 

.1190 

.0548 

.2544 

.2189 

.4408 

.4250 

.7469 

.7428 

2. 0863 

2. 0863 

58 

.0140 

.9120 

.1209 

.  0574 

.  2570 

.2219 

.4446 

.4291 

.7541 

.7501 

.2627 

.2627 

59 
60 

.0156 
0. 0172 

.9143 

.1229 

.  0599 

.2596 

.2249 

.  4485 

.  4331 

.7615 

.7576 

2.5640 

2.5640 

9. 9167 

0. 1249 

0. 0625 

0. 2623 

0.  2279 

0. 4523 

0. 4372 

0.  7689 

0.7652 

Inf. 

Inf. 

TABLE  38.                                           [Page  575    1 

Error  in  Longitude  due  to  one  minute  Error  of  Latitude. 

2 

3  — 

Latitude.  • 

03  d 

00 -a 

3 

0° 

5° 

10° 

15° 

•20° 

•25° 

30° 

35° 

40° 

45° 

60° 

66° 

60° 

66° 

70° 

75° 

o 

0 

/ 

1 

1 

, 

, 

, 

1 

/ 

/ 

, 

/ 

/ 

/ 

1 

/ 

O 

o 

10 

110 

.4 

.4 

.4 

.5 

.5 

.6 

.7 

.8 

1.0 

1.8 

L8 

2.9 

110 

10 

?.o 

.4 

.4 

.5 

.6 

.7 

.8 

1.0 

1.2 

1.6 

2.6 

20 

80 

.4 

.  0 

.6 

.7 

.9 

1.1 

1.5 

2.3 

30 

40 

.5 

.6 

.8 

1.0 

1.3 

40 

50 

.7 

.9 

1.2 

50 

60 
10 

.9 

.8 

.9 

1.2 

1.8 

3.0 

105 

60 
10 

105 

.8 

.8 

.3 

.3 

.4 

.4 

.5 

.6 

9.0 

.8 

.8 

.4 

.4 

.5 

.6 

.7 

.9 

1.2 

L6 

2.7 

20 

80 

.8 

.4 

.5 

.6 

.7 

.8 

1.1 

1.5 

2.4 

30 

40 

.4 

.5 

.6 

.  t 

1.0 

1.3 

40 

50 

.4 

.6 

.8 

1.2 

50 

60 

.6 

.9 

60 

15 

100 

.2 

.2 

.2 

.3 

.3 

.4 

.4 

.5 

.6 

.8 

1.1 

1.6 

2.9 

100 

15 

20 

.2 

,2 

.8 

.3 

.4 

.5 

.5 

.7 

.9 

1.1 

1.6 

2.7 

20 

80 

.2 

.8 

.8 

.4 

.5 

.6 

.8 

1.1 

1.5 

2.4 

30 

40 

.2 

.3 

.4 

.6 

.7 

.9 

1.3 

2.1 

40 

50 

.8 

.4 

.6 

.8 

1.2 

50 

60 

.8 

.6 

.9 

.5 

.6 

.8 

1.1 

1.7 

3.0 

95 

60 
15 

15 

95 

.1 

.1 

.2 

.2 

.3 

.3 

.4 

20 

.1 

.2 

.  2 

.8 

.3 

.4 

.5 

.6 

.8 

1.1 

1.6 

2.8 

20 

80 

.2 

.2 

.3 

.4 

.5 

.6 

.8 

LO 

L5 

2.5 

80 

40 

.2 

.3 

.4 

.5 

.7 

.9 

1.3 

2.1 

40 

50 

.3 

.4 

.6 

.8 

1.1 

50 

60 

.2 

.3 

.6 

.9 

60 

20 

90 

.0 

.0 

.1 

.1 

.1 

.2 

.2 

.3 

.4 

.6 

.7 

1.1 

1.6 

3.0 

90 

20 

80 

.0 

.1 

.1 

.2 

.2 

.3 

.4 

.5 

.7 

1.0 

L5 

2.7 

80 

40 

.0 

.1 

.2 

.3 

.8 

.5 

.6 

.9 

1.3 

2.2 

40 

50 

.0 

.1 

.2 

.4 

.5 

.8 

1.1 

50 

60 

.0 

.2 

.3 

.5 

.9 

60 

70 

.0 

.2 

.6 

1.1 

LO 

L6 

3.1 

70 

20 

85 

.1* 

.1* 

.0 

.0 

.0 

.1 

.1 

.2 

.3 

.3 

.5 

.7 

85 

20 

80 

.1* 

.0 

.0 

.1 

.1 

.2 

.2 

.4 

.5 

.7 

LO 

L5 

2.7 

30 

40 

.1* 

.0 

.0 

.1 

.2 

.3 

.4 

.6 

.9 

1.3 

2.3 

40 

50 

.1* 

.0 

.1 

.2 

.8 

.5 

.7 

1.1 

50 

60 

.2* 

.0 

.1 

.3 

.5 

.9 

60 

70 
20 

.3* 

.0 

.2 

.6 

1.1 

.1 

.1 

.2 

TT 

.5 

.9 

1.5 

3.1 

70 

80 

.2* 

.2* 

.1* 

.1* 

.1* 

.0 

.0 

.0 

80 

20 

80 

.2* 

.2* 

.1* 

.0 

.0 

.1 

.1 

.2 

.3 

.4 

.6 

.9 

1.5 

2.8 

30 

40 

.2* 

.2* 

.1* 

.0 

.1 

.2 

.3 

.4 

.6 

.9 

1.3 

2.4 

40 

50 

.8* 

.2* 

.1* 

.1 

.2 

.3 

.5 

.7 

1.1 

50 

60 

.4* 

.2* 

.0 

.1 

.3 

.5 

.9 

60 

70 
20 

75 

.6* 

.3* 

.0 

.2 

.6 

1.2 

.1* 

.0 

To" 

.1 

.2 

.3 

.6 

1.2 

70 

.3* 

.3* 

.2* 

.2* 

.2* 

.1* 

.1* 

.1* 

75 

20 

80 

.8* 

.3* 

.2* 

.2* 

.1* 

.1* 

.0 

.1 

.1 

.2 

.4 

.6 

.9 

1.5 

3.0 

30 

40 

.4* 

.3* 

.2* 

.1* 

.1* 

.0 

.1 

.2 

.4 

.5 

.8 

1.3 

2.5 

40 

50 

.4* 

.3* 

.2* 

.1* 

.0 

.1 

.3 

.5 

.7 

1.1 

50 

60 

.6* 

.4* 

.2* 

.1* 

.1 

.3 

.5 

.9 

60 

70 
20 

1.2* 

.6* 

.3* 

.0 

.2 

.6 

1.2 

.2* 

.2* 

.2* 

.2* 

.2* 

.2* 

.2* 

.2* 

70 

70 
20 

70 

.4* 

.4* 

.3* 

.8* 

.8* 

.3* 

.2* 

.2* 

80 

.4* 

.4* 

.3* 

.3* 

.2* 

.2* 

.1* 

.1* 

.0 

.0 

.1 

.2 

.6 

.8 

L5 

3.1 

30 

40 

.5* 

.4* 

.3* 

.8* 

.2* 

.1* 

.0 

.1 

.2 

.3 

.5 

.8 

1.3 

2.6 

40 

50 

.6* 

.5* 

.3* 

.2* 

.2* 

.0 

.1 

.3 

.4 

.7 

1.1 

50 

60 

.9* 

.6* 

.4* 

.3* 

.1* 

.1 

.2 

.5 

.9 

60 

70 

1.2* 

.6* 

.3* 

.1* 

.2 

.6 

L2 

70 

•h 

H  *^ 

s 

0° 

6° 

10° 

15° 

20° 

26° 

80° 

86° 

40° 

46° 

60° 

66° 

60° 

65° 

70° 

76° 

«g 

Ph 

Latitude. 

Page  576] 

TABLE  39. 

Amplitudes. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

o°.o 

0°.6 

1°.0 

1°.5 

2^.0 

2°.  5 

8°.0 

8°.  6 

4°.0 

4°.  5 

5°.0 

o°.5 

6°.0 

o 

0 

0 

0 

0 

0 

0 

o 

0 

0 

0 

0 

o 

0 

0 

0 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

4.5 

5.0 

5.5 

6.0 

0 

10 

0.0 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.1 

4.6 

5.1 

5.6 

6.1 

10 

15 

0.0 

0.5 

1.5 

2.1 

2.6 

3.1 

3.6 

4.2 

4.7 

5.2 

5.7 

6.2 

15 

20 

0.0 

0.5 

1.1 

1.6 

2.1 

2.7 

3.2 

3.7 

4.3 

4.8 

5.3 

5.8 

6.4 

20 

25 

0.0 

0.5 

1.1 

1.6 

2.2 

2.8 

3.3 

3.8 

4.4 

5.0 

5.5 

6.0 

6.6 

25 

30 

0.0 

0.6 

1.2 

1.7 

2.3 

2.9 

3.4 

4.0 

4.6 

5.2 

5.8 

6.3 

6.9 

30 

32 

0.0 

0.6 

1.2 

1.8 

2.4 

2.9 

3.5 

4.1 

4.7 

5.3 

5.9 

6.5 

7.0 

32 

34 

0.0 

0.6 

1.2 

1.8 

2.4 

3.0 

3.6 

4.2 

4.8 

5.4 

6.0 

6.6 

7.2 

34 

36 

0.0 

0.6 

1.2 

1.8 

2.5 

3.1 

3.7 

4.3 

4.9 

5.6 

6.1 

6.8 

7.4 

36 

38 

0.0 

0.6 

1.3 

1.9 

2.5 

3.2 

3.8 

4.4 

5.1 

5.7 

6.3 

7.0 

7.6 

38 

40 

0.0 

0.7 

1.3 

2.0 

2.6 

3.3 

3.9 

4.6 

5.2 

5.9 

6.5 

7.2 

7.8 

40 

42 

0.0 

0.7 

1.3 

2.0 

2.7 

3.4 

4.0 

4.7 

5.4 

6.1 

6.7 

7.4 

8.0 

42 

44 

0.0 

0.7 

1.4 

2.1 

2.8 

3.5 

4.2 

4.9 

5.6 

6.3 

6.9 

7.6 

8.3 

44 

46 

0.0 

0.7 

1.4 

2.2 

2.9 

3.6 

4.3 

5.0 

5.8 

6.5 

7.2 

7.9 

■8.6 

46 

48 

0.0 

0.7 

1.5 

2.2 

3.0 

3.7 

4.5 

5.2 

6.0 

6.7 

7.5 

8.2 

9.0 
9.3 

48 

50 

0.0 

0.8 

1.5 

2.3 

3.1 

3.9 

4.7 

5.4 

6.2 

7.0 

7.8 

8.6 

50 

51 

0.0 

0.8 

1.6 

2.4 

3.2 

4.0 

4.8 

5.6 

6.4 

7.2 

8.0 

8.8 

9.5 

51 

52 

0.0 

0.8 

1.6 

2.4 

3.3 

4.1 

4.9 

5.7 

6.5 

7.3 

8.1 

9.0 

9.7 

52 

53 

0.0 

0.8 

1.6 

2.5 

3.3 

4.2 

5.0 

5.8 

6.7 

7.5 

8.3 

9.2 

10.0 

53 

54 

0.0 

0.9 

1.7 

2.5 

3.4 

4.3 

5.1 

6.0 

6.8 

7.7 

8.5 

8.7 

9.4 
9.6 

0.2 

54 

55 

0.0 

0.9 

1.7 

2.6 

3.5 

4.4 

5.2 

6.1 

7.0 

7.9 

10.5 

55 

56 

0.0 

0.9 

1.8 

2.7 

3.6 

4.5 

5.4 

6.3 

7.2 

8.1 

9.0 

9.9 

0.8 

56 

57 

0.0 

0.9 

1.8 

2.7 

3.7 

4.6 

5.5 

6.4 

7.4 

8.3 

9.2 

10.1 

1.1 

57 

58 

0.0 

0.9 

1.9 

2.8 

3.8 

4.7 

5.7 

6.6 

7.6 

-8.5 

9.5 

0.4 

1.4 

58 

59 

0.0 

1.0 

1.9 

2.9 

3.9 

4.9 

5.8 

6.8 

7.8 

8.8 

9.7 

0.7 

1.7 

59 
60 

60 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

7.0 

8.0 

9.0 

10.0 

11.0 

12.1 

61 

0.0 

1.0 

2.1 

3.1 

4.1 

5.2 

6.2 

7.2 

8.3 

9.3 

0.3 

1.4 

2.5 

61 

62 

0.0 

1.1 

2.1 

3.2 

4.3 

5.3 

6.4 

7.5 

8.5 

9.6 

0.7 

1.8 

2.9 

62 

63 

0.0 

1.1 

2.2 

3.3 

4.5 

5.5 

6.6 

7.  7 

8.8 

9.9 

1.1 

2.2 

3.4 

63 

64 

0.0 

1.1 

2.3 

3.4 

4.6 

5.7 

6.9 

S.O 

9.2 

10.3 

1.5 

2.6 

3.9 

64 

65.0 

0.0 

1.2 

2.4 

3.5 

4.8 

5.9 

7.1 

8.3 

9.5 

10.7 

11.9 

13.1 

14.4 

65.0 

5.5 

0.0 

1.2 

2.4 

3.6 

4.8 

6.0 

7.2 

8.5 

9.7 

0.9 

2.1 

3.4 

4.6 

5.5 

6.0 

0.0 

1.2 

2.5 

3.7 

4.9 

6.1 

7.4 

8.6 

9.9 

1.1 

2.4 

3.6 

4.9 

6.0 

6.5 

0.0 

1.2 

2.5 

3.8 

5.0 

6.3 

7.5 

8.8 

10.1 

1.3 

2.6 

3.9 

5.2 

6.5 

7.0 

0.0 

1.3 

2.6 

3.8 

5.1 

6.4 

7.7 

9.0 

0.3 

1.6 

2.9 

4.2 

5.5 

7.0 

67.5 

0.0 

1.3 

2.6 

3.9 

5.2 

6.5 

7.9 

9.2 

10.5 

11.8 

13.2 

14.5 

15.9 

67.5 

8.0 

0.0 

1.3 

2.7 

4.0 

5.3 

6.7 

8.0 

9.4 

0.7 

2.1 

3.5 

4.8 

6.2 

8.0 

8.5 

0.0 

1.4 

2.7 

4.1 

5.4 

6.8 

8.2 

9.6 

1.0 

2.4 

3.8 

5.2 

6.6 

8.5 

9.0 

0.0 

1.4 

2.8 

4.2 

5.5 

7.0 

8.4 

9.8 

1.2 

2.6 

4.1 

5.5 

7.0 

9.0 

9.5 

0.0 

1.4 

2.9 

4.3 

5.7 

7.2 

8.6 

10.0 

1.5 

2.9 

4.4 

5.9 

7.4 

9.5 

70.0 

0.0 

1.5 

2.9 

4.4 

5.8 

7.3 

8.8 

10.3 

11.8 

13.3 

14.8 

16.3 

17.8 

70.0 

0.5 

0.0 

1.5 

3.0 

4.5 

6.0 

7.5 

9.0 

0.5 

2.1 

3.6 

5.1 

6.7 

8.2 

0.5 

1.0 

0.0 

1.5 

3.1 

4.6 

6.2 

7.7 

9.3 

0.8 

2.4 

3.9 

5.5 

7.1 

8.7 

1.0 

1.5 

0.0 

1.6 

3.2 

4.7 

6.3 

7.9 

9.5 

1.1 

2.7 

4.3 

5.9 

7.8 

9.2 

1.5 

2.0 

0.0 

1.6 

3.2 

4.9 
5.0 

6.5 
6.7 

8.1 

9.8 

1.4 

3.0 

4.7 

6.4 

8.1 

9.8 

2.0 

72.5 

0.0 

1.7 

3.3 

8.3 

10.0 

11.7 

13.4 

15.1 

16.9 

18.6 

20.3 

72.5 

3.0 

0.0 

1.7 

3.4 

5.1 

6.9 

8.6 

0.3 

2.0 

3.8 

5.5 

7.4 

9.1 

0.9 

3.0 

3.5 

0.0 

1.8 

3.5 

5.2 

7.1 

8.8 

0.6 

2.4 

4.2 

6.0 

7.9 

9.7 

1.6 

3.5 

4.0 

0.0 

1.8 

3.6 

5.4 

7.3 

9.1 

0.9 

2.8 

4.6 

6.5 

8.4 

20.3 

2.3 

4.0 

4.5 

0.0 

1.9 

3.7 

5.6 

7.5 

9.4 

1.3 

3.2 

5.1 

7.1 

9.0 

1.0 

3.0 

4.5 

75.0 

0.0 

1.9 

3.8 

5.8 

7.7 

9.7 

11.7 

13.6 

15.6 

17.7 

19.7 

21.7 

23.8 

75.0 

5.5 

0.0 

2.0 

3.9 

6.0 

8.0 

10.0 

2.1 

4.1 

6.2 

8.3 

20.4 

2.5 

4.7 

5.5 

6.0 

0.0 

2.1 

4.0 

6.2 

8.3 

0.4 

2.5 

4.6 

6.8 

8.9 

1.1 

3.3 

5.6 

6.0 

6.5 

0.0 

2.1 

4.2 

6.4 

8.6 

0.8 

3.0 

5.2 

7.4 

9.6 

1.9 

4.2 

6.6 

6.5 

7.0 

0.0 

2.2 

4.4 

6.6 

8.9 

1.2 

3.5 

5.8 

8.1 

20.4 

2.8 

5.2 

7.7 

7.0 

TABLE 

39. 

[Page 

577 

Amplitud 

es. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

6°.0 

6°.  6 

;°.o 

7°.  5 

8°,0    j 

8°.o    j    9°.0    , 

9°,  5 

10°.0 

10°.  5 

11°.0 

11°.  5      12°.0 

o 

o 

o 

o 

o 

.    °             °      \ 

0 

o 

o 

o 

0 

o 

o 

0 

6.0 

6.5 

7.0 

7.5 

8.0 

8.5       9.0  1 

9.5 

10.0 

10.5 

11.0 

11.5 

12.0 

0 

10 

6.1 

6.6 

7.1 

7.6 

8.1 

8.6  ;    9.1  1 

9.7 

0.1 

0.7 

1.2 

1.7 

2.2 

10 

15 

6.2 

6.7 

7.2 

7.8 

8.3 

8.8  1     9.3 

9.8 

0.4 

0.9 

1.4 

1.9 

2.5 

15 

20 

6.4 

6.9 

7.4 

8.0 

8.5 

9.1  1    9.6  : 

10.1 

0.7 

1.2 

1.7 

2.  3       2.  8  1 

20 

25 
30 

6.6 

7.1 

7.7 

8.3 

8.8 

9.4  1     9.9 

0.5 

1.1 

1.6 

2.2 

2.8 

3.3 

25 
30 

6.9 

7.5 

8.1 

8.7 

9.3 

9.8     10.4 

11.0 

11.5 

12.1 

12.7 

13.3 

13.9 

82 

7.0 

7.7 

8.3 

8.8 

9.5 

10.0       0.6 

1.2 

1.8 

2.4 

3.0 

3.6 

4.2 

32 

34 

7.2 

7.8 

8.5 

9.0 

9.7 

0.  3       0.  8 

1.5 

2.1 

2.7 

3.3 

3.9 

4.5 

34 

36 

7.4 

8.0 

8.7 

9.3 

9.9 

0.5  1     1.1 

1.8 

2.4 

3.0 

3.6 

'4.3 

4.9 

36 

38 

7.6 

8.2 

8.9 

9.5 

10.2 

0.8  !     1.4 

2.1 

2.7 

3.4 

4.0 

4.7 

5.3 

38 

40 

7.8 

8.5 

9.1 

9.8 

10.5 

11.1     11.7 

12.4 

13.1 

13.8 

14.4 

15.1 

15.7 

40 

42 

8.0 

8.8 

9.4 

10.1 

0.8 

1.5       2.1 

2.8 

3.5 

4.2 

4.8 

5.6 

6.2 

42 

44 

8.3 

9.1 

9.7 

0.5 

1.1 

1.9       2.5 

3.3 

4.0 

4.7 

5.3 

6.1 

6.8 

44 

46 

8.6 

9.4 

10.1 

0.8 

1.5 

2. 3       3. 0 

3.8 

4.5 

5.2 

5.9 

6.7 

7.4 

46 

48 
50 

9.0 

9.7 

0.5 

1.2 

2.0 

2. 8       3. 5 

4.3 

5.0 

5.8 

6.6 

7.3 

8.1 

48 

9.3 

10.1 

10.9 

11.7 

12.5 

13.3     14.1 

14.9 

15.7 

16.5 

17.3 

18.1      18.9 

50 

51 

9.5 

0.4 

1.2 

2.0 

2.8 

3. 6       4. 4 

5.2 

6.0 

6.8 

7.  7 

8.5  ,     9.3 

51 

52 

9.7 

0.6 

1.4 

2.2 

3.1 

3. 9       4.  7 

5.6 

6.4 

7.2 

8.1 

8. 9  i     9.  7 

52 

53 

10.0 

0.8 

1.7 

2.5 

3.4 

4.2       5.1 

5.9 

6.8 

7.6 

8.5 

9. 4     20.  2 

53 

54 

0.2 

1.1 

2.0 

2.8 

3.7 

4.6       5.4 

6.3 

7.2 

8.1 

8.9 

9. 8       0.  7 

54 

55 

10.5 

11.4 

12.3 

13.1 

14.0 

14.9     15.8 

16.7 

17.6 

18.5 

19.4 

20.3     21.2 

55 

56 

0.8 

1.7 

2.6 

3.5 

4.4 

6.3  i    6.2 

7.2 

8.1 

9.0 

9.9 

0.9       1.8 

56 

57 

1.1 

2.0 

2.9 

3.9 

4.8 

5. 8       6. 7 

7.7 

8.6 

9.6 

20.5 

1.5       2.4 

57 

58 

1.4 

2.3 

3.3 

4.3 

5.2 

6.  2       7. 2 

8.2 

9.1 

20.1 

1.1 

2.1  i     3.1 

58 

59 
60 

1.7 

2.7 

3.7 

4.7 

5.7 

6.  7       7.  7 

8.7 

9.7 

0.7 

1.7 

2.8 

3.8 
24.6 

59 
60 

12.1 

13.1 

14.1 

15.1 

16.2 

17.2  i  18.2 

19.3 

20.3 

21.4     22.4 

23.5 

61 

2.5 

3.5 

4.6 

5.6 

6.7 

7.8  i     8.8 

9.9 

1.0 

2.1  1     3.1 

4.3       5.4 

61 

62 

2.9 

3.9 

5.1 

6.1 

7.3 

8.4       9.4 

20.6 

1.7 

2.9  1     3.9 

5.2       6.3 

62 

63 

3.4 

4.4 

5.6 

6.7 

7.9 

9. 0     20. 1 

1.3 

2.5 

3.7 

4.8 

6.1  i     7.2 

63 

64 

3.9 
14.4 

5.0 

6.2 

7.3 

8.5 

9.  7       0. 9 

2.1 

3.3 

4.6 

5.7 

7.1 

28.2 

8.3 

64 

65.0 

15.5 

16.8 

18.0 

19.3 

20.5     21.7 

23.0 

24.2 

25.6  1  26.8 

29.5 

65.0 

5.5 

4.6 

5.8 

7.1 

8.3 

9.6 

0.9       2.2 

3.5 

4.7 

6.1 

7.4 

8.  7     30. 1 

5.5 

6.0 

4.9 

6.2 

7.4 

8.7 

20.0 

1.3 

2.6 

3.9 

5.3 

6.6 

8.0 

9.3       0.7 

6.0 

6.5 

5.2 

6.5 

7.8 

9.1 

0.4 

1.8 

3.1 

4.4 

5.8 

7.2 

8.6 

30.0       1.4 

6.5 

7.0 
67.  5 

5.5 

6.8 

8.2 

9.5 
19.9 

0.9 

2.2 

3.6 

5.0 

6.4 

7.8 

9.2 
29.9 

0.7       2.1 
31.4     .32.9 

7.0 

15.9 

17.2 

18.6 

21.3 

22.7     24.1 

25.5 

27.0 

28.4 

67.5 

8.0 

6.2 

7.6 

9.0 

20.4 

1.8 

3. 2       4.  7 

6.1 

7.6 

9.1 

30.6 

2.  2       3.  7 

8.0 

8.5 

6.6 

8.0 

9.4 

0.9 

2.3 

3. 8       5. 3 

6.8 

8.3 

9.8 

1.4 

3. 0       4. 6 

8.5 

9.0 

7.0 

8.4 

9.9 

1.4 

2.8 

4. 4       5. 9 

7.4 

9.0 

30.6 

2.2 

3.8       5.5 

9.0 

9.5 

7.4 

8.9 

20.4 

1.9 

3.4 

5. 0       6. 5 
25.  6  ;  27. 2 

8.1 
28.8 

9.7 

1.4 

3.0 

4.7       6.4 

9.5 
70.0 

70.0 

17.8 

19.3 

20.9 

22.4 

24.0 

.30.5 

32.2 

33.9 

35.7  1  37.4 

0.5 

8.2 

9.8 

1.4 

3.0 

4.6 

6. 3       7. 9 

9.6 

1.3 

3.1 

4.9 

6.  7       8. 5 

0.5 

1.0 

8.7 

20.3 

2.0 

3.6 

^  5.3 

7. 0       8.  7 

30.5 

2.2 

4.0 

5.9 

7.  8       9.  7 

1.0 

1.5 

9.2 

0.9 

2.6 

4.3 

6.0 

7.  8       9. 5 

1.4 

3.2 

5.0 

7.0 

8. 9     40. 9 

1.5 

2.0 

9.8 

1.5 

3.2 

5.0 

6.8 

8.6  1  30.4 

2.3 

4.2 

6.1 

8.1 

40.  2       2.  3 

2.0 

72.5 

20.3 

22.1 

23.9 

25.7 

27.6 

29.5     31.4 

33.3 

35.3 

37.3 

39.4 

41. 5     43.  7 

72.5 

3.0 

0.9 

2.8 

4.6 

6.5 

8.4 

30.4  1     2.4 

4.4 

6.5 

8.6 

40.8 

3. 0       5. 3 

3.0 

3.5 

1.6 

3.5 

5.4 

7.4 

9.3 

1.4  1     3.4 

5.5 

7.7 

9.9 

2.2 

4.6 

7.0 

3.5 

4.0 

2.3 

4.3 

6.2 

8.3 

30.3 

2. 5  1     4. 6 

6.8 

9.1 

41.4 

3.8 

6.3 

8.9 

4.0 

4.5 

3.0 

5.1 

7.1 

9.3 

1.4 

3.6  1     5.8 

8.2 

40.5 

3.0 

5.6 

8.2 

51.1 

4.5 

75.0 

23.8 

26.0 

28.1 

30.3 

32.5 

34.8 

37.2 

39.6 

42.1 

44.8 

47.5 

50.4 

53.5 

75.0 

5.5 

4.7 

6.9 

9.1 

1.4 

3.8 

6.2 

8.7 

41.2 

3.9 

6.7 

9.6 

2.8 

6.2 

5.5 

6.0 

5.6 

7.9 

30.2 

2.6 

5.1 

7.7 

40.3 

3.0 

5.9 

8.9 

52.1 

5.5 

9.3 

6.0 

6.5 

6.6 

9.0 

1.4 

4.0 

6.6 

9.3 

2.1 

5.0 

8.1 

51.3 

4.8 

8.7 

63.0 

6.5 

7.0 

7.7 

30.2 

2.8 

5.5 

8.2 

41.1 

4.1 

7.2 

50.5 

4.1  '     8.0 

62.4 

7.6 

7.0 

'2US9—0S- 


-37 


Page  578] 

TABLE  39. 

Amplitudes. 

Lati- 
tude. 

Declination. 

Lati- 
tude. 

12°.0  1 

12°.  6 

18°.0 

1S°.5 

14°.0 

14°.  5 

15°.0 

15°.  6 

1«°.0 

16°.  5 

17°.0 

17°,  5 

18°.0 

o 

o 

c 

o 

o 

o 

o                o        1 

o      . 

o 

o 

o 

o 

o 

o 

0 

12.0 

12.5 

13.0 

13.5 

14.0 

14.5 

15.0 

15.5 

16.0 

16.5 

17.0 

17.5 

18.0 

0 

10 

2.2 

2.7 

3.2 

3.7 

4.2 

4.7 

5.3 

5.8 

6.3 

6.8 

7.3 

7.9 

8.3 

10 

15 

2.5 

2.9< 

►    3.5 

4.0 

4.5 

5.0 

5.6 

6.1 

6.6 

7.1 

7.  7 

8.2 

8.7 

15 

20 

2.8 

3.3 

3.8 

4.4 

4.9 

5.5 

6.0 

6.5 

7.1 

7.6 

8.1 

8.7 

9.2 

20 

25 

3.3 

3.8 

4.4 

4.9 

5.5 

6.1 

6.6 

7.1 

7.7 

8.3 

8.8 

9.4 

9.9 

25 

80 

13.9 

14.5 

15.0 

15.6 

16.2 

16.8 

17.4 

18.0 

18.6 

19.2 

19.7 

20.3 

20.9 

30 

32 

4.2 

4.8 

5.3 

6.0 

6.6 

7.2 

7.8 

8.4 

9.0 

9.6 

20.2 

0.8 

1.4 

32 

34 

4.5 

5.1 

5.7 

6.4 

7.0 

7.6 

8.2 

8.8 

9.5 

20.0 

0.7 

1.3 

1.9 

34 

36 

4.9 

5.5 

6.1 

6.8 

7.4 

8.0 

8.7 

9.3 

20.0 

0.5 

1.2 

1.8 

2.5 

36 

38 

5.3 

6.0 

6.6 

7.2 

7.9 

8.5 

9.2 

9.8 

0.5 

1.1 

1.8 

2.4 

3.1 

38 
40 

40 

15.7 

16.4 

17.1 

17.8 

18.4 

19.1 

19.7 

20.4 

21.1 

21.8 

22.4 

23.1 

23.8 

41 

6.0 

6.7 

7.3 

8.0 

8.7 

9.4 

20.0 

0.8 

1.4 

2.1 

2.8 

3.5 

4.2 

41 

42 

6.2 

6.9 

7.6 

8.3 

9.0 

9.7 

0.4 

1.1 

1.8 

2.5 

3.2 

3.9 

4.6 

42 

43 

6.5 

7.2 

7.9 

8.6 

9.3 

20.0 

0.7 

1.4 

2.2 

2.9 

3.6 

4.3 

5.0 

43 

44 
45 

6.8 
17.1 

7.5 

8.2 
18.5 

8.9 

9.6 

0.4 
20.7 

1.1 

1.8 

2.6 

3.3 

4.0 

4.7 
25.  2 

5.4 

44 

17.8 

19.3 

20.0 

21.5 

22.2 

23.0 

23.7 

24.4 

25.9 

45 

46 

7.4 

8.2 

8.9 

9.6 

0.4 

1.1 

1.9 

2.6 

3.4 

4.1 

4.9 

5.7 

6.4 

46 

47 

7.7 

8.5 

9.3 

20.0 

0.8 

1.5 

2.3 

3.1 

3.8 

4.6 

5.4 

6.2 

6.9 

47 

48 

8.1 

8.9 

9.7 

0.4 

1.2 

2.0 

2.8 

3.6 

4.3 

5.1 

5.9 

6.7 

7.5 

48 

49 

8.5 

9.3 

20.1 

0.8 

1.6 

2.4 

3.2 

4.1 

4.9 

5.7 

6.5 

7.3 

8.1 

28.7 

49 

50 

18.9 

19.7 

20.5 

21.3 

22.1 

22.9 

23.7 

24.6 

25.4 

26.2 

27.0 

27.9 

50 

51 

9.3 

20.1 

0.9 

1.8 

2.6 

3.5 

4.3 

5.1 

6.0 

6.8 

7.6 

8.5 

9.4 

51 

52 

9.7 

0.6 

1.4 

2.3 

3.1 

4.0 

4.9 

5.7 

6.6 

7.5 

8.3 

9.2 

30.1 

52 

53 

20.2 

1.1 

1.9 

2.8 

3.7 

4.6 

5.5 

6.4 

7.3 

8.2 

9.0 

30.0 

0.9 

53 

54 

0.7 

1.6 

2.5 

3.4 

4.3 

5.2 

6.1 

7.1 

8.0 

8.9 

9.8 

0.8 

1.7 

54 

55 

21.2 

22.2 

23.1 

24.0 

24.9 

25.9 

26.8 

27.8 

28.7 

29.7 

30.6 

31.6 

32.6 

55 

56 

1.8 

2.8 

3.7 

4.7 

5.6 

6.6 

7.6 

8.6 

9.5 

30.5 

1.5 

2.5 

3.6 

56 

57 

2.4 

3.4 

4.4 

5.4 

6.4 

7.4 

8.4 

9.4 

30.4 

1.4 

2.5 

3.5 

4.6 

57 

58 

3.1 

4.1 

5.1 

6.1 

7.2 

8.2 

9.2 

30.3 

1.3 

2.4 

3.5 

4.6 

5.7 

58 

59 

3.8 

4.8 

5.9 

6.9 

8.0 

9.1 

30.2 

1.3 

2.3 

3.5 

4.6 

5.7 

6.9 

59 

60 

24.6 

25.6 

26.7 

27,8 

28.9 

30.1 

31.2 

32.3 

33.4 

34.6 

35.8 

36.9 

38.2 

60 

61 

5.4 

6.5 

7.6 

8.8 

9.9 

1.1 

2.2 

3.5 

4.6 

5.8 

7.1 

8.3 

9.6 

61 

62 

6.3 

7.5 

8.6 

9.8 

31.0 

2.2 

3.4 

4.7 

5.9 

7.2 

8.5 

9.8 

41.2 

62 

63 

7.2 

8.5 

9.7 

31.0 

2.2 

3.5 

4.7 

6.1 

7.4 

8.7 

40.1 

41.5 

2.9 

63 

64 

8.3 

9.6 

30.9 

2.2 

3.5 

4.8 

6.2 

7.6 

9.0 

40.4 

1.8 

3.3 

4.8 

64 

65.0 

29.5 

30.8 

32.2 

33.5 

34.9 

36.3 

37.8 

39.2 

40.7 

42.2 

43.8 

45.4 

47.0 

65.0 

5.5 

30.1 

1.5 

2.9 

4.3 

5.7 

7.1 

8.6 

40.1 

1.6 

3.2 

4.8 

6.5 

8.2 

5.5 

6.0 

0.7 

2.2 

3.6 

5.0 

6.5 

8.0 

9.5 

1.1 

2.7 

4.3 

5.9 

7.7 

9.4 

6.0 

6.5 

1.4 

2.9 

4.3 

5.8 

7.3 

8.9 

40.5 

2.1 

3.8 

5.4 

7.1 

8.9 

50.8 

6.5 

7.0 

2.1 

3.6 

5.1 

6.7 

8.2 

9.8 

1.5 

3.2 

4.9 

6.6 

8.4 

50.3 

2.3 

7.0 

67.5 

32.9 

34.4 

36.0 

37.6 

39.2 

,^.8 

42.6 

44.3 

46.1 

47.9 

49.8 

51.8 

53.9 

67.5 

8.0 

3.7 

5.3 

6.9 

8.6 

40.2 

1.9 

3.7 

5.5 

7.4 

9.3 

51.3 

3.4 

5.6 

8.0 

8.5 

4.6 

6.2 

7.9 

9.6 

1.3 

3.1 

4.9 

6.8 

8.8 

50.8 

2.9 

5.1 

7.5 

8.5 

9.0 

5.5 

7.2 

8.9 

40.7 

2.5 

4.3 

6.2 

8.2 

50.3 

2.4 

4.6 

7.0 

9.6 

9.0 

9.5 
70.0 

6.4  !     8.2 

40.0 

1.8 
43.0 

3.7 

5.6 

7.6 

9.7 

1.9 

4.2 

6.5 

9.1 

61.9 

9.5 

37.4 

39.3 

41.1 

45.0 

47.0 

49.2 

51.4 

53.7 

56.1 

58.7 

61.5 

64.6 

70.0 

0.5 

8.5 

40.4 

2.4 

4.4 

6.4 

8.6 

50.8 

3.2 

5.7 

8.3 

61.1 

4.3 

7.8 

0.5 

1.0 

9.7 

1.7 

3.7 

5.8 

8.0 

50.3 

2.6 

5.2 

7.9 

60.7 

3.9 

7.5 

71.7 

1.0 

1.5 

40.9 

3.0 

5.1 

7.4 

9.7 

2.1 

4.6 

7.4 

60.3 

3.5 

7.1. 

71.4 

6.9 

1.5 

2.0 

2.3 
43.  7 

4.4 

6.7 

9.1 

!  51.5 

4.1 

6.9 

9.9 

3.1 

6.8 

71.1 

6.7 

90.0 

2.0 

72.5 

46.0 

48.4 

50.9 

53.6 

56.4 

59.4 

62.7 

66.4 

70.9 

76.5 

90.0 

72.5 

3.0 

5.3 

7.7 

50.3 

3.0 

5.9 

8.9 

62.2 

6.1 

70.6 

6.3 

90.0 

3.0 

3.5 

7.0 

9.6 

2.3 

5.3 

8.4 

61.8 

5.6 

70.3 

6.1 

90.0 

3.5 

4.0 

8.9 

51.7 

4.7 

7.9 

61.4 

5.3 

9.8 

75.9 

90.0 

4.0 

4.5 

51.1 

4.1 

7.3 

60.9 

;     4.9 

9.5 

75.5 

90.0 

4.5 

TABLE 

39. 

[Page  579    | 

Amplitudes. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

18°.0 

18°.  5 

19°.0 

19°.  5 

20°.  0 

20°.  5 

21°.0 

21°.  6 

22°.0 

22°.  6 

28°.  0 

28°.  5 

24°.0 

o 

Q 

o 

o 

0 

o 

o 

o 

o 

o 

o 

o 

0 

o 

o 

0 

18.0 

18.5 

19.0 

19.5 

20.0 

20.5 

21.0 

21.5 

22.0 

22.5 

23.0 

23.5 

24.0 

0 

10 

8.3 

8.8 

9.3 

9.8 

0.3 

0.8 

1.3 

1.8 

2.3 

2.9 

3.4 

3.9 

4.4 

10 

15 

8.7 

9.2 

9.7 

20.2 

0.7 

1.3 

1.8 

2.3 

2.8 

3.3 

3.9 

4.4 

4.9 

15 

20 

9.2 

9.7 

20.3 

0.8 

1.4 

1.9 

2.4 

3.0 

3.5 

4.0 

4.6 

5.1 

5.7 

20 

25 
30 

9.9 
20.9 

20.5 
21.5 

1.1 
22.1 

1.6 

2.2 

2.7  1     3.3 

3.9 

4.4 

5.0 

5.5 

6.1 

6.7 

25 

22.7 

23.3 

23.8 

24.4 

25.0 

25.6 

26.2 

26.8 

27.4 

28.0 

30 

32 

1.4 

2.0 

2.6 

3.2 

3.8 

4.4 

5.0v 

5.6 

6.2 

6.8 

7.4 

8.0 

8.7 

32 

34 

1.9 

2.5 

3.1 

3.8 

4.4 

5.0 

5.6 

6.2 

6.9 

7.5 

8.1 

8.7 

9.4 

34 

36 

2.5 

3.1 

3.7 

4.4 

5.0 

5.7 

6.3 

6.9 

7.6 

8.2 

8.9 

9.5 

30.2 

36 

38 

3.1 

3.8 

4.4 

5.1 

5.7 

6.4 

7.0 

7.  7 

8.4 

9.1 

9.7 

30.4 

1.1 

38 

40 

23.9 

24.4 

25.1 

25.8 

26.5 

27.2 

27.9 

28.6 

29.3 

30.0 

30.7 

31.3 

32.1 

40 

41 

4.2 

4.8 

5.5 

6.2 

6.9 

7.7 

8.3 

9.1 

9.8 

0.5 

1.2 

1.8 

2.6 

41 

42 

4.6 

5.3 

6.0 

6.7 

7.4 

8.1 

8.8 

9.6 

30.3 

1.0 

1.7 

2.4 

3.2 

42 

43 

5.0 

5.7 

6.4 

7.2 

7.9 

8.6 

9.3 

30.1 

0.8 

1.6 

2.3 

3.0 

3.8 

43 

44 

5.4 

6.2 

6.9 

7.7 

8.4 

9.1 

9.8 

0.6 

1.4 

2.2 

2.9 

3.6 

4.4 

44 

45 

25.9 

26.7 

27.4 

28.2 

28.9 

29.7 

30.4 

31.2 

32.0 

32.8 

33.5 

34.3 

35.1 

45 

46 

6.4 

7.2 

7.9 

8.7 

9.5 

30.3 

1.0 

1.8 

2.6 

3.4 

4.2 

5.0 

5.8 

46 

47 

6.9 

7.7 

8.5 

9.3 

30.1 

0.9 

1.7 

2.5 

3.3 

4.1 

4.9 

5.7 

6.6 

47 

48 

7.5 

8.3 

9.1 

9.9 

0.7 

1.6 

2.4 

3.2 

4.0 

4.9 

5.7 

6.5 

7.4 

48 

49 

8.1 

28.7 

8.9 

9.7 

30.6 

1.4 

2.3 

3.1 

4.0 

4.8 

5.7 

6.5 
37.4 

7.4 

8.3 

49 

50 

29.6 

30.4 

31.3 

32.1 

33.0 

33.9 

34.8 

35.6 

36.5 

38.3 

39.2 

50     - 

51 

9.4 

30.3 

1.1 

2.0 

2.9 

3.8 

4.7 

5.6 

6.5 

7.4 

8.4 

9.3 

40.2 

51 

52 

30.1 

1.0 

1.9 

2.8 

3.7 

4.7 

5.6 

6.5 

7.5 

8.4 

9.4 

40.3 

1.3 

52 

53 

0.9 

1.8 

2.7 

3.7 

4.6 

5.6 

6.6 

7.5 

8.5 

9.5 

40.5 

1.4 

2.5 

53 

54 

1.7 

2.7 

3.6 

4.6 

5.6 

6.6 

7.6 

8.6 

9.6 

40.6 

1.7 

2.6 

3.8 

54 

55 

32.6 

33.6 

34.6 

35.6 

36.6 

37.6 

38.7 

39.7 

40.8 

41.9 

42.9 

44.0 

45.2 

55 

56 

3.6 

4.6 

5.6 

6.7 

7.7 

8.8 

9.8 

41.0 

2.1 

3.2 

4.3 

5.4 

6.7 

56 

57 

4.6 

5.6 

6.7 

7.8 

8.9 

40.0 

41.1 

2.3 

3.5 

4.6 

5.8 

7.0 

8.3 

57 

58 

5.7 

6.8 

7.9 

9.1 

40.2 

1.4 

2.5 

3.8 

5.0 

6.2 

7.5 

8.8 

50.1 

58 

59 
60.0 

6.9 

8.0 

9.2 

40.4. 

1.6 

2.8 

4.1 

5.4 

6.7 

8.0 

9.3 

50.7 

2.2 

59 

38.2 

39.4 

40.6 

41.9 

43.2 

44.5 

45.8 

47.2 

48.6 

49.9 

51.4  i  52.9 

54.4 

60.0 

0.5 

8.9 

40.1 

1.4 

2.7 

4.0 

5.4 

6.7 

8.1 

9.6 

51.0 

2.5 

4.1 

5.7 

0.5 

1.0 

9.6 

0.9 

2.2 

3.5 

4.9 

6.3 

7.7 

9.1 

50.6 

2.1 

3.7 

5.3 

7.0 

1.0 

1.5 

40.4 

1.7 

3.0 

4.4 

5.8 

7.3 

8.7 

50.2 

1.7 

3.3 

5.0 

6.7 

8.5 

1.5 

2.0 
62.5 

1.2 

2.5 

3.9 

5.3 

6.8 

8.3 

9.8 

1.3 

2.9 

4.6 

6.3 

8.1 

60.0 

2.0 

42.0 

43.4 

44.9 

46.3 

47.8 

49.4 

51.0 

52.6 

54.2 

56.0 

57.8 

59.7 

61.7 

62.5 

3.0 

2.9 

4.3 

5.9 

7.4 

8.9 

50.5 

2.2 

3.9 

5.6 

7.5 

9.4 

61.4 

3.6 

3.0 

3.5 

3.8 

5.3 

6.9 

8.5 

50.1 

1.7 

3.5 

5.3 

7.1 

9.1 

61.1 

3.4 

5.7 

3.5 

4.0 

4.8 

6.4 

8.0 

9.7 

1.3 

3.0 

4.9 

6.7 

8.7 

60.7 

3.0 

5.5 

8.1 

4.0 

4.5 
65.0 

5.9 

7.5 

9.2 

50.9 

2.6 

4.5 

6.4 

8.4 

60.5 
62.5 

2.8 

5.2 

7.8 

70.9 
74.4 

4.5 

47.0 

48.7 

50.4 

52.2 

54.0 

56.0 

58.0 

60.2 

64.9 

67.6 

70.6 

65.0 

5.5 

8.2 

50.0 

1.8 

3.6 

5.6 

7,6 

9.8 

2.2 

4.7 

7.3 

70.4 

4.1 

8.9 

5.5 

6.0 

9.4 

1.3 

3.2 

5.1 

7.3 

9.4 

61.8 

4.4 

7.1 

70.2 

3.8 

8.6 

90.0 

6.0 

6.5 

50.8 

2.7 

4.7 

6.8 

9.1 

61.4 

4.0 

6.8 

70.0 

3.7 

8.4 

90.0 

6.5 

7.0 

2.3 

4.3 

6.4 

8.7 

61.1 

3.7 

6.5 

9.8 

3.5 

8.3 

90.0 

7.0 

67.5 

53.9 

56.0 

58.3 

60.7 

63.4 

66.2 

69.5 

73.3 

78.2 

90.0 

67.5 

8.0 

5.6 

7.9 

60.3 

3.0 

5.9 

9.2 

73.0 

8.1 

90.0 

8.0 

8.5 

7.5 

60.0 

2.6 

5.6 

8.9 

72.8 

7.9 

90.0 

8.5 

9.0 

9.6 

2.3 

5.3 

8.7 

72.7 

7.7 

90.0 

9.0 

9.5 

61.9 

5.0 

8.4 

72.4 

7.6 

90.0 

9.5 

70.0 

64.6 

69.1 

72.2 

77.4 

90.0 

70.0 

0.5 

7.8 

71.9 

7.2 

90.0 

0.5 

1.0 

71.7 

7.1 

90.0 

1.0 

1.5 

6.9 

90.0 

1.5 

2.0 

90.0 

2.0 

Page  580] 

TABLE 

39. 

Amplitudes. 

Declination. 

Lati- 
tude. 

Lati- 
tude. 

24°.0 

24°.  5 

25°.0 

25°.  6 

26°.  0 

26°.  6 

27°.0 

27°.5 

28°.  0 

28°.  6 

29°.  0 

29°.5 

80°.  0 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

0 

24.0 

24.5 

25.0 

25.5 

26.0 

26.5 

27.0 

27.5 

28.0 

28.5 

29.0 

29.5 

30.0 

0 

4 

4.1 

4.6 

5.1 

5.6 

6.1 

6.6 

7.1 

7.6 

8.1 

8.6 

9.1 

9.6 

0.1 

4 

8 

4.3 

4.8 

t.3 

5.8 

6.3 

6.8 

7.3 

7.8 

8.3 

8.8 

9.3 

9.8 

0.3 

8 

12 

4.6 

5.1 

5.6 

6.1 

6.6 

7.1 

7.6 

8.1 

8.7 

9.2 

9.7 

30.2 

0.7 

12 

16 

5.0 

5.6 

6.1 

6.6 

7.1 

7.6 

8.2 

8.7 

9.2 

9.8 

30.3 

0.8 

1.3 
32.1 

16 

20 

25.7 

26.2 

26.7 

27.3 

27.8 

28.3 

28.9 

29.4 

30.0 

30.5 

31.1 

31.6 

20 

22 

6.0 

6.6 

7.1 

7.  7       8. 2 

8.8 

9.3 

9.9 

0.4 

1.0 

1.5 

2.1 

2.6 

22 

24 

6.4 

7.0 

7.6 

8.1 

8.7 

9.2 

9.8 

30.4 

0.9 

1.5 

2.0 

2.6 

3.2 

24 

26 

6.9 

7.5 

8.1 

8.6 

9.2 

9.7 

30.3 

0.9 

1.5 

2.1 

2.6 

3.2 

3.8 

26 

28 

7.4 

8.0 

8.6 

9.2 

9.8 

30.3 

0.9 

1.5 

2.1 

2.7 

3.3 

3.9 

4.5 

28 

30 

28.0 

28.6 

29.2 

29.8 

30.4 

31.0 

31.6 

32.2 

32.8 

33.4 

34.0 

34.7 

35.3 

30 

31 

8.3 

8.9 

9.5 

30.1 

0.8 

1.4 

2.0 

2.6 

3.2 

3.8 

4.5 

5.1 

5.7 

31 

32 

8.7 

9.3 

9.9 

0.5 

1.1 

1.7 

2.4 

3.0 

3.6 

4.2 

4.9 

5.5 

6.1 

32 

33 

9.0 

9.6 

30.2 

0.9 

1.5 

2.1 

2.8 

3.4 

4.0 

4.7 

5.3 

6.0 

6.6 

33 

34 
35 

9.4 

29.8 

30.0 

0.6 

31.3 

1.9 
32.3 

2.6 
33.0 

3.2 

3.8 

4.5 

5.1 

5.8 

6.4 

7.1 

34 

30.4 

31.1 

31.7 

33.6 

34.3 

35.0 

35.6 

36.3  !  36.9 

37.6 

35 

36 

30.2 

0.8 

1.5 

2.1 

2.8 

3.5 

4.1 

4.8 

5.5 

6.1 

6.8 

7.5 

8.2 

36 

37 

0.6 

1.3 

1.9 

2.6 

3.3 

4.0 

4.6 

5.3 

6.0 

6.7 

7.4 

8.1 

8.8 

37 

38 

1.1 

1.7 

2.4 

3.1 

3.8 

4.5 

5.2 

5.9 

6.6 

7.3 

8.0 

8.7 

9.4 

38 

39 

1.6 

2.2 

2.9 

3.6 

4.3 

5.0 

5.7 

6.5 

7.2 

7.9 

8.6 

9.3 

40.0 

39 

40 

40 

32.1 

32.8 

33.5 

34.2 

34.9 

35.6 

36.3 

37.1 

37.8 

38.5 

39.3 

40.0 

40.7 

41 

2.6 

3.3 

4.1 

4.8 

5.5 

6.2 

7.0 

7.7 

8.5 

9.2 

40.0 

0.7 

1.5 

41 

42 

3.2 

3.9 

4.7 

5.4 

6.1 

6.9 

7.7 

8.4 

9.2 

9.9 

0.7 

1.5 

2.3 

42 

43 

3.8 

4.5 

5.3 

6.1 

6.8 

7.6 

8.4 

9.2 

9.9 

40.7 

1.5 

2.3 

3.1 

43 

44 

4.4 

5.2 

6.0 

6.8 

7.5 

8.3 

9.1 

40.0 

40.7 

1.6 

2.4 

3.2 

4.0 

44 

45 

35.1 

35.9 

36.7 

37.5 

38.3 

39.1 

39.9 

40.8 

41.6 

42.5 

43.3 

44.1 

45.0 

45 

46 

5.8 

6.6 

7.5 

8.3 

9.1 

40.0 

40.8 

1.7 

2.5 

3.4 

4.3 

5.1 

6.0 

46 

47 

6.6 

7.4 

8.3 

9.1 

40.0 

0.9 

1.7 

2.6 

3.5 

4.4 

5.3 

6.2 

7.1 

47 

48 

7.4 

8.3 

9.2 

40.0 

0.9 

1.8 

2.7 

3.6 

4.6 

5.5 

6.4 

7.4 

8.3 

48 

49 
50 

8.3 
39.2 

9.2 

40.1 

1.0 

1.9 

2.8 

3.8 

4.7 

5.7 

6.7 

7.6 

8.6 

9.6 

49 

40.2 

41.1 

42.0 

43.0 

43.9 

44.9 

45.9 

46.9 

47.9 

48.9 

50.0 

51.1 

50 

51 

40.2 

1.2 

2.2 

3.2 

4.1 

5.1 

6.2 

7.2 

8.2 

9.3 

50.4 

1.5 

2.6 

51 

52 

1.3 

2.3 

3.3 

4.4 

5.4 

6.4 

7.5 

8.6 

9.7 

50.8 

2.0 

3.1 

4.3 

52 

53 

2.5 

3.5 

4.6 

5.7 

6.7 

7.8 

9.0 

50.1 

51.3 

2.5 

3.7 

4.9 

6.2 

53 

54 

3.8 

4.9 

6.0 

7.1 

8.2 

9.4 

50.6 

1.8 

3.0 

4.3 

5.6 

6.9 

8.3 

54 

55.0 

45.2 

46.3 

47.5 

48.6 

49.8 

51.1 

52.3 

53.6 

54.9 

56.3 

57.7 

59.1 

60.7 

55.0 

5.5 

5.9 

7.1 

8.3 

.9.5 

50.7 

2.0 

3.3 

4.6 

6.0 

7.4 

8.9 

60.4 

2.0 

5.5 

6.0 

6.7 

7.9 

9.1 

50.4 

1.6 

2.9 

4.3 

5.7 

7.1 

8.6 

60.1 

1.7 

3.4 

6.0 

6.5 

7.5 

8.8 

50.0 

1.3 

2.6 

3.9 

5.4 

6.8 

8.3 

9.9 

1.5 

3.2 

5.0 

6.5 

7.0 

8.3 

9.6 

0.9 

2.2 

3.6 

5.0 

6.5 

8.0 

9.5 

61.2 

2.9 

4.7 

6.6 

7.0 

57.5 

49.2 

50.5 

51.9 

53.2 

54.7 

56.2 

57.7 

59.3 

60.9 

62.6 

64.5 

66.4 

68.5 

57.v5 

8.0 

50.1 

1.5 

2.9 

4.3 

5.8 

7.4 

8.9 

60.6 

2.4 

4.2 

6.2 

8.3 

70.7 

8.0 

8.5 

1.1 

2.5 

4.0 

5.5 

7.0 

8.6 

60.3 

2.1 

3.9 

6.0 

8.1 

70.4 

3.1 

8.5 

9.0 

2.2 

3.6 

5.1 

6.7 

8.3 

60.0 

1.8 

3.7 

5.7 

7.9 

70.3 

3.0 

6.2 

9.0 

9.5 

3.3 

4.8 

6.4 

8.0 

9.7 

1.5 

3.4 

5.5 

7.7 

70.1 

2.8  I    5.9 

80.1 

9.5 

60.0 

54.4 

56.0 

57.7 

59.4 

61.2 

63.2 

65.2 

67.4 

69.9 

72.6 

75.8 

80.0 

90.0 

60.0 

0.5 

5.7 

7.4 

9.1 

61.0 

2.9 

5.0 

7.2 

9.6 

72.4 

5.8 

9.9 

90.0 

0.5 

1.0 

7.0 

8.8 

60.7 

2.6 

4.7 

7.0 

9.5 

72.3 

5.5 

9.8 

90.0 

1.0 

1.5 

8.5 

60.3 

2.3 

4.4 

6.7 

9.2 

72.0 

5.4 

9.7 

90.0 

1.5 

2.0 

60.0 
61.7 

2.0 

4.2 

6.5 

9.0 

71,9 

5.2 

9.6 

90.0 

2.0 

62.5 

63.9 

66.2 

68.8 

71.7 

75.1 

9.5 

90.0 

62.5 

3.0 

3.6 

6.0 

8.6 

71.5 

4.9 

9.4 

90.0 

3.0 

3.5 

5.7 

8.3 

71.3 

4.8 

9.3 

90.0 

3.5 

4.0 

8.1 

71.1 

4.6 

9.2 

90.0 

4.0 

4.5 

70.9 

4.4 

9.0 

90.0 

4.5 

TABLE 

40. 

[Page 

581 

Correction  of  the  Amplitude  as  observed  on 

the  Apparent  Horizon. 

Declination.  . 

Lati- 
tude. 

Lati- 
tude. 

0° 

5° 

10° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

0 

0 

0 

0 

o 

0 

o 

o 

o 

o 

0 

o 

0 

o 

0 

0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0 

5 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

5 

10 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

10 

15 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.2 

.  2 

.2 

15 

20 
24 

.2 

.2 

2 

.2 

.2 

.2 

.3 

.3 

.3 

.3 

.3 

.3 

.3 
0.4 

20 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.3 

0.4 

24 

28 

.3 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

28 

32 

.4 

.4 

.4 

.4 

.4 

.4 

.4 

.5 

.5 

.5 

.5 

.5 

.  0 

32 

36 

.5 

.5 

.5 

.5 

.5 

.5 

.5 

.5 

.6 

.6 

.6 

.6 

.6 

36 

38 
40 

.5 

.5 

.5 

.5 

.6 

.6 

.6 

.6 

.6 

.6 

.6 

.7 

.7 

38 
40 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.7 

0.7 

0.7 

0.7 

42 

.6 

.6 

.6 

.6 

.6 

.7 

.7 

.7 

.7 

.7 

.8 

.8 

.8 

42 

44 

.6 

.6 

.7 

.7 

.7 

.7 

.7 

.7 

.8 

.8 

.8 

.9 

.9 

44 

46 

.7 

.7 

.7 

.7 

.  7 

.8 

.8 

.8 

.8 

.9 

.9 

.9 

1.0 

46 

48 
50 

.7 
0.8 

.8 

.8 

.8 

.8 

.8 

.8 

.9 

.9 

1.0 

1.0 

1.0 

.1 

48 
50 

0.8 

0.8 

0.8 

0.9 

0.9 

0.9 

0.9 

1.0 

1.1 

1.1 

1.1 

1.3 

52 

.8 

.9 

.9 

.9 

.9 

1.0 

1.0 

1.0 

.1 

.2 

.2 

.3 

.5 

52 

54 

.9 

.9 

1.0 

1.0 

1.0 

.1 

.1 

.1 

.2 

.3 

.4 

.  .5 

.8 

54 

56 

1.0 

1.0 

.1 

.1 

.1 

.2 

.2 

.2 

.3 

.5 

.6 

.8 

2.2 

56 

58 

.1 

.1 

.2 

.2 

.2 

.3 

.3 

.4 

.5 

.7 

.9 

2.3 

3.2 

58 

60 

1.2 

1.2 

1.3 

1.3 

1.3 

1.4 

1.5 

1.6 

1.7 

2.0 

2.4 

3.4 

60 

62 

.3 

.3 

.4 

.4 

.4 

.6 

.7 

.8 

2.1 

.5 

3.5 

62 

64 

.4 

.4 

.5 

.5 

.6 

.8 

.9 

2.2 

.6 

3.7 

64 

66 

.5 

.5 

.7 

.7 

.9 

2.0 

2.3 

.8 

3.8 

66 

68 

.6 

.7 

.9 

2.0 

2.2 

.4 

.9 

4.0 

68 

70 

1.8 

1.9 

2.1 

2.3 

2.6 

3.1 

4.3 

70 

72 

2.0 

2.1 

.5 

.8 

3.3 

4.6 

72 

74 

.2 

.5 

3.0 

3.5 

4.8 

74 

76 

.6 

3.0 

.8 

5.2 

76 

78 

3.1 

.6 

5.7 

78 

80 

3.8 

4.4 

80 

Page  582] 

TABLE  41. 

Natural  Sines  and  Cosines. 

Prop. 

0° 

1 

3 

2° 

8° 

4 

o 

Prop. 

parts 
29 

parts 
8 

M. 

N.  sine. 

N.cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 
99863 

N.  sine 

N.,cos. 

0 

0 

00000 

100000 

01745 

99985 

03490 

99939 

05234 

06976 

99756 

60 

2 

0 

1 

00029 

100000 

01774 

99984 

03519 

99938 

05263 

99861 

07005 

99754 

59 

2 

1 

2 

00058 

100000 

01803 

99984 

03548 

99937 

05292 

99860 

07034 

99752 

58 

2 

1 

3 

00087 

1(^)000 

01832 

99983 

03577 

99936 

05321 

99858 

07063 

99750 

57 

2 

2 

4 

00116 

lOOOiX) 

01862 

99983  . 

03606 

99935 

05350 

99857 

07092 

99748 

56 

2 

2 

5 

00145 

100000 

01891 

99982 

03635 

99934 

05379 

99855 

07121 

99746 

55 

2 

3 

6 

00175 

100000 

01920 

99982 

036tM 

99933 

05408 

99854 

071.50 

99744 

.54 

2 

3 

7 

00204 

100000 

01949 

99981 

03693 

99932 

05437 

99852 

07179 

99742 

53 

2 

4 

8 

00233 

100000 

01978 

99980 

03723 

99931 

05466 

99851 

07208 

99740 

52 

2 

4 

9 

00262 

100000 

02007 

99980 

03752 

99930 

05495 

99849 

07237 

997.38 

51 

2 

5 

10 

00291 

100000 

02036 

99979 

03781 

99929 

05524 

99847 

07266 

99736 

50 

2 

5 

11 

00320 

99999 

02065 

99979 

03810 

99927 

05553 

99846 

07295 

99734 

49 

2 

6 

12 
13 

00349 
00378 

99999 
99999 

02094 
02123 

99978 
99977 

03839 

99926 

05582 
05611 

99844 
99842 

07324 
07353 

99731 
99729 

48 

2 

6 

03868 

99925 

47 

2 

7 

14 

00407 

99999 

02152 

99977 

03897 

99924 

05640 

99841 

07.382 

99727 

46 

2 

7 

15 

00436 

99999 

02181 

99976 

03926 

99923 

05669 

998.39 

07411 

99725 

45 

2 

8 

16 

00465 

99999 

02211 

99976 

0.3955 

99922 

05698 

99838 

07440 

99723 

44 

8 

17 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

9 

18 
19 

00524 
00553 

99999 

02269 
02298 

99974 
99974 

04013 
04042 

99919 

057.36 
05785 

99834 
99833 

07498 

99719 

42 
41 

1  , 

9 

99998 

99918 

07527 

99716 

10 

20 

00582 

99998 

02327 

99973 

04071 

99917 

0.5814 

99831 

07556 

99714 

40 

10 

21 

00611 

99998 

02356 

99972 

04100 

99916 

05844 

99829 

07585 

99712 

.39 

11 

22 

00640 

99998 

02385 

99972 

04129 

99915 

0,5873 

99827 

07614 

99710 

38 

11 

23 

00669 

99998 

02414 

99971 

04159 

99913 

05902 

99826 

07643 

99708 

37 

12 

24 

00698 

99998 
99997 

02443 

99970 
99969 

04188 
04217 

99912 
99911 

05931 
05960 

99824 
99822 

07672 
07701 

99705 
99703 

36 
35 

12 

25 

00727 

02472 

13 

26 

00756 

99997 

02501 

99969 

04246 

99910 

05989 

99821 

07730 

99701 

34 

13 

27 

00785 

99997 

02530 

99968 

04275  '  99909 

06018 

99819 

07759 

99699 

33 

14 

28 

00814 

99997 

02560 

99967 

04304  I  99907 

06047 

99817 

07788 

99696 

32 

14 

29 

00844 

99996 

02589 

99966 

04333  1  99906 

06076 

99815 

07817 

99694 

31 

15 
15 

30 
31 

00873 

99996 

02618 

99966  04362  j  99905 

06105 
06134 

99813 
99812 

07846 

99692 

30 
29 

00902 

99996 

02647 

99965 

04391 

99904 

07875 

99689 

15 

32 

00931 

99996 

02676 

99964 

04420 

99902 

06163 

99810 

07904 

99687 

28 

16 

33 

00960 

99995 

02705 

99963 

04449 

99901 

06192 

99808 

07933 

99685 

27 

16 

34 

00989 

99995 

02734 

99963 

04478 

99900 

06221 

99806 

07962 

99683 

26 

17 

35 

01018 

99995 

02763 

99962 

04507 

99898 

06250 

99804 

07991 

99680 

25 

17 

36 

01047 

99995 

02792 

99961 

04536 
04565 

99897 
99896 

06279 

99803 
99801 

08020 

99678 

24 

18 

37 

01076 

99994 

02821 

99960 

06308 

08049 

99676 

23 

18 

38 

01105 

99994 

02850 

99959  04594  j  99894 

06337 

99799 

08078 

99673 

22 

19 

39 

01134 

99994 

02879 

99959 

04623  1  99893 

06366 

99797 

08107 

99671 

21 

1 

19 

40 

01164 

99993 

02908 

99958 

04653 

99892 

06395 

99795 

08136 

99668 

20 

20 

41 

01193 

99993 

02938 

99957 

04682 

99890 

06424 

99793 

08165 

99666 

19 

20 

42 

01222 

99993 

02967 

99956 
99955 

04711 

99889 

06453 
06482' 

99792 
99790 

08194 
08223 

99664 

18 

21 

43 

01251 

99992 

02996 

04740 

99888 

99661 

17 

21 

44 

01280 

99992 

03025 

99954 

04769 

99886 

06511 

99788 

08252 

99659 

16 

1 

22 

45 

01309 

99991 

03054 

99953 

04798 

99885 

06540 

99786 

08281 

99657 

15 

22 

46 

01338 

99991 

03083 

99952 

04827 

99883 

06569 

99784 

08310 

99654 

14 

0 

23 

47 

01367 

99991 

03112 

99952 

04856 

99882 

06598 

99782 

08339 

99652 

13 

0 

23 

48 

01396 

99990 

03141 

99951 

04885 

99881 

06627 
06656 

99780 
99778 

08368 

99649 
99647 

12 

U 

0 
0 

24 

49 

01425 

99990 

03170 

99950 

04914 

99879 

08397 

24 

50 

01454 

99989 

03199 

99949 

04943 

99878 

06685 

99776 

08426 

99644 

10 

0 

25 

51 

01483 

99989 

03228 

99948 

04972 

99876 

06714 

99774 

08455 

99642 

9 

0 

25 

52 

01513 

99989 

03257 

99947 

05001 

99875 

06743 

99772 

08484 

99639 

8 

0 

26 

53 

01542 

99988 

03286 

99946 

050.30 

99873 

06773 

99770 

08513 

99637 

7 

0 

26 

27 

54 
55 

01571 
01600 

99988 
99987 

03316 

99945 
99944 

050-59 
05088 

99872 
99870 

06802 

99768 
99766 

08542 
08571 

99635 
99632 

6 
5 

0 
0 

03345 

06831 

27 

56 

01629 

99987 

03374 

99943 

05117 

99869 

06860 

99764 

08600 

99630 

4 

0 

28 

57 

01658 

99986 

03403 

99942 

05146 

99867 

06889 

99762 

08629 

99627 

3 

0 

28 

58 

01687 

99986 

03432 

99941 

05175 

99866 

06918 

99760 

08658 

99625 

2 

0 

29 

59 

01716 

99985 

03461 

99940 

05205 

99864 

06947 

99758 

08687 

99622 

1 

0 

29 

60 

01745 

99985 

03490 

99939 

05234 

99863 
N.  sine. 

06976 

99756 
N.  sine. 

08716 

99619 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  COS. 

N.  COS. 

N.  sine. 

M. 

89° 

88° 

87° 

86° 

8 

j° 

TABLE  41. 

[Page  583 

Natural  Sines  and  Cosines. 

Prop. 

parts 

29 

5 

o 

6° 

7 

o 

8 

o 

9° 

Prop, 
parts 

4 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.sine. 

N.cos. 

N.  sine. 

N.  COS. 

N.  .sine.  N.  cos. 

0 

0 

08716 

99619 

10453 

99452 

12187 

99255 

13917 

99027 

15643  98769 

60 

4 

0 

1 

08745 

99617 

10482 

99449 

12216 

99251 

13946 

99023 

15672  1  98764 

59 

4 

1 

2 

08774 

99614 

10511 

99446 

12245 

99248 

13975 

99019 

15701  98760 

58 

4 

1 

3 

08803 

99612 

10540 

99443 

12274 

99244 

14004 

99015 

15730  ;  98755 

57 

4 

2 

4 

08831 

99609 

10569 

99440 

12302 

99240 

14033 

99011 

15758 

98751 

56 

4 

2 

5 

08860 

99607 

10597 

99437 

12331 

99237 

14061 

99006 

15787 

98746 

55 

4 

3 

6 

7 

08889 
08918 

99604 
99602 

10626 

99434 

12360 
12389 

99233 
99230 

14090 

99002 

15816 
15845 

98741 

54 
53 

4 
4 

3 

10655 

99431 

14119 

98998 

98737 

4   8 

08947 

99599 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

3 

4 

9 

08976 

99596 

10713 

99424 

12447 

99222 

14177 

98990 

15902 

98728 

51 

3 

5 

10 

09005 

99594 

10742 

99421 

12476 

99219 

14205 

98986 

15931 

98723 

50 

3 

5 

11 

09034 

99591 

10771 

99418 

12504 

99215 

14234 

98982 

15959 

98718 

49 

3 

6 

12 

09063 

99588 

10800 
10829 

99415 
99412 

12533 

99211 

14263 
14292 

98978 

15988 

98714 
98709 

48 
47 

3 
3 

6 

13 

09092 

99586 

12562 

99208 

98973 

16017 

7  14 

09121 

99583 

10858 

99409 

12591 

99204 

14320 

98969 

16046 

98704 

46 

3 

7  1  15 

09150 

99580 

10887 

99406 

12620 

99200 

14349 

98965 

16074 

98700 

45 

3 

8  1  16 

09179 

99578 

10916 

99402 

12649 

99197 

14378 

98961 

16103  98695 

44 

3 

8  1  17 

09208 

99575 

10945 

99399 

12678 

99193 

14407 

98957 

16132 

98690 

43 

3 

9  18 
9  19 

09237 

99572 
99570 

10973 
11002 

99396 
99393 

12706 

99189 

14436 
14464 

98953 

16160 
16189 

98686 

42 
41 

3 
3 

09266 

12735 

99186 

98948 

98681 

10  i  20 

09295 

99567 

11031 

99390 

12764 

99182 

14493 

98944 

16218 

98676 

40 

3 

10  '  21 

09324 

99564 

11060 

99386 

12793 

99178 

14522 

98940 

16246 

98671 

39 

3 

11  22 

09353 

99562 

11089 

99383 

12822 

99175 

14551 

98936 

16275 

98667 

38 

3 

11  !  23 

09382 

99559 

11118 

99380 

12851 

99171 

14580 

98931 

16304 

98662 

37 

2 

12 

24 

09411 

99556 

11147 

99377 

12880 

99167 

14608 

98927 

16333 

98657 

36 
35 

2 

2 

12 

25 

09440 

99553 

11176 

99374 

12908 

99163 

14637 

98923 

16361 

98652 

13  26 

09469 

99551 

11205 

99370 

12937 

99160 

14666 

98919 

16390 

98648 

34 

2 

13  27 

09498 

99548 

11234 

99367 

12966 

99156 

14695 

98914 

16419  1  98ft43 

33 

9 

14  28 

09527 

99545 

11263 

99364 

12995 

99152 

14723 

98910 

16447  :  98638 

32 

2 

14  29 

09556 

99542 

11291 

99360 

13024 

99148 

14752 

98906 

16476  1  98633 

31 

2 

15  30 
15  31 

09585 

99540 

11320 

99357 

13053 

99144 

14781 
14810 

98902 
98897 

16505 

98629 

30 
29 

2 

09614 

99537 

11349 

99354 

13081 

99141 

16533 

98624 

2 

15  32 

09642 

99534 

11378 

99351 

13110 

99137 

14838 

98893 

16562 

98619 

28 

2 

16  33 

09671 

99531 

11407 

99347 

13139 

99133 

14867 

98889 

16591 

98614 

27 

2 

16  i  34 

09700 

99528 

11436 

99344 

13168 

99129 

14896 

98884 

16620 

98609 

26 

2 

17  35 

09729 

99526 

11465 

99341 

13197 

99125 

14925 

98880 

16648 

98604 

25 

2 

17  36 

18  !  37 

09758 
09787 

99523 

11494 

99337 
99334 

13226 

99122 

14954 
14982 

98876 
98871 

16677 
16706 

98600 

24 

2 

99520 

11523 

13254 

99118 

98595 

23 

2 

18  38 

09816 

99517 

11552 

99331 

13283 

99114 

15011 

98867 

16734 

98590 

22 

19  39 

09845 

99514 

11580 

99327 

13312 

99110 

15040 

98863 

-16763  98585 

21 

19  •   40 

09874 

99511 

11609 

99324 

13341 

99106 

15069 

98858 

16792  98580 

20 

20  41 

09903 

99508 

11638 

99320 

13370 

99102 

15097 

98854 

16820  98575 

19 

20 

42 
43 

09932 

99506 

11667 

99317 

13399 
13427 

99098 

15126 

98849 
98845 

16849  98570 

18 
17 

21 

09961 

99503 

11696 

99314 

99094 

15155 

16878  j  98565 

21  44 

09990 

99500 

11725 

99310 

13456 

99091 

15184 

98841 

16906  98561 

16 

22  45 

10019 

99497 

11754 

99307 

13485 

99087 

15212 

98836 

16935  98556 

15 

22  46 

10048 

99494 

11783 

99303 

13514 

99083 

15241 

98832 

16964  98551 

14 

23  i  47 

10077 

99491 

11812 

99300 

13543 

99079 

15270 

98827 

16992  !  98546 

13 

J 

23  i  48 

24  49 

10106 

99488 

11840 

99297 
99293 

13572 
13600 

99075 

15299 

98823 

17021 
17050 

98541 

12 

10135 

99485 

11869 

99071 

15327 

98818 

98536 

11 

24  50 

10164 

99482 

11898 

99290 

13629 

99067 

15356 

98814 

17078  !  98531 

10 

25  j  51 

10192 

99479 

11927 

99286 

13658 

99063 

15385 

98809 

17107 

98526 

9 

25  52 

10221 

99476 

11956 

99283 

13687 

99059 

15414 

98805 

17136 

98521 

8 

26  53 

10250 

99473 

11985 

99279 

13716 

99055 

15442 

98800 

17164 

98516 

7 

0 

26  54 

27  55 

10279 

99470 

12014 

99276 

13744 
13773 

99051 

15471 

98796 

17193 

98511 

6 
5 

0 

10308 

99467 

12043 

99272 

99047 

15500 

98791 

17222  98506 

0 

27  i  56 

10337 

99464 

12071 

99269 

13802 

99043 

15529 

98787 

17250  98501 

4 

0 

28  '  57 

10366 

99461 

12100 

99265 

13831 

99039 

15557 

98782 

17279  98496 

3 

0 

28  ;  58 

10395 

99458 

12129 

99262 

13860 

99035 

15586 

98778 

17308  }  98491 

2 

0 

29 

59 

10424 

99455 

12158 

99258 

13889 

99031 

15615 

98773 

17336  98486 

1 

0 

29 

60 

10453 

99452 

12187 

99255 

13917 

99027 

15643 

98769 

17365  98481 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS.  i  N.  sine. 

M. 

1 

8 

JO 

88 

o 

8 

2° 

8 

1° 

80° 

Page  584] 

TABLE  41. 

Natural  Sines  and  Cosines. 

Prop. 

10°     1 

11 

o 

12°     1 

18°     1 

14°      1 

Prop. 

parts 
28 

1 

1 

parte 
6 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 

0 

17365 

98481 

19081 

98163 

20791 

97815 

22495 

97437 

24192 

97030 

60 

6 

0 

1 

17393 

98476 

19109 

98157 

20820 

97809 

22523 

97430 

24220  97023 

59 

6 

1 

2 

17422 

98471 

19138 

98152 

20848 

97803 

22552 

97424 

24249  97015 

58 

6 

1 

3 

17451 

98466 

19167 

98146 

20877 

97797 

22580 

97417 

24277  97008 

57 

6 

2 

4 

17479 

•98461 

19195 

98140 

20905 

97791 

22608 

97411 

24305 

97001 

56 

6 

2 

5 

17508 

98455 

19224 

98135 

20933 

97784 

22637 

97404 

24333 

96994 

55 

6 

3 

6 

17537 

98450 

19252 

98129 

20962 

97778 
97772 

22665 
22693 

97398 
97391 

24362 
24390 

96987 
'96980' 

54 

5 

3 

7 

17565 

98445 

19281 

98124 

20990 

53 

5 

4 

8 

17594 

98440 

19309 

98118 

21019 

97766 

22722 

97384 

24418 

96973 

52 

5 

4 

9 

17623 

98435 

19338 

98112 

21047 

97760 

22750 

97378 

24446 

96966 

51 

5 

5 

10 

17651 

98430 

19366 

98107 

21076 

97754 

22778 

97371 

24474 

96959 

50 

5 

5 

11 

17680 

98425 

19395 

98101 

21104 

97748 

22807 

97365 

24503 

96952 

49 

5 

6 

12 
13 

17708 

98420 

19423 

98096 
98090 

21132 
21161 

97742 

22835 

97358 
97351 

24531 

96945 

48 

47 

5 

6 

17737 

98414 

19452 

97735 

22863 

24559 

96937 

5 

7 

14 

17766 

98409 

19481 

98084 

21189 

97729 

22892 

97345 

24587 

96930 

46 

5 

7 

15 

17794 

98404 

19509 

98079 

21218 

97723 

22920 

97338 

24615 

96923 

45 

5 

7 

16 

17823 

98399 

19538 

98073 

21246 

97717 

22948 

97331 

24644 

96916 

44 

4 

8 

17 

17852 

98394 

19566 

98067 

21275 

97711 

22977 

97325 

24672 

96909 

43 

4 

8  18  1 

17880 

98389 

19595 

98061 
98056 

21303 

97705 

23005 

97318 

24700 

24728 

96902 
96894 

42 
41 

4 

9 

19 

17909 

98383 

19623 

21331  97698 

23033 

97311 

4 

9 

20 

17937 

98378 

19652 

98050 

21360  97692 

23062 

97304 

24756 

96887 

40 

4 

10 

21 

17966 

98373 

19680 

98044 

21388  1  97686 

23090 

97298 

24784 

96880 

39 

4 

10 

22 

17995 

98368 

19709 

98039 

21417  !  97680 

23118 

97291 

24813 

96873 

38 

4 

11 

23 

18023 

98362 

19737 

98033 

21445  j  97673 

23146 

97284 

24841 

96866 

37 

4 

11 
12 

24 
25 

18052 

98357 

19766 
19794' 

98027 
98021 

21474 

97667 
97661 

23175 

97278 

24869 
24897 

96858 
96851 

36 
35 

4 

18081 

98352 

21502 

23203. 

97271 

4 

12 

26 

18109 

98347 

19823 

98016 

21530  j  97655 

23231 

97264 

24925 

96844 

34 

3 

13 

27 

18138 

98341 

19851 

98010 

21559  97648 

23260 

97257 

24954 

96837 

33 

3 

13 

28 

18166 

98336 

19880 

98004 

21587  1  97642 

23288 

97251 

24982 

96829 

32 

3 

14 

29 

18195 

98331 

19908 

97998 

21616  1  97636 

23316 

97244 

25010 

96822 

31 

3 

14 
14 

30 
31 

18224 

98325 

19937 
19965 

97992 
97987 

21644 

97630 
97623 

23345 
23373 

97237 
97230 

25038 
25066 

96815 
96807 

30 
29 

3 

18252 

98320 

21672 

3 

15 

32 

18281 

98315 

19994 

97981 

21701  1  97617 

23401 

97223 

25094 

96800 

28 

3 

15 

33 

18309 

98310 

20022 

97975 

21729  1  97611 

2.3429 

97217 

25122 

96793 

27 

3 

16 

34 

18338 

98304 

20051 

97969 

21758  97604 

23458 

97210 

25151 

96786 

26 

3 

16 

35 

18367 

98299 

20079 

97963 

21786  97598 

23486 

97203 

25179  1  96778 

25 

3 

17 
17 

36 
37 

18395 
18424 

98294 

20108 

97958 
97952 

21814  i  97592 
21843  ;  97585 

23514 
23542 

97196 
97189 

25207  96771 
25235  1  96764 

24 
23 

2 
2 

,  98288 

20136 

18 

38 

18452 

1  98283 

20165 

97946 

21871  97579 

23571 

97182 

25263  '   96756 

22 

2 

18 

39 

18481 

98277 

20193 

97940 

21899  97573 

23599 

97176 

25291  96749 

21 

2 

19 

40 

18509 

98272 

20222 

97934 

21928  97566 

2.3627 

97169 

25320  96742 

20 

2 

19 

41 

18538 

98267 

20250 

97928 

21956  97560 

23656 

97162 

25:348  96734 

19 

2 

20 
20 

42 
43 

18567 
18595 

98261 

20279 

97922 
97916 

21985  \   97553 

23684 

97155 
97148' 

25376  96727 
25404  96719 

18 
17 

2 

98256 

20307 

1  22013 

97547 

23712 

2 

21 

44 

18624 

[  98250 

20336 

97910 

22041 

97541 

23740 

97141 

25432  i  96712 

16 

2 

21 

45 

18652 

;  98245 

20364 

97905 

22070 

97534 

23769 

97134 

25460  96705 

15 

2 

21 

46 

18681 

98240 

20393 

97899 

22098 

97528 

23797 

97127 

25488  96697 

14 

22 

47 

18710 

98234 

20421 

97893 

22126 

97521 

23825 

97120 

25516  96690 

13 

22 
23 

48 
49 

18738 
18767 

98229 
98223 

20450 
20478 

97887 
,'97881 

22155 

97515 
97508 

23853 

23882 

97113 
97106 

25545  96682 
25573  :  96675 

12 
11 

22183 

23 

50 

18795 

98218 

20507 

97875 

22212 

97502 

23910 

97100 

25601   96667 

10 

24 

51 

18824 

98212 

20535 

t  97869 

22240 

97496 

23938 

97093 

25629  96660 

9 

24 

52 

18852 

98207 

20563 

:  97863 

22268 

97489 

23966 

,  97086 

25657  96653 

8 

25 

53 

18881 

98201 

20592 

!  97857 

22297 

i  97483 

23995 

'  97079 

25685  96645 

/ 

25 
26 

54 
55 

18910 

98196 

20620 
20649 

i  97851 
97845 

22325 
22353 

97476 
97470 

24023 
24051 

1  97072 
97065 

25713  96638 

6 
5 

18938 

98190 

25741 

96630 

26 

56 

18967 

98185 

20677 

97839 

22382 

97463 

24079 

97058 

25769 

1  96623 

4 

0 

27 

57 

18995 

,  98179 

20706 

97833 

22410 

i  97457 

24108 

97051 

25798  I  96615 

3 

1  0 

27 

58 

19024 

j  98174 

20734 

97827 

22438 

97450 

24136 

97044 

25826  96608 

2 

0 

28 

59 

19052 

1  98168 

20763 

97821 

22467 

I  97444 

24164 

i  97037 

25854 

i  96600 

1 

0 

28 

60 

19081 

98163 

20791 

97815 

22495 

!  97437 

24192 

;  97030 

25882 

96593 

0 

0 

N.  CO.". 

1  N.  sine. 

N.  COS. 

j  N.sine. 

N.  COS. 

j  N.  sine. 

N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

7«° 

7 

s° 

77° 

7 

fl° 

75° 

TABLE  41. 

[Page  585 

Natural  Sines  and  Cosines. 

Prop. 

parts 

27 

1 

5° 

16 

o 

1' 

o 

18° 

19° 

Prop. 

parts 

9 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  CCS. 

N.siiie. 

N.co.s. 

N.  sine. 

N.cos. 

N.  sine. 

N.  COS. 

0 

0 

25882 

96593 

27564 

96126 

29237 

95630 

30902 

95106 

32557 

94552 

60 

9 

0 

1 

25910 

96585 

27592 

96118 

29265 

95622 

30929 

95097 

32584 

94542 

59 

9 

1 

2 

25938 

96578 

27620 

96110 

29293 

95613 

30957 

95088 

32612 

94533 

58 

9 

1 

3 

25966 

96570 

27648 

96102 

29321 

95605 

30985 

95079 

32639  94523 

57 

9 

2 

4 

25994 

96562 

27676 

96094 

29348 

95596 

31012 

95070 

32667  94514 

56 

8 

2 

5 

26022 

96555 

27704 

96086 

29376 

95588 

31040 

95061 

32694  i  94504 

55 

8 

3 

6 

26050 

96547 
96540 

27731 

96078 
96070 

29404 

95579 
95571 

31068 
31095 

95052 
95043" 

32722 

94495 
94485 

54 
53 

8 
8 

3 

7 

26079 

27759 

29432 

32749 

4 

8 

26107 

96532 

27787 

96062 

29460 

95562 

31123 

95033 

32777 

94476 

52 

8 

4 

9 

26135 

96524 

27815 

96054 

29487 

95554 

31151 

95024 

32804 

94466 

51 

8 

5 

10 

26163 

96517 

27843 

96046 

29515 

95545 

31178 

95015 

32832 

94457 

50 

8 

5 

11 

26191 

96509 

27871 

96037 

29543 

95536 

31206 

95006 

32859 

94447 

49 

7 

5 

12 

26219 

96502 
96494 

27899 
27927 

96029 

29571 

95528 

31233 
31261 

94997 

32887 
32914 

94438 
94428 

48 
47 

7 
7 

6 

13 

26247 

96021 

29599 

95519 

94988 

6 

14 

26275 

96486 

27955 

96013 

29626 

95511 

31289 

94979 

32942 

94418 

46 

7 

'  7 

15 

26303 

96479 

27983 

96005 

29654 

95502 

31316 

94970 

32969 

94409 

45 

7 

7 

16 

26331 

96471 

28011 

95997 

29682 

95493 

31344 

94961 

32997  94399 

44 

7 

8 

17 

26359 

96463 

28039 

95989 

29710 

95485 

31372 

94952 

33024  i  94390 

43 

6 

8 

18 
19 

26387 

96456 

28067 

95981 

29737 

95476 

31399 
31427 

94943 
94933 

33051 
33079" 

94380 

42 

6 
6 

9 

26415 

96448 

28095 

95972 

29765 

95467 

94370 

41 

9 

20 

26443 

96440 

28123 

95964 

29793 

95459 

31454 

94924 

33106  (  94361 

40 

6 

9 

21 

26471 

96433 

28150 

95956 

29821 

95450 

31482 

94915 

33134  '  94351 

39 

6 

10 

22 

26500 

96425 

28178 

95948 

29849 

95441 

31510 

94906 

33161  94342 

38 

6 

10 

23 

26528 

96417 

28206 

95940 

29876 

95433 

31537 

94897 

33189  94332 

37 

6 

11 

24 

26556 

96410 

28234 
28262 

95931 
95923 

29904 
29932 

95424 
95415 

31565 

94888 
94878 

33216  94322 

36 
35 

5 
5 

11 

25 

26584 

96402 

31593 

33244  94313 

12 

26 

26612 

96394 

28290 

95915 

29960 

95407 

31620 

94869 

33271  94303 

34 

5 

12 

27 

26640 

96386 

28318 

95907 

29987 

95398 

31648 

94860 

33298  ;  94293 

33 

5 

13 

28 

26668 

96379 

28346 

95898 

30015 

95389 

31675 

94851 

33326  ,  94284 

32 

5 

13 

29 

26696 

96371 

28374 

95890 

30043 

95380 

31703 

94842 

33353  94274 

31 

5 

14 
14 

30 
31 

26724 

96363 

28402 

95882 

30071 

95372 
95363 

31730 
31758 

94832 
94823 

33381  94264 
33408  94254 

30 
29 

5 

26752 

96355 

28429 

95874 

30098 

4 

14 

32 

26780 

96347 

28457 

95865 

30126 

95354 

31786 

94814 

33436  ;  94245 

28 

4 

15 

33 

26808 

96340 

28485 

95857 

30154 

95345 

31813 

94805 

33463  ;  94235 

27 

4 

15 

34 

26836 

96332 

28513 

95849 

30182 

95337 

31841 

94795 

33490  i  94225 

26 

4 

16 

35 

26864 

96324 

28541 

95841 

30209 

95328 

31868 

94786 

33518  ,  94215 

25 

4 

16 
17 

36 
37 

26892 

96316 

28569 
28597 

95832 
95824 

30237 
30265 

95319 
95310 

31896 
31923 

94777 

33545  ;  94206 
33573  1  94196 

24 
23" 

4 

26920 

96308 

94768 

3 

17 

38 

26948 

96301 

28625 

95816 

30292 

95301 

31951 

94758 

33600  ,  94186 

22 

3 

18 

39 

26976 

96293 

28652 

95807 

30320 

95293 

31979 

94749 

33627  94176 

21 

3 

18 

40 

27004 

96285 

28680 

95799 

30348 

95284 

32006 

94740 

33655  94167 

20 

3 

18 

41 

27032 

96277 

28708 

95791 

30376 

95275 

32034 

94730 

33682  94157 

19 

3 

19 
19 

42 
43 

27060 

96269 
96261 

28736 
28764 

95782 
95774 

30403 

95266 
95257 

32061 

94721 
94712 

33710 
33737 

94147 

18 

3 
3 

27088 

30431 

32089 

94137 

17 

20 

44 

27116 

96253 

28792 

95766 

30459 

95248 

32116 

94702 

33764  !  94127 

16 

2 

20 

45 

27144 

96246 

28820 

95757 

30486 

95240 

32144 

94693 

33792 

94118 

15 

2 

21 

46 

27172 

96238 

28847 

95749 

30514 

95231 

32171 

94684 

33819 

94108 

14 

2 

21 

47 

27200 

96230 

28875 

95740 

30542 

95222 

32199 

94674 

33846 

94098 

13 

2 

22 

48 

27228 

96222 

28903 

95732 
95724 

30570 

95213 
95204 

32227 
32254 

94665 
94656 

33874 

94088 

12 

2 

22 

49 

27256 

96214 

28931 

30597 

33901 

94078 

11 

2 

23 

50 

27284 

96206 

28959 

95715 

30625 

95195 

32282 

94646 

33929 

94068 

10 

23 

51 

27312 

96198 

28987 

95707 

30653 

95186 

32309 

94637 

33956 

94058 

9 

23 

52 

27340 

96190 

29015 

95698 

30680 

95177 

32337 

94627 

33983 

94049 

8 

24 

53 

27368 

96182 

29042 

95690 

30708 

95168 

32364 

94618 

34011 

94039 

7 

24 
25 

54 
55 

27396 

96174 
96166 

29070 
29098 

95681 
95673 

30736 

95159 
95150 

32392 
32419 

94609 
'94599 

34038 

94029 

6 

27424 

30763 

34065 

94019 

5 

25 

56 

27452 

96158 

29126 

95664 

30791 

95142 

32447 

94590 

34093 

94009 

4 

26 

57 

27480 

96150 

29154 

95656 

30819 

95133 

32474 

94580 

34120 

93999 

3 

0 

26 

58 

27508 

96142 

29182 

95647 

30846 

95124 

32502 

94571 

34147 

93989 

2 

0 

27 

59 

27536 

96134 

29209 

95639 

30874 

95115 

32529 

94561 

34175 

93979 

1 

0 

27 

60 

27564 

96126 

29237 

95630 

30902 

95106 

32557 

94552 

34202 

93969 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

X.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

7 

t° 

7S 

t° 

7 

i° 

71° 

70° 

Page  586]                  TABLE  41. 

Natural  Sines  and  Cosines. 

Prop. 

parts 

87 

M. 

20' 

21°      1 

22° 

28° 

24° 

Prop. 

parts 

11 

N.  sine.   N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine.  N.  cos. 

0 
0 

1 
1 

2 
2 
3 
3 

4 
4 
5 
5 
5 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

34202 
34229 
34257 
34284 
34311 
34339 
34366 
34393 
34421 
34448 
34475 
34503 
34530 

93969 
93959 
93949 
98939 
93929 
93919 
93909 
93899 
93889 
93879 
93869 
93859 
93849 

35837 
35864 
358^1 
35918 
35945 
35973 
36000 
36027 
36054 
36081 
36108 
36135 
36162 

93358 
93348 
93337 
93327 
93316 
93306 
93295 

37461 
37488 
37515 
37542 
37569 
37595 
37622 

92718 
92707 
92697 
92686 
92675 
926(>4 
92653 
92642 
92631 
92620 
92609 
92598 
92587 

39073 
39100 
39127 
39153 
39180 
39207 
39234 

92050 
92039 
92028 
92016 
92005 
91994 
91982 

40674 
40700 
40727 
40753 
40780 
40806 
40833 

91355 

9i:i43 

91331 
91319 
91307 
91295 
91283 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 
49 
48 
47 
46 
45 
44 
43 
42 

11 

11 

11 

10 

10 

10 

10 

10 

10 

9 

9 

9 

9 

9 

8 

8 

8 

8 

8 

93285 
93274 
93264 
93253 
93243 
93232 

37649 
37676 
37703 
37730 
37757 
37784 

39260 
39287 
39314 
39341 
39367 
39394 

91971 
91959 
91948 
91936 
91925 
91914 

40860 
40886 
40913 
40939 
40966 
40992 

91272 
91260 
91248 
91236 
91224 
91212 
91200 
91188 
91176 
91164 
91152 
91140 

6 

6 

7 

7 

8 

8 

9 

9 

9 

10 

10 

11 

11 

12 

12 

13 

13 

14 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55^ 

56 

57 

58 

59 

60 

34557 
34584 
34612 
34639 
34666 
34694 

93839 
93829 
93819 
93809 
93799 
93789 

36190 
36217 
36244 
36271 
36298 
36325 
36352 
36379 
36406 
36434 
36461 
36488 

93222 
93211 
93201 
93190 
93180 
93169 
93159 
93148 
93137 
93127 
93116 
93106 

37811 
37838 
37865 
37892 
37919 
37946 
37973 
37999 
38026 
38053 
38080 
38107 
38134 
38161 
38188 
38215 
38241 
38268 
38295 
38322 
38349 
38376 
38403 
38430 
38456 
38483 
38510 
38537 
38564 
38591 
38617 
38644 
38671 
38698 
38725 
38752 

92576 
92565 
92554 
92543 
92532 
92521 
92510 
92499 
92488 
92477 
92466 
92455 
92444 
92432 
92421 
92410 
92399 
92388 
92377 
92366 
92355 
92343 
92332 
92321 
92310 
92299 
92287 
92276 
92265 
92254 
92243 
92231 
92220 
92209 
92198 
92186 

39421 
39448 
39474 
39501 
39528 
39555 
39581 
39608 
39635 
39661 
39688 
39715 

91902 
91891 
91879 
91868 
91856 
91845 
91833 
91822 
91810 
91799 
91787 
91775 
91764 
91752 
91741 
91729 
91718 
91706 
91694 
91683 
91671 
91660 
91648 
91636 

41019 
41045 
41072 
41098 
41125 
41151 

34721 
34748 
34775 
34803 
34830 
34857 

93779 
93769 
93759 
93748 
93738 
93728 

41178 
41204 
41231 
41257 
41284 
41310 

91128 
91116 
91104 
91092 
91080 
91068 

41  i  8 
40  !  7 
39  '  7 
38   7 
37   7 
36   7 

34884 
34912 
34939 
34966 
34993 
35021 

93718 
93708 
93698 
93688 
93677 
93667 

36515 
36542 
36569 
36596 
36623 
36650 

93095 
93084 
93074 
93063 
93052 
93042 
93031 
93020 
93010 
92999 
92988 
92978 

39741 
39768 
39795 
39822 
39848 
39875 
39902 
39928 
39955 
39982 
40008 
40035 

41337 
41363 
41390 
41416 
41443 
41469 

91056 
91044 
91032 
91020 
91008 
90996 

35 
34 
33 
32 
31 
30 

6 
6 
6 
6 
6 
6 

14 
14 
15 
15 
16 
16 
17 
17 
18 
18 
18 
19 
19 
20 
20 
21 
21 
22 
22 
23 
23 
23 
24 
24 
25 
25 
26 
26 
27 
27 

35048 
35075 
35102 
35130 
35157 
35184 

93657 
93647 
93637 
93626 
93616 
93606 

36677 
36704 
36731 
36758 
36785 
36812 

41496 
41522 
41549 
41575 
41602 
41628 

90984 
90972 
90960 
90948 
90936 
90924 

29 
28 
27 
26 
25 
24 

5 
5 
5 
5 
5 
4 

35211 
35239 
35266 
35293 
35320 
35347 

93596 
93585 
93575 
93565 
93555 
93544 

36839 
36867 
36894 
36921 
36948 
36975 

92967 
92956 
92945 
92935 
92924 
92913 
92902' 
92892 
92881 
92870 
92859 
92849 
92838 
92827 
92816 
92805 
92794 
92784 

40062 
40088 
40115 
40141 
40168 
40195 
40221 
40248 
40275 
40301 
40328 
40355 
40381 
40408 
40434 
40461 
40488 
40514 
40541' 
40567 
40594 
40621 
40647 
40674 

91625 
91613 
91601 
91590 
91578 
91566 

41655 
41681 
41707 
41734 
41760 
41787 

90911 
90899 
90887 
90875 
90863 
90851 
90839 
90826 
90814 
90802 
90790 
90778 
90766 
90753 
90741 
90729 
90717 
90704 

23 
22 
21 
20 
19 
18 

4 
4 
4 
4 
3 
3 

35375 
35402 
35429 
35456 
35484 
35511 

93534 
93524 
93514 
93503 
93493 
93483 

37002 
37029 
37056 
37083 
37110 
37137 

91555 
91543 
91531 
91519 
91508 
91496 
91484 
91472 
91461 
91449 
91437 
91425 

41813 
41840 
41866 
41892 
41919 
41945 
41972 
41998 
42024 
42051 
42077 
42104 

17 
16 
15 
14 
13 
12 

3 
3 
3 
3 
2 
2 

35538 
35565 
35592 
35619 
35647 
35674 

93472 
93462 
93452 
93441 
93431 
93420 

37164 
37191 
37218 
37245 
37272 
37299 

38778 
38805 
38832 
38859 
38886 
38912 

92175 
92164 
92152 
92141 
92130 
92119 

11 

10 

9 

8 
7 
6 

2 
2 

2 

35701 
35728 
35755 
35782 
35810 
35837 

93410 
93400 
93389 
93379 
93368 
93358 

37326 
37353 
37380 
37407 
37434 
37461 

92773 
92762 
92751 
92740 
92729 
92718 

38939 
38966 
38993 
39020 
39046 
39073 

92107 
92096 
92085 
92073 
92062 
92050 

91414 
91402 
91390 
91378 
91366 
91355 

421.30 
42156 
42183 
42209 
42235 
42262 

90692 
90680 
90668 
90655 
90643 
90631 

5 
4 
3 
2 

1 
0 

0 
0 
0 

— 

N.  coe. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

09° 

68° 

67° 

66° 

65° 

!   1 

TABLE  41.                  [Page  587 

Natural  Sines  and  Cosines. 

Prop. ' 

s 

•5° 

26° 

27° 

28° 

29° 

Prop. 

parts 

14 

26   M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

X.  sine.  j.  N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0    0 

42262 

90631 

43837 

89879 

45399  89101 

46947 

88295 

48481 

87462 

60 

14 

0   1 

42288 

90618 

43863 

89867 

45425  1  89087 

46973 

88281 

48506 

87448 

59 

14 

1   2 

42315 

90606 

43889 

89854 

45451  i  89074 

46999 

88267 

48532 

87434 

58 

14 

1   3 

42341 

90594 

43916 

89841 

45477  '   89061 

47024 

88254 

48557 

87420 

57 

13 

2  1  4 

42367 

90582 

43942 

89828 

45503  89048 

47050 

88240 

48583 

87406 

56 

13 

2  i  5 

42394 

90569 

43968 

89816 

45529  89035 

47076 

88226 

48608 

87391 

55 

13 

3  j  6 
3  ;  7 

42420 

90557 
90545 

43994 

89803 

45554  !  89021 

47101 

88213 
88199 

48634 
48659 

87377 

54 

13 

42446 

44020 

89790 

45580  89008 

47127 

87363 

53 

12 

3  i  8 

42473 

90532 

44046 

89777 

45606  88995 

47153 

88185 

48684 

87349 

52 

12 

4   9 

42499 

90520 

44072 

89764 

45632  88981 

47178 

88172 

48710 

87335 

51 

12 

4  10 

42525 

90507 

44098 

89752 

45658  88968 

47204 

88158 

48735 

87321 

50 

12 

5  1  n 

42552 

90495 

44124 

89739 

45684  88955 

47229 

88144 

48761 

87306 

49 

11 

5  12 

42578 

90483 

44151 

89726 

45710  88942 

47255 
47281 

88130 

48786 

87292 
87278 

48 

11 

6  1  13 

42604 

90470 

44177 

89713 

45736  (  88928 

88117 

48811 

47 

11 

6  14 

42631 

90458 

44203 

89700 

45762 

88915 

47306 

88103 

48837 

87264 

46 

11 

7  1  15 

42657 

90446 

44229 

89687 

45787 

88902 

47332 

88089 

48862 

87250 

45 

11 

7  '  16 

42683 

90433 

44255 

89674 

45813 

88888 

47358 

88075 

48888 

87235 

44 

10 

7  !  17 

42709 

90421 

44281 

89662 

45839 

88875 

47383 

88062 

48913 

87221 

43 

10 

8  I  18 
8  19 

42736 

90408 

44307 

89649 

45865  1  88862 

47409 

88048 
88034 

48938 
48964 

87207 

42 
41 

10 

42762 

90396 

44333 

89636 

45891  i  88848 

47434 

87193 

10 

9  20 

42788 

90383 

44359 

89623 

45917  ;  88835 

47460 

88020 

48989 

87178 

40 

9 

9  j  21 

42815 

90371 

44385 

89610 

45942  88822 

47486 

88006 

49014 

87164 

39   9 

10  22 

42841 

90358 

44411 

89597 

45968  '  88808 

47511 

87993 

49040 

87150 

38   9 

10  i  23 

42867 

90346 

44437 

89584 

45994  88795 

47537 

87979 

49065 

87136 

37   9 

10 

24 
25 

42894 

90334 
90321. 

44464 

89571 
89558 

46020  i  88782 
46046  88768 

47562 

47588 

87965 
87951 

49090 
49116 

87121 
87107 

36   8 
35  ;    8 

n 

42920 

44490 

11 

26 

42946 

90309 

44516 

89545 

46072  88755 

47614 

87937 

49141 

87093 

34  1  8 

12 

27 

42972 

90296 

44542 

89532 

46097  88741 

47639 

87923 

49166 

87079 

33  1  8 

12  i  28 

42999 

90284 

44568 

89519 

46123  88728 

47665 

87909 

49192 

87064 

32   7 

13  •  29 

43025 

90271 

44594 

89506 

46149  88715 

47690 

87896 

49217 

87050 

31   7 

13  !  30 

43051 

90259 

44620 

89493 

46175  88701 

47716 
47741 

87882 

49242 

87036 
87021 

30   7 
29   7 

13  1  31 

43077 

90246 

44646 

89480 

46201  j  88688 

87868 

49268 

14  !  32 

43104 

90233 

44672 

89467 

46226  '   88674 

47767 

87854 

49293 

87007 

28  '     7 

14  !  33 

43130 

90221 

44698 

89454 

46252  i  88661 

47793 

87840 

49318 

86993 

27  1  6 

15  ;  34 

43156 

90208 

44724 

89441 

46278  !  88647 

47818 

87826 

49344 

86978 

26   6 

15  35 

43182 

90196 

44750 

89428 

46304  88634 

47844 

87812 

49369 

86964 

25   6 

16  36 

43209 
43235 

90183 
90171 

44776 

89415 
89402 

46330  88620 

47869 

87798 

49394 
49419 

86949 

24 
23 

6 

16 

37 

44802 

46355  i  88607 

47895 

87784= 

86935 

5 

16 

38 

43261 

90158 

44828 

89389 

46381  88593 

47920 

87770' 

49445 

86921 

22   5 

17 

39 

43287 

90146 

44854 

89376 

46407  88580 

47946 

87756 

49470 

86906 

21   5 

17 

40 

43313 

90133 

44880 

89363 

46433  ;  88566 

47971 

87743 

49495 

86892 

20   5 

18 

41 

43340 

90120 

44906 

89350 

46458  1  88553 

47997 

87729 

49521 

86878 

19   4 

18 

42 

43366 
43392 

90108 

44932 

89337 
89324 

46484 
46510 

88539 

48022 

87715 
87701 

49546 
49571 

86863 

18  .     4 
17   4 

19  43 

90095 

44958 

88526 

48048 

86849 

19  44 

43418 

90082 

44984 

89311 

46536  88512 

48073 

87687 

49596 

86834 

16   4 

20  45 

4:W45 

90070 

45010 

89298 

46561  88499 

48099 

87673 

49622 

86820 

15   4 

20  i  46 

43471 

90057 

45036 

89285 

46587  ;  88485 

48124 

87659 

49647 

86805 

14   3 

20  '  47 

43497 

90045 

45062 

89272 

46613  88472 

48150 

87645 

49672 

86791 

13   3 

21  '  48 
21  49 

43523 

90032 

45088 
45114 

89259 

46639  i  88458 

48175 

87631 

49697 
49723 

86777 

12   3 

43549 

90019 

89245 

46664  88445 

48201 

87617 

86762 

11   3 

22  50 

43575 

90007 

45140 

89232 

46690 

88431 

48226 

87603 

49748 

86748 

10   2 

22  51 

43602 

89994 

45166 

89219 

46716 

88417 

48252 

87589 

49773 

86733 

-9   2 

23  ;  52 

43628 

89981 

45192 

89206 

46742 

88404 

48277 

87575 

49798 

86719 

8   2 

23  53 

43654 

89968 

45218 

89193 

46767 

88390 

48303 

87561 

49824 

86704 

7   2 

23  1  54 

24  i  55 

43680 
43706 

89956 
89943 

45243 

89180 

46793 

88377 
88363 

48328 
48354 

87546 
87532 

49849 

49874 

86690 

86675 

6   1 
5   1 

45269 

89167 

46819 

24  56 

43733 

89930 

45295 

89153 

46844  i  88349 

48379 

87518 

49899 

86661 

4   1 

25 

57 

43759 

89918 

45321 

89140 

46870  88336 

48405 

87504 

49924 

86646 

3  j  1 

25 

58 

43785 

89905 

45347 

89127 

46896 

88322 

48430 

87490 

49950 

86632 

2   0 

26 

59 

43811 

89892 

45373 

89114 

46921 

88308 

48456 

87476 

49975 

86617 

1  !  0 

26 

60 

43837 

89879 

45399 

89101 

46947 

88295 

48481 

87462 

50000 

86603 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  cos. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

64 

1° 

6 

i° 

62° 

61° 

60° 

Page  588] 

TABLE  41. 

Natural  Sines  and  Cosines. 

Prop. 

80°    ■  1 

81°      1 

82°     1 

88°     1 

3^ 

[° 

! 

Prop. 

parts. 
25 

1 

parts. 
16 

M. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.*ine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 

0 

50000 

86603 

51504 

85717 

52992 

84805 

54464 

83867 

55919 

82904 

60 

16 

0 

1 

50025 

86588 

51529 

85702 

53017  !  84789  | 

54488 

83851 

55943 

82887 

59 

16 

1 

2 

50050 

86573 

51554 

85687 

53041 

84774 

54513 

83835 

55968 

82871 

58 

15 

1 

3 

50076 

iS559 

51579 

85672 

53066 

84759 

54537 

83819 

55992 

82855 

57 

15 

2 

4 

50101 

86544 

51604 

85657 

53091 

84743 

54561 

83804 

56016 

82839 

66 

15 

2 

5 

50126 

86530 

51628 

85642 

53115 

84728 

54586 

83788 

56040 

82822 

55 

15 

3 

6 

50151 

86515 

51653 

85627 
85612 

53140 

84712 

54610 

83772 
83756 

56064 

82806 
82790 

54 
53 

14 
14 

3 

7 

50176 

86501 

51678 

53164 

84697 

54635 

56088 

3 

8 

50201 

86486 

51703 

85597 

53189 

84681 

54659 

83740 

56112 

82773 

52 

14 

4 

9 

50227 

86471 

51728 

85582 

53214 

84666 

54683 

83724 

56136 

82757 

51 

14 

4 

10 

50252 

86457 

51753 

85567 

53238 

84650 

54708 

83708 

56160 

82741 

50 

13 

5 

11 

50277 

86442 

51778 

85551 

53263 

84635 

54732 

83692 

56184 

82724 

49 

13 

5 
5 

12 
13 

50302 
50327 

86427 

51803 

85536 
85521 

53288 
53312 

84619 
84604 

54756 
'54781 

83676 

56208 

82708 

48 

13 

86413 

51828 

83660 

56232 

82692 

47 

13 

6 

14 

50352 

86398 

51852 

85506 

53337 

84588 

54805 

83645 

56256 

82675 

46 

12 

6 

15 

50377 

86384 

51877 

85491 

53361  84573 

54829 

83629 

56280 

82659 

45 

12 

7 

16 

50403 

86369 

51902 

85476 

53386  84557 

54854 

83613 

56305 

82643 

44 

12 

7 

17 

50428 

86354 

51927 

85461 

53411  84542 

54878 

8.3597 

56329 

82626 

43 

11 

8 
8 

18 
19 

50453 

50478 

86340 
86325 

51952 
51977 

85446 
85431 

53435 

84526 
84511 

54902 

83581 

56353 

82610 
82593 

42 

11 

53460 

54927 

83565 

56377 

41 

11 

8 

20 

50503 

86310 

52002 

85416 

53484  84495 

54951 

83549 

56401 

82577 

40 

11 

9 

21 

50528 

86295 

52026 

85401 

53509 

84480 

54975 

83533 

56425 

82561 

39 

10 

9 

22 

50553 

86281 

52051 

85385 

53534 

84464 

54999 

83517 

56449 

82544 

38 

10 

10 

23 

50578 

86266 

52076 

85370 

53558 

84448 

55024 

83501 

56473 

82528 

37 

10 

10 

24 

50603 

86251 

52101 

85355 

53583 

84433 
84417 

55048 

83485 

56497 
56521 

82511 

36 
35 

10 
9 

10 

25 

50628 

86237 

52126 

85340 

53607 

55072 

■  83469 

82495 

11 

26 

50654 

86222 

52151 

85325 

53632  84402 

55097 

83453 

56545 

82478 

34 

9 

11 

27 

50679 

86207 

52175 

85310 

53656  84386 

55121 

83437 

56569 

82462 

33 

9 

12 

28 

50704 

86192 

52200 

85294 

53681  84370 

55145 

83421 

56593 

82446 

32 

9 

12 

29 

50729 

86178 

52225 

85279 

53705  !  84355 

55169  i  8.3405 

56617 

82429 

31 

8 

13 

30 

50754 

86163 

52250 

85264 

53730 

84339 

55194  !  83389 

56641 

82413 

30 
29 

8 
8 

13 

31 

50779 . 

86148 

52275 

85249 

53754 

84324 

55218 

83373 

56665 

82396 

13 

32 

50804 

86133 

52299 

85234 

53779 

84308 

55242 

83356 

56689 

82380 

28 

7 

14 

33 

50829 

86119 

52324 

85218 

53804 

84292 

55266 

83340 

56713 

82363 

27 

7 

14 

34 

50854 

86104 

52349 

85203 

53828 " 

•  84277 

55291 

83324 

56736 

82347 

26 

/ 

15 

35 

50879 

86089 

52374 

85188 

53853 

84261 

55315 

83308 

56760 

82330 

25 

( 

15 
15 

36 
37 

50904 
'  50929 

86074 
86059 

52399 

85173 

53877 

84245 
84230' 

55339 

83292 
83276 

56784 

82314 

24 
23 

6 
6 

52423 

85157 

53902 

55363 

56808 

82297 

16 

38 

50954 

86045 

52448 

85142 

53926 

84214 

55388 

83260 

56832 

82281 

22 

6 

16 

39 

50979 

86030 

52473 

85127 

53951 

84198 

55412 

83244 

56856 

82264 

21 

6 

17 

40 

51004 

86015 

52498 

85112 

53975 

84182 

55436 

83228 

56880 

82248 

20 

o 

17 

41 

51029 

86000 

52522 

85096 

54000 

84167 

55460 

83212 

56904 

82231 

19 

0 

18 

42 
43 

51054 
51079 

85985 
85970 

52547 

85081 

54024 
54049 

84151 

55484 

83195 

56928 

82214 

18 
17 

o 

5~ 

18 

52572 

85066 

84135 

55509 

83179 

56952 

82198 

18 

44 

51104 

85956 

52597 

85051 

54073 

84120 

55533 

83163 

56976 

82181 

16 

4 

19 

45 

51129 

85941 

52621 

85035 

54097 

84104 

55557 

83147 

57000 

82165 

15 

4 

19 

46 

51154 

85926 

52646 

85020 

54122 

84088 

55581 

83131 

57024 

82148 

14 

4 

20 

47 

51179 

85911 

52671 

85005 

54146 

84072 

55605 

83115 

57047 

82132 

13 

3 

20 

48 

51204 

85896 

52696 

84989 

54171 

84057 
84041 

55630 

8.3098 

57071 

82115 

12 
11 

3 
3 

20 

49 

51229 

85881 

52720 

84974 

54195 

55654 

83082 

57095 

82098 

21 

50 

51254 

85866 

52745 

84959 

54220  i  84025 

55678 

83066 

57119 

82082 

10 

3 

21 

51 

51279 

85851 

52770 

84943 

54244  ,  84009 

55702  j  83050 

57143 

82065 

9 

2 

22 

52 

51304 

85836 

52794 

84928 

54260  !  83994 

55726  i  83034 

57167 

82048 

8 

2 

22 

53 

51329 

85821 

52819 

84913 

54293 

83978 

55750  i  8.3017 

57191 

82032 

7 

2 

23 
23 

54 
55 

51354 

85806 

52644 
52869 

84897 

54317 
54342 

83962 
83946 

55775 
55799' 

83001 

57215 
57238 

82015 

6 
5 

2 

1 

51379 

85792 

84882 

82985 

81999 

23 

56 

51404 

85777 

52893 

84866 

54366 

83930 

55823 

82969 

57262 

81982 

4 

1 

24 

57 

51429 

85762 

52918 

84851 

54391 

83915 

55847 

82953 

57286 

81965 

3 

1 

24 

58 

51454 

85747 

52943 

84836 

54415 

83899 

55871 

829.36 

57310 

81949 

2 

1 

25 

59 

51479 

85732 

52967 

84820 

54440 

83883 

55895 

82920 

57334 

81932 

1 

0 

25 

60 

51504 

85717 

52992 

84805 

54464 

. 83867 

55919 

82904 

57358 

81915 

0 

0 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

M. 

59° 

5 

*° 

67° 

56° 

5 

6° 

TABLE  41. 

[Page  589  [ 

Natural  Sines  and  Cosines. 

Prop. 

85°      1 

86°      1 

S', 

° 

38° 

89° 

Prop. 

parts 
23 

t 

parts 
18 

M. 

N.  sine. 

N.  COS. 

X.  sine.  ] 

N.  COS. 

X.  .sine. 

N.  COS. 

X.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

0 

0 

57358 

81915 

58779 

80902 

60182 

79864 

61566 

78801 

62932 

77715 

60 

18 

0 

1 

57381 

81899 

58802 

80885 

60205 

79846 

61589 

78783 

62955 

77696 

59 

18 

1 

9 

57405 

81882 

58826 

80867 

60228 

79829 

61612 

78765 

62977 

77678 

58 

17 

1 

3 

57429 

81865 

58849 

80850 

60251 

79811 

61635 

78747 

63000 

77660 

57 

17 

2 

4 

57453 

81848 

58873 

80833 

60274 

79793 

61658 

78729 

63022 

77641 

56 

17 

2 

o 

57477 

81832 

58896 

80816 

60298 

79776 

61681 

78711 

63045 

77623 

55 

17 

2 
3 

6 

7 

57501 

81815 

58920 

80799 

60321 
60344 

79758 

61704 

78694 
78676 

63068 
63090 

77605 
77586 

54 

16 

57524 

81798 

58943 

80782 

79741 

61726 

53 

16 

3 

8 

57548 

81782 

58967 

80765 

60367 

79723 

61749 

78658 

63113 

77568 

52 

16 

3 

9 

57572 

81765 

58990 

80748 

60390 

79706 

61772 

78640 

63135 

77550 

51 

15 

4 

10 

57596 

81748 

59014 

80730 

60414 

79688 

61795 

78622 

63158 

77531 

50 

15 

4 

11 

57619 

81731 

59037 

80713 

60437 

79671 

61818 

78604 

63180 

77513 

49 

15 

5 

12 

57643 

81714 

59061 

80696 
80679 

60460 
60483 

79653 

61841 

78586 

63203 
63225 

77494 

48 
47 

14 

5 

13 

57667 

81698 

59084 

79635 

61864 

78568 

77476 

14 

5 

14 

57691 

81681 

59108 

80662 

60506 

79618 

61887 

78550 

63248 

77458 

46 

14 

6 

15 

57715 

81664 

59131 

80644 

60529 

79600 

61909 

78532 

63271 

77439 

45 

14 

6 

16 

57738 

81647 

59154 

80627 

60553 

79583 

61932 

78514 

63293 

77421 

44 

13 

7 

17 

57762 

81631 

59178 

80610 

60576 

79565 

61955 

78496 

63316 

77402 

43 

13 

7 
7 

18 
19 

57786 

81614 

59201 

80593 
80576 

60599 

79547 

61978 
62001 

78478 

63338 

77384 

42- 

13 

57810 

81597 

59225 

60622 

79530 

78460 

63361 

77366 

41 

12 

8 

20 

57833 

81580 

59248 

80558 

60645 

79512 

62024 

78442 

63383 

77347 

40 

12 

8 

21 

57857 

81563 

59272 

80541 

60668 

79494 

62046 

78424 

63406 

77329 

39 

12 

8 

22 

57881 

81546 

59295 

80524 

60691 

79477 

62069 

78405 

63428 

77310 

38 

11 

9 

23 

57904 

81530 

59318 

80507 

60714 

79459 

62092 

78387 

63451 

77292 

37 

11 

9 

24 

57928 

81513 

59342 
59365 

80489 
80472 

60738 

79441 

62115 
62138 

78369 
78351 

63473 

77273 

36 

11 

10 

25 

57952 

81496 

60761 

79424 

6:3496 

77255 

35 

11 

10 

26 

57976 

81479 

59389 

80455 

60784 

79406 

62160 

78333 

63518 

77236 

34 

10 

10 

27 

57999 

81462 

59412 

80438 

60807 

79388 

62183 

78315 

6;?540 

77218 

33 

10 

11 

28 

58023 

81445 

59436 

80420 

60830 

79371 

62206 

78297 

63563 

77199 

32 

10 

11 

29 

58047 

81428 

59459 

80403 

60853 

79353 

62229 

78279 

63585 

77181 

31 

9 

12 

30 

58070 

81412 

.  59482 
59506 

80386 
80368 

60876 
60899 

79335 
79318 

62251 
62274 

78261 

63608 
63630 

77162 

30 
29 

9 
9 

12 

31 

58094 

81395 

78243 

77144 

12 

32 

58118 

81378 

59529 

80351 

60922 

79300 

62297 

78225 

63653 

77125 

28 

8 

13 

33 

58141 

81361 

59552 

80334 

60945 

79282 

62320 

78206 

63675 

77107 

27 

8 

13 

34 

58165 

81344 

59576 

80316 

60968 

79264 

62342 

78188 

63698 

77088 

26 

8 

13 

35 

58189 

81327 

59599 

80299 

60991 

79247 

62365 

78170 

63720 

77070 

25 

8 

14 

36 

58212 

81310 

59622 

80282 

61015 
61038 

79229 

62388 
62411 

78152 

63742 

77051 
77033 

24 
23 

7 

7 

14 

37 

58236 

81293 

59646 

80264 

79211 

78134 

63765 

15 

38 

58260 

81276 

59669 

80247 

61061 

79193 

62433 

78116 

63787 

77014 

22 

7 

15 

39 

58283 

81259 

59693 

80230 

61084 

79176 

62456 

78098 

63810 

76996 

21 

6 

15 

40 

58307 

81242 

59716 

80212 

61107 

79158 

62479 

78079 

63832 

76977 

20 

6 

16 

41 

58330 

81225 

59739 

80195 

61130 

79140 

62502 

78061 

63854 

76959 

19 

6 

16 

42 

58354 

81208 

59763 

80178 

61153 

79122 
79105 

62524 
62547 

78043 
78025 

63877 

76940 
76921 

18 
17 

5 
5 

16 

43 

58378 

81191 

59786 

80160 

61176 

63899 

17 

44 

58401 

81174 

59809 

80143 

61199 

79087 

62570 

78007 

63922 

76903 

16 

5 

17 

45 

58425 

81157 

59832 

80125 

61222 

79069 

62592 

77988 

63944 

76884 

15 

5 

18 

46 

58449 

81140 

59856 

80108 

61245 

79051 

62615 

77970 

63966 

76866 

14 

4 

18 

47 

58472 

81123 

59879 

80091 

61268 

79033 

62638 

77952 

63989 

76847 

13 

4 

18 
19 

48 
49 

58496 

81106 

59902 

80073 

61291 

79016 

62660 

77934 

64011' 

76828 
76810 

12 
11 

4 

58519 

81089 

59926 

80056 

61314 

78998 

62683 

77916 

64033 

3 

19 

50 

58543 

81072 

59949 

80038 

61337 

78980 

62706 

77897 

64056 

76791 

10 

3 

20 

51 

58567 

81055 

59972 

80021 

61360 

78962 

62728 

77879 

64078 

76772 

9 

3 

20 

52 

58590 

81038 

59995 

80003 

61383 

78944 

62751 

77861 

64100 

76754 

8 

2 

20 

53 

58614 

81021 

60019 

79986 

61406 

78926 

62774 

77843 

64123 

76735 

7 

2 

21 

21 

54 
55' 

58637 
58661 

81004 

60042 

79968 

61429 
"61451 

78908 

62796 
62819 

77824 
77806' 

64145 

76717 

6 

2 

80987 

60065 

79951 

78891 

64167 

76698 

5 

2 

21 

56 

58684 

80970 

60089 

79934 

61474 

78873 

62842 

77788 

64190 

76679 

4 

1 

22 

57 

58708 

80953 

60112 

79916 

61497 

78855 

62864 

77769 

64212 

76661 

3 

1 

22 

58 

58731 

80936 

60135 

79899 

61520 

78837 

62887 

77751 

64234 

76642 

2 

1 

23 

59 

58755 

80919 

60158 

79881 

61543 

78819 

62909 

77733 

64256 

76623 

1 

0 

23 

60 

58779 

80902 

60182 

79864 

61566 

78801 

62932 

77715 

64279 

76604 

0 

0 

N.  COS. 

N.  sine. 

K.  COS. 

N.  sine. 

K.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.  cos. 

X.  sine. 

M. 

5 

1° 

bS 

° 

5 

>o 

5 

1° 

Q< 

0° 

Page  590] 

TABLE  41. 

Natural  Sines  and  Cosines. 

Prop. 

40°       1 

41°      1 

42°     1 

48 

o 

44 

o 

Prop. 

parts 
22 

1 

parts 
19 

19 

M. 

N.  sine. 

N.cos. 

N.  sine. 
65606 

N.  COS. 

N.sine. 

N.  COS. 

N.sine. 

N.  COS. 

N.  sine. 

N.  COS. 

0 

0 

64279 

76604 

75471 

66913 

74314 

68200 

73135 

69466 

71934 

60 

0 

1 

64301 

76586 

65628 

75452 

66935 

74295 

68221 

73116 

69487 

71914 

59 

19 

1 

2 

64323 

7fi567 

65650 

75433 

66956 

74276 

68242 

73096 

69508 

71894 

58 

18 

1 

3 

64346 

76548 

65672 

75414 

66978 

74256 

68264 

73076 

69529 

71873 

57 

18 

1 

4 

64368 

76530 

65694 

75395 

66999 

74237 

68285 

73056 

69549 

71853 

56 

18 

2 

5 

64390 

76511 

65716 

75375 

67021 

74217 

68306 

73036 

69570 

71833 

55 

17 

2 
3 

6 

64412 

76492 
76473 

65738 

75356 
75337 

67043 

74198 
74178 

68327 

73016 

69591 

71813 
71792 

54 
53 

17 

7 

64435 

65759 

67064 

68349 

72996 

69612 

17 

3 

8 

64457 

76455 

65781 

75318 

67086 

74159 

68370 

72976 

69633 

71772 

52 

16 

3 

9 

64479 

76436 

65803 

75299 

67107 

74139 

68391 

72957 

69654 

71752 

51 

16 

4 

10 

64501 

76417 

65825 

75280 

67129 

74120 

68412 

72937 

69675 

71732 

50 

16 

4 

11 

64524 

76398 

65847 

75261 

67151 

74100 

68434 

72917 

69696 

71711 

49 

16 

4 
5 

12 
13 

64546 
64568 

76380 

65869 

75241 
75222 

67172 
67194 

74080 

68455 

72897 

69717 
69737 

71691 
71671 

48 
47 

15 
15 

76361 

65891 

74061 

68476 

72877 

5 

14 

64590 

76342 

65913 

75203 

67215 

74041 

68497 

72857 

69758 

71650 

46 

15 

6 

15 

64612 

76323 

65935 

75184 

67237 

74022 

68518 

72837 

69779 

71630 

45 

14 

6 

16 

64635 

76304 

65956 

75165 

67258 

74002 

68539 

72817 

69800 

71610 

44 

14 

6 

17 

64657 

76286 

65978 

75146 

67280 

73983 

68561 

72797 

69821 

71590 

43 

14 

7 
7 

18 
19 

64679 
64701 

76267 
76248 

66000 
66022 

75126 
75107 

67301 

73963 

68582 

72777 
72757 

69842 
69862 

71569 
71549 

42 
41 

13 

67323 

73944 

68603 

13 

7 

20 

64723 

76229 

66044 

75088 

67344 

73924 

68624 

72737 

69883 

71529 

40 

13 

8 

21 

64746 

76210 

66066 

75069 

67366 

73904 

68645 

72717 

69904 

71508 

39 

12 

8 

22 

64768 

76192 

66088 

75050 

67387 

73885 

68666 

72697 

69925 

71488 

38 

12 

8 

23 

64790 

76173 

66109 

75030 

67409 

73865 

68688 

72677 

69946 

71468 

37 

12 

9 

24 

64812 

76154 

66131 

75011 

67430 

73846 

68709 
68730 

72657 
72637 

69966 
69987 

71447 

36 

11 

11 

9 

25 

64834 

76135 

66153 

74992 

67452 

73826 

71427 

35 

10 

26 

64856 

76116 

66175 

74973 

67473 

73806 

68751 

72617 

70008 

71407 

34 

11 

10 

27 

64878 

76097 

66197 

74953 

67495 

73787 

68772 

72597 

70029 

71386 

33 

10 

10 

28 

64901 

76078 

66218 

74934 

67516 

73767 

68793 

72577 

70049 

71366 

32 

10 

11 

29 

64923 

76059 

66240 

74915 

67538 

73747 

68814 

72557 

70070 

71.345 

31 

10 

11 
11 

30 
31 

64945 
64967 

76041 
76022 

66262 

74896 
74876 

67559 

73728 
73708 

68835 

72537 
72517 

70091 
70112 

71325 

30 

29 

10 
9 

66284 

67580 

68857 

71305 

12 

32 

64989 

76003 

66306 

74857 

67602 

73688 

68878 

72497 

70132 

71284 

28 

9 

12 

33 

65011 

75984 

66327 

74838 

67623 

73669 

68899 

72477 

70153 

71264 

27 

9 

12 

34 

65033 

75965 

66349 

74818 

67645 

73649 

68920 

72457 

70174 

71243 

26 

8 

13 

35 

65055 

75946 

66371 

74799 

67666 

73629 

68941 

72437 

70195 

71223 

25 

8 

13 
14 

36 
37 

65077 

75927 

66393 

74780 

67688 
67709 

73610 

68962 

72417 
72397 

70215 

71203 

24 
23 

8 
7 

65100 

75908 

66414 

74760 

73590 

68983 

70236 

71182 

14 

38 

65122 

75889 

66436 

74741 

67730 

73570 

69004 

72377 

70257 

71162 

22 

7 

14 

39 

65144 

75870 

66458 

74722 

67752 

73551 

69025 

72357 

70277 

71141 

21 

7 

15 

40 

65166 

75851 

66480 

74703 

67773 

73531 

69046 

72337 

70298 

71121 

20 

6 

15 

41 

65188 

75832 

66501 

74683 

67795 

73511 

69067 

72317 

70319 

71100 

19 

6 

15 
16 

42 

65210 

75813 

66523 
66545 

74664 

67816 
67837 

73491 

69088 

72297 

70339 

71080 
71059 

18 
17 

6 

43 

65232 

75794 

74644 

73472 

69109 

72277 

70360 

0 

16 

44 

65254 

75775 

66566 

74625 

67859 

73452 

69130 

72257 

70381 

71039 

16 

5 

17 

45 

65276 

75756 

66588 

74606 

67880 

73432 

69151 

72236 

70401 

71019 

15 

5 

17 

46 

65298 

75738 

66610 

74586 

67901 

73413 

69172 

72216 

70422 

70998 

14 

4 

17 

47 

65320 

75719 

66632 

74567 

67923 

73393 

69193 

72196 

70443 

70978 

13 

4 

18 
18 

48 
49 

65342 
65364 

75700 

66653 

74548 

67944 

73373 

69214 
69235 

72176 
72156 

70463 
70484 

70957 

12 

4 

75680 

66675 

74528 

67965 

73353 

70937 

11 

3 

18 

50 

65386 

75661 

66697 

74509 

67987 

73333 

69256 

72136 

70505 

70916 

10 

3 

19 

51 

65408 

75642 

66718 

74489 

68008 

73314 

69277 

72116 

70525 

70896 

9 

3 

19 

52 

65430 

75623 

66740 

74470 

68029 

73294 

69298 

72095 

70546 

70875 

8 

3 

19 

53 

65452 

75604 

66762 

74451 

68051 

73274 

69319 

72075 

70567 

70855 

/ 

2 

20 
20 

54 
55 

65474 

75585 

66783 
66805 

74431 

68072 

73254 
73234 

69340 

72055 
72035 

70587 
70608 

70834 
70813" 

6 
5 

2 
2 

65496 

75566 

74412 

68093 

69361 

21 

56 

65518 

75547 

66827 

74392 

68115 

73215 

69382 

72015 

70628 

70793 

4 

I 

21 

57 

65540 

75528 

66848 

74373 

68136 

73195 

69403 

71995 

70649 

70772 

3 

1 

21 

58 

65562 

75509 

66870 

74353 

68157 

73175 

69424 

71974 

70670 

70752 

2 

1 

22 

59 

65584 

75490 

66891 

74334 

68179 

73155 

69445 

71954 

70690 

70731 

1 

0 

22 

60 

65606 

75471 

66913 

74314 

68200 

73135 

69466 

71934 

70711 

70711 

0 

0 

— 

N.cos. 

i  N.slne. 

N.  COS. 

N.sine. 

N.  COS. 

N.  sine. 

N.  COS. 

N.  sine. 

N.COS. 

N.  sine. 

M. 

49° 

48° 

47° 

46° 

46° 

TABLE  42. 

Page  591 

Logarithms  of  Numbers. 

No. 

1 100. 

Log.  0.00000 ^2.00000.   1 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1 

0.00000 

21 

1. 32222 

41 

1.61278 

61 

1. 78533 

81 

1. 90849 

2 

0. 30103 

22 

1. 34242 

42 

1. 62325 

62 

1.  79239 

82 

1.91381 

3 

0.47712 

23 

1.36173 

43 

1. 63347 

63 

1.  79934 

83 

1. 91908 

4 

0.  60206 

24 

1. 38021 

44 

1. 64345 

64 

1.80618 

84 

1. 92428 

5 
6 

0.  69897 

25 
"26 

1.39794 

45 
46 

1. 65321 

65 

1.  81291 

85 

1. 92942 

0.  77815 

1. 41497 

1. 66276 

66 

1.  81954 

86 

1. 93450 

7 

0.  84510 

27 

1.43136 

47 

1. 67210 

67 

1. 82607 

87 

1. 93952 

8 

0. 90309 

28 

1.44716 

48 

1. 68124 

68 

1. 83251 

88 

1.94448 

9 

0.  95424 

29 

1. 46240 

49 

1. 69020 

69 

1. 83885 

89 

1.94939 

10 

1.  00000 

30 

1.47712 

50 

1. 69897 

70 

1. 84510 

90 

1. 95424 

11 

1.  04139 

31 

1.  49136 

51 

1.  70757 

71 

1. 85126 

91 

1. 95904 

12 

1.07918 

32 

1.50515 

52- 

1.  71600 

72 

1. 85733 

92 

1. 96379 

13 

1.11394 

33 

1. 51851 

53 

1. 72428 

73 

1. 86332 

93 

1. 96848 

14 

1. 14613 

34 

1. 53148 

54 

1.  73239 

74 

1. 86923 

94 

1. 97313 

15 

1. 17609 

35 

1.  54407 

55 

1. 74036 

75 

1. 87506 

95 

1.97772 

16 

1. 20412 

36 

1. 55630 

56 

1. 74819 

76 

1. 88081 

96 

1. 98227 

17 

1. 23045 

37 

1.56820 

57 

1. 75587 

77 

1. 88649 

97 

1. 98677 

18 

1.  25527 

38 

1.57978 

58 

1. 76343 

78 

1. 89209 

98 

1. 99123 

19 

1. 27875 

39 

1.59106 

59 

1. 77085 

79 

1. 89763 

99 

1. 99564 

20 

1.  30103 

40 

1. 60206 

60 

1. 77815 

80 

1. 90309 

100 

2. 00000 

Page  592] 

TABLE  42. 

Logarithms  of  Numbers. 

No. 

100 1600 

Log.  00000- 

—20412. 

No. 

0 

1 

'■    i 

8 

00130 
00561 
00988 
01410 
01828 
02243 
02653 
03060 
03463 
03862 
04258 
04650 
05038 
05423 
05805 

4 

5      0 

7 

8 

9 

100 
101 
102 
103 
104 
105 
106 
107 
108 
109 

OOOOO 
00432 
008t)0 
01284 
01703 

00043 

00475 

00903 

0132^ 

01745 

02160 

02572 

02979 

03383 

03782 

04179 

04571 

04961 

05346 

05729 

00087 
00518 
00945 
01368 
01787 
02202 
02612 
03019 
03423 
03822 
04218 
04610 
04999 
05385 
05767 

00173 
00604 
01030 
01452 
01870 
02284 
02694 
03100 
03503 
03902 
04297 
04689 
05077 
05461 
05843 

00217  '   00260 
00647   00689 

00303 
00732 
01157 
01578 
01995 
02407 
02816 
03222 
03623 
04021 
04415 
04805 
05192 
05576 
05956 
06333 
06707 
07078 
07445 
07809 

00346 
00775 
01199 
01620 
02036 
02449 
02857 
03262 
03663 
04060 

00389 

00817 

01242 

01662  , 

02078 

02490 

02898  1 

03302 

03703 

04100 

4S  !  42 

01072 
01494 
01912 
02325 
02735 
03141 
03543 
03941 

01115 
01536 
01953 

1 

2 
3 
4 

5 
6 

7 
8 
9 

4 

9 

13 

17 
22 
26 
30 
34 
39 

4 
8 

13 
17 
21 
25 
29 
34 
38 

02119 
02531 
02938 
03:342 
03743 

02366 
02776 
03181 
03583 
03981 

110 
111 
112 
113 
114 
115 
116 
117 
118 
119 

04139 
04532 
04922 
05308 
05690 
06070 
06446 
06819 
07188 
07555 

04336 
04727 
05115 
05500 
05881 
06258 
06633 
07004 
07372 
07737 
08099 
08458 
08814 
09167 
09517 
09864 
10209 
10551 
10890 
11227 
11561 
11893 
12222 
12548 
12872 

04376 

04766 

05154 

05538 

05918 

06296' 

06670 

07041 

07408 

07773 

08135 

08493 

08849 

09202 

09552 

04454 
04844 
05231 
05614 
05994 

04493 
04883 
05269 
05652 
06032 

T 
2 
3 

4 
5 

6 

7 
8 
9 

41 

4 

8 
12 
16 
21- 
25 
29 
33 
37 

40 

4 

8 
12 
16  • 
20 
24 
28 
32 
36 

06108 
06483 
06856 
07225 
07591 
07954 
08314 
08672 
09026 
09377 

06145 
06521 
06893 
07262 
07628 

06183 
06558 
06930 
07298 
07664 
08027 
08386 
08743 
09096 
09447 

06221 
06595 
06967 
07335 
07700 
08063 
08422 
08778 
09132 
09482 

06371 
06744 
07115 
07482 
07846 

06408 
06781 
07151 
07518 
07882 

120 
121 
122 
123 
124 
125 
126 
127 
128 
129 

07918 
08279 
08636 
08991 
09342 
09691 
10037 
10380 
10721 
11059 
11394 
11727 
12057 
12385 
12710 
13033 
13354 
13672 
13988 
14301 

07990 
08350 
08707 
09061 
09412 

08171 
08529 
08884 
09237 
09587 

08207 
08565 
08920 
09272 
09621 

08243 
08600 
08955 
09307 
09656 
10003 
10346 
10687 
11025 
11361 

2 
3 
4 
5 
6 
7 
8 
9 

89 

4 
8 
12 
16 
20 
23 
27 
31 
35 

88 

4 
8 
11 
15 
19 
23 
27 
30 
34 

09726 
10072 
10415 
10755 
11093 
11428 
11760 
12090 
12418 
12743 

09760 
10106 
10449 
10789 
11126 

09795 
10140 
10483 
10823 
11160 

09830 
10175 
10517 
10857 
11193 

09899 
10243 
10585 
10924 
11261 

09934 
10278 
10619 
10958 
11294 

09968 

10312- 

10653 

10992 

11327 

11661 

11992 

12320 

12646 

12969 

130 
131 
132 
133 
134 
135 
136 
137 
138 
139 

11461 
11793 
12123 
12450 
12775 

11494 
11826 
12156 
12483 
12808 

11528 
11860 
12189 
12516 
12840 
13162 
13481 
13799 
14114 
14426 
14737 
15045 
15351 
15655 
15957 

11594 
11926 
12254 
12581 
12905 

11628 
11959 
12287 
12613 
12937 

11694 
12024 
12352 
12678 
13001 

87 

36 

1 
2 
3 

4 
5 
6 
7 
8 
9 

4 

7 

11 
15 
19 
22 
26 
30 
33 

4 

7 

11 
14 
18 
22 
25 
29 
32 

13066 
13386 
13704 
14019 
14333 

13098 
13418 
13735 
14051 
14364 

13130 
13450 
13767 
14082 
14395 

13194 
13513 
13830 
14145 
14457 
14768 
15076 
15381 
15685 
15987 

13226 
13545 
13862 
14176 
14489 

13258 
13577 
13893 
14208 
14520 

13290 
13609 
13925 
14239 
14551 

13322 
13640 
13956 
14270 
14582 
14891 
15198 
15503 
15806 
16107 
16406 
16702 
16997 
17289 
17580 
17869 
18156 
18441 
18724 
19005 

140 
141 
142 
143 
144 
145 
146 
147 
148 
149 
150 
151 
152 
153 
154 
155 
156 
157 
158 
159 

14613 
14922 
15229 
15534 
15836 
16137 
16435 
16732 
17026 
17319 

14644 
14953 
15259 
15564 
15866 

14675 
14983 
15290 
15594 
15897 

14706 
15014 
15320 
15625 
15927 
16227 
16524 
16820 
17114 
17406 

14799 
15106 
15412 
15715 
16017 

14829 
15137 
15442 
15746 
16047 
16346 
16643 
16938 
17231 
17522 
17811 
18099 
18384 
18667 
18949 
19229 
19507 
19783 
20058 
20330 

14860 
15168 
15473 
15776 
16077 
16376 
16673 
16967 
17260 
17551 

1~ 
2 
3 
4 
5 
6 
7 
8 
9 

85 

"4" 
7 
11 
14 
18 
21 
25 
28 
32 

84 

3 
7 
10 
14 
17 
20 
24 
27 
31 

16167 
16465 
16761 
17056 
17348 
17638 
17926 
18213 
18498 
18780 

16197 
16495 
16791 
17085 
17377 

16256 
16554 
16850 
17143 
17435 

16286 
16584 
16879 
17173 
17464 
17754 
18041 
18327 
18611 
18893 
19173 
19451 
19728 
20003 
20276 

16316 
16613 
16909 
17202 
17493 

17609 
17898 
18184 
18469 

18752 

17667 
17955 
18241 
18526 
18808 

17696 
17984 
18270 
18554 
18837 

17725 
18013 
18298 
18583 
18865 

17782 

18070 

18355 

18639 

18921 

19201' 

19479 

19756 

20030 

20303. 

17840 
18127 
18412 
18696 
18977 

2 
3 
4 

5 
'6 

7 
8 

88 

32 

3 
7 
10 
13 
17 
20 
23 
26 
30 

3 
6 
10 
13 
16 
19 
22 
26 
29 

19033 
19312 
19590 
19866 
20140 

19061 
19340 
19618 
19893 
20167 

19089 
19368 
19645 
19921 
20194 

19117 
19396 
19673 
19948 
20222 

19145 
19424 
19700 
19976 
20249 

19257 
19535 
19811 
20085 
20358 

8 

19285 
19562 
19838 
20112. 
20385 

No. 

0 

1 

2 

s 

4 

5   1   6 

7 

0 

^ 

TABLE  4:2. 
Logarithms  of  Nximbers. 

[Page  593 

N( 

-2200 

Log.  20412 

-34242.     1 

No. 

0 

1 

2 

8 

4 

5 

6 

7 

« 

9 

160 
161 
162 
163 
164 
165 
166 
167 
168 
169 

20412 
20683 
20952 
21219 
21484 

20439 
20710 
20978 
21245 
21511 

20466 
20737 
21005 
21272 
21537 

20493 
20763 
21032 
21299 
21564 
21827 
22089 
22350 
22608 
22866 

20520 
20790 
21059 
21325 
21590 
21854 
22115 
22376 
22634 
22891 

20548 
20817 
21085 
21352 
21617 
21880 
22141 
22401 
22660 
22917 
23172 
23426 
23679 
23930 
24180 

20575 
20844 
21112 
21378 
21643 
21906 
22167 
22427 
22686 
22943 
23198 
23452 
23704 
23955 
24204 
24452 
24699 
24944 
25188 
25431 
25672 
25912 
26150 
26387 
26623 
26858 
27091 
27323 
27554 
27784 
28012 
28240 
28466 
28691 
28914 
29137 
29358 
29579 
29798 
30016 
30233 
30449 
30664 
30878 
31091 
31302 
31513 
31723 
31931 
32139 

20602 
20871 
21139 
^405 
21669 
21932 
22194 
22453 
22712 
22968 
23223 
23477 
23729 
23980 
24229 

20629 
20898 
21165 
21431 
21696 
21958 
22220 
22479 
22737 
22994 
23249 
23502 
23754 
24005 
24254 

20656 
20925 
21192 
21458 
21722 

1 

2 
3 
4 
5 

6 

7 
8 
9 

31 

3 
6 
9 
12 
16 
19 
22 
25 
28 

30 

3 
6 
9 
12 
15 
18 
21 
24 
27 

21748 
22011 
22272 
22531 
22789 

21775 
22037 
22298 
22557 
22814 

21801 
22063 
22324 
22583 
22840 

21985 
22246 
22505 
22763 
23019 
23274 
23528 
23779 
24030 
24279 

170 
171 
172 
173 
174 
175 
176 
177 
178 
179 

23045 
23300 
23553 
23805 
24055 
24304 
24551 
24797 
25042 
25285 

23070 
23325 
23578 
23830 
24080 
24329 
24576 
24822 
25066 
25310 

23096 
23350 
23603 
23855 
24105 
24353 
24601 
24846 
25091 
25334 

23121  23147 
23376  23401 

29 

28 

23629 
23880 
24130 
24378 
24625 
24871 
25115 
25358 

23654 
23905 
24155 

1 
2 
3 
4 
5 
6 
7 
8 
9 

3 
6 
9 
12 
15 
17 
20 
23 
26 

3 

6 
8 
11 
14 
17 
20 
22 
25 

24403 
24650 
24895 
25139 
25382 

24428 
24674 
24920 
25164 
25406 
25648 
25888 

24477 
24724 
24969 
25212 
25455 
25696 
25935 
26174 
26411 
26647 
26881 
27114 
27346 
27577 
27807 
28035 
28262 
28488 
28713 
28937 
29159 
29380 
29601 
29820 
30038 
30255 
30471 
30685 
30899 
31112 
31323 
31534 
31744 
31952 
32160 
32366 
32572 
32777 
32980 
33183 
33385 
33586 
33786 
33985 
34183 

24502 
24748 
24993 
25237 
25479 
25720 
25959 
26198 
2frl35 
26670 
26905 
27138 
27370 
27600 
27830 
28058 
28285 
28511 
28735 
28959 
29181 
29403 
29623 
29842 
30060 
30276 
30492 
30707 
30920 
31133 
31345 
31555 
31765 
31973 
32181 
32387 
32593 
32797 
33001 
33203 
33405 
33606 
33806 
34005 
34203 

24527 
24773 
25018 
25261 
25503 

180 
181 
182 
183 
184 

25527 
25768 
26007 
26245 
26482 

25551 
25792 
26031 
26269 
26505 

25575 
25816 
26055 
26293 
26529 

25600  25624 
25840  25864 

25744 
25983 
26221 
26458 
26694 

1 
2 
3 
4 
5 
6 
7 
8 
9 

27 

3 
5 
8 
11 
14 
16 
19 
22 
24 

26 

26316  26M0     26364 
26553  26576  |  26600 
26788  26811  26834 
27021  27045  1  27068 
27254  27277  27300 
27485  27508  ;  27531 
27715  27738  27761 

3 
5 
8 
10 
13 
16 
18 
21 
23 

185 
186 
187 
188 
189 

26717 
26951 
27184 
27416 
27646 

26741 
26975 
27207 
27439 
27669 
27898 
28126 
28353 
28578 
28803 
29026 
29248 
29469 
29688 
29907 
30125 
30341 
30557 
30771 
30984 

26764 
26998 
27231 
27462 
27692 
27921 
28149 
28375 
28601 
28825 
29048 
29270 
29491 
29710 
29929 
30146 
30363 
30578 
30792 
31006 

26928 
27161 
27393 
27623 
27852 
28081 
28307 
28533 
28758 
28981 
29203 
29425 
29645 
29863 
30081 

190 
191 
192 
193 
194 

27»75 
28103 
28330 
28556 

28780 

27944  27967 
28171   28194 
28398  1  28421 
28623  28646 
28847  '  28870 
29070  29092 
29292  29314 
29513  29535 
29732  29754 
29951  29973 
30168  30190 
30384  30406 
30600  30621 
30814  30835 
31027  31048 
31239  31260 
31450  '   31471 
31660  31681 
31869  31890 
32077  i  32098 

27989 
28217 
28443 
28668 
28892 
29115 
29336 
29557 
29776 
29994 
30211 
30428 
30&43 
30856 
31069 
31281 
31492 
31702 
31911 
32118 

25 

24 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 

4 
5 
6 
7 
8 
9 

3 
5 
8 
10 
13 
15 
18 
20 
23 

2 

5 
7 
10 
12 
14 
17 
19 
22 

195 
196 
197 
198 
199 

29003 
29226 
29447 
29667 
29885 

200 
201 
202 
203 
204 

30103 
30320 
30535 
30750 
30963 

30298 
30514 
30728 
30942 
31154 

23 

~2" 
5 

7 
9 

12 

14 

16 

18 

21 

22 

2 

4 

7 

9 

11 

13 

15 

18 

20 

205 
206 
207 
208 
209 
210 
211 
212 
213 
214 

31175 
31387 
31597 
31806 
32015 

31197 
31408 
31618 
31827 
32035 

31218 
31429 
31639 
31848 
32056 

31366 
31576 
31785 
31994 
32201 
32408 
32613 
32818 
33021 
33224 
33425 
33626 
33826 
34025 
34223 

32222 
32428 
32634 

32838 
33041 

32243 
32449 
32654 
32858 
33062 
33264 
33465 
33666 
33866 
34064 

32263 
32469 
32675 
32879 
33082 
33284 
33486 
33686 
33885 
34084 

32284  '   32305  \   32325 
32490  1  32510  32531 

32346 
32552 
32756 
32960 
33163 

32695  32715 
32899  32919 
33102  33122 

32736 
32940 
33143 

1 
2 
3 
4 

5 
6 

7 
8 
9 

21 

"2~ 
4 

20 

2 

4 

215 
216 
217 
218 
219 

33244 
33445 
33646 
33846 
34044 

33304 
33506 
33706 
33905 
34104 

33325 
33526 
33726 
33925 
34124 

33345 
33546 
33746 
33945 
34143 

33365 
33566 
33766 
33965 
34163 

6   6 
8  !  8 
11  !  10 
13  12 
15  14 
17  16 

No. 

0 

1 

2 

3    '        4 

5 

6 

7 

« 

9 

19 

18 

22489—03- 


-38 


Page  594] 

TABLE  42. 

Logarithms  ( 

3f  Numbers. 

Xo.  2200 280C 

. 

Log.  34242- 

— M716. 

Ko. 

«    1 

1    i 

2 

3 

4 

5    1 
34341 

0   1 

7 

8 

9 

220 

34242 

34262 

34282 

34301 

34321 

34361 

34380 

34400 

34420 

221 

34439 

34459 

34479 

34498 

34518 

34537 

34557 

34577 

34596 

34616 

20 

222 

34635 

34655 

34674 

34694 

34713 

34733 

34753 

34772 

34792 

34811 

1 

2 

223 

34830 

348o0 

;34869 

34889 

34908 

34928 

34947 

34967 

34986 

35005 

2 

4 

224 

35025 

35044  1 

35064 

35083 

35102 
35295 

35122 
35315 

35141 
35334 

35160 
35353 

35180 

35199 
35392 

3 
4 

6 

8 

225 

35218 

35238 

35257 

35276 

35372 

226 

35411 

35430 

35449 

35468 

35488 

35507 

35526 

35545 

35564 

35583 

5 

10 

227 

35603 

35622 

35641 

35660 

35679 

35698 

35717 

35736 

35755 

35774 

6 

12 

228 

35793 

35813 

35832 

35851 

35870 

35889 

35908 

35927 

35946 

35965 

V 

14 

229 

35984 

36003 
36192 

36021 

36040 

36059 

36078 

36097 

36116 

36135 

36154 

8 
9 

16 

18 

230 

36173 

36211 

36229 

36248 

36267 

36286 

36305 

36324 

Sfi.^l9 

231 

36361 

36380 

36399 

36418 

36436 

36455 

36474 

36493 

36511  !  36530 

19 

232 

36549 

36568 

36586 

36605 

36624 

36642 

36661 

36680 

36698  36717 

1 

2 

233 

36736 

36754 

36773 

36791 

36810 

36829 

36847 

36866 

36884  36903 

9 

4 

234 

36922 

36940 

36959 

36977 

36996 

37014 

37033 

37051 

37070  37088 

3 
4 

6 

8 

235 

37107 

37125 

37144 

37162 

37181 

37199 

37218 

37236 

37254 

37273 

236 

37291 

37310 

37328 

37346 

37365 

37383 

37401 

37420 

37438 

37457 

5 

10 

237 

37475 

37493 

37511 

37530 

37548 

37566 

37585 

37603 

37621 

37639 

6 

11 

238 

37658 

37676 

37694 

37712 

37731 

37749 

37767 

37785 

37803 

37822 

7 

13 

239 

37840 

37858 

37876 

37894 

37912 

37931 

37949 

37967 

37985  38003 

8 
9 

15 
17 

240 
241 

38021 
38202 

38039 
38220 

38057 
38238 

38075 
38256 

38093 
38274 

38112 
38292 

38130 
38310 

38148 
38328 

38166  ;  38184 
38346  1  38364 

18 

242 

38382 

38399 

38417 

38435 

38453 

38471 

38489 

38507 

38525 

38543 

1 
2 
3 
4 

2 
4 
5 

7 

243 

38561 

38578 

38596 

38614 

38632 

38650. 

38668 

38686 

38703 

38721 

244 

38739 

38757 

38775 

38792 

38810 

38828 

38846  , 

38863 

38881 

38899 

245 

38917 

38934 

38952 

38970 

38987 

39005 

39023 

39041 

39058 

39076 

246 

39094 

39111 

39129 

39146 

39164 

39182 

39199 

39217 

39235  39252 

5 

Q 

247 

39270 

39287 

39305 

39322 

39340 

39358 

39375 

39393 

39410 

39428 

6 

11 

248 

39445 

39463 

39480 

39498 

39515 

39533 

39550 

39568 

39585 

39602 

7 

13 

249 

39620 

39637 

39655 

39672 

39690 

39707 . 

39724 

39742 

39759 
39933 

39777 

8 
9 

It 

250 

39794 

39811 

39829 

39846 

39863 

39881 

39898 

39915 

39950 

251 

39967 

39985 

40002 

40019 

40037 

40054 

40071 

40088 

40106 

40123 

252 

40140 

40157 

40175 

40192 

40209 

40226 

40243 

40261 

40278 

40295 

253 

40312 

40329 

40346 

40364 

40381 

40398 

40415 

40432 

40449 

40466 

1 

2 

254 

40483 

40500 

40518 
40688 

40535 
40705 

40552 
40722 

40569 

40586 

40603 
40773 

40620 

40637 

2 
3 

3 
5 

255 

40654 

40671 

40739 

40756 

40790 

40807 

256 

,  40824 

40841 

40858 

40875 

40892 

40909 

40926 

40943 

40960 

40976 

4 

7 

257 

40993 

41010 

41027 

41044 

41061 

41078 

41095 

41111 

41128 

41145 

5 

9 

258 

41162 

41179 

41196 

41212 

41229 

41246 

41263 

41280 

41296 

41313 

6 

10 

259 

41330 

41347 

41363 

41380 

41397 

41414 

41430 

41447 

41464 

41481 

7 
8 
9 

12 
14 
15 

260 

41497 

41514 

41531 

41547 

41564 

41581 

41597 

41614 

41631 

41647 

261 
262 

41664 
41830 

41681 
41847 

41697 
41863 

41714 
41880 

41731 
41896 

41747 
41913 

41764 

41780 

41 797 

41814 

41929 

41946 

41963 

41979 

16 

263 

41996 

42012 

42029 

42045 

42062 

42078 

42095 

42111 

42127 

42144 

1 

2 

264 

42160 

42177 

42193 

42210 

42226 

42243 

42259 
42423 

42275 

42292 

42308 

2 
3 

3 
5 

265 

42325 

42341 

42357 

42374 

42390 

42406 

42439 

42455 

42472 

266 

42488 

42504 

42521 

42537 

42553 

42570 

42586 

42602 

42619 

42635 

4 

6 

267 

42651 

42667 

42684 

42700 

42716 

42732 

42749 

42765 

42781 

42797 

5 

8 

268 

42813 

42830 

42846 

42862 

42878 

42894 

42911 

42927 

42943 

42959 

6 

10 

269 

42975 

42991 

43008 

43024 

43040 

43056 
43217 

43072 
43233 

43088 
43249 

43104 

43120 

7 
8 

11 
13 

270 

43136 

43152 

43169 

43185 

43201 

43265 

43281 

271 
272 

43297 
43457 

43313 
43473 

43329 
43489 

43345 
43505 

43361 
43521 

43377 
43537 

43393 
43553 

43409 
43569 

43425 
43584 

43441 
43600 

9 

14 

15 

273 

43616 

43632 

43648 

43664 

43680 

43696 

43712 

43727 

43743 

43759 

1 

2 

274 

43775 

43791 

43807 

43823 

43838 

43854 
44012 

43870 
44028 

43886 
44044 

43902 

43917 

2 
3 

3 
5 

275 

43933 

43949 

i  43965 

43981 

i  43996 

44059 

i  44075 

276 

44091 

44107 

44122 

44138 

!  44154 

44170 

44185 

44201 , 

44217 

44^32 

4 

6 

277 

44248 

44264 

44279 

i  44295 

44311 

44326 

44342 

44358 

44373 

44389 

5 

8 

278 

44404 

44420 

44436 

44451 

44467 

44483 

44498 

44514 

44529 

44545 

6 

9 

279 

44560 

44576 

44592 

44607 

44623 

i 

,  44638 

44654 

44669 

44685 

44700 

8 
9 

11 
12 

,14 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

TABLE  42. 

Logarithms  of  Numbers. 

[Page  595 

No.  2800 3400. 

Log.  44716 53148. 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

» 

1 

280 

281 
282 
283 
284 
285 
286 
287 
288 
289 

44716 
44871 
45025 
45179 
45332 

44731 
44886 
45040 
45194 
45347 

44747 
44902 
45056 
45209 
45362 
45515 
45667 
45818 
45969 
46120 

44762 
44917 
45071 
45225 
45378 

44778 

44932 

45086  1 

45240  ! 

45393  1 

45545 

45697 

45849 

46000 

46150 

44793 
44948 
45102 
45255 
45408 
45561 
45712 
45864 
46015 
46165 

44809 
44963 
45117 
45271 
45423 

44824 
44979 
45133 
45286 
45439 
45591 
45743 
45894 
46045 
46195 

44840  44855 
44994  45010 
45148  45163 
45301  45317 
45454  1  45469 

16 

1 
2 
3 
4 
5 
6 
7 
8 
9 

2 

3 

5 

6 

8 

10 

11 

13 

14 

45484 
45637 
45788 
45939 
46090 

45500 
45a52 
45803 
45954 
46105 

45530 
45682 
45834 
45984 
46135 

45576 
45728 
45879 
46030 
46180 

45606 

45758  1 

45909 

46060 

46210 

46359" 

46509 

46657 

46805 

46953 

45621 
45773 
45924 
46075 
46225 

290 
291 
292 
293 
294 
295 
296 
297 
298 
299 

46240 
46389 
46538 
46687 
46835 

46255 
46404 
46553 
46702 
46850 

46270 
46419 
46568 
46716 
46864 
47012 
47159 
47305 
47451 
47596 

46285 
46434 
46583 
46731 
46879 
47026 
47173 
47319 
47465 
47611 

46300 
46449 
46598 
46746 
.  46894 
47041 
47188 
47334 
47480 
47625 

46315 
46464 
46613 
46761 
46909 
47056 
47202 
47349 
47494 
47640 

46330 
46479 
46627 
46776 
46923 

56345 
46494 
46642 
46790 
46938 

46374 
46523 
46672 
46820 
46967 
47114 
47261 
47407 
47553 
47698 

1 

15 

1 
2 
3 
4 
5 
6 
7 
8 
9 

2 

3 

5 

6 

8 

9 

11 

12 

14 

46982 
47129 
47276 
47422 
47567 

46997 
47144 
47290 
47436 

47582 

47070 
47217 
47363 
47509 
47654 

47085 
47232 
47378 
47524 
47669 

47100 
47246 
47392 
47538 
47683 

300 
301 
302 
303 
304 

47712 
47857 
48001 
48144 
48287 

47727 
47871 
48015 
48159 
48302 

47741 
47885 
48029 
48173 
48316 

47756 
47900 
48044 
48187 
48330 

47770 
47914 
48058 
48202 
48344 

47784 
47929 
48073 
48216 
48359 

47799 
47943 
48087 
48230 
48373 

47813 
47958 
48101 
48244 
48387 

47828  47842 
47972  47986 
48116  48130 
48259  48273 
48401  i  48416 

1 

305 
306 
307 
308 
309 

48430 
48572 
48714 
48855 
48996 

48444 
48586 
48728 
48869 
49010 

48458 
48601 
48742 
48883 
49024 

48473 
48615 
48756 
48897 
49038 

48487 
48629 
48770 
48911 
49052 

48501 
48643 
48785 
48926 
49066 

48515 
48657 
48799 
48940 
49080 

48530 
48671 
48813 
48954 
49094 
49234 
49374 
49513 
49651 
49790 
49927 
50065 
50202 
50338 
50474 
50610 
50745 
50880 
51014 
51148 

48544  1  48558 

14 

48827 
48968 
49108 
49248 
49388 
49527 
49665 
49803 
49941 
50079 
50215 
50352 
50488 
50623 
50759 
50893 
51028 
51162 
51295 
51428 
51561 
51693 
51825 
51957 
52088 
52218 
52349 
52479 
52608 
52737 
52866 
52994 
53122 

48841 
48982 
49122 
492(32 
49402 
49541 
49679 
49817 
49955 
50092 
50229 
50365 
50501 
50637 
50772 
50907 
51041 
51175 
51308 
51441 
51574 
51706 
51838 
51970 
52101 
52231 
52362 
52492 
52621 
52750 
52879 
53007 
53135 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
3 
4 
6 
7 
8 

10 
11 
13 

310 
311 
312 
313 
314 

49136 
49276 
49415 
49554 
49693 

49150 
49290 
49429 
49568 
49707 

49164 
49304 
49443 
49582 
49721 
49859 
49996 
50133 
50270 
50406 

49178 
49318 
49457 
49596 
49734 
49872 
50010 
50147 
50284 
50420 

49192 
49332 
49471 
49610 
49748 

49206 
49346 
49485 
49624 
49762 

49220 
49360 
49499 
49638 
49776 

315 
316 
317 
318 
319 

49831 
49969 
50106 
50243 
50379 

49845 
49982 
50120 
50256 
50393 
50529 
50664 
50799 
50934 
51068 

49886 
50024 
50161 
50297 
50433 
50569 
50705 
50840 
50974 
51108 

49900 
50037 
50174 
50311 
50447 

49914 
50051 
50188 
50325 
50461 

1 

18 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
3 
4 
5 
7 
8 
9 
10 
12 

320 
321 
322 
323 
324 

50515 
50651 
50786 
50920 
51055 

50542 
50678 
50813 
50947 
51081 

50556 
50691 
50826 
50961 
51095 

50583 
50718 
50853 
50987 
51121 

50596 

50732 

50866 

51001 

51135 

51268' 

51402 

51534 

51667 

51799 

325 
326 
327 
328 
329 

51188 
51322 
51455 
51587 
51720 

51202 
51335 
51468 
51601 
51733 

51215 
51348 
51481 
51614 
51746 

51228 
51362 
51495 
51627 
51759 
51891 
52022 
52153 
52284 
52414 

51242 
51375 
51508 
51640 
51772 

51255 

51388 
51521 
51654 
51786 

51282 
51415 
51548 
51680 
51812 
51943 
52075 
52205 
52336 
52466 

1 

330 
331 
332 
333 
334 

51851 
51983 
52114 
52244 
52375 

51865 
51996 
52127 
52257 

52388 

51878 
52009 
52140 
52270 
52401 

51904 
52035 
52166 
52297 
52427 

51917 
52048 
52179 
52310 
52440 

51930 
52061 
52192 
52323 
52453 

1 
2 

3 
4 
5 

6 
7 
8 
9 

12 

1 
2 
4 
5 
6 
7 
8 
10 
11 

335 
336 
337 
338 
339 

52504 
52634 
52763 
52892 
53020 

52517 
52647 
52776 
52905 
53033 

52530 
52660 
52789 
52917 
53046 

52543 
52673 

52802 
52930 
53058 

52556 
52686 
52815 
52943 
53071 

52569 
52699 
52827 
52956 
53084 

52582 
52711 
52840 
52969 
53097 

52595 
52724 
52853 
52982 
53110 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Page  596] 

TABLE  42. 

Logarithms  of  Numbers. 

No. 

S400 lOOC 

. 

Log.  53148 60206.   1 

No. 

0 

1 

2 

3 

4 

5 

G 

7 

8 

9 

1 

340 

:^i 

342 
343 
344 
345 
346 
347 
348 
349 
350 
351 
352 
353 
354 

53148 
53275  1 
53403 
53529 
53^56 
53782  1 
53908  ' 
54033  ! 
54158  ' 
54283 
.  54407 
54531 
54654 
54777 
54900 

53161 
53288 
53415 
535* 
53668 
53794 
53920 
54045 
54170 
54295 
54419 
54543 
54667 
54790 
54913 

53173 

53301 

53428 

53555 

53681 

53807" 

53933 

54058 

54183 

54307 

54432 

54555 

54679 

54802 

54925 

53186 

53314 

53441 

53567 

53694  ' 

53820  1 

53945  : 

54070 

54195 

54320 

53199 
53326 
53453 
53580 
53706 
5.3832 
53958 
54083 
54208 
54332 

53212 
53339 
5;i466 
53593 
53719 
53845 
5.3970 
54095 
54220 
54345 

53224 
53352 
53479 
5.3605 
53732 
53857 
53983 
54108 
54233 
.54357 

53237 
53364 
5,3491 
53618 
53744 
53870 
5,3995 
54120 
54245 
54370 
54494 
54617 
5-^741 
54864 
54986 
55108 
55230 
55352 
5,5473 
55594 

53250 
53377 
53504 
53631 
53757 
53882 
,54008 
,54133 
54258 
54382 
54506 
54630 
54753 
54876 
54998 
55121 
55242 
55364 
55485 
55606 

53263 
53390 
,5.3517 
53643 
53769 
53895 
54020 
,54145 
54270 
54394 
54518 
54642 
54765 
54888 
55011 

Vi 

1 

2 
3 
4 
5 

/ 
8 
9 

1 
3 
4 
5 
7 
8 
9 
10 
12 

54444 
54568 
54691 
54814 
54937  : 

54456 
54580 
54704 
54827 
54949 

54469 
54593 
54716 
548.39 
.54962. 
55084 
55206 
55328 
55449 
55570 

54481 
54605 
54728 
54851 
54974 
55096 
55218 
55;i40 
55461 
55582 

355 
356 
357 
358 
359 

55023 
,55145 
55267 
55388 
55509 

550;i5 
55157 
55279 
55400 
55522 

55047 
55169 
55291 
55413 
55534 

55060 
55182 
55303 
55425 
55546 

55072 
55194 
55315 
55437 
55558 

55133 
55255 
55376 
55497 
55618 
55739 
55859 
55979 
56098 
56217^ 

1 
2 
3 
4 
5 
6 
7 
8 
9 

12 

1 
2 
4 
5 
6 
7 
8 

10 
11 

360 
361 
362 
363 
364 

55630 
55751  1 
55871 
55991  ' 
56110  i 

55642 
55763 
55883 
56003 
56122 

55654 
55775 
55895 
56015 
56134 

55666 
55787 
55907  i 
56027 
56146 

55678 
55799 
55919 
56038 
56158 

55691 
55811 
55931 
56050 
56170 

55703 
55823 
55943 
56062 
56182 

55715 
55835 
55955 
56074 
56194 
56312 
5&431 
56549 
56667 
56785 

55727 

,55847 
55967 
56086 
56205 

365 
366 
367 
368 
369 

56229  , 
56348 
56467 
56585 
56703  ' 

56241 
56360 
56478 
56597 
56714 
56832 
56949 
57066 
57183 
57299 

56253 
56372 
56490 
56608 
56726 
56844 
56961 
57078 
57194 
57310 

56265 
56384 
56502 
56620 
56738 

56277 
56396 
56514 
56632 
56750 

56289 
56407 
56526 
56644 
56761 

56301 
56419 
56538 
56656 
56773 

56324 
56443 
56561 
56679 
56797 
56914 
57031 
57148 
57264 
57380 
57496 
57611 
57726 
57841 
57955 

56336 
56455 
56573 
56691 
56808 

370 
371 
372 
373 
374 

56820 
56937 
57054 
57171 

57287 

56855 
56972 
57089 
57206 
57322 

56867 
56984 
57101 
57217 
57334 

56879 
56996 
57113 
57229 
57345 

56891 
57008 
57124 
57241 
57357 

56902 
57019 
57136 
57252 
57368 

56926 
57043 
57159 
57276 
57392 
57507 
57623 
57738 
57852 
57967 

11 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
6 
7 
8 
9 
10 

375 
376 
377 
378 
379 

57403 
57519 
57634 
57749 
57864 

57415 
57530 
57646 
57761 

57875 

57426 
57542 
57657 

57772 
57887 

57438 
57553 
57669 

57784 
57898 

57449 
57565 
57680 
57795 
57910 

57461 
57576 
57692 
57807 
57921 

57473 
57588 
57703 
.57818 
579,33 

57484 
57600 
,57715 
57830 
57944 

380 
381 
382 
383 
384 

57978 
58092 
58206 
58320 
58433 

57990 
58104 
58218 
58331 
58444 

58001 
58115 
58229 
58343 
58456 

58013 
58127 
58240 
58354 
58467 

58024 
581.38 
58252 
58365 

58478 

58035 
58149 
58263 
58377 
58490 

58047 
58161 
58274 
58388 
58501 

58058 
58172 
58286 
58399 
.58512 

58070 
58184 
58297 
,58410 
58524 

58081 
58195 
58309 
58422 
58535 
5864? 
58760 
58872 
58984 
59095 

385 
386 
387 
388 
389 

58546 
58659 
58771 
58883 
58995 

58557 
58670 
58782 
58894 
59006 

58569 
58681 
58794 
58906 
59017 

58580 
58692 
58805 
58917 
59028 

58591 
58704 
58816 
58928 
59040 

58602 
58715 
58827 
58939 
59051 

58614 
58726 
58838 
58950 
59062 

58625 
58737 
58850 
58961 
59073 

58636 
58749 
58861 
58973 
59084 

10 

390 
391 
392 
393 
394 

59106 

59218 

59329 

59439 

59550 

59660" 

59770 

59879 

59988 

60097 

0 

59118 
59229 
59340 
59450 
59561 
59671 
59780 
59890 
59999 
60108 

1 

59129 
59240 
59351 
59461 
59572 
59682 
59791 
59901 
60010 
60119 

59140 

59251 

59362 

59472 

59583 

59693' 

59802 

59912 

60021 

60130 

59151 

59262 

59373 

59483 

59594 

59704' 

59813 

59923 

60032 

60141 

59162 
59273 
59384 
59494 
59605 
i  59715 
59824 
59934 
60043 
60152 

59173 
59284 
59.395 
.59506 
,59616 
"59726 
59835 
59945 
60054 
60163 

59184 
59295 
59406 
59517 
59627 
59737 
59846 
59956 
60065 
60173 

59195 
59306 
59417 
59528 
59638 

59207 
,59318 
59428 
59539 
59649 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 

5 
6 

7 
8 
9 

395 
396 
397 
398 
399 

59748 
59857 
59966 
60076 
60184 

59759 
59868 
59977 
60086 
60195 

No. 

2 

S 

4 

o 

G 

7 

8 

!  » 

1 

No. 

TABLE  42. 

Logarithms  of  Numbers. 

[Page  597 

4000 1600. 

Log.  60206 66276.   1 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

400 
401 
402 
403 
404 

60206 
60314 
60423 
60531 
60638 
60746 
60853 
60959 
61066 
61172 
6f278 
61384 
61490 
61595 
61700 

60217 
60325 
60433 
60541 
60649 
60756 
60863 
60970 
61077 
61183 

60228 
60336 
60444 
60552 
60660 

60239 
60347 
60455 
60563 
60670 

60249 
60358 
60466 
60574 
60681 

60260 
60369 
60477 
60584 
60692 

60271 
60379 
60487 
60595 
60703 

60282 
60390 
60498 
60606 
60713 

60293 
60401 
60509 
60617 
60724 

60304 
60412 
60520 
60627 
60735 
60842" 
60949 
61055 
61162 
61268 
61374 
61479 
61584 
61690 
61794 
61899 
62003 
62107 
62211 
62315 

11 

1 
2 

3 
4 
5 
6 

7 
8 
9 

1 
2 

3 
4 
6 

7 

8 

9 

10 

405 
406 
407 
408 
409 

60767 
60874 
60981 
61087 
61194 

60778 
60885 
60991 
61098 
61204 

60788 
60895 
61002 
61109 
61215 

60799 
60906 
61013 
61119 
61225 

60810 
60917 
61023 
61130 
61236 

60821 
60927 
61034 
61140 
61247 

60831 
60938 
61045 
61151 
61257 

410 
411 

412 
413 
414 

61289 
61395 
61500 
61606 
61711 

61300 
61405 
61511 
61616 
61721 

61310 
61416 
61521 
61627 
61731 

61321 
61426 
61532 
61637 
61742 

61331 
61437 
61542 
61648 
61752 

61342 
61448 
61553 
61658 
61763 
61868 
61972 
62076 
62180 
62284 
62387 
62490 
62593 
62696 
62798 

61352 
61458 
61563 
61669 
61773 
61878 
61982 
62086 
62190 
62294 
62397 
62500 
62603 
62706 
62808 
62910 
63012 
63114 
63215 
63317 

61363 
61469 
61574 
61679 
61784 
61888 
61993 
62097 
62201 
62304 
62408 
62511 
62613 
62716 
62818 
62921 
63022 
63124 
63225 
63327 
63428 
63528 
63629 
63729 
63829 
63929 
64028 
64128 
64227 
64326 

415 
416 
417 
418 
419 
420 
421 
422 
423 
424 

61805 
61909 
62014 
62118 
62221 
62325 
62428 
62531 
62634 
62737 

61815 
61920 
62024 
62128 
62232 
62335 
62439 
62542 
62644 
62747 

61826 
61930 
62034 
62138 
62242 
62346 
62449 
62552 
62655 
62757 
62859 
62961 
63063 
63165 
63266 
63367 
63468 
63568 
63669 
63769 

61836 
61941 
62045 
62149 
62252 
62356 
62459 
62562 
62665 
62767 
62870 
62972 
63073 
63175 
63276 

61847 
61951 
62055 
62159 
62263 
62366 
62469 
62572 
62675 
62778 
62880 
62982 
63083 
63185 
63286 

61857 
61962 
62066 
62170 
62273 
62377 
62480 
62583 
62685 
62788 

62418 
62521 
62624 
62726 
62829 

1 
2 

3 
4 
5 
6 
7 
8 
9 

10 

1 

2 
3 
4 
5 

6 

7 
8 
9 

425 
4^6 
427 
428 
429 
430 
431 
432 
433 
434 

62839 
62941 
63043 
63144 
63246 

62849 

62951 

63053 

63155 

63256 

63357' 

63458 

63558 

63659 

63759 

62890 
62992 
63094 
63195 
63296 

62900 
63002 
63104 
63205 
63306 

62931 
63033 
63134 
63236 
63337 
63438 
63538 
63639 
63739 
63839 

63347 
63448 
63548 
63649 
63749 

63377 
63478 
63579 
63679 
63779 

63387 
63488 
63589 
63689 
63789 

63397 
63498 
63599 
63699 
63799 
63899 
63998 
64098 
64197 
64296 

63407 
63508 
63609 
63709 
63809 
63909 
64008 
64108 
64207 
64306 

63417 
63518 
63619 
63719 
63819 
63919 
64018 
64118 
64217 
64316 

435 
436 
437 
438 
439 
440 
441 
442 
443 
444 
445 
446 
447 
448 
449 

63849 
63949 
64048 
64147 
64246 . 

63859 
63959 
64058 
64157 
64256 

63869 
63969 
64068 
64167 
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63879 
63979 
64078 
64177 
64276 

63889 
63988 
64088 
64187 
64286 

63939 
64038 
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64237 
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64345 
64444 
64542 
64640 
64738 

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64552 
64650 
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64365 
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64562 
64660 
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64375 
64473 
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64670 
64768 
64865 
64963 
65060 
&5157 
65254 

64385 
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64582 
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65021 

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65040 
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64856 
64953 
65050 
65147 
65244 

64885 
64982 
65079 
65176 
65273 

6t895 
64992 
65089 
65186 
65283 

6^904 
65002 
65099 
65196 
65292 

1 
2 

3 
4 
5 
6 

7 
8 
9 

9 

450 
451 
452 
453 
454 

65321 
65418 
65514 
65610 
65706 

65331 
65427 
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65619 
65715 

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65437 
65533 
65629 
65725 

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65543 
65639 
65734 

65360 
65456 
65552 
65648 
65744 

65369 
65466 
65562 
65658 
65753 

65379 
65475 
65571 
65667 
65763 

65389 
65485 
65581 
65677 

65772 

1 
2 
3 
4 
5 
5 
6 
7 
8 

455 
456 
457 
458 
459 

65801 
65896 
65992 
66087 
66181 

65811 
65906 
66001 
66096 
66191 

65820 
65916 
66011 
66106 
66200 

65830 
65925 
66020 
66115 
66210 

65839 
65935 
66030 
66124 
66219 

65849 
65944 
66039 
66134 
66229 

65858 
65954 
66049 
66143 
66238 

65868 
65963 
66058 
66153 
66247 

65877 
65973 
66068 
66162 
66257 

65887 
65982 
66077 
66172 
66266 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

Page  598] 

TABLE  42. 

Logarithms 

of  Numbers. 

No. 

4600 5200. 

« 

Log.  66276- 

^71600. 

No.  . 

0 

1 

2 

8 

4 

fi 

7 

8 

9 

460 
461 

66276 
66370 

66285 
66380 

6()295 
66389 

66304 
66398 

66314 
66408 

66323 
66417 

66332 
66427 

66342 
66436 

66351 
66445 

66361 
66455 

•10 

1 
1 
2 

462 

66464 

66474 

66483 

66492 

66502 

66511 

66521 

66530 

66539 

66549 

1 

463 

66558 

6659r 

66577 

66586 

66596 

66605 

66614 

66624 

66633 

66642 

2 

464 

66652 

66661 
66755^ 

66671 
66764 

66680 
66773" 

66689 
66783 

66699 
66792 

66708 
66801 

66717 

66727 
66820 

66736 
66829 

3 
4 

5 
6 

3 
4 
5 

465 

66745 

66811 

466 

66839 

66848 

66857 

66867 

66876 

66885 

66894 

66904 

(>6913 

66922 

467 

66932 

66941 

66950 

66960 

66969 

66978 

(56987 

66997 

67006 

67015 

1^ 

468 

67025 

67034 

67043 

67052 

67062 

67071 

67080 

67089 

67099 

67108 

8 
9 

1 

469 

67117 

67127 

67136 

67145 
67237 
67330 

67154 

67164 

67173 

67182 
67274 

67191 
67284 

67201 
67293 

8 
9 

470 

67210 

67219 

67228 

67247 
67339 

67256 

67265 

471 

67302 

6731 1 

67321 

67348 

67357 

67367 

67376 

67385 

472 

67394 

{)7403 

67413 

67422 

67431 

67440 

67449 

67459 

67468 

67477 

473 

67486 

67495 

67504 

67514 

67523 

67532 

67541 

67550 

67560 

67569 

474 
475 

67578 
67669^ 

67587 
67679 

67596 
67688 

67605 
67697 

67614 
67706 

67624 
67715 

67633 
67724' 

67642 
677^3 

67651 
67742 

67660 

67752 

476 

67761 

67770 

67779 

67788 

67797 

67806 

67815 

67825 

67834 

67843 

477 

67852 

67861 

67870 

67879 

67888 

67897 

67906 

67916 

67925 

67934 

478 

67943 

67952 

67961 

67970 

67979 

67988 

67997 

68006 

68015 

68024 

479 

68034 
68124 

68043 
68133 

68052 
68142 

68061 
68151 

68070 
68160 

68079 
68169" 

68088 
68178 

68097 
68187 

68106 
68196 

68115 
68205 

480 

481 

68215 

68224 

68233 

68242 

68251 

68260 

68269 

68278 

68287 

68296 

482 

68m5 

68314 

68323 

68332 

68341 

68350 

68:^59 

68368 

68377 

68386 

483 

484 
485 
486 

68395 
68485 
68574 
68664 

68404 
68494 

68583' 
68673 

68413 
68502 
68592 
68681 

68422 
68511 

68431 
68520 

68440 
68529 

68449 
68538 
68628 
68717 

68458 
68547 

68467 
68556 

68476 
68565 

9 

68601 
68690 

68610 
68699 

68619 

68708 

68637 
68726 

68646 
68735 

68655 
68744 

1 

1 

487 

68753 

68762 

68771 

68780 

68789 

68797 

68806 

68815 

68824 

68833 

9 

2 

488 

68842 

68851 

68860 

68869 

68878 

68886 

68895 

68904 

68913 

68922 

;] 

o 

489 
490 

68931 

68940 
69028 

68949 
69037 

68958 
69046 

68966 
69055 

68975 
69064 

68984 
69073 

68993 
69082 

69002 
69090 

69011 

4 
5 

4 

5 

69020 

69099 

491 

69108 

69117 

69126 

69135 

69144 

69152 

69161 

69170 

69179 

69188 

6 

5 

492 

69197 

69205 

69214 

69223 

69232 

69241 

69249 

69258 

69267 

69276 

7 

6 

493 

69285 

69294 

69302 

69311 

69320 

69329 

69338 

69346 

69355 

69364 

8 

7 

494 

69373 

69381 

69390 

69399 

69408 

69417 

69425 

69434 

69443 

69452 

9 

8 

495 
496 

69461 
69548 

69469 
69557 

69478 
69566 

69487 
69574 

69496 
69583 

69504 
69592 

69513 
69601 

69522 
69609 

69531 
69618 

69539 
69627 

497 

69636 

69644 

69653 

69662 

69671 

69679 

69688 

69697 

69705 

69714 

498 

69723 

69732 

69740 

69749 

69758 

69767 

69775 

69784 

69793 

69801 

499 

69810 
69897 

69819 

69827 

69836 

69845 

69854 
69940 

69862 
69949 

69871 
69958 

69880 
69966 

69888 
69975 

500 

69906 

69914 

69923 

69932 

501 

69984 

69992 

70001 

70010 

70018 

70027 

70036 

70044 

70053 

70062 

502 

70070 

70079 

70088 

70096 

70105 

70114 

70122 

70131 

70140 

70148 

503 

70157 

70165 

70174 

70183 

70191 

70200 

70209 

70217 

70226 

70234 

504 

70243 

70252 

70260 

70269 

70278 

70286 

70295 
70381' 

70303 
70389 

70312 

70398 

70321 

505 

70329 

70338 

70346 

70355 

70364 

70372 

70406 

506 

70415 

70424 

70432 

70441 

70449 

70458 

70467 

70475 

70484 

70492 

507 

70501 

70509 

70518 

70526 

70535 

70544 

70552 

70561 

70569 

70578 

508 
509 

70586 
70672 

70595 
70680 

70603 
70689 

70612 
70697 

70621 
70706 

70629 
70714 
70800 

70638 
70723 

70808 

70646 
70731 

70817 

70655 
70740 
70825 

70663 
70749 

„ 

8 

510 

70757 

70766 

70774 

70783 

70791 

70834 

511 

70842 

70851 

70859 

70868 

70876 

70885 

70893 

70902 

70910 

70919 

1 

1 

512 

70927 

70935 

70944 

70952 

70961 

70969 

70978 

70986 

70995 

71003 

?. 

2 

513 

71012 

71020 

71029 

71037 

71046 

71054 

71063 

71071 

71079 

71088 

3 

2 

514 

71096 

71105 

71113 

71122 

71130 

71139 

71147 

71155 
71240 

71164 
71248 

71172 
71257 

4 
5 

3 
4 

515 

71181 

71189 

71198 

71206 

71214 

71223 

71231 

516 

71265 

71273 

71282 

71290 

71299 

71307 

71315 

71.324 

71332 

71341 

6 

5 

517 

71349 

71357 

71366 

71374 

71383 

71391 

71399 

71408 

71416 

71425 

7 

6 

518 

71433 

71441 

71450 

71458 

71466 

71475 

71483 

71492 

71500 

71508 

8 

6 

519 

71517 

71525 

71533 

71542 

71550 

71559 

71567 

71575 

71584 

71592 

9 

7 

No. 

0 

1 

2 

« 

4 

5 

6 

7 

8 

9 

1 

TABLE  42. 

Logarithms  of  Numbers. 

[Page  699 

No 

5200 5800. 

Log.  71600 76343. 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

520 
521 
522 
523 
524 
525 
526 
527 
528 
529 
530 
531 
532 
533 
534 
535 
536 
537 
538 
539 
540 
541 
542 
543 
544 
545 
546 
547 
548 
549 
550 
551 
552 
553 
554 
555 
556 
557 
558 
559 
560 
561 
562 
563 
564 
565 
566 
567 
568 
569 

71600 
71684 
71767 
71850 
71933 

71609 
71692 
71775 
71858 
71941 

71617 
71700 
71784 
71867 
71950 

71625 
71709 
71792 
71875 
71958 

71634 
71717 
71800 
71883 
71966 

71642 
71725 
71809 
71892 
71975 

71650 
71734 
71817 
71900 
71983 

71659 
71742 
71825 
71908 
71991 

71667 
71750 
71834 
71917 
71999 
72082 
72165 
72247 
72329 
72411 
72493 
72575 
72656 
72738 
72819 
72900 
72981 
73062 
73143 
73223 

71675 
71759 
71842 
71925 
72008 
72090 
72173 
72255 
72337 
72419 

9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
5 
6 
7 
8 

72016 
72099 
72181 
72263 
72346 
72428 
72509 
72591 
72673 
72754 
~  72835 
72916 
72997 
73078 
73159 

72024 
72107 
72189 
72272 
72354 

72032 
72115 
72198 
72280 
72362 

72041 
72123 
72206 

72288 
72370 

72049 
72132 

72214 
72296 

72378 

72057 
72140 
72222 
72304 

72387 

72066 
72148 
72230 
72313 
72395 

72074 
72156 
72239 
72321 
72403 

72436 

72518 
72599 
72681 
72762 

72444 
72526 
72607 
72689 
72770 

72452 
72534 
72616 
72697 

72779 

72460 
72542 
72624 

72705 

72787 

72469 
72550 
72632 
72713 
72795 

72477 
72558 
72640 
72722 
72803 

72485 
72567 
72648 
72730 
72811 

72501 
72583 
72665 
72746 
72827 
72908 
72989 
73070 
73151 
73231 

72843 
72925 
73006 
73086 
73167 

72852 
72933 
73014 
73094 
73175 

7^860 
72941 
73022 
73102 
73183 

72868 
72949 
73030 
73111 
73191 
73272 
73352 
73432 
73512 
73592 

72876 
72957 
73038 
73119 
73199 
73280 
73360 
73440 
73520 
73600 
73679 
73759 
73838 
73918 
73997 

72884 
72965 
73046 
73127 
73207 
73288 
73368 
73448 
73528 
73608 

72892 
72973 
73054 
73135 
73215 
73296 
73376 
73456 
73536 
73616 

73239 
73320 
73400 
73480 
73560 

73247 
73328 
73408 

73488 
73568 

73255 
73336 
73416 
73496 
73576 

73263 
73344 
73424 
73504 
73584 

73304 
73384 
73464 
73544 
73624 

73312 
73392 
73472 
73552 
73632 

8 

73640 
73719 
73799 
73878 
73957. 
74036 
74115 
74194 
74273 
74351 

73648 
73727 
73807 
73886 
73965 

73656 
73735 
73815 
73894 
73973 

73664 
73743 
73823 
73902 
73981 

73672 
73751 
73830 
73910 
73989 

73687 
73767 
73846 
73926 
74005 

73695 
73775 
73854 
73933 
74013 

73703 
73783 
7.3862 
73941 
74020 
74099 
74178 
74257 
74335 
74414 
74492 
74570 
74648 
74726 
74803 

73711 
73791 
73870 
73949 
74028 
74107 
74186 
74265 
74343 
74421 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
2 

3 

4 
5 
6 
6 

7 

74044 
74123 
74202 
74280 
74359 

74052 
74131 
74210 
74288 
74367 

74060 
74139 
74218 
74296 
74374 

74068 
74147 
74225 
74304 
74382 

74076 
74155 
74233 
74312 
74390 

74084 
74162 
74241 
74320 
74398 

74092 
74170 
74249 
74327 
74406 

74429 
74507 
74586 
74663 
74741 

74437 
74515 
74593 
74671 
74749 

74445 
74523 
74601 
74679 
74757 

74453 
74531 
74609 
74687 
74764 

74461 
74539 
74617 
74695 
74772 

74468 
74547 
74624 
74702 
74780 

74476 
74554 
74632 
74710 

74788 

74484 
74562 
74640 
74718 
74796 

74500 
74578 
74656 
74733 
74811 
74889 
74966 
75043 
75120 
75197 
75274 
75351 
75427 
75504 
75580 

74819 
74896 
74974 
75051 

75128 

74827 
74904 
74981 
75059 
75136 

74834 
74912 
74989 
75066 
75143 

74842 
74920 
74997 
75074 
75151 

74850 
74927 
75005 
75082 
75159 

74858 
74935 
75012 
75089 
75166 

74865 
74943 
75020 
75097 
75174 

74873 
74950 
75028 
75105 
75182 

74881 
74958 
75035 
75113 
75189 
75266 
75343 
75420 
75496 
75572 
'75648 
75724 
75800 
75876 
75952 

75205 
75282 
75358 
75435 
75511 
75587 
75664 
75740 
75815 
75891 

75213 
75289 
75366 
75442 
75519 
75595 
75671 
75747 
75823 
75899 

75220 
75297 
75374 
75450 
75526 
75603 
75679 
75755 
75831 
75906 

75228 
75305 
75381 
75458 
75534 
75610 
75686 
75762 
75838 
75914 

75236 
75312 
75389 
75465 
75542 
75618 
75694 
75770 
75846 
75921 

75243 
75320 
75397 
75473 
75549 
75626 
75702 
75778 
75853 
75929 

75251 
75328 
75404 
75481 
75557 
75633 
75709 
75785 
75861 
75937 

75259 
75335 
75412 
75488 
75565 
75641 
75717 
75793 
75868 
75944 

7 

570 
571 
572 
573 
574 

75656 
757.32 
75808 
75884 
75959 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
3 
4 
4 
5 
6 
6 

575 

576 
577 
578 
579 

75967 
76042 
76118 
76193 

76268 

75974 
76050 
76125 
76200 
76275 

75982 
76057 
76133 
76208 
76283 

75989 
76065 
76140 
76215 
76290 

75997 
76072 
76148 
76223 
76298 

76005 
76080 
76155 
76230 
76305 

76012 
76087 
76163 
762.38 
76313 

76020 
76095 
76170 
76245 
76320 

76027 
76103 
76178 
76253 
76328 

76035 
76110 
76185 
76260 
76335 

No. 

0 

1 

8 

» 

4 

5 

« 

7 

8 

9 

1 

Page  600J 

TABLE  42. 
Logarithms  of  Numbers. 

No. 

5800 WOO. 

Log.  76343 80618.   1 

No. 

580 
581 
582 
583 
584 
585 
586 
587 
588 
589 
590 
591 
592 
593 
594 

0 

1    • 

i 

3 

4 

5 

6 

7 

76395 
76470 
76545 
76619 
76693 
"76768 
76842 
76916 
76989 
77063 
77137 
77210 
77283 
77357 
77430 

8 

0 

1 

76343 

76418 

76492 

76567 

76641 

76716 

76790 

76864 

76938 

77012 

"77085" 

77159 

77232 

77305 

77379 

1 

76360 
76425 
76500 
765y 
76649 

;  76723 

'  76797 

76871 

7«>945 

77019 

" 77093" 

■  77166 
77240 
77313 
77386 

76358 
76433 
76507 
76582 
7(5656 

"76730" 
76805 
76879 
76953 
77026 

"77100" 
77173 
77247 
77320 
77393 

76365 
76440 
76515 
76589 
76664 

76373 
76448 
76522 
76597 
76671 

76380 
76455 
76530 
76604 
76678 

76388 
76462 
76537 
76612 
76686 

76403 
76477 
76552 
76626 
76701 
76775 
76849 
76923 
76997 
77070 
77144 
77217 
77291 
77364 
77437 

76410 
76485 
76559 
76634 
76708 

8 

1 
2 
3 
4 

6 
6 
7 
8 
9 

1 
2 
2 
3 
4 
6 
6 
6 
7 

76738 
76812 
76886 
76960 
77034 

76745 
76819 
76893 
76967 
77041 

76753 
76827 
76901 
76975 
77048 

76760 
76834 
76908 
76982 
77056 
77129 
77203 
77276 
77349 
77422 

76782 
76856 
76930 
77004 
77078 
77151 
77225 
77298 
77371 
77444 

77107 
77181 
77254 
77327 
77401 

77115 
77188 
77262 
77335 
77408 

77122 
77195 
77269 
77342 
77415 

595 
596 
597 
598 
599 

77452 
77525 
77597 
77670 
77743 

77459 
77532 
77605 
77677 
77750 

77466 
77539 
77612 
77685 
77757 

77474 
77546 
77619 
77692 
77764 

77481 
77554 
77627 
77699 
77772 

77488 
77561 
77634 
77706 
77779 

77495 
77568 
77641 
77714 
77786 

77503 

77576 

77648 

77721 

77793 

77866" 

77938 

78010 

78082 

78154 

77510 

77583 

77656 

77728 

77801 

77873" 

77945 

78017 

78089 

78161 

78233 

78305 

78376 

78447 

78519 

77517 
77590 
77J563 
77735 
77808 
77880 
77952 
78025 
78097 
78168 

600 
601 
602 
603 
604 

77815 
77887 
77960 
78032 
78104 

77822 

77895 

77967 

78039 

78111 

78183" 

78254 

78326 

78398 

78469 

77830 
77902 
77974 
78046 
78118 
78190 
78262 
78333 
78405 
78476 
78547 
78618 
78689 
78760 
78831 

77837- 
77909 
77981 
78053 
78125 

77844 
77916 
77988 
78061 
78132 

77851 
77924 
77996 
78068 
78140 
78211 
78283 
78355 
78426 
78497 

77859. 
77931 
78003 
78075 
78147 

7 

605 
606 
607 
608 
609 

78176 
78247 
78319 
78390 
78462 

78197 
78269 
78340 
78412 
78483 

78204 
78276 
78347 
78419 
78490 

78219 
78290 
78362 
78433 
78504 

^  78226 
78297 
78369 
78440 
78512 

78240 
78312 
78383 
78455 
78526 

1 
2 
3 
4 
5 
6 
-7 
8 
9 

1 
1 
2 
3 
4 
4 
5 
6 
6 

610 
611 
612 
613 
614 
615 
616 
617 
618 
619 

78533 
78604 
78675 
78746 
78817 
78888 
78958 
79029 
79099 
79169 

78540 
78611 
78682 
78753 

78824 

78554 
78625 
78696 
78767 
78838 
78909 
78979 
79050 
79120 
79190 

78561 
78633 
78704 
78774 
78845 

78569 
78640 
78711 
78781 
78852 
78923 
78993 
79064 
79134 
79204 

78576 
78647 
78718 
78789 
78859 
78930 
79000 
79071 
79141 
79211 

78583 
78654 
78725 
78796 
78866 
78937 
79007 
79078 
79148 
79218 

78590 
78661 
78732 
78803 
78873 
78944 
79014 
79085 
79155 
79225 

78597 
78668 
78739 
78810 
78880 
78951 
79021 
79092 
79162 
79232 

78895 
78965 
79036 
79106 
79176 

78902 
78972 
79043 
79113 
79183 

78916 
78986 
79057 
79127 
79197 

620 
621 
622 
623 
624 
625 
62(5 
627 
628 
629 

79239 
79309 
79379 
79449 
79518 

79246 
79316 
79386 
79456 
•  79525 

79253 
79323 
79393 
79463 
79532 

79260 
79330 
79400 
79470 
79539 

79267 
79337 
79407 
79477 
79546 

79274 
79344 
79414 
79484 
79553 

79281 
79351 
79421 
79491 
79560 

79288 
79358 
79428 
79498 
79567 

79295 
79365 
79435 
79505 
79574 
79644 
79713 
79782 
79851 
79920 
79989 
80058 
80127 
80195 
80264 
80332 
80400 
80468 
80536 
80604 

79302 
79372 
79442 
79511 
79581 

79588 
79657 
79727 
79796 
79865 
799;?4 
80003 
80072 
80140 
80209 
8d277 
80346 
80414 
80482 
80550 

79595 
79664 
79734 
79803 

79872 

79602 
79671 
79741 
79810 
79879 

79609 

79678 
79748 
79817 
79886 

79616 
79685 
79754 
79824 
79893 

79623 
79692 
79761 
79831 
79900 

79630 
79699 
79768 
79837 
79906 

79637 
79706 
79775 
79844 
79913 
79982 
80051 
80120 
80188 
80257 
80325 
80393 
80462 
80530 
80598 

79650 
79720 
79789 
79868 
79927 

6 

630 
631 
632 
633 
634 
635 
636 
637 
638 
639 

79941 
80010 
80079 
80147 
80216 
80284 
80353 
80421 
80489 
80557 

79948 
80017 
80085 
80154 
80223 
80291 
80359 
80428 
80496 
805^4 

79955 
80024 
80092 
80161 
80229 

79962 
80030 
80099 
80168 
80236 

79969 

80037 

80106 

80175 

80243 

80312" 

80380 

80448 

80516 

80584 

79975 
80044 
80113 
80182 
80250 
80318 
80387 
80455 
80523 
80691 

79996 

80065 

80134 

80202 

80271 

80339" 

80407 

80475 

80543 

80611 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
1 
2 
2 
3 
4 
4 
5 
5 

80298 
80366 
80434 
80502 
80570 

80305 
80373 
80441 
80509 
80577 

No. 

0 

1 

2 

3 

4 

o 

6 

7 

8 

9 

1 

TABLE  42. 

[Page  601 

Logarithms 

of  Numbers. 

No 

.  6400 7000. 

Log.  80G18 84510.    1 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

640 
641 

80618 
80686 

80625 
80693 

80632 
80699 

80638 
80706 

80645 
80713k 

80652 
80720 

80659 

80726 

80665 
80733 

80672 
80740 

80679 

80747 

1  ' 

1 

642 

80754 

80760 

80767 

80774 

80781 

80787 

80794 

80801 

80808 

80814 

1  1  1 

643 

80821 

80828 

80835 

80841 

80848 

80855 

80862 

80868 

80875 

80882 

2  i  1 

644 
645 

80889 

80895 

80902 

80909 

80916 

80922 

80929 

80936 

80943 

80949 

3  ;  2 

4  i  3 

5  4 

6  1  4 

7  i  5 

8  ;  6 

9  6 

■  80956 

80963 

80969 

80976 

80983 

80990 

80996 

81003 

81010 

81017 

646 

81023 

81030 

81037 

81043 

81050 

81057 

81064 

81070 

81077 

81084 

647 

81090 

81097 

81104 

81111 

81117 

81124 

81131 

81137 

81144 

81151 

648 

81158 

81164 

81171 

81178 

81184 

81191 

81198 

81204 

81211 

81218 

649 

81224 

81231 

81238 

81245 

81251 

81258 

81265 

81271 

81278 

81285 

650 

81291 

81298 

81305 

81311 

81318 

81325 

81331 

81338 

81345 

81351 

651 

81358 

81365 

81371 

81378 

81385 

81391 

81398 

81405 

81411 

81418 

652 

81425 

81431 

81438 

81445 

81451 

81458 

81465 

81471 

81478 

81485 

653 

81491 

81498 

81505 

81511 

81518 

81525 

81531 

81538 

81544 

81551 

654 

81558 

81564 

81571 

81578 

81584 

81591 

81598 

81604 
'81671 

81611 
81677 

81617 

655 

81624 

81631 

81637 

81644 

81651 

81657 

81664 

81684 

656 

81690 

81697 

81704 

81710 

81717 

81723 

81730 

81737 

81743 

81750 

657 

81757 

81763 

81770 

81776 

81783 

81790 

81796 

81803 

81809 

81816 

658 

81823 

81829 

81836 

81842 

81849 

81856 

81862 

81869 

81875 

81882 

659 

81889 

81895 

81902 
81968 

81908 
81974 

81915 
81981 

81921 

81987 

81928 

81935 

81941 
82007' 

81948 
82014 

660 

81954 

81961 

81994 

82000 

661 

82020 

82027 

82033 

82040 

82046 

82053 

82060 

82066 

82073 

82079 

662 

82086 

82092 

82099 

82105 

82112 

82119 

82125 

82132 

82138 

82145 

663 

82151 

82158 

82164 

82171 

82178 

82184 

82191 

82197 

82204 

82210 

664 
665 

82217 

82223 

82230 

82236 

82243 

82249 

82256 

82263 

82269 
82334 

82276 

82282 

82289 

8229"5 

82302 

82308 

82315 

82321 

82328 

82341 

666 

82347 

82354 

82360 

82367 

82373 

82380 

82387 

82393 

82400 

82406 

667 

82413 

82419 

82426 

82432 

82439 

82445 

82452 

82458 

82465 

82471 

668 

82478 

82484 

82491 

82497 

82504 

82510 

82517 

82523 

82530 

82536 

669 

82543 

82549 

82556 

82562 

82569 

82575 

82582 

82588 

82595 

82601 

670 

82607 

82614 

82620 

82627 

82633 

82640 

82646 

82653 

82659 

82666 

671 

82672 

82679 

82685 

82692 

82698 

82705 

82711 

82718 

82724 

82730 

672 

-  82737 

82743 

82750 

82756 

82763 

82769 

82776 

82782 

82789 

82795 

673 

82802 

82808 

82814 

82821 

82827 

82834 

82840 

82847 

82853 

82860 

674 

82866 

82872 

82879 

82885 

82892 

82898 

82905 

82911 

82918 
82982 

82924 

675 

82930 

82937 

82943 

82950 

82956 

82963 

82969 

82975 

82988 

676 

82995 

83001 

83008 

83014 

83020 

83027 

83033 

83040 

83046 

83052 

677 

83059 

83065 

83072 

83078 

83085 

83091 

83097 

83104 

83110 

83117 

678 

83123 

83129 

83136 

83142 

83149 

83155 

83161 

83168 

83174 

83181 

679 
680 

83187 

83193 

83200 

83206 

83213 

83219 

83225' 
83289 

83232 
83296 

83238 
83302 

83245 

83308 

83251 

83257 

83264 

83270 

83276 

83283 

681 

83315 

83321 

83327 

83334 

83340 

83347 

83353 

83359 

83366 

83372 

682 

83378 

83385 

83391 

83398 

83404 

83410 

83417 

83423 

83429 

83436 

683 

83442 

83448 

83455 

83461 

83467 

8.3474 

83480 

8.3487 

83493 

83499 

684 
685 

83506 
83569 

83512 
83575 

83518 

83525 

83531 

83537 
83601 

83544 
83607 

83550 
83613 

83556 
83620 

83563 
83626 

83582 

83588 

83594 

686 

83632 

83639 

83645 

83651 

83658 

83664 

83670 

83677 

83683 

83689 

687 

83696 

83702 

83708 

83715 

83721 

83727 

83734 

83740 

83746 

83753 

688 
689 

83759 
83822 

83765 
83828 

83771 
83835 

83778 
83841 

83784 
83847 

83790 
83853 

83797 
83860 

83803 
83866 

83809 
83872 

83816 
83879 

!   6 

690 

83885 

83891 

83897 

83904 

83910 

83916 

83923 

83929 

83935 

83942 

691 

83948 

83954 

83960 

83967 

83973 

83979 

83985 

83992 

83998 

84004 

1   1 

692 

84011 

84017 

84023 

84029 

84036 

84042 

84048 

84055 

84061 

84067 

2   1 

693 

84073 

84080 

84086 

84092 

84098 

84105 

84111 

84117 

84123 

84130 

3   2 

694 

84136 

84142 

84148 

84155. 

84161 

84167 

84173 

84180 

84186 
84248 

84192 
84255 

4  2 

5  3 

695 

84198 

84205 

84211 

84217 

84223 

84230 

84236 

84242 

696 

84261 

84267 

84273 

84280 

84286 

84292 

84298 

84305 

84311 

84317 

6  ,  4 

697 

84323 

84330 

84336 

84342 

84348 

84354 

84361 

84367 

84373 

84379 

7  !  4 

698 

84386 

84392 

84398 

84404 

84410 

84417 

84423 

84429 

84435 

84442 

8   5 

699 

84448 

84454 

84460 

84466 

84473 

84479 

84485 

84491 

84497 

84504 

9  ;  5 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Pag 

e602] 

TABLE  42. 

IjOgarithms  of  Numbers. 

No.  7000 7600. 

Log.  84510 88081.    1 

No. 

0 

1 

i 

8    1 

4 

6    1 

6 

7   1 

8 

1 

700 
701 
702 
703 
704 

84510 
84572 
84634 
84696 
84757 

84516 
84578 
84640 
84796 
84763 

84522 
84584 
84646 
84708 
84770 

84528 
84590 
84652 
84714 
84776 

84535 
84597- 
84658  1 
84720 
84782 

84541 
84603 
84665 
84726 
84788 

84547  84553 
84609  84615 
84671  84677 
84733  84739 
84794  !  84800 

84559 

84566 

1 
1 

7 

84621  ! 
84683  i 
84745  ! 
84807  ; 

84628 
84689 
84751 
84813 

1 

2  i 

3  I 
.4 

5  ! 

6  i 

7  -i 
8 
9 

1 
1 
2 
3 
4 
4 
5 
6 
6 

705 
706 
707 
708 
709 
710 
711 
712 
713 
714 

84819 
84880 
■  84942 
85003 
85065 

84825  { 
84887 
84948 
85009 
85071  ' 

84831 
84893 
84954 
85016 
85077 
85138 
85199 
85260 
85321 
85382 

84837 
84899 
84960 
•  85022 
85083 

84844 
84905 
84967 
85028 
85089 

84850  1 
84911  ' 
84973  ' 
85034  < 
85095  i 
85156 
85217 
85278 
85339 
85400 

84856  i  84862 
84917  !  84924 
84979  84985 
85040  85046 
85101  !  85107 
85163  85169 

84868  : 
84930  i 
84991 
85052 
85114 

84874 
84936 
84997 
85058 
85120 

85126 
85187 
85248 
85309 
85370 

85132 
85193 
85254 
85315 
85376 

85144 
85205 
85266 
85327 
85388 

85150 
85211 
85272 
85333 
85394 

85175 
85236 
85297 
85358 
85418 

85181 
85242 
85303 
85364 
85425 

85224  ' 
85285 
85345 
85406 

85291 
85352 
85412 

715 
716 
717 
718 
719 

85431 
85491 
85552 
85612 
85673 

85437 
85497 
85558 
85618 
85679 

85443 
85503 
85564 
85625 
85685 

85449 
85509 
85570 
85631 
85691 

85455 
85516 
85576 
85637 
85697 

85461 
85522 
85582 
85643 
85703 

85467  85473 
85528  85534 
85588  85594 
85649  1  85655 
85709  i  85715 

85479  1 

85540 

85600 

85661 

85721 

85485 
85546 
85606 
85667 

85727 

720 
721 
722 
723 

724 
725 
726 

727 
728 
729 

85733 
85794 
85854 
85914 
85974 

85739 
85800 
85860 
85920 
85980 

85745 
85806 
85866 
85926 
85986 

85751 
85812 
85872 
85932 
85992 
86052 
86112 
86171 
86231 
86291 

85757 
85818 
85878 
85938 
85998 

85763 
85824 
85884 
85944 
86004 
86064 
86124 
86183 
86243 
86303 

85769  :  85775 
85830  1  85836 
85890  1  85896 
85950  85956 

85781 
85842 
85902 
85962 
86022 

85788 
85848 
85908 
85968 
86028 
86088 
86147 
86207 
86267 
86326 
86386 
86445 
86504 
86564 
86623 

86010 

86070  ■' 

86130 

86189 

86249 

86308 

86016 

1 
2 
3 
4 
5 
6 
7 
8 
9 

6 

1 
1 
2 
2 
3 
4 
4 
5 
5 

86034 
86094 
86153 
86213 
86273 

86040 
86100 
86159 
86219 
86279 

86046 
86106 
86165 
86225 
86285 

86058 
86118 
86177 
86237 
86297 

86076 
86136 
86195 
86255 
86314 

86082 
86141 
86201 
86261 
86320 

730 
.  731 
732 
733 
734 

86332 
86392 
86451 
86510 
86570 

86338 
86398 
86457 
86516 
86576 
86635 
86694 
86753 
86812 
86870 

86344 
86404 
86463 
86522 
86581 
86641 
86700 
86759 
86817 
86876 
86935 
86994 
87052 
87111 
87169 

86350 
86410 
86469 
86528 
86587 
86646 
86705 
86764 
86823 
86882 

86356 
86415 
86475 
86534 
86593 

86362 
86421 
86481 
86540 
86599 

86368  i  86374 
86427  ■   86433 
86487  86493 
8a546  86552 
86605  86611' 

86380 
86439 
86499 
86558 
86617 

735 
736 
737 
738 
739 

86629 
86688 
86747 
86806 
86864 

86652 
86711 
86770 
86829 
86888 

86658 
86717 
86776 
86835 
86894 

86664  86670  i  86676 

86682 
86741 
86800 
86859 
86917 

86723 
86782 
.86841 
86900 

86729  86735 
86788  86794 
86847  1  86853 
86906  1  86911 

740 
741 
742 
743 
744 

86923 
86982 
87040 
87099 

87157 

86929 
86988 
87046 
87105 
87163 

86941 
86999 
87058 
87116 
87175 

86947 
87005 
87064 
87122 
87181 

86953 
87011 
87070 
87128 
87186 

86958 
87017 
87075 
87134 
87192 

86964 
87023 
87081 
87140 
87198 

1  86970 
87029 

1  87087 
87146 
87204 

86976 
87035 
87093 
87151 
87210 
87268 
87326 
87384 
87442 
87500 

745 
746 
747 

748 
749 

87216 
87274 
87332 
87390 
87448 

87221 
87280 
87338 
87-396 
87454 

87227 
87286 
87344 
87402 
87460 

87233 
87291 
87349 
87408 
87466 

87239 
87297 
87355 
87413 
87471 

87245 
87303 
87361 
87419 

87477 

87251 
87309 
87367 
87425 
87483 

87256 
87315 
87373 
87431 
87489 

87262 
87320 
87379 
87437 
87495 

1 
2 
3 
4 

5 
6 
7 
8 
9 

5 

750 
751 
752 
753 
754 

87506 
87564 
87622 
87679 
87737 

87512 
87570 
87628 
1  87685 
87743 

87518 
87576 
87633 
87691 

87749 

87523 
87581 
87639 
87697 
87754 

87529 
87587 
87645 
87703 
87760 

87535 
87593 
87651 
87708 
87766 

87541 
87599 
87656 
87714 
87772 

87547 
87604 
87662 
87720 
87777 

87552 
87610 
87668 
87726 
87783 

875"58 
87616 
87674 
87731 
87789 

1 

1 
2 
2 

3 
3 
4 
4 
5 

755 
756 

757 
758 
759 

87795 
87852 
87910 
87967 
88024 

87800 
87858 
87915 
87973 
88030 

87806 

87864 

;  87921 

!  87978 

88036 

87812 
87869 
87927 
87984 
88041 

87818 
87875 
87933 
87990 
88047 

87823 
87881 
87938 
87996 
88053 

87829 
87887 
87944 
88001 
88058 

87835 
87892 
87950 
88007 
88064 

87841 
87898 
87955 
88013 
88070 

87846 
87904 
87961 
88018 
88076 

No. 

0 

1 

1    ^ 

8 

4 

5 

6 

' 

8 

» 

1 

TABLE  42. 

[Page  603 

Logarithms  of  Numbers. 

No. 

7600 8200. 

Log.  88081 91381.   1 

No. 

0 

1 

2 

8 

* 

5 

6 

7 

8 

9 

760 
761 

88081 
88138 

88087 
88144 

88093 
88150 

88098 
88156 

88104 
88161 

88110 
88167 

88116 
88173 

88121 
88178 

88127 
88184 

88133 
88190 

1  6 

762 

88195 

88201 

88207 

88213 

88218 

88224 

88230 

88235 

88241 

88247 

1    1 

763 

88252 

88258 

88264 

88270 

88275 

88281 

88287 

88292 

88298 

88304 

2   1 

764 
765 

88309 
"88366 

88315 
88"372 

88321 

88326 

88332 

88338 

88343 

88349 
88406 

88355 
88412 

88360 
88417 

3  i  2 

A            O 

88377 

88383 

88389 

88:395 

88400 

5 
6 

7 

3 
4 
4 

766 

88423 

88429 

88434 

88440 

•88446 

88451 

88457 

88463 

88468 

88474 

767 

88480 

88485 

88491 

88497 

88502 

88508 

88513 

88519 

88525 

88530 

768 

88536 

88542 

88547 

88553 

88559 

88564 

88570 

88576 

88581 

88587 

769 

88593 

88598 

88604 

88610 

88615 
88672 

88621 
88677 

88627 
88683 

88632 
88689 

88638 
88694 

88643 
88700 

9  1  5 

770 

88649 

88655 

88660 

88666 

771 

88705 

88711 

88717 

88722 

88728 

88734 

88739 

88745 

88750 

88756 

772 

88762 

88767 

88773 

88779 

88784 

88790 

88795 

88801 

88807 

88812 

773 

88818 

88824 

88829 

88835 

88840 

88846 

88852 

88857 

88863 

88868 

774 
775 

88874 
88930 

88880 

88885 

88891 

88897 

88902 

88908 

88913 

88919 
88975 

88925 

88936 

88941 

88947 

88953 

88958 

88964 

88969 

88981 

776 

88986 

88992 

88997 

89003 

89009 

89014 

89020 

89025 

89031 

89037 

777 

89042 

89048 

89053 

89059 

89064 

89070 

89076 

89081 

89087 

89092 

778 

89098 

89104 

89109 

89115 

89120 

89126 

89131 

89137 

89143 

89148 

779 

89154 

89159 

89165 

89170 

89176 

89182 
89237 

89187 

89193 

89198 

89204 
89260 

780 

89209 

89215 

89221 

89226 

89232 

89243 

89248 

89254 

781 

89265 

89271 

89276 

89282 

89287 

89293 

89298 

89304 

89310 

89315 

782 

89321 

89326 

89332 

89337 

89343 

89348 

89354 

89360 

89365 

89371 

783 

89376 

89382 

89387 

-  89393 

89398 

89404 

89409 

89415 

89421 

89426 

784 

89432 

89437 

89443 

89448 

89454 

89459 
89515 

89465 
89520 

89470 
89526 

89476 
89531 

89481 
89537 

785 

89487 

89492 

89498 

89504 

89509 

786 

89542 

89548 

89553 

89559 

89564 

89570 

89575 

89581 

89586 

89592 

787 

89597 

89603 

89609 

89614 

89620 

89625 

89631 

89636 

89642 

89647 

788 

89653 

89658 

89664 

89669 

89675 

89680 

89686 

89691 

89697 

89702 

789 
790 

89708 

89713 

89719 

89724 

89730 

89735 

89741 

89746 

89752 

89757 

89763 

89768 

89774 

89779 

89785 

89790 

89796 

89801 

89807 

89812 

791 

89818 

89823 

89829 

898^4 

89840 

89845 

89851 

89856 

89862 

89867 

792 

89873 

89878 

89883 

89889 

89894 

89900 

89905 

89911 

89916 

89922 

793 

89927 

89933 

89938 

89944 

89949 

89955 

89960 

89966 

89971 

89977 

794 

89982 

89988 

89993 

89998 

90004 

90009 

90015 
90069 

90020 
90075 

90026 
90080 

90031 
90086 

795 

90037 

90042 

90048 

90053 

90059 

90064 

796 

90091 

90097 

90102 

90108 

90113 

90119 

90124 

90129 

90135 

90140 

797 

90146 

90151 

90157 

90162 

90168 

90173 

90179 

90184 

90189 

90195 

798 

90200 

90206 

90211 

90217 

90222 

90227 

90233 

90238 

90244 

90249 

799 
800 

90255 
90309 

90260 

90266 

90271 
90325 

90276 

90282 

90287 

90293 
90:347 

90298 
90352 

90;304 
90358 

90314 

90320 

90331 

90336 

90342 

801 

90363 

90369 

90374 

90380 

90385 

90390 

90396 

90401 

90407 

90412 

802 

90417 

90423 

90428 

90434 

90439 

90445 

90450 

90455 

90461 

9046() 

803 

90472 

90477 

90482 

90488 

90493 

90499 

90504 

90509 

90515 

90520 

804 

90526 

90531 

90536 

90542 

90547 

90553 

90558 

90563 
90617 

90569 
90623" 

90574 
90628 

805 

90580 

90585 

90590 

90596 

90601 

90607 

90612 

806 

90634 

90639 

90644 

90650 

90655 

90660 

90666 

90671 

90677 

90682 

807 

90687 

90693 

90698 

90703 

90709 

90714 

90720 

90725 

90730 

907:36 

808 
809 

90741 
90795 

90747 
90800 

90752 
90806 

90757 
90811 

90763 
90816 

90768 
90822 

90773 
90827 

90779 
90832 

90886 

90784 
90838 
90891 

90789 
90843 

5 

810 

90849 

90854 

90859 

90865 

90870 

90875 

90881 

90897 

811 

90902 

90907 

90913 

90918 

90924 

90929 

90934 

90940 

90945 

90950 

1 

1 

812 

90956 

90961 

90966 

90972 

90977 

90982 

90988 

90993 

90998 

91004 

2 

1 

813 

91009 

91014 

91020 

91025 

91030 

91036 

91041 

91046 

91052 

91057 

3 

2 

814 

91062 

91068 

91073 

91078 
91132^ 

91084 
91137 

91089 
91142 

91094 
91148 

91100 
91153 

91105 

91110 

4 
5 

2 
3 

815 

91116 

91121 

91126 

91158 

91164 

816 

91169 

91174 

91180 

91185 

91190 

91196 

91201 

91206 

91212 

91217 

6 

3 

817 

91222 

91228 

91233 

91238 

91243 

91249 

91254 

91259 

91265 

91270 

7 

4 

818 

91275 

91281 

91286 

91291 

91297 

91302 

91307 

91312 

91318 

91323 

8 

4 

819 

91328 

91334 

91339 

91344 

91350 

91355 

91360 

91365 

91371 

91376 

9 

5 

No. 

0 

1 

2 

3 

4 

5 

« 

7 

8 

9 

1 

Page  604] 

TABLE  42. 

Logarithms 

of  Numbers. 

No. 

8200 8800. 

Log.  91381 94448 

No. 

0 

1 

2 

S 

4 

5 

6 

7 

8 

9 

1 

820 
821 

91381 
91434 

91387 
91440 

91392 
91445 

91397 
91450 

91403 
91466 

91408 
91461 

91413 
91466 

91418  91424 

91429 
91482 

6 

91471 

91477 

822 

91487 

91492 

91498 

91503 

91608 

91514 

91619 

91524 

91629 

91535 

1 

1 

823 

91540 

9154» 

91551 

91556 

91561 

91566 

91572 

91577 

91682 

91687 

1 

824 

91593 

91598 

91603 

91609 

91614 

91619 

91624 

91630  91635 

91640 

3 
4 

2 
3 
4 
4 
6 
5 

825 

91645 

91661 

91656 

91661 

91666 

91672 

91677 

91682  91687 

91693 

826 

91698 

91703 

91709 

91714 

91719 

91724 

91730 

91735  91740 

91745 

6 

827 

91751 

91756 

91761 

91766 

91772 

91777 

91782 

91787  91793 

91798 

828 

91803 

91808 

91814 

91819 

91824 

91829 

91834 

91840  91845 

91850 

8 
9 

829 

91855 

91861 

91866 

91871 

91876 

91882 

91887 

91892  91897 

91903 

830 

91908 

91913 

91918 

91924 

91929 

91934 

91939 

91944  91950 

91955 

831 

91960 

91965 

91971 

91976 

91981 

91986 

91991 

91997  92002 

92007 

832 

92012 

92018 

92023 

92028 

92033 

92038 

92044 

92049  92054 

92059 

833 

92065 

92070 

92075 

92080 

92085 

92091 

92096 

92101  92106 

92111 

834 

92117 

92122 

92127 

92132 

92137 

92143 

92148 

92153  92158 
92205'  92210 

92163 

835 

92169 

92174 

92179 

92184 

92189 

92195 

92200 

92215 

836 

92221 

92226 

92231 

92236 

92241 

92247 

92252 

92257  92262 

92267 

837 

92273 

92278 

92283 

92288 

92293 

92298 

92304 

92309  92314 

92319 

838 

92324 

92330 

92335 

92340 

92345 

92360 

92355 

92361  92366 

92371 

839 

92376 

92381 

92387 

92392 

92397 

92402 
92454 

92407 
92459 

92412  92418 
92464  92469 

92423 
92474 

840 

92428 

92433 

92438 

92443 

92449 

841 

92480 

92485 

92490 

92495 

92500 

92505 

92511 

92616  92521 

92526 

842 

92531 

92536 

92542 

92547 

92552 

92557 

92562 

92567  92572 

92578 

843 
844 

92583 
92634 

92588 
92639 

92593 
92645 

92598 
92650 

92603 
92655 

92609 
92660 

92614  J 
92665 

92619  92624 
92670  92676 
92722  92727 

92629 
92681 

5 

845 

92686 

92691 

92696 

92701 

92706 

92711 

92716 

92732 

846 

92737 

92742 

92747 

92752 

92758 

92763 

92768 

92773  92778 

92783 

1 
2 

1 

1 
9 

847 

92788 

92793 

92799 

92804 

92809 

92814 

92819 

92824  92829 

92834' 

848 

92840 

92845 

92860 

92855 

92860 

92865 

92870 

92876  92881 

92886 

849 

92891 

92896 

92901 

92906 

92911 

92916 

92921 

92927 

92932 
92983 

92937 

4 
5 

2 

3 

850 

92942 

92947 

92952 

92967 

92962 

92967 

92973 

92978 

92988 

851 

92993 

92998 

93003 

93008 

93013 

93018 

93024 

93029  93034 

93039 

6 

3 

852 

93044 

93049 

93054 

~  93059 

93064 

93069 

93075 

93080  93085 

93090 

7 

4 

853 

93095 

93100 

93106 

93110 

93115 

93120 

93125 

93131  93136 

93141 

8 

4 

854 

93146 

93151 

93156 

93161 

93166 
93217 
93268 

93171 
93222 
93273 

93176 

93181  93186 

93192 

9 

5 

855 
856 

93197 
93247 

93202 
93252 

93207 
93258 

93212 
93263 

93227 
93278 

93232  93237 
93283  93288 

93242 
93293 

857 

93298 

93303 

93308 

93313 

93318 

93323 

93328 

93334  93339 

93344 

858 

93349 

93354 

93359 

93364 

93369 

93374 

93379 

93384  93389 

93394 

859 

93399 

93404 

93409 

93414 

93420 

93425 

93430 

93435 

93440 
93490 

93445 

860 

93450 

93455 

93460 

93465 

93470 

93475 

93480 

93486 

93495 

861 

93500 

93505 

93510 

93515 

93520 

93526 

93631 

93536  :  93541 

93546 

862 

93551 

93556 

93561 

93566 

93571 

93576 

93581 

93586  93591 

93596 

863 

93601 

93606 

93611 

93616 

93621 

93626 

93631 

93636  93641 

93646 

864 
865 

93651 
93702 

93656 
93707 

93661 
93712 

93666 
93717 

93671 
93722 

93676 
93727 

93682 

93687  93692 
93737  93742 

93697 
93747 

93732 

866 

93752 

93757 

93762 

93767 

93772 

93777 

93782 

93787  93792 

93797 

867 

93802 

93807 

93812 

93817 

93822 

93827 

93832 

93837  93842 

93847 

868 
869 

93852 
93902 

93857 
93907 

93862 
93912 
93962 

93867 
93917 
93967 

93872 
93922 

93877 
93927 

93882 
93932 
93982 

93887  93892 
93937  93942 
9398;  "93992 

93897 
93947 

4 

870 

93952 

93957 

93972 

93977 

93997 

871 

94002 

94007 

94012 

94017 

94022 

94027 

94032 

94037  i  94042 

94047 

1 

0 

872 

94052 

94057 

94062 

94067 

94072 

94077 

94082 

94086  94091 

94096 

2 

1 

873 

94101 

94106 

94111 

94116 

94121 

94126 

94131 

94136  1  94141 

94146 

3 

1 

874 

94151 

94156 

94161 

94166 

94171 

94176 

94181 

94186 

94191 
94240 

94196 
94245 

4 
5 

2 
2 

875 

94201 

94206 

94211 

94216 

94221 

94226 

94231 

94236 

876 

94250 

94255 

94260 

94265 

94270 

94275 

94280 

94285 

94290 

94295 

6 

2 

877 

94300 

94305 

94310 

94316 

94320 

94325 

94330 

94335 

94340 

94345 

7 

3 

878 

94349 

94354 

94359 

94364 

94369 

94374 

94379 

94384 

94389 

94394 

8 

3 

879 

94399 

94404 

94409 

94414 

94419 

94424 

94429 
6 

94433 

94438 

94443 

9 

4 

No. 

0 

1    ■ 

2 

3 

4 

5 

i   ' 

'  8 

9 

1 

TABLE  42. 

[Page  605 

Logarithms 

of  Numbers. 

No. 

8800 9400. 

L 

og.  94448   97313 

No. 

0 

94448 
94498 

1 

2 

3 

4 

9 

6 

7 

8 

9 

1 

880 

881 

94453 
94503 

94458 
94507 

94463 
94512 

94468 
94517 

94473 
94522 

94478 
94527 

94483 
94532 

94488 
94537 

94493 
94542 

5 

882 

94547 

94552 

94557 

94562 

94567 

94571 

94576 

94581 

94586 

94591 

1 

1 

883 

94596 

94601 

94606 

94611 

94616 

94621 

94626 

94630 

94635 

94640 

2 

1 

884 
8'85 

94645 
94694 

94650 
94699 

94655 
94704 

94660 
94709 

94665 

94670 

94675 
94724 

94680 
94729 

94685 
94734 

94689 
94738 

3 
4 
5 
6 

7 
8 
9 

2 
2 
3 
3 
4 
4 
5 

94714 

94719 

886 

94743 

94748 

94753 

94758 

94763 

94768 

94773 

94778 

94783 

94787 

887 

94792 

94797 

94802 

94807 

94812 

94817 

94822 

94827 

94832 

94836 

888 

94841 

94846 

94851 

94856 

94861 

94866 

94871 

94876 

94880 

94885 

889 
890 

94890 
94939 

94895 

94900 

94905 

94910 

94915 

94919 

94924 

94929 

94934 
94983 

94944 

94949 

94954 

94959 

94963 

94968 

94973 

94978 

891 

94988 

94993 

94998 

95002 

95007 

95012 

95017 

95022 

95027 

95032 

892 

95036 

95041 

95046 

95051 

95056 

95061 

95066 

95071 

95075 

95080 

893 

95085 

95090 

95095 

95100 

95105 

95109 

95114 

95119 

95124 

95129 

894 

95134 

95139 

95143 

95148 

95153 

95158 

95163 

95168 

95173 
95221 

95177 
95226 

895 

95182 

95'187 

95192 

95197 

95202 

95207 

95211 

95216 

896 

95231 

95236 

95240 

95245 

95250 

95255 

95260 

95265 

95270 

95274 

897 

95279 

95284 

95289 

95294 

95299 

95303 

95308 

95313 

95318 

95323 

898 

95328 

95332 

95337 

95342 

95347 

95352 

95357 

95361 

95366 

95371 

899 
900 

95376 

95381 

95386 

95390 

95395 

95400 

95405 

95410 

95415 

95419 

95424 

95429 

95434 

95439 

95444 

95448 

95453 

95458  95463 

95468 

901 

95472 

95477 

95482 

95487 

95492 

95497 

95501 

95506  95511 

95516 

902 

95521 

95525 

95530 

95535 

95540 

95545 

95550 

95554  95559 

95564 

903 

95569 

95574 

95578 

95583 

95588 

95593 

95598 

95602  ,  95607 

95612 

904 

95617 

95622 

95626 

95631 

95636 

95641 

95646 

95650 

95655 
95703 

95660 
95708 

905 

95665 

95670 

95674 

95679 

95684 

95689 

95694 

95698 

906 

95713 

95718 

95722 

95727 

95732 

95737 

95742 

95746  i  95751 

95756 

907 

95761 

95766 

95770 

95775 

95780 

95785 

95789 

95794  1  95799 

95804 

908 

95809 

95813 

95818 

95823 

95828 

95832 

95837 

95842  1  95847 

95852 

909 

'  95856 

95861 

95866 
95914 

95871 
95918 

95875 
95923 

95880 

95885 

95890  !  95895 
95938  95942 

95899 
95947 

910 

95904 

95909 

95928 

95933 

911 

95952 

95957 

95961 

95966 

95971 

95976 

95980 

95985  I  95990 

95995 

912 

95999 

96004 

96009 

96014 

96019 

96023 

96028 

96033 

96038 

96042 

913 

96047 

96052 

96057 

96061 

96066 

96071 

96076 

96080 

96085 

96090 

914 

96095 

96099 

96104 

96109 

96114 

96118 

96123 

96128 

96133 

96137 

915 

96142 

96147 

96152 

96156 

96161 

96166 

96171 

96175 

96180 

96185 

916 

96190 

96194 

96199 

96204 

96209 

96213 

96218 

96223  t  96227 

96232 

917 

96237 

96242 

96246 

96251 

96256 

96261 

96265 

96270 

96275 

96280 

918 

96284 

96289 

96294 

96298 

96303 

96308 

96313 

96317 

96322 

9(i327 

919 

96332 

96336 

96341 
96388 

96346 
96393 

96350 
96398 

96355 
96402 

96360 
96407 

96365 

96369 

96374 

920 

96379 

96384 

96412 

96417 

96421 

921 

96426 

96431 

96435 

96440 

96445 

96450 

96454 

96459  !  96464 

96468 

922 

96473 

96478 

96483 

96487 

96492 

96497 

96501 

96506 

96511 

96515 

923 

96520 

96525 

96530 

96534 

96539 

96544 

96548 

96553 

96558 

96562 

924 
925 

96567 

96572 

96577 

96581 

96586 

96591 

96595 

96600 

96605 

96609 

96614 

96619 

96624 

96628 

96633 

96638 

96642 

96647 

96652 

96(556 

926 

96661 

96666 

96670 

96675 

96680 

96685 

96689 

96694 

96699 

96703 

927 

96708 

96713 

96717 

96722 

96727 

96731 

96736 

96741 

96745 

96750 

928 
929 
930 

96755 
96802 

96759 
96806 
96853 

96764 
96811 
96858 

96769 
96816 
96862 

96774 
96820 

96778 
96825 

96783 
96830 

96788 
96834 
96881 

96792 
96839 
96886 

96797 
96844 

4 

96848 

96867 

96872 

96876 

96890 

931 

96895 

96900 

96904 

96909 

96914 

96918 

96923 

96928 

96932 

96937 

1 :  0 

932 

96942 

96946 

96951 

96956 

96960 

96965 

96970 

96974 

96979 

96984 

2   1 

933 

96988 

96993 

96997 

97002 

97007 

97011 

97016 

97021 

97025 

97030 

3   1 

934 
935 

97035 

970.39 

97044 

97049 

97053 

97058 

97063 

97067 

97072 
97118 

97077 
97123" 

4 
5 

2 
•  2 

97081 

97086 

97090 

97095 

97100 

97104 

97109 

97114 

936 

97128 

97132 

97137 

97142 

97146 

97151 

97155 

97160 

97165 

97169 

6 

2 

937 

97174 

97179 

97183 

97188 

97192 

97197 

97202 

97206 

97211 

97216 

7 

3 

938 

97220 

97225 

97230 

97234 

97239 

97243 

97248 

97253 

97257 

97262 

8 

3 

939 

No. 

97267 

97271 

97276 

97280 

97285 

97290 

97294 

97299 

97304 

97308 

^ 

4 

0        1 

o 

3 

4 

5 

6 

7 

8 

9 

1 

Page  606] 

TABLE  42. 

Logarithms 

of  Numbers. 

No. 

9400 10000. 

Log.  97313- 

99996. 

No. 

0 

1 

i 

8 

4 

5 

* 

1 

8   1   » 

940 

97313 

97317 

97322 

97327 

97331 

97336 

97340 

97345 

1 
97350  97354 

5 

941 

97359 

97364 

97368 

97373 

97377 

97382 

97387 

97391 

97396  97400 

942 

97405 

97410 

97414 

97419 

97424 

97428 

97433 

97437 

97442  97447 

1    1 

943 

97451 

97456 

97460 

97465 

97470 

97474 

97479 

97483 

97488  97493 

2   1 

944 
945 

97497 

97502 

97506 

97511 

97516 

97520 

97525 

97529 

97534 

97539 

97585 

3  !  2 

4  1  2 

97543 

97548 

97552 

97557 

97562 

97566 

97571 

97575 

97580 

946 

97589 

97594 

97598 

97603 

97607 

97612 

97617 

97621 

97626  \   97630 

5  1  3 

947 

97635 

97640 

97644 

97649 

97653 

97658 

97663 

97667 

97672  97676 

6  i  3 

948 

97681 

97685 

97690 

97695 

97699 

97704 

97708 

97713 

97717  !  97722 

7  !  4 

949 
950' 

97727 

97731 

,  97736 

97740 

97745 
97791 

97749 
97795 

97754 
97800 

97759 
97804 

97763  i  97768 
97809^  97813 

8  ;  4 

9  i  5 

97772 

97777 

97782 

97786 

951 

97818 

97823 

97827 

97832 

97836 

97841 

97845 

97850 

97855  '  97859 

952 

97864 

97868 

97873 

97877 

97882 

97886 

97891 

97896 

97900  97905 

953 

97909 

97914 

97918 

97923 

97928 

97932 

97937 

97941 

97946  i  97950 

954 

97955 

97959 

97964 

97968 

97973 

97978 

97982 
98028 

97987 
98032 

97991  1  97996 

955 

98000 

98005 

98009 

98014 

98019 

98023 

9803.7  1  98041 

956 

98046 

98050 

98055 

98059 

98064 

98068 

98073 

98078 

98082  !  98087 

957 

98091 

98096 

98100 

98105 

98109 

98114 

98118 

98123 

98127  1  98132 

958 

98137 

98141 

98146 

98150 

98155 

98159 

98164 

98168 

98173  1  98177 

959 

98182 
98227 

98186 

98191 

98195 

98200 
98245 

98204 

98209 

98214 

98218  !  98223 
98263  98268 

960 

98232 

98236 

98241 

98250 

98254 

98259 

961 

98272 

98277 

98281 

98286 

98290 

98295 

98299 

98304 

98308  98313 

962 

98318 

98322 

98327 

98331 

98336 

98340 

98345 

98349 

98354  98358 

963 

98363 

98367 

98372 

98376 

98381 

98385 

98390 

98394 

98399  98403 

964 
965 

98408 
98453 

98412 
98457 

98417 

98421 

98426 

98430 

98435 

98439 

98444  ,  98448 

98462 

98466 

98471 

98475 

98480 

98484 

98489  98493. 

966 

98498 

98502 

98507 

98511 

98516 

98520 

98525 

98529 

98534  98538 

967 

98543 

98547 

98552 

98556 

98561 

98565 

98570 

98574 

98579  1  98583 

968 

98588 

98592 

98597 

98601 

98605 

98610 

98614 

98619 

98623  98628 

969 
970 

98632 

98637 

98641 

98646 

98650 

98655 

98659 

98664 
98709 

98668  :   98673 
98713  98717 

98677 

98682 

98686 

98691 

98695 

98700 

98704 

971 

98722 

98726 

98731 

98735 

98740 

98744 

98749 

98753 

98758  98762 

972 

98767 

98771 

98776 

98780 

98784 

98789 

98793 

98798 

98802  98807 

973 

98811 

98816 

98820 

98825 

98829 

98834 

98838 

98843 

98847  :  98851 

974 

98856 

98860 

98865 

98869 

98874 

98878 

98883 

98887 

98892 

98896 
98941 

975 

9890'0 

98905 

98909 

98914 

98918 

98923 

98927 

98932 

98936 

976 

98945 

98949 

98954 

98958 

98963 

98967 

98972 

98976 

98981  98985 

977 

98989 

98994 

98998 

99003 

99007 

99012 

99016 

99021 

99025 

99029 

978 

99034 

99038 

99043 

99047 

99052 

99056 

99061 

99065 

99069 

99074 

979 

99078 

99083 
99127 

99087 

99092 

99096 
99140 

99100 
99145 

99105 
99149 

99109 
99154 

99114 

99118 
99162 

980 

99123 

99131 

99136 

99158 

981 

99167 

99171 

99176 

99180 

99185 

99189 

99193 

99198 

99202 

99207 

982 

99211 

99216 

99220 

99224 

99229 

99233 

99238 

99242 

99247 

99251 

983 

99255 

99260 

99264 

99269 

99273 

99277 

99282 

99286 

99291 

99295 

984 

99300 

99304 

99308 

99313 

99317 

99322 

99326 

99330 

99335 

99339 

985 

99344 

99348 

99352 

99357 

99361 

99366 

99370 

99374 

99379 

99383 

986 

99388 

99392 

99396 

99401 

99405 

99410 

99414 

99419 

99423 

99427 

987 

99432 

99436 

99441 

99445 

99449 

99454 

99458 

99463 

99467 

99471 

988 
989 
990 

99476 
99520 

99480 
99524 

99484 
99528 

99489 
99533 

99493 
99537 

99498 
99542 

99502 
99546 

99506 
99550 

99511  1  99515 

99555 

99559 
99603 

4 

99564 

99568 

99572 

99577 

99581 

99585 

99590 

99594 

99599 

991 

99607 

99612 

99616 

99621 

99625 

99629 

99634 

99638 

99642 

99647 

1  '  0 

992 

99651 

99656 

99660 

99664 

99669 

99673 

99677 

99682 

99686 

99691 

2   1 

993 

99695 

99699 

99704 

99708 

99712 

99717 

99721 

99726 

99730 

99734 

3   1 

994 
995 

99739 

99782' 

99743 

99787 

99747 
99791 

99752 
99795 

99756 

99760 
99804~ 

99765 
99808 

99769 
99813 

99774 
99817 

99778 
99822 

4  2 

5  i  2 

99800 

996 

99826 

99830 

99835 

99839 

99843 

99848 

99852 

99856 

99861   99865 

6   2 

997 

99870 

99874 

99878 

99883 

99887 

99891 

99896 

99900 

99904  99909 

7   3 

998 

99913 

99917 

99922 

99926 

99930 

99935 

99939 

99944 

99948  99952 

n    ! 

999 

99957 

99961 

99965 

99970 

99974 

99978 

99983 

99987 

99991 

99996 
0 

9  ;    4 

No. 

0 

1 

2 

8 

4 

5 

a 

7 

8 

TABLE  43.                                           [Page  607 

Logarithmic  Sines,  Tangents,  and  Secants  to  every  Point  and  Quarter  Point  of  the  Compass. 

Points. 

Sine.            1          Cosine.          1      Tangent. 

Cotangent. 

Secant. 

Cosecant. 

0 

1 

Inf.  neg.             10. 00000        Inf.  neg. 
8.69080               9.99948  j         8.69132 
8.99130  i            9.99790           8.99340 
9.16652              9.99527  i        9.17125 

infinite. 
11.  30868 
11.00660 
10.  82875 

10.00000 
10.00052 
10. 00210 
10. 00473 

Infinite. 
11. 30920 
11. 00870 
10.  83348 

8 
71 

1 

u 

9. 29024 
9. 38557 
9. 46282 
9. 52749 

9. 99157 
9. 98679 
9. 98088 
9. 97384 

9. 29866 
9.  39879 
9. 48194 
9. 55365 

10.  70134 
10. 60121 
10. 51806 
10. 44635 

10. 00843 
10.  01321 
10. 01912 
10. 02616 

10.  70976 
10.  61443 
10. 53718 
10. 47251 

7 

6| 
6J 
6i 

2 

2i 
21 

9. 58284 
9. 63099 
9. 67339 
9. 71105 

9. 96562 
9. 95616 
9. 94543 
9. 93335 

9. 61722 
9.  67483 
9. 72796 
9.  77770 

10. 38278 
10. 32517 
10. -27204 
10.  22230 

10. 03438 
10. 04384 
10. 05457 
10. 06665 

10.41716 
10. 36901 
10. 32661 
10. 28895 

6 

5^ 
5i 

3 
3i 

31 

9.74474 
9. 77503 
9. 80236 
9. 82708 

9. 91985 
9. 90483 
9. 88819 
9. 86979 

9. 82489 
9.  87020 
9.91417 
9. 95729 

10. 17511 
10. 12980 
10. 08583 
10. 04271 

10. 08015 
10.  09517 
10. 11181 
10. 13021 

10. 25526 
10.22497 
10. 19764 
10. 17292 

5 
4| 

^ 

4i 

4 

9. 84949 

9. 84949 

10.00000 

10. 00000          10. 15051 

10. 15051 

4 

Cosine. 

Sine. 

Cotangent. 

Tangent.           Cosecant. 

Secant. 

Points. 

Page  608j 

TABLE  U. 

Log.  Sines,  Tangents,  and  Secants. 

0" 

179° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff.  1'. 

Cosecant. 

Tangent. 

Diff.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

12  0  0 

0  0  0 

Inf.  neg. 

lniinit«. 

Inf.  neg. 

Infinite. 

10.  00000 

10.00000 

60 

1 

11  59  52 

0  8 

6.46373  30103 

13.  53627 

6. 46373 

30103 

13.53627 

00000 

00000 

59 

2 

59  44 

0  16 

76476  17609 

23524 

76476  17609 

23524 

00000 

00000 

58 

3 

59  3t5 

0  24 

94085  12494 

05915 

94085  12494 

05915 

00000 

00000 

57 

4 

59  28 

0  3? 
0  0  40 

7.06579  j  9691 
7. 16270  7918 

12. 93421 

7.  06579 

9691 

12. 93421 
12.  83730 

00000 

00000 

56 
55 

5 

11  59  20 

12.  83730 

7. 16270 

7918 

10.00000 

10.  00000 

6 

59  12 

0  48 

24188  6694 

75812 

24188 

6694 

75812 

00000 

00000 

54 

7 

59  4 

0  56 

30882  1  5800 

69118 

.30882 

5800 

69118 

00000 

00000 

53 

8 

58  56 

1  4 

36682  5115 

63318 

36682 

5115 

63318 

00000 

00000 

52 

9 
10 

58  48 
11  58  40 

1  12 

41797  4576 

58203 

41797 

4576 

58203 

00000 

00000 

51 
50 

0  1  20 

7. 46373 

4139 

12. 53627 

7. 46373 

4139 

12. 53627 

10.  00000 

10. 00000 

11 

58  32 

1  28 

50512 

3779 

49488 

50512 

3779 

49488 

00000 

00000 

49 

12 

58  24 

1  36 

54291 

3476 

45709 

54291 

3476 

45709 

00000 

00000 

48 

13 

58  16 

1  44 

57767 

3218 

42233 

57767 

3219 

42233 

00000 

00000 

47 

14 
15 

58  8 

1  52 

60985 

2997 

39015 

60986 

2996 

39014 

00000 

00000 
10. 00000 

46 
45 

11  58  0 

0  2  0 

7. 63982 

2802 

12. 36018 

7. 63982 

2803 

12.  36018 

10. 00000 

16 

57  52 

2  8 

66784 

2633 

33216 

66785 

2633 

33215 

00000 

00000 

44 

17 

57  44 

2  16 

69417 

2483 

30583 

69418 

2482 

30582 

00001 

9. 99999 

43 

18 

57  36 

2  24 

71900 

2348 

28100 

71900 

2348 

28100 

00001 

99999 

42 

19 
20 

57  28 
11  57  20 

2  32 
0  2  40 

74248 
7.  76475 

2227 
2119 

25752 
12. 23525 

74248 
7.  76476 

2228 

25752 

00001 

99999 

41 
'40 

2119 

12.  23524 

10. 00001 

9. 99999 

21 

57  12 

2  48 

78594 

2021 

21406 

78595 

2020 

21405 

00001 

99999 

39 

22 

57  4 

2  56 

80615 

1930 

19385 

80615 

1931 

19385 

00001 

99999 

38 

23 

56  56 

3  4 

82545 

1848 

17455 

82546 

1848 

17454 

00001 

99999 

37 

24 

56  48 

3  12 
0  3  20 

84393 

1773 

15607 
12. 13834 

84.394 

1773 
1704 

15606 

00001 

99999 

36 
35 

25 

11  56  40 

7.86166  1  1704 

7. 86167 

12. 13833 

10. 00001 

9. 99999 

26 

56  32 

3  28 

87870  1  1639 

12130 

87871 

1639 

12129 

00001 

99999 

34 

27 

56  24 

3  36 

89509  !  1579 

10491 

89510 

1579 

10490 

00001 

99999 

33 

28 

56  16 

3  44 

91088 

1524 

08912 

91089 

1524 

08911 

00001 

99999 

32 

29 

56  8 

3  52 

92612 

1472 

07388 

92613  1473 

07387 

00002 

99998 

31 

30 

11  56  0 

0  4  0 

7.  94084 

1424 

12. 05916 

7. 94086 

1424 

12.  05914 

10.  00002 

9. 99998 

30 

31 

55  52 

4  8 

95508 

137£i 

04492 

95510 

1379 

04490 

00002 

99998 

29 

32 

55  44 

4  16 

96887 

1336 

03113 

96889 

1336 

03111 

00002 

99998 

28 

33 

55  36 

4  24 

98223 

1297 

01777 

98225 

1297 

01775 

00002 

99998 

27 

34 

55  28 

4  32 

99520 

1259 

00480 

99522 

1259 

00478 

00002 

99998 
9. 99998 

26 
25 

35 

11  55  20 

0  4  40 

8.00779  1  1223 

11. 99221 

8. 00781 

1223 

11.99219 

10.  00002 

36 

55  12 

4  48 

02002 

-1190 

97998 

02004 

1190 

97996 

00002 

99998 

24 

37 

55  4 

4  56 

03192 

1158 

96808 

03194 

1159 

96806 

00003 

99997 

23 

38 

54  56 

5  4 

04350 

1128 

95650 

04353 

1128 

95647 

00003 

.  99997 

22 

39 

54  48 

5  12, 
0  5  20 

05478 

1100 

94522 

05481 

1100 

94519 

00003 

99997 

21 

40 

11  54  40 

8.  06578 

1072 

11. 93422 

8. 06581 

1072 

11. 93419 

10. 00003 

9. 99997 

20 

41 

54  32 

5  28 

07650 

1046 

92350 

07653 

1047 

92347 

00003 

99967 

19 

42 

54  24 

5  36 

08696 

1022 

91.304 

08700 

1022 

91300 

00003 

99997 

18 

43 

54  16 

5  44 

09718 

999 

90282 

09722 

998 

90278 

00003 

99997 

17 

44 
45 

54  8 

5  52 

10717 

976 

89283 

10720 

976 

89280 

00004 

99996 

16 

11  54  0 

0  6  0 

8. 11693 

954 

11. 88307 

8. 11696 

955 

11.  88304 

10. 00004 

9. 99996 

15 

46 

53  52 

6  8 

12647 

934 

87353 

12651 

934 

87349 

00004 

99996 

14 

47 

53  44 

6  16 

13581 

914 

86419 

13585 

915 

86415 

00004 

99996 

13 

48 

53  36 

6  24 

14495 

896 

85505 

14500 

895 

85500 

00004 

99996 

12 

49 

53  28 

6  32 

15391 

877 

84609 

15395 

878 

84605 

00004 

99996 

11 
10 

50 

11  53  20 

0  6  40 

8. 16268 

860 

11. 83732 

8. 16273 

860 

11.  83727 

10. 00005 

9. 99995 

51 

53  12 

6  48 

17128 

843 

82872 

17133 

843 

82867 

00005 

99995 

9 

52 

53  4 

6  56 

17971 

827 

82029 

17976 

828 

82024 

00005 

99995 

8 

53 

52  56 

7  4 

18798 

812 

81202 

18804 

812 

81196 

00005 

99995 

/ 

54 
55 

52  48 

7  12 

19610 

797 

80390 

19616 

797 

80384 

00005 

99995 

6 

11  52  40 

0  7  20 

8. 20407 

782 

11. 79593 

8. 20413 

782 

11. 79587 

10. 00006 

9. 99994 

5 

56 

52  32 

7  28 

21189 

769 

78811 

21195 

769 

78805 

00006 

99994 

4 

57 

52  24 

7  36 

21958 

755 

78042 

21964 

756 

78036 

00006 

99994 

3 

58 

52  16 

7  44 

22713 

743 

77287 

22720 

742 

77280 

00006 

99994 

2 

59 

52  8 

7  52 

23456 

730 

76544 

23462 

730 

76538 

00006 

99994 

1 

60 
M. 

52  0 

8  0 

24186 

.  717 

75814 

24192 

718 

75808 

00007 

99993 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Dlff.l'. 

Secant. 

Cotangent.  Diflf.l'. 

Tangent. 

Cosecant. 

Sine. 

M. 

90° 

89° 

- 

TABLE  44. 

[Page  609 

1° 

l,og.  Sines,  Tangents,  and  Secants 

178° 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Dia.  1'. 

Cosecant. 

Tangent. 

Diff.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

11  52  0 

0  8  0 

8.24186 

717 

11.  75814 

8. 24192 

718 

11.  75808 

10.  00007 

9. 99993 

60 

1 

51  52 

8  8 

24903 

706 

75097 

24910 

706 

75090 

00007 

99993 

59 

2 

51  44 

8  16 

25609 

695 

74391 

25616 

696 

74384 

00007 

99993 

58 

3 

51  36 

8  24 

26304 

684 

73696 

26312 

684 

73688 

00007 

99993 

57 

4 
5 

51  28 

8  32 

26988 

673 

73012 

26996 

673 

73004 

00008 
10. 00008 

99992 

56 
55 

11  51  20 

0  8  40 

8. 27661 

663 

11. 72339 

8. 27669 

663 

11. 72331 

9. 99992 

6 

51  12 

8  48 

28324 

653 

71676 

28332 

654 

71668 

00008 

99992 

54 

7 

51  4 

8  56 

28977 

644 

71023 

28986 

643 

71014 

00008 

99992 

53 

8 

50  56 

9  4 

29621 

634 

70379 

29629 

634 

70371 

00008 

99992 

52 

9 
10 

50  48 

9  12 

30255 

624 

69745 

30263 

625 

69737 

00009 

99991 

51 

11  50  40 

0  9  20 

8. 30879 

616 

11. 69121 

8. 30888 

617 

11.69112 

10. 00009 

9. 99991 

50 

11 

50  32 

9  28 

31495 

608 

68505 

31505 

607 

68495 

00009 

99991 

49 

12 

50  24 

9  36 

32103 

599 

67897 

32112 

599 

67888 

00010 

99990 

48 

13 

50  16 

9  44 

32702 

590 

67298 

32711 

591 

67289 

00010 

99990 

47 

14 

50  8 

9  52 

33292 

583 

66708 

33302 

584 

66698 

00010 

99990 

46 
45 

15 

11  50  0 

0  10  0 

8. 33875 

575 

11.  66125 

8. 33886 

575 

11.66114 

10.  00010 

9. 99990 

16 

49  52 

10  8 

34450 

568 

65550 

34461 

568 

65539 

00011 

99989 

44 

17 

49  44 

10  16 

35018 

560 

64982 

35029 

561 

64971 

00011 

99989 

43 

18 

49  36 

10  24 

35578 

553 

64422 

35590 

553 

64410 

00011 

99989 

42 

19 
20 

49  28 
11  49  20' 

10  32 
0  10  40 

36131 

547 

63869 

36143 

546 

63857 

00011 

99989 

41 

8. 36678 

539 

11. 63322 

8.  36689 

540 

11. 63311 

10. 00012 

9.  99988 

40 

21 

49  12 

10  48 

37217 

533 

62783 

37229 

533 

62771 

00012 

99988 

39 

22 

49  4 

10  56 

37750 

526 

62250 

37762 

527 

62238 

00012 

99988 

38 

23 

48  56 

11  4 

38276 

520 

61724 

38289 

520 

61711 

00013 

99987 

37 

24 

48  48 

11  12 

38796 

514 

61204 

38809 

514 

61191 

00013 

99987 

36 

25 

11  48  40 

0  11  20 

8. 39310 

508 

11. 60690 

8. 39323 

509 

11. 60677 

10.00013 

9. 99987 

35 

26 

48  32 

11  28 

39818 

502 

60182 

39832 

502 

60168 

00014 

99986 

34 

27 

48  24 

11  36 

40320 

496 

59680 

40334 

496 

59666 

00014 

99986 

33 

28 

48  16 

11  44 

40816 

491 

59184 

40830 

491 

59170 

00014 

99986 

32 

29 

48  8 

11  52 

41307 

485 

58693 

41321 

486 

58679 

00015 

99985 

31 

30 

11  48  0 

0  12  0 

8. 41792 

480 

11. 58208 

8. 41807 

480 

11. 58193 

10. 00015 

9. 99985 

30 

31 

47  52 

12  8 

42272 

474 

57728 

42287 

475 

57713 

00015 

99985 

29 

32 

47  44 

12  16 

42746 

470 

57254 

42762 

470 

57238 

00016 

99984 

28 

33 

47  36 

12  24 

4.3216 

464 

56784 

43232 

464 

567()8 

00016 

99984 

27 

34 
35 

47  28 

12  32 

43680 

459 

56320 

43696 

460 

56304 

00016 

99984 

26 

11  47  20 

0  12  40 

8.44139 

455 

11. 55861 

8.  44156 

455 

11. 55844 

10.  00017 

9. 99983 

25 

36 

47  12 

12  48 

44594 

450 

55406 

44611 

450 

55389 

00017 

99983 

24 

37 

47  4 

12  56 

45044 

445 

54956 

45061 

446 

54939 

00017 

99983 

23 

38 

46  56 

13  4 

45489 

441 

54511 

45507 

.  441 

54493 

00018 

99982 

22 

39 
40 

46  48 

13  12 

45930 

436 

54070 

45948 

437 

54052 

00018 
To.  00018 

99982 
9. 99982 

21 
20 

11  46  40 

0  13  20 

8. 46366 

433 

11, 53634 

8. 46385 

432 

11. 53615 

41 

46  32 

13  28 

46799 

427 

5.3201 

46817 

428 

53183 

00019 

99981 

19 

42 

46  24 

13  36 

47226 

424 

52774 

47245 

424 

52755 

00019 

99981 

18 

43 

46  16 

13  44 

47650 

419 

52350 

47669 

420 

52.331 

00019 

99981 

17 

44 

46  8 

13  52 

48069 

416 

51931 

48089 

416 

51911 

00020 

99980 

16 

15 

45 

11  46  0 

0  14  0 

8. 48485 

411 

11.51515 

8.  48505 

412 

11. 51495 

10. 00020 

9. 99980 

46 

45  52 

14  8 

48896 

408 

51104 

48917 

408 

51083 

oa)2i 

99979 

14 

47 

45  44 

14  16 

49304 

404 

50696 

49325 

404 

50675 

00021 

99979 

13 

48 

45  36 

14  24 

49708 

400 

50292 

49729 

401 

50271 

00021 

99979 

12 

49 

45  28 

14  32 

50108 

396 

49892 

50130 

397 

49870 

00022 

99978 

11 
10 

50 

11  45  20 

0  14  40 

8. 50504 

393 

11. 49496 

8. 50527 

393 

11. 49473 

10. 00022 

9.  99978 

51 

45  12 

14  48 

50897 

390 

49103 

50920 

390 

49080 

00023 

99977 

9 

52 

45  4 

14  56 

51287 

386 

48713 

51310 

386 

48690 

00023 

99977 

8 

/53 

44  56 

15  4 

51673 

382 

48327 

51696 

383 

48304 

00023 

99977 

/ 

54 

44  48 

15  12 

52055 

379 

47945 

52079 

380 

47921 

00024 

99976 

6 

55 

11  44  40 

0  15  20 

8. 52434 

376 

11. 47566 

8. 52459 

376 

11. 47541 

10.  00024 

9. 99976 

5 

56 

44  32 

15  28 

52810 

373 

47190 

52835 

373 

47165 

00025 

99975 

4 

57 

44  24 

15  36 

53183 

369 

46817 

53208 

370 

46792 

00025 

99975 

3 

58 

44  16 

15  44 

53552 

367 

46448 

53578 

367 

46422 

00026 

99974 

2 

59 

44  8 

15  52 

53919 

363 

46081 

53945 

363 

46055 

0002(1 

99974 

1 

60 

44  0 

16  0 

54282 

360 

45718 

54308 

361 

45692 

00026 

99974 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.  1'. 

Secant. 

Cotangent. 

Diff.  1'. 

Tangent. 

Cosecant. 

Sine. 

M. 

91° 

88°  1 

22489—03- 


-39 


Page  610] 

TABLE  44. 

2° 

Log.  Sines,  Tangents,  and  Secants 

177° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff.l'. 

Cosecant. 

Tangent. 

Diff.  1'. 

Cotangent. 

Secant. 

Co.slne. 

M. 

0 

11  44  0 

0  16  0 

8. 54282 

360 

11. 45718 

8. 54308 

361 

11.45692 

10.  00026 

9. 99974 

60 

1 

43  52 

16  8 

54642 

357 

45358 

54669 

358 

45331 

00027 

99973 

59 

2 

43  44 

16  16 

54999 

355 

45001 

55027 

355 

44973 

00027 

99973 

58 

3 

43  36 

16  24 

55354 

351 

44646 

55382 

352 

44618 

00028 

99972 

57 

4 

5 

43  28 

16  32 

55705 

349 

44295 

55734 

349 

44266 

00028 

99972 

56 

11  43  20 

0  16  40 

8. 56054 

346 

11. 43946 

8. 56083 

346 

11.43917 

10.  00029 

9. 99971 

55 

6 

43  12 

16  48 

56400 

343 

43600 

5t>429 

344 

.  43571 

00029 

99971 

54 

1 

43  4 

16  56 

56743 

341 

43257 

56773 

341 

43227 

00030 

99970 

53 

8 

42  56 

17  4 

57084 

337 

42916 

57114 

338 

42886 

00030 

99970 

52 

9 
10 

42  48 

17  12 

57421 

336 

42579 

57452 

336 

42548 

00031 

99969 

51 

11  42  40 

0  17  20 

8. 57757 

332 

11. 42243 

8. 57788 

333 

11.42212 

10. 00031 

9. 99969 

50 

11 

42  32 

17  28 

58089 

330 

41911 

58121 

330 

41879 

00032 

99968 

49 

12 

42  24 

17  36 

58419 

328 

41581 

58451 

328 

41549 

00032 

99968 

48 

13 

42  16 

17  44 

58747 

325 

41253 

58779 

326 

41221 

00033 

99967 

47 

14 

42  8 

17  52 

59072 

323 

40928 

59105 

323 

40895 

00033 

99967 

46 
45 

15 

11  42  0 

0  18  0 

8. 59395 

320 

11. 40605 

8. 59428 

321 

11. 40572 

10.  00033 

9. 99967 

16 

41  52 

18  8 

59715 

318 

40285 

59749 

319 

40251 

00034 

99966 

44 

17 

41  44 

18  16 

60033 

316 

39967 

60068 

316 

39932 

00034 

99966 

43 

18 

41  36 

18  24 

60349 

313 

39651 

60384 

314 

39616 

00035 

99965 

42 

19 
20 

41  28 

18  32 

60662 

311 

39338 

60698 

311 

39302 

00036 

99964 

41 
40 

11  41  20 

0  18  40 

8. 60973 

309 

11. 39027 

8. 61009 

310 

11.  38991 

10.  00036 

9. 99964 

21 

41  12 

18  48 

61282 

307 

38718 

61319 

307 

38681 

00037 

99963 

39 

22 

41  4 

18  56 

61589 

305 

38411 

61626 

305 

38374 

00037 

99963 

38 

23 

40  56 

19  4 

61894 

302 

38106 

61931 

303 

38069 

00038 

99962 

37 

24 
25 

40  48 

19  12 

62196 

301 

37804 

62234 

301 

37766 

00038 

99962 

36 
35~ 

11  40  40 

0  19  20 

8. 62497 

298 

11. 37503 

8.  62535 

299 

11. 37465 

10. 00039 

9. 99961 

26 

40  32 

19  28 

62795 

296 

37205 

62834 

297 

37166 

00039 

99961 

34 

27 

40  24 

19  36 

63091 

294 

36909 

63131 

295 

36869 

00040 

99960 

33 

28 

40  16 

19  44 

63385 

293 

36615 

63426 

292 

36574 

00040 

99960 

32 

29 
30 

40  8 

19  52 

63678 

290 

36322 

63718 

291 

36282 

00041 

99959 

31 

11  40  0 

0  20  0 

8. 63968 

288 

11. 36032 

8. 64009 

289 

11. 35991 

10. 00041 

9. 99959 

30 

31 

39  52 

20  8 

64256 

287 

35744 

64298 

287 

35702 

00042 

99958 

29 

32 

39  44 

20  16 

64543 

284 

35457 

64585 

285 

35415 

00042 

99958 

28 

33 

39  36 

20  24 

64827 

283 

35173 

64870 

284 

35130 

00043 

99957 

27 

34 

39  28 

20  32 

65110 

281 

34890 

65154 

281 

34846 

00044 

99956 

26 

35 

11  39  20 

0  20  40 

8. 65391 

279 

11. 34609 

8.  65435 

280 

11. 34565 

10. 00044 

9. 99956 

25 

36 

3i^  12 

20  48 

65670 

277 

34330 

65715 

278 

34285 

00045 

99955 

24 

37 

39  4 

20  56 

65947 

276 

34053 

65993 

276 

34007 

00045 

99955 

23 

38 

38  56 

21  4 

66223 

274 

33777 

66269 

274 

33731 

00046 

99954 

22 

39 

38  48 

21  12 

66497 

272 

33503 

66543 

273 

33457 

00046 

99954 
9. 99953 

21 
20 

40 

11  38  40 

0  21  20 

8. 66769 

270 

11. 33231 

8. 66816 

271 

11. 33184 

10.  00047 

41 

38  32 

21  28 

67039 

269 

32961 

67087 

269 

32913 

00048 

99952 

19 

42 

38  24 

21  36 

67308 

267 

32692 

67356 

268 

32644 

00048 

99952 

18 

43 

38  16 

21  44 

67575 

266 

32425 

67624 

266 

32376 

00049 

99951 

17 

44 

38  8 

21  52 

67841 

263 

32159 

67890 

264 

32110 

00049 

99951 

16 

45 

11  38  0 

0  22  0 

8.  68104 

263 

11. 31896 

8. 68154 

263 

11.  31846 

10. 00050 

9. 99950 

15 

46 

37  52 

22  8 

68367 

260 

31633 

68417 

261 

31583 

00051 

99949 

14 

47 

37  44 

22  16 

68627 

259 

31373 

68678 

260 

31322 

00051 

99949 

13 

48 

37  36 

22  24 

68886 

258 

31114 

68938 

258 

31062 

00052 

99948 

12 

49 

37  28 

22  32 

69144 

256 

30856 

69196 

257 

30804 

00052 

99948 
9. 99947 

11 
10 

50 

11  37  20 

0  22  40 

8. 69400 

254 

11. 30600 

8. 69453 

255 

11. 30547 

10. 00053 

51 

37  12 

22  48 

69654 

253 

30.346 

69708 

254 

30292 

00054 

99946 

9 

52 

37  4 

22  56 

69907 

252 

30093 

69962 

252 

30038 

00054 

99946 

8 

53 

36  56 

23  4 

70159 

250 

29841 

70214 

251 

29786 

00055 

99945 

7 

54 

36  48 

23  12 
0  23  20 

70409 

249 

29591 

70465 

249 

29535 

00056 

99944 

6 

55 

11  36  40 

8. 70658 

247 

11. 29342 

8.  70714 

248 

11. 29286 

10.00056 

9. 99944 

5 

56 

36  32 

23  28 

70905 

246 

29095 

70962 

246 

29038 

00057 

99943 

4 

57 

36  24 

23  36 

71151 

244 

28849 

71208 

245 

28792 

00058 

99942 

3 

58 

36  16 

23  44 

71395 

243 

28605 

71453 

244 

28547 

00058 

99942 

2 

59 

36  8 

23  52 

71638 

242 

28362 

71697 

243 

28303 

00059 

99941 

1 

60 

36  0 

24  0 

71880 

240 

28120 

71940 

241 

28060 

00060 

99940 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.  1'. 

Secant. 

Cotangent. 

Diff.l'. 

Tangent. 

Cosecant. 

Sine. 

M. 

92° 

87° 

TABLE  44. 

[Page  611 

3° 

Log.  Sines,  Tangents,  and  Secants 

176° 

M. 

Hour  *.  M. 

Hour  P.  M. 

Sine. 

Difl.  1'. 

Cosecant. 

Tangent. 

Diff.  1'. 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

11  36  0 

0  24  0 

8. 71880 

240 

11. 28120 

8. 71940 

241 

11. 28060 

10. 00060 

9. 99940 

60 

1 

35  52 

24  8 

72120 

239 

27880 

72181 

239 

27819 

00060 

99940 

59 

?. 

35  44 

24  16 

72359 

238 

27641 

72420 

239 

27580 

00061 

99939 

58 

8 

35  36 

24  24 

72597 

237 

27403 

72659 

237 

27341 

00062 

99938 

0/ 

4 

35  28 

24  32 

72884 

235 

27166 

72896 

236 

27104 

00062 

99938 

56 
55 

5 

11  35  20 

0  24  40 

8. 73069 

234 

11. 26981 

8.  73132 

234 

11.  26868 

10.  00068 

9.  99937 

6 

35  12 

24  48 

73303 

232 

26697 

73366 

234 

26634 

000«)4 

99986 

54 

7 

35  4 

24  56 

73535 

232 

26465 

73600 

232 

26400 

000(>1 

99936 

53 

8 

34  56 

25  4 

73767 

230 

26233 

73832 

231 

26168 

00065 

99935 

52 

9 

34  48 

25  12 

73997 

229 

26003 

74063 

229 

25937 
11. 25708 

00066 
10.  00066 

99934 

51 
50 

10 

11  34  40 

0  25  20 

8. 74226 

228 

11. 25774 

8.  74292 

229 

9. 99934 

11 

34  32 

25  28 

74454 

226 

25546 

74521 

227 

25479 

00067 

99933 

49 

12 

34  24 

25  36 

74680 

226 

25320 

74748 

226 

25252 

00068 

99982 

48 

13 

34  16 

25  44 

74906 

224 

25094 

74974 

225 

25026 

00068 

99932 

47 

14 

34  8 

25  52 

75130 

223 

24870 

75199 

224 

24801 

00069 

99931 
'9.  99930 

46 
45 

15 

11  34  0 

0  26  0 

8. 75353 

222 

11.24647 

8.  75423 

222 

11.  24577 ! 10. 00070 

18 

33  52 

26  8 

75575 

220 

24425 

75645 

222 

24355 

00071 

99929 

44 

17 

33  44 

26  16 

75795 

220 

24205 

75867 

220 

24183 

00071 

99929 

43 

18 

33  36 

26  24 

76015 

219 

23985 

76087 

219 

23913 

00072 

99928 

42 

19 

33  28 

26  82 

76234 

217 

23766 

76306 

219 

23694 

00073 

99927 

41 
40 

?.o 

11  33  20 

0  26  40 

8. 76451 

216 

11. 23549 

8.  76525 

217 

11.  23475 

10. 00074 

9. 99926 

21 

33  12 

26  48 

76667 

216 

23333 

76742 

216 

23258 

00074 

99926 

39 

22 

33  4 

26  56 

76883 

211 

23117 

76958 

215 

23042 

00075 

99925 

38 

28 

82  56 

27  4 

77097 

213 

22903 

77173 

214 

22827 

00076 

99924 

37 

24 

32  48 

27  12 

77310 

212 

22690 

77387 

213 

22613 

00077 

99923 

36 
35 

2o 

11  82  40 

0  27  20 

8. 77522 

211 

11. 22478 

8.  77600 

211 

11. 22406 

10. 00077 

9. 99923 

26 

32  32 

27  28 

77733 

210 

22267 

77811 

211 

22189 

00078 

99922 

34 

27 

32  24 

27  36 

77943 

209 

22057 

78022 

210 

21978 

00079 

99921 

33 

28 

32  16 

27  44 

78152 

208 

21848 

78232 

209 

21768 

00080 

99920 

32 

29 

32  8 

27  52 

78360 

208 

21640 

78441 

208 

21559 

00080 

99920 

31 
30 

80 

11  32  0 

0  28  0 

8.  78568 

206 

11.  21432 

8. 78649 

206 

11.21351 1 10. 00081 

9. 99919 

81 

31  52 

28  8 

78774 

205 

21226 

78855 

206 

21145 

00082 

99918 

29 

82 

31  44 

28  16 

78979 

204 

21021 

79061 

205 

20989 

00088 

99917 

28 

88 

31  36 

28  24 

79188 

203 

20817 

79266 

204 

20784 

00083 

99917 

27 

84 

31  28 

28  82 

79386 

202 

20614 

79470 

203 

20580  i   00084 

99916 
9.  99915 

26 
25 

85 

11  31  20 

0  28  40 

8.  79588 

201 

11.20412 

8. 79673 

202 

11.20827110.00085 

8fi 

31  12 

28  48 

79789 

201 

20211 

79875 

201 

20125;   00086 

99914 

24 

87 

31  4 

28  56 

79990 

199 

20010 

80076 

201 

19924 

00087 

99918 

23 

88 

30  56 

29  4 

80189 

199 

19811 

80277 

199 

19728 

00087 

99913 

22 

89 

30  48 

29  12 

80388 

197 

19612 

80476 

198 

19524 

00088 

99912 

21 

40 

11  30  40 

0  2v^  20 

8. 80585 

197 

11.19415 

8. 80674 

198 

11.19326  10.00089 

9.99911 

20 

41 

30  32 

29  28 

80782 

196 

19218 

80872 

196 

19128 

00090 

99910 

19 

42 

30  24 

29  36 

80978 

195 

19022 

81068 

196 

18982 

00091 

99909 

18 

48 

30  16 

29  44 

81173 

194 

18827 

81264 

195 

18736 

00091 

9<>909 

17 

44 

30  8 

29  52 
0  30  0 

81367 
8.81560' 

193 

18633 

81459 

194 

18541 

00092 

99908 

16 

45 

11  30  0 

192 

11. 18440 

8.  816.53 

193 

11.18847  10.00098 

9. 99907 

15 

46 

29  52 

30  8 

81752 

192 

18248 

81846 

192 

18154 

00094 

99906 

14 

47 

29  44 

30  m 

81944 

190 

18056 

82038 

192 

17962 

00095 

99905 

18 

48 

29  36 

30  24 

82134 

190 

1 7866 

82280 

190 

17770 

00096 

99904 

12 

49 
50 

29  28 
11  29  20 

80  82 
0  80  40 

82824 
8.82513 

189 

17676 

82420 

190 

17580 

00096 

99904 

11 

188 

11.17487 

8.  82610 

189 

11. 173V.0 

10.  00097 

9. 99903 

10 

51 

29  12 

-  80  48 

82701 

187 

17299 

82799 

188 

17201 

00098 

99902 

9 

52 

29  4 

30  56 

82888 

187 

17112 

82987 

188 

17013 

00099 

99901 

8 

58 

28  56 

31  4 

83075 

186 

16925 

83175 

186 

16825 

00100 

99900 

/ 

54 
55 

28  48 
11  28  40 

31  12 
0  31  20 

83261 

185 

16739 

88361 

186 

16689 

00101 

99899 

6 
5 

8. 88446 

184 

11.16554 

8. 83547 

185 

11.16458 

10.00102 

9.  99898 

56 

28  32 

81  28 

83680 

188 

16370 

88732 

184 

16268 

00102 

99898 

4 

57 

28  24 

31  m 

83813 

183 

16187 

83916 

184 

16084 

00108 

99897 

3 

58 

28  16 

31  44 

88996 

181 

16004 

84100 

182 

15900 

00104 

99896 

2 

59 

28  8 

31  52 

84177 

181 

15828 

84282 

182 

15718 

00105 

99895 

1 

60 
M. 

28  0 

32  0 

S4:ioS 

181 

15642 

84464 

182 

15536 

00106 

99894 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.  1'. 

Secant. 

Cotangent. 

Diff.  1'. 

Tangent.  Cosecant. 

Sine. 

M. 

93° 

86°  1 

Page  612] 

TABLE  44. 

4° 

Log.  Sines,  Tangents,  and  Secants 

175° 

M. 

Hour  A.  M. 

Hour  p.  K. 

Sine. 

Diff.l'. 

Cosecant. 

Tangent. 

Diff.l'. 

1 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

11  28  0 

0  32  0 

8. 84358 

181 

11. 15642 

8.84464 

182 

11. 15536 

10.  00106 

9. 99894 

60 

1 

27  52 

32  8 

84539 

179 

15461 

84646 

180 

15354 

00107 

99893 

59 

2 

27  44 

32  16 

84718 

179 

15282 

84826 

180 

15174 

00108 

99892 

58 

3 

27  36 

32  24 

84897 

178 

15103 

85006 

179 

14994 

00109 

99891 

57 

4 

27  28 

32  3f 

85075 

177 

14925 

85185 

.  178 

14815 

00109 

99891 

56 
55 

5 

11  27  20 

0  32  40 

8. 85252 

177 

11. 14748 

8. 85363 

177 

11. 14637 

10.  00110 

9. 99890 

6 

27  12 

32  48 

85429 

176 

14571 

85540 

177 

14460 

00111 

99889 

54 

7 

27  4 

32  56 

85605 

175 

14395 

8.5717 

176 

14283 

00112 

99888 

53 

8 

26  56 

33  4 

85780 

175 

14220 

85893 

176 

14107 

00113 

99887 

52 

9 
10 

26  48 
11  26  40 

33  12 

85955 

173 

14045 

86069 

174 

13931 

00114 

99886 

51 
50 

0  33  20 

8. 86128 

173 

11. 13872 

8. 86243 

174 

11. 1.3757 

10. 00115 

9. 99885 

11 

26  32 

33  28 

86301 

173 

13699 

86417 

174 

13583 

00116 

99884 

49 

12 

26  24 

33  36 

86474 

171 

13526 

86591 

172 

13409 

00117 

99883 

48 

13 

26  16 

33  44 

86645 

171 

13355 

86763 

172 

13237 

00118 

99882 

47 

14 

26  8 

33  52 

86816 

171 

13184 

86935 

171 

13065 

00119 

99881 

46 

45 

15 

11  26  0 

0  34  0 

8. 86987 

169 

11. 13013 

8. 87106 

171 

11. 12894 

10. 00120 

9. 99880 

16 

25  52 

34  8 

87156 

169 

12844 

87277 

170 

12723 

00121 

99879 

44 

17 

25  44 

34  16 

87325 

169 

12675 

87447 

169 

12553 

00121 

99879 

43 

18 

25  36 

34  24 

87494 

167 

12506 

87616 

169 

12384 

00122 

99878 

42 

19 
20 

25  28 
11  25  20 

34  32 

87661 

168 

12339 

87785 

168 

12215 

00123 

99877 

41 
40 

0  34  40 

8. 87829 

166 

11.12171 

8. 87953 

167 

11. 12047 

10. 00124 

9. 99876 

21 

25  12 

34  48 

87995 

166 

12005 

88120 

167 

11880 

00125 

99875 

39 

22 

25  4 

34  56 

88161 

165 

11839 

88287 

166 

11713 

00126 

99874 

38 

23 

24  56 

35  4 

88326 

164 

11674 

88453 

165 

11547 

00127 

99873 

37 

24 

24  48 

35  12 

88490 

164 

11510 

88618 

165 

11382 

00128 

99872 

36 
35 

25 

11  24  40 

0  35  20 

8. 88654 

163 

11. 11346 

8. 88783 

165 

11. 11217 

10.  00129 

9. 99871 

26 

24  32 

35  28 

88817 

163 

11183 

88948 

163 

11052 

00130 

99870 

34 

27 

24  24 

35  36 

88980 

162 

11020 

89111 

163 

10889 

00131 

99869 

33 

28 

24  16 

35  44 

89142 

162 

•  10858 

89274 

163 

10726 

00132 

99868 

32 

29 

24  8 

35  52 

89304 

160 

10696 

89437 

161 

10563 

00133 

99867 

31 

30 

11  24  0 

0  36  0 

8. 89464 

161 

11. 10536 

8. 89598 

162 

11. 10402 

10. 00i;34 

9. 99866 

30 

31 

23  52 

36  8 

89625 

159 

10375 

89760 

160 

10240 

00135 

99865 

29 

32 

23  44 

36  16 

89784 

159 

10216 

89920 

160 

10080 

00136 

99864 

28 

33 

23  36 

36  24 

89943 

159 

10057 

90080 

160 

09920 

00137 

99863 

27 

34 
35 

23  28 

36  32 

90102 

158 

09898 

90240 

159 

09760 

001.38 

99862 

26 

11  23  20 

0  36  40 

8. 90260 

157 

11. 09740 

8. 90399 

158 

11. 09601 

10.  00139 

9. 99861 

25 

36 

23  12 

36  48 

90417 

157 

09583 

90557 

158 

09443 

00140 

99860 

24 

37 

23  4 

36  56 

90574 

156 

09426 

90715 

157 

09285 

00141 

99859 

23 

38 

22  56 

37  4 

90730 

155 

09270 

90872 

157 

09128 

00142 

99858 

22 

39 

22  48 

37  12 

90885 

155 

09115 

91029 

156 

08971 

00143 

99857 

21 

40 

11  22  40 

0  37  20 

8. 91040 

155 

11. 08960 

8.  91185 

155 

11. 08815 

10. 00144 

9.  99856 

20 

41 

22  32 

37  28 

91195 

154 

08805 

91340 

155 

08660 

00145 

99855 

19 

42 

22  24 

37  36 

91349 

153 

08651 

91495 

155 

08505 

00146 

99854 

18 

43 

22  16 

37  44 

91502 

153 

08498 

91650 

153 

083.50 

00147 

99853 

17 

44 

22  8 

37  52 

91655 

152 

08345 

91803 

154 

08197 

00148 

99852 

16 

15 

45 

11  22  0 

0  38  0 

8.91807 

152 

11.08193 

8. 91957 

153 

11.08043 

10. 00149 

9. 99851 

46 

21  52 

38  8 

91959 

151 

08041 

92110 

152 

07890 

00150 

99850 

14 

47 

21  44 

38  16 

92110 

151 

07890 

92262 

152 

07738 

00152 

99848 

13 

48 

21  36 

38  24 

92261 

150 

07739 

92414 

151 

07586 

00153 

99847 

12 

49 

21  28 

38  32 

92411 

150 

07589 

92565 

151 

07435 

00154 

99846 

11 

50 

11  21  20 

0  38  40 

8. 92561 

149 

11.074.39 

8.  92716 

150 

11. 07284 

10.  001.55 

9. 99845 

JO 

51 

21  12 

38  48 

92710 

149 

07290 

92866 

150 

07134 

00156 

99844 

9 

52 

21  4 

38  56 

92859 

148 

07141 

93016 

149 

06984 

00157 

99843 

8 

53 

20  56 

39  4 

93007 

147 

06993 

93165 

148 

0683.5 

00158 

99842 

7 

54 

20  48 

39  12 

93154 

147 

06846 

93313 

149 

06687 

00159 

99841 

6 

55 

11  20  40 

0  39  20 

8. 93301 

147 

11. 06699 

8. 93462 

147 

11.06538 

10.  00160 

9. 99840 

5 

56 

20  32 

39  28 

93448 

146 

06552 

93609 

147 

06.391 

00161 

99839 

4 

57 

20  24 

39  36 

93594 

146 

06406 

93756 

147 

06244 

00162 

99838 

3 

58 

20  16 

39  44 

93740 

145 

06260 

93903 

146 

06097 

00163 

99837 

2 

59 

20  8 

39  52 

93885 

145 

06115 

94049 

146 

05951 

00164 

998.36 

1 

60 

20  0 

40  0 

94030 

144 

05970 

94195 

145 

05805 

00166 

99834 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff.l'. 

Secant. 

Cotangent. 

Diff.l'. 

Tangent. 

Cosecant. 

Sine. 

M. 

94° 

85°  1 

TABLE  44. 

[Page  613 

Log. 

Sines,  Tangents,  and  Secants. 

6° 

A 

A         B 

B 

C 

C    174° 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

11  20  00 

0  40  00 

8. 94030 

0 

11.05970 

8.  94195 

0 

11.  05805 

10. 00166 

0 

9. 99834 

60 

1 

19  52 

40  08 

94174 

2 

05826 

94340 

2 

05660 

00167 

0    99833  1 

59 

">, 

19  44 

40  16 

94317 

4 

05683 

94485 

4 

05515 

00168 

0 

99832 

58 

w 

19  36 

40  24 

94461 

7 

05539 

94630 

7 

05370 

00169 

0 

99831 

57 

4 
5 

19  28 
11  19  20 

40  32 

94603 

9 

05397 

94773 

9 

05227 

00170 

0 

93830 

56 

0  40  40 

8. 94746 

11 

11.  05254 

8. 94917 

11 

11. 05088 

10.00171 

0 

9. 99829 

55 

(\ 

19  12 

40  48 

94887 

13 

05113 

95060 

13 

04940 

00172 

0 

99828 

54 

7 

19  04 

40  56 

95029 

15 

04971 

95202 

15 

04798 

00173 

0 

99827 

53 

8 

18  56 

41  04 

95170 

18 

04830 

95344 

18 

04656 

00175 

0 

99825 

52 

9 

18  48 

41  12 

95310 

20 

04690 

95486 
8.95627 

20 
22 

04514 
11.04873 

00176 

0   99824 

51 
50" 

10 

11  18  40 

0  41  20 

8. 95450 

22 

11.04550 

10.00177 

0  i 9.  99823 

n 

18  82 

41  28 

95589 

24 

04411 

95767 

24 

04233 

00178 

0   99822 

49 

1^ 

18  24 

41  36 

95728 

26 

04272 

95908 

27 

04092 

00179 

0   99821 

48 

ia 

18  16 

41  44 

95867 

29 

041.33 

96047 

29 

03953 

00180 

0    99820 

47 

14 
15 

18  08 

41  52 

96005 

31 

03995 

96187 

31 

03813 

00181 
10.00183 

0   99819 
0  19.99817 

46 

45 

11  18  00 

0  42  00 

8.  96143 

33 

11.03857 

8. 96325 

83 

11.08675 

18 

17  52 

42  08 

96280 

35 

03720 

96464 

35 

08536 

00184 

0 

99816 

44 

17 

17  44 

42  16 

96417 

37 

03583 

96602 

38 

03398 

00185 

0 

99815 

48 

IS 

17  36 

42  24 

96553 

89 

03447 

96739 

40 

03261 

00186 

0 

99814 

42 

19 

17  28 

42  82 

96689 

42 
44 

08311 
11.03175 

96877 

42 
44 

03123 

00187 

0 

99813 

41 

90 

11  17  20 

0  42  40 

8. 96825 

8.  97013 

11.02987 

10. 00188 

0 

9. 99812 

40 

?A 

17  12 

42  48 

96960 

46 

03040 

97150 

46 

02850 

00190 

0 

99810 

39 

22 

17  04 

42  56 

97095 

48 

02905 

97285 

49 

02715 

00191 

0 

99809 

38 

28 

16  56 

43  04 

97229 

50 

02771 

97421 

51 

02579 

00192 

0 

99808 

37 

24 

16  48 

43  12 

97368 

53 
55 

02637 

97556 

53 

02444 

00193 

0 

99807 

36 
35 

2ft 

11  16  40 

0  43  20 

8. 97496 

11.02504 

8. 97691 

55 

11.  02309 

10.00194 

1  9.99806 

26 

16  32 

43  28 

97629 

57 

02371 

97825 

58 

02175 

00196 

1   99804 

34 

27 

16  24 

43  36 

97762 

59 

02238 

97959 

60 

02041 

00197 

1   99803 

88 

28 

16  16 

43  44 

97894 

61 

02106 

98092 

62 

01908 

00198 

99802 

32 

29 
80 

16  08 

43  52 

98026 

64 

01974 
11. 01843 

98225 

&4 

01775 

00199 

99801 

31 
30 

11  16  00 

0  44  00 

8. 98157 

66 

8.  98358 

66 

11.01642 

10. 00200 

9. 99800 

81 

15  52 

44  08 

98288 

68 

01712 

98490 

69 

01510 

00202 

99798 

29 

82 

15  44 

44  16 

98419 

70 

01581 

98622 

71 

01378 

00203 

99797 

28 

88 

15  36 

44  24 

98549 

72 

01451 

98753 

73 

01247 

00204 

99796 

27 

34 

15  28 

44  82 

98679 

75 

01321 

98884 

75 

01116 
11.00985 

00205 

99795 

26 
25 

85 

11  15  20 

0  44  40 

8. 98808 

77 

11.01192 

8. 99015 

77 

10. 00207 

9. 99793 

86 

15  12 

44  48 

98937 

79 

01068 

99145 

80 

00855 

00208 

99792 

24 

87 

15  04 

44  56 

99066 

81 

00934 

99275 

82 

00725 

00209 

99791 

23 

88 

14  56 

45  04 

99194 

83 

00806 

99405 

84 

00595 

00210 

99790 

22 

39 

14  48 

45  12 

99322 

86 

00678 

99534 

86 
89 

00466 

00212 

99788 

21 
20 

40 

11  14  40 

0  45  20 

8. 99450 

88 

11.00550 

8. 99662 

11.00888 

10.  00213 

9. 99787 

41 

14  32 

45  28 

99577 

90 

00423 

99791 

91 

00209 

00214 

99786 

19 

42 

14  24 

45  36 

99704 

92 

00296 

99919 

93 

00081 

00215 

99785 

18 

48 

14  16 

45  44 

99880 

94 

00170 

9.00046 

95 

10.  999,54 

00217 

99783 

17 

44 
45 

14  08 

45  52 

99956 

96 

00044 
10. 99918 

00174 
9.00301 

97 
100 

99826 

00218 
To.  00219 

1  1  99782 
1  9.99781 

16 
15 

11  14  00 

0  46  00 

9. 00082 

99 

10.99699 

46 

18  52 

46  08 

00207 

101 

99793 

00427 

102 

99573 

00220 

1  1   99780 

14 

47 

18  44 

46  16 

00332 

108 

99668 

00553 

104 

99447 

00222 

1  i   99778 

13 

48 

13  36 

46  24 

00456 

105 

99544 

00670 

106 

99321 

00223 

99777 

12 

49 
50 

13  28 
11  18  20 

46  32 
0  46  40 

00581 
9.00704 

107 
110 

99419 
10. 99296 

00805 
9. 00930 

108 
111 

99195 

00224 
10.  00225 

99776 
9. 99775 

11 
10 

10.  99070 

51 

13  12 

46  48 

00828 

112 

99172 

01055 

113 

98945 

00227 

99773 

9 

52 

13  04 

46  56 

00951 

114 

99049 

01179 

115 

98821 

00228 

99772 

8 

58 

12  56 

47  04 

01074 

116 

98926 

•  01303 

117 

98697 

00229 

99771 

7 

54 
55 

12  48 

47  12 
0  47  20 

01196 
9.01318 

118 
121 

98804 
10. 98682 

01427 

120 
122 

98578 
10.98450 

00231 

99769 
99768 

6 
5 

11  12  40 

9.  01550 

10. 00232 

56 

12  32 

47  28 

01440 

123 

98560 

01673 

124 

98827 

00233 

99767 

4 

57 

12  24 

47  36 

01561 

125 

98439 

01796 

126 

98204 

00235 

1  j   99765 

3 

58 

12  16 

47  44 

01682 

127 

98318 

01918 

128 

98082 

00236 

99764 

2 

59 

12  08 

47  52 

01808 

129 

98197 

02040 

131 

97960 

00237 

99763 

1 

60 

12  00 

48  00 

01923 

132 

98077 

02162 

133 

97838 

00239 

99761 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

96° 

A 

A         B 

B 

C 

C    84°  1 

Seconds  of  time 

1» 

•.'=  j  8b 

4' 

5-  i  C    7.  1 

Prop,  parts  of  cols.  -;  B 

(c 

16 
17 

0 

33    49   66 

33    50    66 

0    0    1 

82 

83 

1 

99 
100 

1 

115 
116 

1 

Page  614] 

TABLE  U. 

Log.  Sines,  Tangents,  and  Secants. 

6° 

A             A 

B           B 

C 

C 

178° 

M. 

Hour  A.  M.  Hour  p.  m. 

Sine. 

Diflf. 

Cosecant. 

Tangent.  Diff.  1  Cotangent. 

Secant. 
10.  00239 

Diff. 
0 

Cosine. 

M. 
60 

0 

11  12  00 

0  48  00 

9.01923 

0 

10.  98077 

9.02162   0  10.97838 

9. 99761 

1 

11  52 

48  08 

02043  i  2 

97957 

02283  1  2    97717 

00240 

0 

99760 

59 

2 

11  44  1   48  16 

02163  :  4 

97837 

02404  j  4    97596 

00241 

0 

99759 

58 

3 

11  36 

48  24 

02283  !  6 

97717 

02525  1  6 

97475 

00243 

0 

99757 

57 

4 

11  28 

48  321 

02402 

7 
9 

97598 

02645 

8 
9 

97355 
10^97234 

00244 
10.  00245 

0 
0 

99756 
9. 99755 

56 
55 

5 

11  11  20 

0  48  40 

9. 02520 

10. 97480 

9. 02766 

6 

11  12 

48  48 

02639  1  11 

97361 

02885  1  11 

97115 

00247 

0 

99753 

.54 

7 

11  04 

48  56 

02757  !  13 

97243 

03005  13    96995 

00248 

0 

99752 

53 

8 

10  56 

49  04 

02874 

15 

97126 

03124  15    96876 

00249 

0 

9975] 

52 

9 
10 

10  48 

49  12 
049  20 

02992 

17 

97008 

03242 
9. 03361 

17 
19 

96758 
10. 96639 

00251 
10. 00252 

0 
0" 

99749 

51 

11  10  40 

9.  03109 

19 

10. 96891 

9. 99748 

50 

11 

10  32 

49  28 

03226 

20 

96774 

03479 

21 

96521 

00253 

0 

99747 

49 

12 

10  24 

49  36 

03342 

22 

96658 

03597  23    96403 

00255 

0 

99745 

48 

13 

10  16 

49  44 

03458 

24 

96542 

03714  i  24 

96286 

00256 

0 

99744 

47 

14 
15 

10  08 

49  52 

03574 

26 

96426 

03832  1  26 

96168 

00258 
10. 00259 

0 
0 

99742 

46 
45 

11  10  00 

0  50  00 

9. 03690 

28 

10.  96310 

9.03948  28 

10. 96052 

9. 99741 

16 

9  52 

50  08 

03805 

30 

96195 

04065  1  30 

95935 

00260 

0 

99740 

44 

17 

9  44 

50  16 

03920 

31 

96080 

04181  1  32 

95819 

00262 

0 

99738 

43 

18 

9  36 

50  24 

04034 

33 

95966 

04297  1  34 

95703 

00263 

0 

99737 

42 

19 

9  28 

50  32 
0  50  40 

04149 

35 

95851 

04413  36 

95587 

00264 

0 

99736 

41 
40 

20 

11  9  20 

9. 04262 

37 

10. 95738 

9.04528  !  38 

10. 95472 

10.  00266 

0 

9.  99734 

21 

9  12 

50  48 

04376 

39 

95624 

04643  39 

95357 

00267 

99733 

39 

22 

9  04 

50  56 

04490 

41 

95510 

04758  41 

95242 

00269 

99731 

38 

23 

8  56 

51  04 

04603 

43 

95397 

04873  43    95127 

00270 

99730 

37 

24 

8  48 

51  12 

04715  44 

95285 

04987  i  45 

95013 

00272 

99728 

36 
35 

25 

11  8  40  1  0  51  20 

9.04828  1  46 

10.95172 

9.05101  1  47 

10. 94899 

10. 00273 

9. 99727 

26 

8  32    51  28 

04940  48 

95060 

05214  i  49 

94786 

00274 

99726 

34 

27 

8  24    51  36 

05052 

50 

94948 

05328  1  51 

94672 

00276 

99724 

33 

28 

8  16  1   51  44 

05164 

52 

94836 

05441  !  53 

94559 

00277 

99723 

32 

29 

8  08  i   51  52 

05275 
9. 05386 

54 
56 

94725 

05553  54 

94447 

00279 

99721 
9. 99720 

31 
30 

30 

11  8  00 

0  52  00 

10.  94614 

9.05666  56  10.94334 

10. 00280 

31 

7  52 

52  08 

05497 

57 

94503 

05778  1  58  1   94222 

00282 

99718 

29 

32 

7  44 

52  16 

05607 

59    94393 

05890  1  60    94110 

00283 

99717 

28 

33 

7  36 

52  24 

05717 

61    94283 

06002  62    93998 

00284 

99716 

27 

34 

7  28 

52  32 

05827 

63    94173 

06113  64    93887 

00286 

99714 

26 

35 

11  7  20 

0  52  40 

9.05937  65  10.94063 

9.06224  66  10.93776 

10. 00287 

9. 99713 

25 

36 

7  12 

52  48 

06046  67 

93954 

06335  68    93665 

00289 

99711 

24 

37 

7  04 

52  56 

06155  69 

93845 

06445 

69 

93555 

00290 

99710 

23 

38 

6  56 

53  04 

06264  70 

93736 

06556 

71 

93444 

00292 

99708 

22 

39 
40" 

6  48 

53  12 

06372 
9.  06481" 

72 

93628 

06666 

73 

93334 

00293 

99707 

21 
20 

11  6  40 

0  53  20 

74  10.93519 

9. 06775 

75 

10.  93225 

10.  00295 

9. 99705 

41 

6  32 

53  28 

06589  i  76 

93411 

06885 

77 

93115 

00296 

99704 

19 

42 

6  24 

53  36 

06696 

78 

93304 

06994 

79 

93006 

00298 

99702 

18 

43 

6  16 

53  44 

06804 

80 

93196 

07103 

81 

92897 

00299 

99701 

17 

44 
45 

6  08 

53  52 

06911 

81 

93089 

07211 

83 
84 

92789 

00301 

99699 
9. 99698 

16 
15 

11  6  00 

0  54  00 

9.  07018 

83 

10. 92982 

9.  07320 

10. 92680 

fo.  oote' 

46 

5  52 

54  08 

07124 

85 

92876 

07428 

86 

92572 

00304 

99696 

14 

47 

5  44 

54  16 

07231 

87 

92769 

07536 

88 

92464 

00305 

99695 

13 

48 

5  36 

54  24 

07337 

89 

92663 

07643 

90 

92357 

00307 

99693 

12 

49 

.  5  28 

54  32 

07442 

91 

92558 

07751 

92 

92249 
10. 92142 

00308 

99692 
9. 99690 

11 
10 

50 

11  5  20 

0  54  40 

9. 07548 

93 

10. 92452 

9. 07858 

94 

10. 00310 

51 

5  12 

54  48 

07653 

94 

92347 

07964 

96 

92036 

00311 

99689 

9 

52 

5  04 

54  56 

07758 

96 

92242 

08071 

98 

91929 

.  00313 

99687 

8 

53 

4  56 

55  04 

07863 

98 

92137 

08177 

99 

91823 

00314 

99686 

7 

54 

4  48 

55  12 

07968 

100 

92032 

08283 

101 

91717 

00316 

99684 

6 
5 

55 

11  4  40 

0  55  20 

9. 08072 

102 

10. 91928 

9.  08389 

103 

10.91611 

10. 00317 

1 

9. 99683 

56 

4  32 

55  28 

08176 

104 

91824 

08495 

105 

91505 

00319 

99681 

4 

57 

4  24 

55  36 

08280 

106 

91720 

08600 

107 

91400 

00320 

99680 

3 

58 

4  16 

55  44 

08383 

107 

91617 

08705 

109 

91295 

00322 

99678 

2 

59 

4  08 

55  52 

08486 

109 

91514 

08810 

111 

91190 

00323 

99677 

1 

60 

4  00 

56  00 

08589 

111 

91411 

08914 

113 

91086 

00325 

99675 

0 
M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diflf. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

96° 

A           A 

B          B 

c 

C 

88° 

Seconds  of  time 


Prop,  parts 


of  cols.  < 


2» 

28 
28 
0 


6' 

83 

84 

1 


TABLE  U. 

[Page  615 

Log.  Sines,  Tangents,  and  Secants. 

7° 

A             A 

B 

B 

C 

C    172° 

M. 

Hour  A.  M. 

Hour  P.  M. 
0  56  0 

Sine. 

DiflF. 

Cosecant. 

Tangent.  DiS. 

i  Cotangent. 

Seeant. 

Diff. 

Cosine. 

M. 
60 

0 

n     4  0 

9. 08589 

0 

10.91411 

9. 08914 

0 

10. 91086 

10. 00325 

0 

9.  99675 

1 

3  52 

56  8 

08692 

2 

91308 

09019 

2 

90981 

00326 

0 

99674 

59 

2 

3  44 

56  16 

08795 

3 

91205 

09123 

3 

i   90877 

00328 

0 

99672 

58 

8 

3  36 

56  24 

08897 

5 

91103 

09227 

5 

1   90773 

00330 

0 

99670 

57 

4 
5 

3  28 

56  32 

08999 

6 

8 

91001 
rd."90899 

09330 
9.09434 

7 
8 

i   90670 

00331 

0 

99669 

56 

11  3  20 

0  56  40 

9. 09101 

[10.  90566 

10. 00333 

0 

9. 99667 

55 

6 

3  12 

56  48 

09202 

10 

90798 

09537 

10 

90463 

00334 

0 

99666 

54 

7 

3  4 

56  56 

09304 

11 

90696 

09640 

11 

90360 

00336 

0 

99664 

53 

8 

2  56 

57  4 

09405 

13 

90595 

09742 

13 

90258 

00337 

0 

99663 

52 

9 
10 

2  48 
11  2  40 

57  12 
0  57  20 

09506 
9. 09606 

14 
16" 

90494 
10. 90394 

09845 
9. 09947 

15 
16 

90155 
10. 90053 

00339 

0 

99661 

51 

10. 00341 

0 

9. 99659 

50 

11 

2  32 

57  28 

09707 

18 

90293 

10049 

18 

89951 

00342 

0 

99658 

49 

12 

2  24 

57  36 

09807 

19 

90193 

10150 

20 

89850 

00344 

0 

99656 

48 

13 

2  16 

57  44 

09907 

21 

90093 

10252 

21 

89748 

00345 

0 

99655 

47 

14 

2  8 

57  52 

10006 

22 

89994 

10353 

23 

89647 

00347 

0 

99653 
9. 99651" 

46 
45 

15 

11  2  0 

0  58  0 

9. 10106 

24 

10. 89894 

9. 10454 

24 

10. 89546 

10.  00349 

0 

16 

1  52 

58  8 

10205 

26 

89795 

10555 

26 

89445 

00350 

0 

99650 

44 

17 

1  44 

58  16 

10304 

27 

89696 

10656 

28 

89344 

00352 

0 

99648 

43 

18 

1  36 

58  24 

10402 

29 

89598 

10756 

29 

89244 

00353 

99647 

42 

19 

1  28 

58  32 
0  58  40 

10501 
9. 10599 

30 

89499 

10856 

31 

89144 

00355 

99645 

41 

20 

11  1  20 

32  110.89401 

9. 10956 

33 

10.  89044 

10.  00357 

9. 99643 

40 

21 

1  12 

58  48 

10697 

34    89303 

11056 

34 

88944 

00358 

99642 

39 

22 

1  4 

58  56 

10795 

35    89205 

11155 

36 

88845 

00360 

99640 

38 

23 

0  56 

59  4 

10893 

37    89107 

11254 

37 

88746 

00362 

99638 

37 

24 
25' 

0  48 

59  12 

10990 

38  1   89010 

lia53 

39 

88647 

00363 
10. 00365 

99637 
9. 99635 

36 
35 

11  0  40 

0  59  20 

9. 11087 

40  [10.88913 

9. 11452 

41 

10. 88548 

26 

0  32 

59  28 

11184 

42  !   88816 

11551 

42 

88449 

00367 

1 

99633 

34 

27 

0  24 

59  36 

11281 

43 

88719 

11649 

44 

88351 

00368 

99632 

33 

28 

0  16 

59  44 

11377 

45 

88623 

11747 

46 

88253 

00370 

99630 

32 

29 

0  8 

59  52 

11474 

46 

88526 

11845 

47 

88155 
10.  88057 

00371 
10. 00373 

99629 
9. 99627 

31 
30 

30 

11  0  0 

1  0  0 

9. 11570 

48  110.88430 

9.11943 

49 

31 

10  59  52 

0  8 

11666  i  50    88334 

12040 

51 

87960 

00375 

99625 

29 

32 

59  44 

0  16 

11761 

51    88239 

12138 

52 

87862 

00376 

99624 

28 

33 

59  36 

0  24 

11857 

53  1   88143 

12235 

54 

87765 

00378 

99622 

27 

34 
35 

59  28 

0  32 

11952 

54  !   88048 

12332 
9. 12428 

55 
57 

87668 

00380 
10.  00382 

99620 

26 

10  59  20 

1  0  40 

9. 12047 

56  10.87953 

10. 87572 

9.  99618 

25 

36 

59  12 

0  48 

12142 

58    87858 

12525 

59 

87475 

00383 

99617 

24 

37 

59  4 

0  56 

12236 

59    87764 

12621 

60 

87379 

00385 

99615 

23 

38 

58  56 

1  4 

12331 

61    87669 

12717 

62 

87283 
8/187 

00387 

99613 

22 

39 

58  48 

1  12 

12425 

62  i   87575 

12813 

64 

00388 

99612 

21 

20 

40 

10  58  40 

1  1  20 

9. 12519 

64  (10.87481 

9. 12909 

65 

10. 87091 

10.00390 

9.99610 

41 

58  32 

1  28 

12612 

66  !   87388 

13004 

67 

86996 

00392 

99608 

19 

42 

58  24 

1  36 

12706 

67    87294 

13099 

68 

86901 

00393 

99607 

18 

43 

58  16 

1  44 

12799 

69  •      87201 

13194 

70 

86806 

00395 

99(W5 

17 

44 
45 

58  8 

1  52 

12892 

70  1   87108 

13289 

72 

86711 

00397 

99603 

16 
15 

10  58  0 

1  2  0 

9. 12985 

72  10.87015 

9. 13384 

73 

10. 86616 

10.  00.399 

9.  99()01 

46 

57  52 

2  8 

13078 

74    86922 

13478 

to 

86522 

00400 

99(i00 

14 

47 

57  44 

2  16 

13171 

75 

86829 

13573 

77 

86427 

00402 

99598 

13 

48 

57  36 

2  24 

13263 

77 

86737 

13667 

78 

•  86333 

00404 

99596 

12 

49 
50 

57  28 
10  57  20 

2  32 

1  2  40 

13355 
9. 13447 

78 
80 

86645 
10. 86553 

13761 
9. 13854 

80 
81 

86239 
10.  86146 

00405 

99595 
9. 99593 

11 
10 

10. 00407 

51 

57  12 

2  48 

13539 

82 

8<>461 

13948  i  83 

86052 

00409 

99591 

9 

52 

57  4 

2  56 

13630 

83 

86370 

14041   85 

85959 

00411 

99589 

8 

53 

56  56 

3  4 

13722  85  :   86278  | 

14134  86 

85866 

00412 

99588 

7 

54 
55 

56  48 

3  12 

13813 

87  :   86187 

88  110.86096 

14227  1  88 
9.14320  1  90 

85773 
10.  85680 

00414 
10.  00416 

2 
2 

99586 
9. 99584 

6 

5 

10  56  40 

1  3  20 

9. 13904 

56 

56  32 

3  28 

13994 

90    8600(i 

14412  91 

85588 

00418 

2 

99582 

4 

57 

56  24 

3  36 

14085 

91 

85915 

14.504  i  93 

85496 

00419 

2 

9958 1 

3 

58 

56  16 

3  44 

14175 

93 

85825 

14597 

95 

85403 

00421 

2 

99579 

2 

59 

56  8 

3  52 

14266 

95 

85734 

14688 

96 

85312 

00423 

2 

99577 

1 

60 

56  0 

4  0 

14356  96    85644 

14780 

98 

85220 

00425 

2 

99575 

0 

M. 

Hour  p.  M. 

Hour  AHU. 

Cosine.   Diff.   Secant,  i 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

97^ 

A             A 

B 

B 

C 

C     82°  1 

Seconds  of  time 

1' 

2'    -8' 

4' 

b> 

6^  1  7. 

Prop,  parts  of  cols.  <  B 

12 
12 

0 

24    36 

24    37 

0     1 

48 
49 

1 

60 
61 

1 

72  84 

73  86 
1    1 

Page  616] 

TABLE  44. 

Log.  Sines,  Tangente,  and  Secants. 

8° 

A            A 

B           B 

C 

C 

I'iV 

M. 

Hour  A.  M.  Hour  p.  M. 

Sine.   JDifl.  Cosecant. 

Tangent.  Dili. 

Cotangent. 

Secant. 

Difif. 

Cosine. 

M. 

0 

10  56  0   14  0 

9.14356  1  0  10.85644 

9. 14780   0 

10.  85220 

10.  00425 

0 

9. 99575 

60 

1 

55  52     4  8 

14445  :  1  1   85555 

14872   1 

85128 

00426 

0 

99574 

59 

9 

55  44  ■   4  16 

14535   3  i   85465 

14963  1  3    85037 

00428 

0 

99572 

58 

3 

55  36  I    4  24 

14624   4    85376 

15054   4    84946 

00430 

0 

99570 

57 

4 
5 

55  28  1    4  32 
10  55  20  I  1  4  40 

14714  i  6    85286 
9.14803   7  10,85197 

15145   6    84855 
9.15236  !  7  10.84764 

00432 
10.00434 

0 

99568 

56 
55 

0 

9. 99566 

6 

55  12  :    4  48 

14891  1  8    85109 

15327   9  1   84673 

00435 

0   99565 

54 

7 

55  4     4  56 

14980  1  10 

85020 

15417  10  i   84583 

00437 

0   99563 

53 

8 

54  56  !    5  4 

15069  11 

84931 

15508  12    84492 

00439 

0  ;   99561 

52 

9 

54  48  1    5  12 

15157  13 

84843 

15598  ,   13    84402 

00441 

0 

99559 

51 
50 

10 

10  54  40  1  1  5  20 

9.15245  14  10.84755 

9.15688  14  10.84312 

10.00443 

0 

9. 99557 

11 

54  32  '    5  28 

15333  16    84667 

15777  16    84223 

00444 

0 

99556 

49 

12 

54  24     5  36 

15421   17    84579 

15867  1  17  !   84133 

00446 

0 

99554 

48 

13 

54  16     5  44 

15508  \   18    84492 

15956  19  !   84044 

00448 

0 

99552 

47 

14 

54  8  1    5  52 

15596  20    84404 

16046  20  '   83954 

00450 

0 

99550 

46 

15 

10  54  0  1  6  0 

9.  15683  21  10.  84317 

9.1613.5  i  22  10.83865 

10. 00452 

0 

9. 99548 

45 

16 

53  52     6  8 

15770  23    84230 

16224  [  23    83776 

00454 

99546 

44 

17 

53  44     6  16 

15857  X  24    84143 
15944"^  25    84056 

16312  25  I  "83688 

00455 

99545 

48 

18 

53  36     6  24 

16401  26  '   83599 

00457 

99543 

42 

19 
20 

53  28  1    6  32 

16030 

27 

83970 

16489 

27 

83511 
10.  83423 

00459 

1 

99541 

41 
40 

10  53  20  1  6  40 

9. 16116 

28 

10.  83884 

9. 16577 

29 

10.  00461 

9. 99539 

21 

53  12     6  48 

16203 

30    83797 

16665 

30    83335 

00463 

99537 

39 

22 

53  4     6  56 

16289 

31    83711 

16753 

32    83247 

00465 

99535 

38 

23 

52  56     7  4 

16374  1  32  j   83626 

16841 

33 

83159 

00467 

1    99533 

37 

24 

52  48  1    7  12 

16460  1  34  1   83540 

16928 

35 

83072 

00468 

1    99532 

36 

25 

10  52  40  1  7  20 

9. 16545  ,   35  ilO.  83455 

9. 17016 

36  10.82984 

10. 00470 

1  9.99530 

35 

26 

52  32 

7  28 

16631 

37 

83369 

17103 

37 

82897 

00472 

99528 

34 

27 

52  24 

7  36 

16716 

38 

83284 

17190 

39 

82810 

00474 

99526 

33 

28 

52  16 

7  44 

16801 

39 

83199 

17277 

40 

82723 

00476 

99524 

32 

29 
30 

52  8 
10  52  0 

7  52 
18  0 

16886 

41 

83114 

17363 

42 

82637 

00478 

99522 
9. 99520 

31 
30 

9. 16970 

42 

10. 83030 

9. 17450 

43 

10. 82550 

10. 00480 

31 

51  52  i    8  8 

17055  1  44    82945 

17536 

45 

82464 

00482 

99518 

29 

32 

51  44 

8  16 

17139  45    82861 

17622 

46 

82378 

00483 

99517 

28 

33 

51  36 

8  24 

17223  i  47    82777 

17708 

48 

82292 

00485 

99515 

27 

34 
35 

51  28 

8  32 

17307  48 

82693 
10. 82609 

17794 

49 

82206 

00487- 

99513 

26 
25 

10  51  20  1  8  40 

9. 17391  49 

9.17880 

50 

10. 82120 

10. 00489 

9.99511 

36 

51  12     8  48 

17474 

51 

82526 

17965 

52 

82035 

00491 

.  99509 

24 

37 

51  4  {    8  56 

17558 

52 

82442 

18051 

53 

81949 

00493 

99507 

23 

38 

50  56     9  4 

17641 

54 

82359 

18136 

55 

81864 

00495 

99505 

22 

39 
40 

50  48  1    9  12 

17724 

55 

82276 

18221 

56 

81779 

00497 

99503 

21 

10  50  40  1  9  20 

9. 17807 

56  10.82193 

9. 18306 

58  10.81694 

10. 00499 

1  9.99501 

20 

41 

50  32  I    9  28 

17890  58    82110 

18391 

59    81609 

00501 

1   99499 

19 

42 

50  24  !    9  36 

17973  i  59    82027 

18475 

61 

81525 

00503 

1   99497 

18 

43 

50  16     9  44 

18055  61    81945 

18560 

62 

. 81440 

00505 

1  !  99495 

17 

44 

50  8 

9  52 
1  10  0 

18137  62    81863 
9.18220  i  63  10.81780 

18644 

63 

81356 

00506 

1  i   99494 

16 
15 

45 

10  50  0 

9. 18728 

65  10.81272 

10. 00508 

1  19.99492 

46 

49  52  :   10  8 

18302  i  65  !   81698 

18812 

66 

81188 

00510 

99490 

14 

47 

49  44    10  16 

18383  66    81617 

18896  1  68 

81104 

00512 

1 

99488 

13 

48 

49  36  I   10  24 

18465  68    81535 

18979  i  69 

81021 

00514 

2 

99486 

12 

49 
50 

49  28  1   10  32 

18547  1  69    81453 
9.18628  71  ;iO.  81372 

19063 
9.19146 

71  80937 

72  10780854 

00516 
10. 00518 

2 

2 

99484 
9. 99482 

11 
10 

10  49  20  i  1  10  40 

51 

49  12    10  48 

18709  1  72    81291 

19229 

74    80771 

00520 

2    99480 

9 

52 

49  4    10  56 

18790  73  ;   81210 

19312 

75   •  80688 

■  00522 

2  1  99478 

8 

53 

48  56    11  4 

18871  75    81129 

19395 

76    80605 

00524 

2  i  99476 

7 

54 
55 

48  48    11  12 

18952  76  ■  81048 

19478  i  78  1   80522 

00526 

2  j   99474 

6 

10  48  40  i  1  11  20 

9.19033  i  78  10.80967 

9.19561  '  79  10.80439 

10. 00528 

2  9. 99472 

5 

56 

48  32    11  28 

19113  79  !   80887 

19643  1  81  1   80357 

00530 

2  \      99470 

4 

57 

48  24    11  36 

19193 

80  i   80807 

19725 

82  j   80275 

00532 

2    99468 

3 

58 

48  16    11  44 

19273 

82  I   80727 

19807 

84 

80193 

00534 

2  i   99466 

2 

59 

48  8  i   11  52 

19353 

83 

80647 

19889 

85 

80111 

00536 

2 

99464 

1 

60 
M. 

48  0    12  0 

19433 

85 

80567 

19971 

87 

80029 

00538 

2 

99462 

0 
M. 

Hour  p.  M.  j  Hoxir  a.  m. 

Cosine.   Dlfif. 

Secant. 

Cotangent.  ^  Diff. 

Tangent. 

Cosecant. 

DiflE. 

Sine. 

98° 

A            A 

.  B            B 

C 

C 

81° 

Seconds  of  time 1" 

2» 

8-  j  4« 

o' 

«• 

<• 

fA   11 
Prop,  parts  of  cols.  -JB   11 

[C   1   0 

21 

22 
0 

32    42 
32    43 

1  [   1 

53 
54 

1 

63 

65 

1 

74 

76 
2 

TABLE  U. 

[Page  617 

Log. 

Sines,  Tangents,  and  Secants. 

9° 

A 

A 

B 

B 

C 

C    170° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff.  1  Cosine. 

M. 

0 

10  48  0 

1  12  0 

9. 19433 

0 

10.  80567 

9.  19971 

0 

10.  80029 

10. 00538 

0  9.99462 

60 

1 

47  52 

12  8 

19513 

1 

80487 

20053 

1 

79947 

00540 

0 

99460 

59 

2 

47  44 

12  16 

19592 

3 

80408 

20134 

3 

79865 

00542 

0 

99458 

58 

3 

47  36 

12  24 

19672 

4 

80328 

20216 

4 

79784 

00544 

0 

99456 

57 

4 

47  28 

12  32 

19751 

5 

80249 
10.80170 

20297 

5 

79703 
10.  79622 

00546 
10. 00548 

0 

99454 

56 
55 

5 

10  47  20 

1  12  40 

9. 19830 

6 

9. 20378   6 

0 

9. 99452 

H 

47  12 

12  48 

19909 

8 

80091 

20459 

8 

79541 

00550 

0 

99450 

54 

7 

47  4 

12  56 

19988 

9 

80012 

20540 

9 

79460 

00552 

0 

99448 

53 

8 

46  56 

13  4 

20067 

10 

79933 

20621  10 

79379 

00554 

0 

99446 

52 

9 
10 

46  48 
10  46  40 

13  12 

1  13  20 

20145 
9. 20223 

11 
13 

79855 

20701 

12 
13 

79299 

00556 

0 

99444 

51 
50 

10.  79777 

9. 20782  ' 

10.  79218 

10. 00558 

0  9.99442 

11 

46  32 

13  28 

20302 

14 

79698 

20862  1  14 

79138 

00560 

0 

99440 

49 

12 

46  24 

13  36 

20380 

15 

79620 

20942  16 

79058 

00562 

0 

99438 

48 

13 

46  16 

13  44 

20458 

16 

79.542 

21022 

17 

78978 

00564 

0 

99436 

47 

14 

46  8 

13  52 

20535 

18 

79465 

21102 

18 

78898 

00566 

0 

99434 

46 
45 

15 

10  46  0 

1  14  0 

9. 20613 

19 

10. 79387 

9.21182 

19 

10.  78818 

10.  00568 

9. 99432 

K) 

45  52 

14  8 

20691 

20 

79309 

21261 

21 

78739 

00571 

.  99429 

44 

17 

45  44 

14  16 

20768 

21 

79232 

21341 

22 

78659 

00573 

99427 

43 

18 

45  36 

14  24 

20845 

23 

79155 

21420 

23 

78580 

00575 

99425 

42 

19 

45  28 

14  32 

20922 

24 

79078 

21499 

25 

78501 

00577 

99423 

41 

20 

10  45  20 

1  14  40 

9. 20999 

25 

10.  79001 

9.  21578 

26 

10.  78422 

10. 00579 

9. 99421 

40 

21 

45  12 

14  48 

21076 

26 

>  78924 

21657 

27 

78343 

00581 

99419 

39 

22 

45  4 

14  56 

21153 

28 

78847 

21736 

28 

78264 

00583 

99417 

38 

23 

44  56 

15  4 

21229 

29 

78771 

21814 

30 

78186 

00585 

99415 

37 

24 

44  48 

15  12 

21306 
9. 21382 

30 

78694 

21893 

31 

78107 

00587 

99413 

36 

25 

10  44  40 

1  15  20 

31 

10.  78618 

9.  21971 

32 

10. 78029 

10. 00589 

9.99411 

35 

26 

44  32 

15  28 

21458 

33 

78542 

22049 

34 

77951 

00591 

99409 

34 

27 

44  24 

15  36 

21534 

34 

78466 

22127 

35 

77873 

00593 

99407 

33 

28 

44  16 

15  44 

21610 

35 

78390 

22205 

36 

77795 

00596 

99404 

32 

29 
30 

44  8 

15  52 

21685 

37 

78315 
10.  78239 

22283 

38 

77717 
10.  77639 

00598 

99402 

31 

10  44  0 

1  16  0 

9.  21761 

38 

9. 22361 

39 

10.00600 

9.99400 

30 

31 

43  52 

16  8 

21836 

39 

78164 

22438 

40 

77562 

00602 

99398 

29 

32 

43  44 

16  16 

21912 

40 

78088 

22516 

41 

77484 

00604 

99396 

28 

33 

43  36 

16  24 

21987 

42 

78013 

22593 

43 

77407 

00606 

99394 

27 

34 
35 

43  28 

16  32 

22062 

43 

77938 

22670 

44 

77330 

00608 

99392 

26 

10  43  20 

1  16  40 

9. 22137 

44 

10.  77863 

9. 22747 

45 

10.  77253 

10. 00610 

9. 99390 

25 

36 

43  12 

16  48 

22211 

45 

77789 

22824 

47 

77176 

00612 

99388 

24 

37 

43  4 

16  56 

22286 

47 

77714 

22901 

48 

77099 

00615 

99385 

23 

38 

42  56 

17  4 

22361 

48 

77639 

22977 

49 

77023 

00617 

99383 

22 

39 

42  48 

17  12 

22435 
9.  22509 

49 
50 

77565 
10.  77491 

23054 
9. 23130 

50 
52 

76946 

00619 

99381 

21 

40 

10  42  40 

1  17  20 

10.  76870 

10. 00621 

9. 99379 

20 

41 

42  32 

17  28 

22583 

52 

77417 

23206 

53 

76794 

00623 

99377 

19 

42 

42  24 

17  36 

22657 

53 

77343 

23283 

54 

76717 

00625 

99375 

18 

43 

42  16 

17  44 

22731 

54 

77269 

23359 

56 

76641 

00628 

2 

99372 

17 

44 
45 

42  8 

17  52 

22805 

55 

57 

77195 
10.  77122 

23435 

57 

76565 

00630 

2 

99370 

16 
15 

10  42  0 

1  18  0 

9.  22878 

9.  23510 

58 

10.  76490 

10. 00632 

2 

9. 99368 

46 

41  52 

18  8 

22952 

58 

77048 

23586 

60 

76414 

00634 

2 

99366 

14 

47 

41  44 

18  16 

23025 

59 

76975 

23661 

61 

76339 

00(i36 

2 

99364 

13 

48 

41  36 

18  24 

23098 

60 

76902 

23737 

62 

76263 

00638 

2 

99362 

12 

49 

41  28 

18  32 

23171 
9.  23244 

62 
63 

76829 

23812 

63 
65 

76188 

00641 

2 

99359 

11 
10 

50 

10  41  20 

1  18  40 

10.  76756 

9. 23887 

10.76113 

10.  00643 

2  9,99357 

51 

41  12 

18  48 

23317 

64 

76683 

23962 

66 

76038 

00645 

2 

99355 

9 

52 

41  4 

18  56 

23390 

65 

76610 

24037 

67 

75963 

00(>47 

2 

99353 

8 

53 

40  56 

19  4 

23462 

67 

76538 

24112 

69 

75888 

00649 

2 

99351 

i 

54 
55 

40  48 
10  40  40 

19  12 

23535 
9. 23607 

68 

76465 

24186 

70 

75814 

00652 

2 

99348 

6 

1  19  20 

69 

10.  76393 

9.  24261 

71 

10.  75739 

10. 00654 

2 

9. 99346 

5 

56 

40  32 

19  28 

23679 

71 

76321 

24335 

73 

75665 

00656 

2 

99344 

4 

57 

40  24 

19  36 

23752 

72 

76248 

24410 

74 

75590 

00658 

2 

99342 

3 

58 

40  16 

19  44 

23823 

73 

76177 

24484 

75 

75516 

00660 

2 

99340 

2 

59 

40  8 

19  52 

23895 

74 

76105 

24558 

76 

75442 

00663 

2 

99337 

1 

60 

M. 

40  0 

20  0 

23967 

76 

76033 

24632 

78 

75368 

00665 

2 

99335 

0 
-M. 

Hour  p.  M. 

Hour  A.  M. 

Co.sine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. }   Sine. 

99° 

A 

A 

B 

B 

C 

C     80°  1 

Seconds  of  time 

1«    2»    3^ 

4. 

5' 

6» 

7» 

Prop,  parts  of  cols.  •!  B 

Ic 

9    19    28 
10    19    29 

0    1  i   1 

38 

39 

1 

47 
49 

1 

57 

58 

2 

66 
68 
2 

Page  618] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

10° 

A           A 

B 

B 

C 

C    169° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine.   Diff.  1  Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

10  40  0 

1  20  0 

9.23967   0  10.76033 

9. 24632 

0 

10.75368 

10.00665 

0 

9. 99335 

60 

1 

39  52 

20  8 

24039   1  i   75961 

24706 

1  1 

75294 

00667 

0   99333 

59 

2 

39  44 

20  16 

24110   2  1   75890 

24779   2 

75221 

00669 

0    99331 

58 

:^ 

39  36 

20  24 

24181   3 

75819 

24853   4 

75147 

00672 

0    99328 

57 

4 

39  28 

20  3i 

24253 

5 

75747 
10.  75676 

24926 

5 

6 

75074 
10.  75000 

00674 

0  i   99326 
0  i 9. 99324 

56 
55 

5 

10  39  20 

1  20  40 

9. 24324 

6 

9. 25000 

10. 00676 

6 

39  12 

20  48 

24395 

7 

75605 

25073 

7 

74927 

00678 

0   99322 

54 

7 

39  4 

20  56 

24466 

8 

75534 

25146 

8 

74854 

00681 

0   99319 

53 

8 

38  56 

21  4 

24536 

9 

75464 

25219 

9 

74781 

00683 

0   99317 

52 

9 
10 

38  48 

21  12 

24607 

10 

75393 

25292 

11 
12 

74708 

00685 

0   99315 

51 

10  38  40 

1  21  20 

9. 24677 

11 

10.  75323 

9. 25365 

10.  74635 

10.  00687 

0  9.99313 

50 

11 

38  32 

21  28 

24748 

13 

75252 

25437  13 

74563 

00690 

0   99310 

49 

12 

38  24 

21  36 

24818 

14 

75182 

. 25510  i  14 

74490 

00692 

0  i  99308 

48 

13 

38  16 

21  44 

24888 

15 

75112 

25582 

15 

74418 

00694 

99306 

47 

14 

38  8 

21  52 

24958 

16 

75042 

25655 

16 

74345 

00696 

99304 

46 

15 

10  38  0 

1  22  0 

9. 25028 

17 

10. 74972 

9. 25727 

18 

10.  74273 

10. 00699 

9. 99301 

45 

1(1 

37  52 

22  8 

25098 

18 

74902 

25799 

19 

74201 

00701 

99299 

44 

17 

37  44 

22  16 

25168 

19 

74832 

25871 

20 

74129 

00703 

99297 

43 

18 

37  36 

22  24 

25237 

20 

74763 

25943 

21 

74057 

00706 

99294 

42 

19 

37  28 

22  32 

25307 

22 

74693 

26015 

22 

73985 

00708 

99292 

41 

20 

10  37  20 

1  22  40 

9. 25376 

23 

10. 74624 

9. 26086 

24 

10.  73914 

10. 00710 

9. 99290 

40 

21 

37  12 

22  48 

25445 

24 

74555 

26158 

25, 

73842 

00712 

99288 

39 

22 

37  4 

22  56 

25514 

25 

74486 

26229 

26 

73771 

00715 

99285 

38 

23 

36  56 

23  4 

25583 

26 

74417 

26301 

27 

73699 

00717 

99283 

37 

24 
25 

36  48 

23  12 

25652 

27 

74348 

26372 

28 

73628 

00719 

99281 
9. 99278 

36 
35 

10  36  40 

1  23  20 

9. 25721 

28 

10. 74279 

9. 26443 

29 

10.  73557 

10. 00722 

26 

36  32 

23  28 

25790 

30 

74210 

26514  31 

73486 

00724 

99276 

34 

27 

36  24 

23  36 

25858 

31 

74142 

26585 

32 

73415 

00726 

99274 

33 

28 

36  16 

23  44 

25927 

32 

74073 

26655 

33 

73345 

00729 

99271 

32 

29 
30 

36  8 

23  52 

25995 

33 
34 

74005 

26726 

34 
35 

73274 

00731 

99269 

31 
30 

10  36  0 

1  24  0 

9. 26063 

10.  73937 

9.  26797 

10.  73203 

10. 00733 

9. 99267 

31 

35  52 

24  8 

26131 

35 

73869 

26867 

36 

73133 

00736 

99264 

29 

32 

35  44 

24  16 

26199 

36 

73801 

26937 

38 

73063 

00738 

99262 

28 

33 

35  36 

24  24 

26267 

38 

73733 

27008 

39 

72992 

00740 

99260 

27 

34 

35  28 

24  32 

26335 

39 

73665 

27078 

40 

72922 

00743 

99257 

26 

35 

10  35  20 

1  24  40 

9. 26403 

40 

10. 73597 

9. 27148 

41 

10.  72852 

10. 00745 

9. 99255 

25 

3H 

35  12 

24  48 

26470 

41 

73530 

27218 

42 

72782 

00748 

99252 

24 

37 

35  4 

24  56 

26538 

42 

73462 

27288 

44 

72712 

00750 

99250 

23 

38 

34  56 

25  4 

26605 

43 

73395 

27357 

45 

72643 

00752 

99248 

22 

39 

34  48 

25  12 

26672 

44 

73328 

27427 

46 

72573 

00755 

2 

99245 

21 

40 

10  34  40 

1  25  20 

9. 26739 

45 

10.  73261 

9. 27496 

47 

10.  72504 

10. 00757 

2 

9. 99243 

20 

41 

34  32 

25  28 

26806 

47 

73194 

27566 

48 

72434 

00759 

2 

99241 

19 

42 

34  24 

25  36 

26873 

48 

73127 

27635 

49 

72365 

00762 

2 

99238 

18 

43 

34  16 

25  44 

26940 

49 

73060 

27704 

51 

72296 

00764 

2 

99236 

17 

44 

34  8 

25  52 

27007 

50 

72993 

27773 

52 

72227 

00767 

2 

99233 

16 
15 

45 

10  34  0 

1  26  0 

9.  27073 

51 

10.  72927 

9. 27842 

53 

10.  72158 

10. 00769 

2 

9. 99231 

46 

33  52 

26  8 

27140 

52 

72860 

27911 

54 

72089 

00771 

2 

99229 

14 

47 

33  44 

26  16 

27206 

53 

72794 

27980 

55 

72020 

00774 

2 

99226 

13 

48 

33  36 

26  24 

27273 

55 

72727 

28049  1  56 

71951 

00776 

2 

99224 

12 

49 

33  28 

26  32 

27339 

56 

72661 

28117  !  58 

71883 

00779 

2 

99221 

11 
10 

50 

10  33  20 

1  26  40 

9. 27405 

57 

10. 72595 

9. 28186 

59 

10.  71814 

10. 00781 

2 

9. 99219 

51 

33  12 

26  48 

27471 

58 

72529 

28254 

60 

71746 

00783 

2 

99217 

9 

52 

33  4 

26  56 

27537 

59 

72463 

28323 

61 

71677 

00786 

2 

99214 

8 

53 

32  56 

27  4 

27602 

60 

72398 

28391 

62 

71609 

00788 

2 

99212 

7 

54 

32  48 

27  12 

27668 

61 

72332 

28459 

63 

71541 

00791 

2 
2 

99209 
9. 99207 

5' 

55 

10  32  40 

1  27  20 

9. 27734 

63 

10.  72266 

9. 28527 

65 

10.  71473 

10. 00793 

56 

32  32 

27  28 

27799 

64 

72201 

28595 

66 

71405 

00796 

2 

99204 

4 

57 

32  24 

27  36 

27864 

65 

72136 

28662  \   67 

71338 

00798 

2 

99202 

3 

58 

32  16 

27  44 

27930 

66 

72070 

28730  68 

71270 

00800 

2 

99200 

2 

59 

32  8 

27  52 

27995 

67 

72005 

28798 

69 

71202 

00803 

2 

99197 

1 

60 

32  0 

28  0 

28060 

68 

71940 

28865 

71 

71135 

00805 

2 
Diff. 

99195 

0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent.  Diff. 

Tangent. 

Cosecant. 

Sine. 

M. 

100^ 

A           A 

B 

B 

C 

C     79°  1 

Seconds  of  time 

1. 

2- 

8" 

4" 

5» 

6» 

7' 

Prop,  parts  of  cols,  i  B 

9 
9 
0 

17 

18 

1 

26 

26 
1 

34 
35 

1 

43 

44 

1 

51 

53 

2 

60 

62 

2 

TABLE  U. 

[Page  619 

Log. 

Sines,  Tangents,  and  Secants. 

11° 

A 

A 

B 

B 

C 

C     168° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Diflf. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

10  32  0 

1  28  0 

9. 28060 

0 

10.  71940 

9.  28865 

0 

10.71135 

10.  00805 

0 

9.  99195 

60 

1 

31  52 

28  8 

28125 

1 

71875 

28933 

1 

71067 

00808 

0 

99192 

59 

2 

31  44 

28  16 

28190 

2 

71810 

29000 

2 

71000 

00810 

0 

99190 

58 

8 

31  36 

28  24 

28254 

3 

71746 

29067 

3 

70933 

00818 

0 

99187 

57 

4 

81  28 

28  32 

28319 

4 

71681 

29184 

4 

70866 

00815 

0 

99185 
9. 99182 

56 
55 

5 

10  31  20 

1  28  40 

9. 28384 

5 

10.  71616 

9. 29201 

5 

10.  70799 

10.  00818 

0 

6 

31  12 

28  48 

28448 

6 

71552 

29268 

6 

70732 

00820 

0 

99180 

54 

7 

31  4 

28  56 

28512 

7 

71488 

29335 

8 

70665 

00823 

0 

99177 

58 

8 

30  56 

29  4 

28577 

8 

71423 

29402 

9 

70598 

00825 

0 

99175 

52 

9 
10 

30  48 

29  12 

28641 

9 

71359 

29468 

10 

70532 

00828 

0 

99172 

51 
50 

10  80  40 

1  29  20 

9. 28705 

10 

10. 71295 

9. 29585 

11 

10.  70465 

10.  00830 

0 

9.99170 

n 

30  82 

29  28 

28769 

11 

71281 

29601 

12 

70399 

00833 

0 

99167 

49 

12 

30  24 

29  36 

28833  1  12 

71167 

29668 

13 

70332 

00835 

99165 

48 

18 

30  16 

29  44 

28896 

13 

71104 

29734 

14 

70266 

00838 

99162 

47 

14 

30  8 

29  52 

28960 

14 

71040 

29800 

15 
16 

70200 

00840 

99160 
9. 99157 

46 
45 

15 

10  30  0 

1  30  0 

9.  29024 

16 

10.  70976 

9. 29866 

10.  70134 

10.  00843 

IB 

29  52 

30  8 

29087 

17 

70913 

29932 

17 

70068 

00845 

99155 

44 

17 

29  44 

30  16 

29150 

18 

70850 

29998 

18 

70002 

00848 

99152 

43 

18 

29  36 

30  24 

29214 

19 

70786 

30064 

19 

69936 

00850 

99150 

42 

19 

29  28 

30  32 

29277 

20 

70723 

30130 

20 

69870 

00853 

99147 
9. 99145 

41 
40 

20 

10  29  20 

1  80  40 

9.  29340 

21 

10.  70660 

9.  30195 

22 

10.  69805 

10.  00855 

21 

29  12 

80  48 

29403 

22 

70597 

30261 

23 

69739 

00858 

99142 

39 

22 

29  4 

80  56 

29466 

23 

70534 

30326 

24 

69674 

00860 

99140 

38 

28 

28  56 

31  4 

29529 

24 

70471 

30.391 

25 

69609 

00863 

99137 

87 

24 

28  48 

31  12 
1  31  20 

29591 

25 

70409 

30457 

26 

69543 
10.  69478 

00865 

99135 

36 
35 

25 

10  28  40 

9. 29654 

26 

10. 70346 

9. 30522 

27 

10. 00868 

9. 99182 

26 

28  32 

81  28 

29716 

27 

70284 

30587 

28 

69413 

00870 

99130 

34 

27 

28  24 

31  36 

29779 

28 

70221 

30652 

29 

69.348 

00873 

99127 

38 

28 

28  16 

31  44 

29841 

29 

70159 

30717 

30 

69283 

00876 

99124 

32 

29 
80 

28  8 

31  52 

29903 

30 

70097 

30782 

31 
32 

69218 
10. 69154 

00878 

99122 
9. 99119 

31 
30 

10  28  0 

1  82  0 

9. 29966 

31 

10.  70034 

9. 30846 

10.  00881 

81 

27  52 

82  8 

30028 

32 

69972 

30911 

33 

69089 

00883 

99117 

29 

82 

27  44 

32  16 

30090 

33 

69910 

30975 

35 

69025 

00886 

99114 

28 

88 

27  36 

82  24 

80151 

34 

69849 

31040 

36 

68960 

00888 

99112 

27 

34 
85 

27  28 

32  32 

30213 

35 

69787 

81104. 

37 

68896 

00891 

1 

99109 
9. 99106 

26 
25 

10  27  20 

1  32  40 

9.  30275 

36 

10. 69725 

9.  31168 

38 

10.  68832 

10. 00894 

2 

86 

27  12 

32  48 

30336 

37 

69664 

31233 

39 

68767 

005?&6 

2 

99104 

24 

87 

27  4 

32  56 

80898 

38 

69602 

31297 

40 

68703 

00899 

2 

99101 

23 

88 

26  56 

33  4 

30459 

89 

69541 

31361 

41 

68689 

00901 

2 

99099 

22 

39 

26  48 

83  12 

30521 

40 

69479 

31425 

42 

68575 

00904 

2 
2 

99096 
9. 99093 

21 
20 

40 

10  26  40 

1  33  20 

9. 30582 

41 

10. 69418 

9.  31489 

43 

10.68511 

10. 00907 

41 

26  32 

83  28 

30643 

42 

69357 

31552 

44 

68448 

00909 

2 

99091 

19 

42 

26  24 

33  36 

30704 

43 

69296 

31616 

45 

68384 

00912 

2 

99088 

18 

48 

26  16 

33  44 

80765 

45 

69235 

31679 

46 

68321 

00914 

2 

99086 

17 

44 
45 

26  8 

33  52 

30826 

46 
47 

69174 

31743 

47 

68257 

00917 

2 

2 

99083 

16 
15 

10  26  0 

1  34  0 

9. 30887 

10.69113 

9.  81806 

49 

10. 68194 

10.  00920 

9. 99080 

46 

25  52 

34  8 

30947 

48 

69053 

31870 

50 

68130 

00922 

2 

99078 

14 

47 

25  44 

34  16 

31008 

49 

68992 

31933 

51 

68067 

00925 

2 

99075 

13 

48 

25  86 

34  24 

31068 

50 

68932 

31996 

52 

68004 

00928 

2 

99072 

12 

49 

25  28 

34  82 

31129 

51 

68871 

32059 

53 

67941 

00980 

2 

99070 

11 
10 

50 

10  25  20 

1  34  40 

9. 31189 

52 

10.  68811 

9.  32122 

54 

10. 67878 

10. 00938 

2 

9. 99067 

51 

25  12 

34  48 

31250 

53 

68750 

32185 

55 

67815 

00936 

2 

99064 

9 

52 

25  4 

34  56 

31310 

54 

68690 

82248 

56 

67752 

00938 

2 

99062 

8 

58 

24  56 

35  4 

31370 

55 

68630 

32311 

57 

67689 

00941 

2 

99059 

7 

54 
55 

24  48 

35  12 

31480 

56 

68570 

32373 

58 

67627 

00944 

2 
2 

99056 

6 

10  24  40 

1  35  20 

9.  31490 

57 

10.  68510 

9. 32436 

59 

10. 67564 

10. 00946 

9. 99054 

5 

56 

24  32 

35  28 

31549 

58 

68451 

32498 

60 

67502 

00949 

2 

99051 

4 

57 

24  24 

35  36 

31609 

69 

68391 

32561 

61 

67439 

00952 

2 

99048 

3 

58 

24  16 

35  44 

81669 

60 

68331 

32628 

63 

67877 

00954 

2    99046 

2 

59 

24  8 

35  52 

81728 

61 

68272 

32685 

64 

67315 

00957 

3    99043 

1 

60 

24  0 

36  0 

31788 

62 

68212 

32747 

65 

67253 

00960 

3 

99040 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine.   Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

101° 

A 

A 

B 

B 

C 

C     78°  1 

Seconds  of  time ■  1* 

2' 

3» 

4' 

5»  1  6» 

7' 

Prop,  parts  of  cols.  •{B 

ic 

8 

a 

0 

16 
16 

1 

23 
24 

1 

31 
32 

1 

39  1  47 

40  1  49 

2  !   2 

54 

57 

2 

Page  620] 

TABLE  U. 

Log.  Sines,  Tangents,  and  Secants. 

129 

A            A 

B          B 

C 

C    167° 

M. 

Hour  A.  M. 

Hour  p,  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

DiS. 

Cotangent. 

Secant.  • 

Difl.  j  Cosine. 

M. 
60 

0 

10  24  0 

1  36  0 

9.  31788 

0 

10.  68212 

9. 32747 

0 

10. 67253 

10. 00960 

0  9.99040 

1 

23  52 

36  8 

31847 

1 

68153 

32810   1 

67190 

00962 

0    99088 

59 

2 

23  44 

36  16 

31907 

2 

68093 

32872 

2 

67128 

00965 

0  :      99085 

58 

8 

23  36 

36  24 

31966 

3 

68034 

32933 

3 

67067 

00968 

0    99082 

57 

4 
5 

23  28 
10  23  20 

36  3t 
1  36  40 

82025  j  4 

67975 
10. 67916 

32995 
9.33057 

4 
5 

67005 

00970 
10.  0097'3 

0  '•      99080 
0  9.99027 

56 

55 

9.  32084 

5 

10.  66943 

B 

23  12  1 

36  48 

32143 

6 

67857 

33119 

6 

66881 

00976 

0    99024 

54 

7 

23  4  1 

36  56 

82202 

7 

67798 

33180 

7 

66820 

00978 

0    99022 

53 

8 

22  56 

37  4 

82261 

8 

67739 

33242 

8 

66758 

00981 

0    99019 

52 

9 

22  48 

37  12 

82319 

9 

67681 

33803 

9 

66697 

00984 
10. 00987 

0  ;  99016 
0  9. 99013 

51 
50 

10 

10  22  40 

1  37  20 

9.32378  1  10 

10. 67622 

9. 88365 

10  10.66635  1 

11 

22  32 

37  28 

82437  10 

67563 

33426  11 

66574 

00989 

1    99011 

49 

12 

22  24 

37  36 

82495 

11 

67505 

33487 

12 

66513 

00992 

1    99008 

48 

18 

22  16 

37  44 

32553 

12 

67447 

33548 

13 

66452 

00995 

1    99005 

47 

14 

22  8 

37  52 

32612 

13 
14 

67388 

38609 

14    66391 

00998 

1    99002 

46 
45 

15 

10  22  0 

1  38  0 

9. 32670 

10.  67880 

9. 33670 

15  10.66380 

10. 01000 

1  9.99000 

16 

21  52 

38  8 

32728 

15 

67272 

38731 

16 

66269 

01003 

1   98997 

44 

17 

21  44 

38  16 

82786 

16 

67214 

33792 

17 

66208 

01006 

1   98994 

43 

18 

21  36 

38  24 

32844 

17 

67156 

33853 

18 

66147 

01009 

1  i  98991 

42 

19 
20 

21  28 

38  32 

32902 

18 

67098 

33913 

19 

66087 

01011 
10.01014 

1    98989 
1  9.98986 

41 
40 

10  21  20 

1  38  40 

9. 32960 

19 

10. 67040 

9.  38974 

20  10.66026 

21 

21  12 

38  48 

33018 

20 

66982 

34034 

21    65966 

01017 

1    98983 

.39 

22 

21  4 

38  56 

38075  21 

66925 

34095 

22    65905 

01020 

1    98980 

38 

28 

20  56 

39  4 

33133 

22 

66867 

34155 

28    65845 

01022 

1    98978 

37 

24 

20  48 

39  12 

88190 

28 

66810 

34215 

24 

65785 
10. 65724 

01025 
10.01028 

1    98975 

36 
35 

25 

10  20  40 

1  39  20 

9. 33248 

24 

10.  66752 

9.  34276 

25 

1  9.98972 

26- 

20  32 

39  28 

38805 

25 

66695 

34336 

26  I   6o664 

01031 

1    98969 

34 

27 

20  24 

39  36 

33362 

26 

66638 

34396 

27  1   65604 

01033 

1    98967 

83 

28 

20  16 

39  44 

83420 

27 

66580 

34456 

28 

65544 

01086 

1  '      98964 

32 

29 

20  8 

39  52 

33477  !  28 

66523 

84516 

29 

65484 

01089 

1    98961 

31 

80 

10  20  0 

1  40  0 

9.33534  29 

10. 66466 

9. 34576 

30 

10. 65424 

10. 01042 

1  9.98958 

80 

81 

19  52 

40  8 

33591  29 

66409 

34635 

31 

65365 

01045 

1   98955 

29 

82 

19  44 

40  16 

88647 

30 

66358 

84695 

32  !   65305 

01047 

1   98958 

28 

38 

19  36 

40  24 

83704 

31 

66296 

84755 

83    65245 

01050 

2   98950 

27 

34 
85 

19  28 

40  32 

33761 

32 

66239 

34814 

34    65186 

01053 

2   98947 

26 

25 

10  19  20 

1  40  40 

9.33818 

33 

10.  66182 

9. 34874 

35  10.65126 

10. 01056 

2  9.98944 

36 

19  12 

40  4^ 

33874 

34 

66126 

.34933 

36    65067 

01059 

2    98941 

24 

87 

19  4 

40  56 

38931 

35 

66069 

34992 

37  i   65008 

01062 

2    98988 

23 

88 

18  56 

41  4 

33987 

36 

66013 

35051 

38    64949 

01064 

2    98936 

22 

39 

18  48 

41  12 

34043  i  87 

65957 

8.5111 

39    64889 

01067 

2 

98933 
9. 98930 

21 
20 

40 

10  18  40 

1  41  20 

9. 34100 

38 

10.  65900 

9.  35170 

40  10.64830 

10.01070 

2 

41 

18  32 

41  28 

34156 

39 

65844 

85229 

41  !   64771 

01073 

2 

98927 

19 

42 

18  24 

41  36 

34212 

40 

65788 

85288 

42 

64712 

01076 

2 

98924 

18 

48 

18  16 

41  44 

34268  1  41 

65782 

35347 

43 

64653 

01079 

2 

98921 

17 

44 
45 

18  8 

41  52 

34324  ;  42 

65676 

85405 

44 
45 

64595 

01081 

2 

98919 
9. 98916 

16 
15 

10  18  0 

1  42  0 

9. 34380 

43 

10. 65620 

9.  35464 

10.  64536 

10.  01084 

2 

46 

17  52 

42  8 

34436 

44 

65564 

35523 

46    64477 

01087 

2 

98913 

14 

47 

17  44 

42  16 

34491 

45 

65509 

35581 

47    64419 

01090 

2 

98910 

13 

48 

17  36 

42  24 

34547 

46 

65453 

35640 

48    64360 

01093 

2 

98907 

12 

49 

17  28 

42  32 

34602 

47 

65398 

35698 

49    64302 

01096 

2 

98904 

11 

50 

10  17  20 

1  42  40 

9.84658  1  48 

10. 65342 

9. 35757 

50  110.64243 

10. 01099 

2 

9. 98901 

10 

51 

17  12 

42  48 

34713 

48 

65287 

35815 

51 

641^5 

01102 

2 

98898 

9 

52 

17  4 

42  56 

34769 

49 

65231 

85873 

52 

64127 

01104 

2 

98896 

8 

53 

16  56 

43  4 

34824 

50 

65176 

35981 

53 

64069 

01107 

2 

98893 

7 

54 

16  48 

43  12 

34879 

51 

65121 

85989 

64 

64011 

OHIO 

3 
3' 

98890 
9. 98887 

6 
5 

55 

10  16  40 

1  43  20 

9. 34934 

52 

10. 65066 

9. 36047 

55  10.63953 

10.01113 

56 

16  32 

43  28 

34989 

53 

65011 

36105 

56 

63895 

01116 

3 

98884 

4 

57 

16  24 

43  36 

35044 

54 

64956 

36163 

57 

63837 

01119 

3 

98881 

3 

58 

16  16 

43  44 

35099 

55 

64901 

36221 

58 

63779 

01122 

8 

98878 

2 

59 

16  8 

43  52 

35154 

56 

64846 

36279 

59 

63721 

01125 

3 

98875 

1 

60 

16  0 

44  0 

35209 

57 

64791 

36836 

60 

63664 

01128 

3 
Difl. 

98872 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine,  j  Diflf. 

Secant. 

Cotangent. 

Difif. 

Tangent. 

Cosecant. 

Sine. 

M. 

102 

o 

A           A 

B           B 

C 

C     77°  1 

Seconds  of  time 


Prop,  parts  of  cols. -{B 
C 


TABLE  U. 

[Page  621 

I 

Mg.  Sines,  Tangents,  and  Secants. 

13° 

A 

A 

B 

B 

C 

C    166° 

M. 

Hour  A.M. 

Hour  P.  M. 

Sine. 
9. 35209 

Diff. 

Cosecant. 

Tangent.  Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

0 

10  16  0 

1  44  0 

0 

10.  64791 

9. 36336 

0 

10.  63664 

10.01128 

0 

9. 98872 

1 

15  52 

44  8 

35268 

1 

64737 

36394 

1 

63606 

01181 

0  !   98869  1 

59 

?< 

15  44 

44  16 

35818 

2 

64682 

86452 

2 

68548 

01183 

0 

98867 

58 

8 

15  86 

44  24 

85373 

3 

&4627 

36509 

3 

63491 

01186 

0 

98864 

57 

4 

15  28 

44  32 

35427 

4 

64578 
10.  64519 

36566 

4 
5 

63484 
10.  63876 

01189 

0 

98861 

56 
55 

5 

10  15  20 

1  44  40 

9. 85481 

4 

9. 36624 

10.  01142 

0 

9. 98858 

fi 

15  12 

44  48 

35536 

5 

64464 

86681 

6 

68319 

01145 

0 

98855 

54 

7 

15  4 

44  56 

35590 

6 

64410 

36738 

6 

63262 

01148 

0 

98852 

53 

8 

14  56 

45  4 

85644 

7 

64356 

36795 

7 

63205 

01151 

0 

98849 

52 

9 

14  48 

45  12 

35698 

8 

64302 

36852 

8 

63148 

01154 

0 

98846 

51 

10 

10  14  40 

1  45  20 

9.  ;^752 

9 

10. 64248 

9.  36909 

9 

10. 63091 

10.01157 

9. 98848 

50 

n 

14  82 

45  28 

35806 

10 

64194 

36966 

10 

63034 

01160 

98840 

49 

12 

14  24 

45  86 

35860 

11 

64140 

37023 

11 

62977 

01163 

98887 

48 

i;s 

14  16 

45  44 

85914 

11 

64086 

37080 

12 

62920 

01166 

98834 

47 

14 

14  8 

45  52 

85968 

12 

64082 

37137 

13 

62868 

01169 

98831 

46 
45 

15 

10  14  0 

1  46  0 

9. 86022 

13 

10.  63978 

9. 37193 

14 

10.  62807 

10.01172 

9. 98828 

ifi 

18  52 

46  8 

36075 

14 

63925 

87250 

15 

62750 

01175 

98825 

44 

17 

18  44 

46  16 

36129 

15 

68871 

87306 

16 

62694 

01178 

98822 

43 

18 

18  86 

46  24 

36182 

16 

68818 

37363 

17 

62637 

01181 

98819 

42 

19 

18  28 

46  32 

86236 

17 

63764 

37419 

18 

62581 

01184 

98816 

41 

20 

10  18  20 

1  46  40 

9. 36289 

18 

10.  63711 

9.  37476 

19 

10. 62524 

10.01187 

9. 98813 

40 

21 

13  12 

46  48 

36842 

18 

63658 

37532 

19 

62468 

01190 

98810 

39 

22 

13  4 

46  56 

36895 

19 

68605 

37588 

20 

62412 

01193 

98807 

88 

28 

12  56 

47  4 

36449 

20 

63551 

37644 

21 

62356 

01196 

98804 

37 

24 
25 

12  48 

47  12 

36502 

21 

6,3498 

37700 

22 

62300 

01199 

98801 

36 
35 

10  12  40 

1  47  20 

9. 36555 

22  !l0.6;i445 

9.  37756 

23 

10.  62244 

10. 01202 

9. 98798 

2rt 

12  82 

47  28 

36608 

23 

68392 

37812 

24 

62188 

01205 

98795 

34 

27 

12  24 

47  86 

36660 

24 

68340 

37868 

25 

62182 

01208 

98792 

38 

28 

12  16 

47  44 

36713 

25 

63287 

37924 

26 

62076 

01211 

98789 

32 

29 
30 

12  8 

47  52 

36766 

25 

63284 

37980 

27 

62020 

01214 
10. 01217 

2 

98786 

31 

10  12  0 

1  48  0 

9.  86819 

26  110.63181 

9.  38035 

28 

10. 61965 

9. 98788 

30 

81 

11  52 

48  8 

36871 

27    68129 

38091 

29 

61909 

01220 

2 

98780 

29 

82 

11  44 

48  16 

36924 

28    68076 

38147 

30 

61858 

01223 

2 

98777 

28 

88 

11  86 

48  24 

36976 

29 

6.8024 

38202 

31 

61798 

01226 

2 

98774 

27 

84 
85 

11  28 

48  32 

37028 

30 

62972 

38257 

32 

61743 
10.  61687 

01229 
10. 01232 

2 
2 

98771 

26 
25 

10  11  20 

1  48  40 

9. 37081 

31 

10.  62919 

9. 38813 

32 

9. 98768 

m 

11  12 

48  48 

87183 

32 

62867 

38868  !  33 

61632 

01235 

2 

98765 

24 

87 

11  4 

48  56 

37185 

32 

62815 

88423  1  34 

61577 

012.38 

2 

98762 

23 

88 

10  56 

49  4 

87237 

33 

62763 

38479  i  a5 

61521 

t)1241 

2 

98759 

22 

89 

10  48 

49  12 

87289 

34 

62711 

38534  36 

61466 

01244 

2 

98756 

21 

40 

10  10  40 

1  49  20 

9. 87841 

35 

10.  62659 

9. 38589  37 

10. 61411 

10.01247 

2 

9. 98758 

20 

41 

10  32 

49  28 

87893 

36 

62607 

88644  88 

61856 

01250 

2 

98750 

19 

42 

10  24 

49  86 

87445 

37 

62555 

88699 

39 

61301 

01254 

2 

98746 

18 

48 

10  16 

49  44 

37497 

38 

62503 

88754 

40 

61246 

01257 

2 

98748 

17 

44 
45 

10  8 

49  52 

37549 
9. 37600 

39 

62451 

88808 

42 

61192 
10.  61137 

01260 
10.  01263 

2 
2 

98740 

16 
15 

10  10  0 

1  50  0 

39  10.62400 

9. 38863 

9. 98787 

46 

9  52 

50  8 

37652 

40 

62348 

38918 

43 

61082 

01266 

2 

98784 

14 

47 

9  44 

50  16 

37703 

41 

62297 

38972 

44 

61028 

01269 

2 

98731 

13 

48 

9  36 

50  24 

37755 

42 

62245 

39027 

45 

60973 

01272 

2 

98728 

12 

49 

50 

9  28 

50  32 

37806 
9.37858 

43 
44 

62194 
10. 62142 

39082 

45 

60918 

01275 

2 

98725 

11 
10 

10  9  20 

1  50  40 

9.  39136 

46 

10. e0864 

10. 01278 

3 

9. 98722 

51 

9  12 

50  48 

37909 

45 

62091 

39190 

47 

60810 

01281 

3 

98719 

9 

52 

9  4 

50  56 

37960 

46 

62040 

39245 

48 

60755 

01285 

3 

98715 

8 

58 

8  56 

51  4 

38011 

47 

61989 

39299 

49 

60701 

01288 

3 

98712 

7 

54 

8  48 

51  12 

38062 

47 

61988 

39353 

50 

60647 

01291 

3 

98709 

6 

55 

10  8  40 

1  51  20 

9.88113 

48 

10.  61887 

9. 39407 

51 

10.  60593 

10. 01294 

3 

9. 98706 

5 

56 

8  32 

51  28 

88164 

49 

61836 

39461 

52 

60589 

01297 

3 

98703 

4 

57 

8  24 

51  86 

38215 

50 

61785 

39515 

53 

60485 

01300 

3 

98700 

3 

58 

8  16 

51  44 

38266 

51 

61784 

39569 

54 

60431 

01303 

3 

98697 

2 

59 

8  8 

51  52 

38817 

52 

61683 

39623 

55 

60377 

01306 

3 

98694 

1 

60 
M. 

8  0 

52  0 

38368 

53 

61682 

39677 

56 
Diff. 

60323 
Tangent. 

01310 

3 

98690 

0 
M. 

Hour  P.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Cosecant. 

Diff. 

Sine. 

103° 

A 

A 

B 

B 

C 

C     76°  1 

Seconds  of  time 

1«  i  2' 

3s  ^  4,  ^  5»  j  6' 

7» 

Prop,  parts  of  cols.  <  B 

Ic 

7 
7 
0 

13 
14 

1 

20  26 

21  28 
1     2 

33    39 
8.5    42 

2    2 

46 

49 

3 

Page  622] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

14° 

A 

A 

B           B 

C 

C 

16o° 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 
10.  60323 

Secant. 

Diff. 

Cosine. 

10  8  0 

1  52  0 

9. 38368 

0 

10. 61632 

9. 39677 

0 

10.  01310 

0 

9. 98690 

60 

1 

7  52 

52  8 

3S418 

1  !   61582 

39731 

1 

60269 

01313 

0 

98687 

59 

2 

7  44 

52  16 

38469 

2 

61531 

39785 

9 

60215 

01316 

0 

98684 

58 

3 

7  36 

52  24 

38519 

2 

61481 

39838 

3 

60162 

01319 

0 

98681 

57 

4 

7  28 

52  32* 

38570 

3 

61430 

39892 

3 

60108 

01322 

0 

98(>78 

56 
55 

5 

10  7  20 

1  52  40 

38620 

4 

10.  61380 

9. 39945 

4 

10. 60055 

10. 01325 

0 

9. 98675 

6 

7  12 

52  48 

38670 

5 

61330 

39999 

5 

60001 

01329 

0 

98671 

54 

7 

7  4 

52  56 

38721 

6 

61279 

40052 

6 

599t8 

01332 

0 

98668 

53 

8 

6  56 

53  4 

38771 

7 

61229 

40106 

7 

59894 

01335 

0 

98665 

52 

9 

6  48 

53  12 

38821 

7 

61179 

40159 

8 

59841 

01338 

0 

98662 

51 

10 

10  6  40 

1  53  20 

9. 38871 

8 

10. 61129 

9.40212  i  9 

10. 59788 

10. 01341 

9. 98659 

50 

11 

6  32 

53  28 

38921 

9 

61079 

40266  10 

59734 

01344 

98656 

49 

12 

6  24 

53  36 

38971 

10 

61029 

40319  1  10 

59681 

01348 

98652 

48 

13 

6  16 

53  44 

39021 

11 

60979 

40372  j  11 

59628 

01351 

98649 

47 

14 

6  8 

53  52 

39071 

11 

60929 

40425  1  12 

59575 

01354 

98646 

46 
15 

15 

10  6  0 

1  54  0 

9. 39121 

12  ilO.  60879 

9.40478  i  13 

10.  59522 

10. 01357 

9. 98643 

16 

5  52 

54  8 

39170 

13    60830 

40531  14 

59469 

01360 

98640 

44 

17 

5  44 

54  16 

39220 

14 

60780 

40584  15 

59416 

01364 

98636 

43 

18 

5  36 

54  24 

39270 

15 

60730 

40636  16 

59364 

01367 

98633 

42 

19 
20 

5  28 
10  5  20 

54  32 

39319 

15 

60681 
10. 60631 

40689  17 

59311 

01370 

— J- 

98630 
9. 98627 

41 
40 

1  54  40 

9. 39369 

16 

9.40742  :  17 

10. 59258 

10. 01373 

21 

5  12 

54  48 

39418 

17 

60582 

40795  1  18 

59205 

01377 

98623 

39 

22 

5  4 

54  56 

39467 

18 

60533 

40847  19 

59153 

01380 

98620 

38 

23 

4  56 

55  4 

■  39517 

19 

60483 

40900  20 

59100 

01383 

98617 

37 

24 

4  48. 

55  12 
1  55  20 

39566 
S. 39615 

20 

60434 

40952  !  21 

59048 

01386 

98614 

36 

25 

10  4  40 

20  10.60385 

9.41005  22  10.58995 

10. 01390 

9. 98610 

35 

26 

4  32 

55  28 

39664 

21    60336 

41057  !  23 

58943 

01393 

98607 

34 

27 

4  24 

55  36 

39713 

22    60287 

41109  23 

58891 

01396 

98604 

33 

28 

4  16 

55  44 

39762 

23    60238 

41161  24 

58839 

01399 

2 

98601 

32 

29 

4  8 

55  52 

39811 

24    60189 

41214  25 

58786 

01403 

2 

98597 

31 

30 

10  4  0 

1  56  0 

9.  39860 

24  10.60140 

9.41266  26  10.58734 

10. 01406 

2 

9. 98594 

30 

31 

3  52 

56  8 

39909 

25 

60091 

41318  27 

58682 

01409 

2 

98591 

29 

32 

3  44 

56  16 

39958 

26 

60042 

41370  28 

58630 

01412 

2 

98588 

28 

33 

3  36 

56  24 

40006 

27 

59994 

41422  29 

58578 

01416 

2 

98584 

27 

34 

3  28 

56  32 

40055 

28    59945 

41474  30 

58526 

01419 

2 

2 

98581 
9. 98578 

26 
25 

35 

10  3  20 

1  56  40 

9. 40103 

29  10.59897 

9.41526  30 

10.  58474 

01422 

36 

3  12 

56  48 

40152 

29 

59848 

41578  31 

58422 

01426 

2 

98574 

24 

37 

3  4 

56  56 

40200 

30 

59800 

41629  32 

58371 

01429 

2 

98571 

23 

38 

2  56 

57  4 

40249 

31 

59751 

41681  1  33 

58319 

01432 

2 

98568 

22 

39 

2  48 

57  12 

40297 

32    59703 

41733  1  34 

58267 

01435 

2 

98565 

21 

40 

10  2  40 

1  57  20 

9. 40346 

33 

10.  59654 

9.41784  35  110.58216 

10. 01439 

2 

9. 98561 

20 

41 

2  32 

57  28 

40394 

33 

59606 

41836  36 

58164 

01442 

2 

98558 

19 

42 

2  24 

57  36 

40442 

34 

59558 

41887  !  36 

58113 

01445 

2 

98555 

18 

43 

2  16 

57  44 

40490 

36 

59510 

41939  i  37 

58061 

01449 

2 

98551 

17 

44 

2  8 

57  52 

40538 

36 

59462 

41990 

38 

58010 

01452 

2 

985^8 

16 
15 

45 

10  2  0 

1  58  0 

9. 40586 

37 

10.  59414 

9. 42041 

39 

10.  57959 

10. 01455 

2 

9. 98545 

46 

1  52 

58  8 

40634 

37 

59366 

42093  40  i   57907 

01459 

3 

98541 

14 

47 

1  44 

58  16 

40682 

38 

59318 

42144  41 

57856 

01462 

3 

98538 

13 

48 

1  36 

58  24 

40730 

39 

59270 

42195  42 

57805 

01465 

3 

98535 

12 

49 

1  28 

58  32 

40778 

40 

59222 

42246  43 

57754 

01469 

3 
3 

98531 
9. 98528 

11 
10 

50 

10  1  20 

1  58  40 

9. 40825 

41  :i0.  59175 

9.42297  :  43 

10.  57703 

10. 01472 

51 

1  12 

58  48 

40873 

42 

59127 

42348  i  44 

57652 

01475 

3 

98525 

9 

52 

1  4 

58  56 

40921 

42 

59079 

42399  i  45 

57601 

01479 

3 

98521 

8 

53 

0  56 

59  4 

40968 

43 

59032 

42450 

46 

57550 

01482 

3 

98518 

7 

54 

0  48 

59  12 

41016 

44 

58984 

42501 

47 

48 

57499 

01485 

3 

98515 
9.98511 

6 
5 

55 

10  0  40 

1  59  20 

9. 41063 

45  10.58937 

9. 42552 

10. 57448 

10.  01489 

3 

56 

0  32 

59  28 

41111 

46 

58889 

42603 

49 

57397 

01492 

3 

98508 

4 

57 

0  24 

59  36 

41158 

46 

58842 

42653 

50 

57347 

01495 

3 

98505 

3 

58 

0  16 

59  44 

41205 

47 

58795 

42704 

50 

57296 

01499 

3 

98501 

2 

59 

0  8 

59  52 

41252 

48 

58748 

42755 

51 

57245 

01502 

3 

98498 

1 

60 

0  0 

2  0  0 

41300 

49 

58700 

42805 

52 

57195 

01506 

3 

98494 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

104° 

A 

A 

B            B 

C 

c 

76° 

Seconds  of  time 

1« 

2« 

3» 

4» 

5> 

«• 

7» 

fA 

Prop,  parts  of  cols,  i  B 
IC 

6 

7 
0 

12 
13 
1 

18 
20 

1 

24 

26 

2 

31 

83 

2 

37 

39 

2 

43 
40 
3 

TABLE  44. 

[Page  623 

Log. 

Sines,  Tangents,  and  Secants. 

15° 

A 

A 

B 

B 

C 

C   164° 

M. 
0 

Hour  A.M. 
10  0  0 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff.  Cosine. 

M. 

2  0  0 

9.41300 

0 

10.  58700 

9. 42805 

0 

10. 57195 

10.  01506 

0  ! 9.  98494 

60 

1 

9  59  52     0  8 

41347 

1 

58653 

42856 

1 

57144 

01509 

0   98491 

59 

2 

59  44     0  16 

41394 

2 

5860(5 

42906 

2 

57094 

01512 

0  1   98488  1  58  1 

8 

59  36  1    0  24 

41441 

2 

58559 

42957 

2 

57043 

01516 

0   98484  !  57  I 

4 

59  28     0  32 

41488 

3 

58512 

43007 

3 

56993 

01519 

0 

98481  56 

5 

9  59  20  2  0  40 

9.  41535 

4 

10.  58465 

9. 43057 

4 

10. 56943 

10. 01523 

0 

9.98477  55 

6 

59  12     0  48 

41582 

5 

58418 

43108 

5 

56892 

01526 

0  1  98474 

54 

7 

59  4     0  56 

41628 

5 

58372 

43158 

6 

56842 

01529 

0  1  98471 

53 

8 

58  56  ;    14' 

41675 

6 

58325 

43208 

7 

56792 

01533 

0  ;  98467 

52 

9 
10 

58  48  !    1  12 

41722 

7 

58278 

43258 

7 

56742 

01536 

98464 
9. 98460 

51 
50 

9  58  40  2  1  20 

9.  41768 

8 

10.  58232 

9. 43308 

8 

10. 56692 

10. 01540 

1 

n 

58  32     1  28 

41815 

8 

58185 

43358 

9 

56642 

01543 

98457 

49 

12 

58  24     1  36 

41861 

9 

58139 

43408 

10 

56592 

01547 

98453 

48 

13 

58  16  ,    1  44 

41908 

10 

58092 

43458 

11 

56542 

01550 

98450 

47 

14 
15 

58  8 
9  58  0 

1  52 

41954 
9. 42001 

11 
11 

58046 

43508 

11 

56492 

01553 
10.  01557 

98447 
9.  9844;^ 

46 
45 

2  2  0 

10.  57999 

9. 43558 

12  110.56442 

16 

57  52  i    2  8 

42047 

12 

57953 

43607 

13 

56393 

01560 

98440 

44 

17 

57  44 

2  16 

42093 

13 

57907 

43657 

14 

56343 

01564 

98436 

43 

18 

57  36 

2  24 

42140 

14 

57860 

43707 

15 

56293 

01567 

98433 

42 

19 

57  28 

2  32 

42186 

14 

57814 

43756 
9. 43806 

16 

56244 

01571 
10. 01574 

98429 

41 

20 

9  57  20  i  2  2  40 

9. 42232 

15 

10. 57768 

16 

10.  56194 

1  9. 98426  1  40  | 

21 

57  12  j    2  48 

42278 

16 

57722 

43855 

17 

56145 

01578 

1    98422 

39 

22 

57  4     2  56 

42324 

17 

57676 

43905 

18 

56095 

01581 

1    98419 

38 

23 

56  56 

3  4 

42370 

17 

576.30 

43954 

19  i   56046 

01585 

1  ,   98415 

37 

24 
25 

56  48 

3  12 

42416 

18 

57584 

44004 

20 

55996 

01588 

1    98412  1  36 

9  56  40  i  2  3  20 

9. 42461 

19 

10.  57539 

9. 44053 

20 

10. 55947 

10.  01591 

1  9.98409  1  35 

26 

56  32     3  28 

42507 

20 

57493 

44102 

21 

55898 

01595 

2    98405 

34 

27 

56  24     3  36 

42553 

21 

57447 

44151 

2-2 

55849 

01598 

2    98402 

33 

28 

56  16     3  44 

42599 

21 

57401 

44201 

23 

55799 

01602 

2    98398 

32 

29 
30 

56  8     3  52 

42644 
9. 42690 

22 
23 

57356 
10.57310 

44250 

24 

55750 

01605 

2   98395 

31 

9  56  0 

2  4  0 

9. 44299 

25  ilO.  55701 

10. 01609 

2  9.98391  i  30 

31 

55  52 

4  8 

42735 

24 

57265 

44.348 

25 

55652 

01612 

2   98388  t  29 

32 

55  44     4  16 

42781 

24 

57219 

44397 

26 

55603 

01616 

2  '   98384  28 

33 

55  36  1    4  24 

42826 

25 

57174 

44446 

27 

55554 

01619 

2  i  98381 

27 

34 

55  28  i    4  32 

42872 

26 

57128 
10. 57083 

44495 
9. 44544 

28 

55505 

01623 

2   98377 

26 
25 

35 

9  55  20 

2  4  40 

9.42917 

27 

29 

10.  55456 

10. 01627 

2  9.98373 

36 

55  12 

4  48 

42962 

27 

57038 

44592 

29 

55408 

016.30 

2   98370 

24 

37 

55  4 

4  56 

43008 

28 

56992 

44641 

30 

55359 

01634 

2   98366 

23 

38 

54  56 

5  4 

43053 

29 

56947 

44690 

.31 

55310 

01637 

2   98363 

22 

39 
40 

54  48 
9  54  iO' 

5  12 

43098 

30 
30 

56902 

44738 
9. 44787 

32 
33 

55262 
10. 55213 

01641 
10.  01644 

2   98359  1  21 
2  9.  98356  i  20 

2  5  20 

9.  43143 

10. 56857 

41 

54  32 

5  28 

43188 

31 

56812 

44836 

34 

55164 

01648 

2 

98352  19 

42 

54  24 

5  36 

43233 

32 

56767 

44884 

34 

55116 

01651 

2 

98349  18 

43 

54  16 

5  44 

43278 

33 

56722 

44933 

35 

55067 

01655 

3 

98345  17 

44 

54  8 

5  52 

43323 
9. 43367 

33 
34 

56677 

44981 
9. 45029 

36 
37 

55019 
10. 54971 

01658 
10.  01662 

3 

98342  t  16 

45 

9  54  0 

2  6  0 

10. 56633 

3  9. 98338  15  1 

46 

53  52 

6  8 

4.3412 

35 

56588 

45078 

38 

54922 

01666 

3   98.334  14  I 

47 

53  44     6  16 

43457 

36 

56543 

45126 

38 

54874 

01669 

3   98331 

13 

48 

53  36  i    6  24 

43502 

36 

56498 

45174 

39 

54826 

01673 

3   98327 

12 

49 
50 

53  28 

6  32 
2  6  40 

43546 

37 

56454 

45222 
9. 45271 

40 
41 

54778 
10. 54729 

01676 
10. 01680 

3 
3 

98324 

11 
10 

9  53  20 

9. 43591 

38 

10.  56409 

9. 98320 

51 

53  12  i    6  48. 

43635 

39 

56365 

45319 

42 

54681 

01683 

3 

98317 

9 

52 

53  4  ■    6  56 

43680 

39 

56320 

45367 

43 

54633 

01687 

3 

98313 

8 

53 

52  56 

7  4 

43724 

40 

56276 

45415 

43 

54585 

01691 

3 

98309 

7 

54 
55 

52  48 
9  52  40 

7  12 
2  7  20 

43769 
9743813 

41 
42 

56231 

45463 
9.45511 

44 
45 

54537 

01694 
10.01698 

3 
3 

98306 
9.  98302 

6 

5 

10. 56187 

10. 54489 

56 

52  32 

7  28 

43857 

43 

56143 

45559 

46 

54441 

01701 

3 

98299 

4 

57 

52  24 

7  36 

43901 

43 

56099 

45606 

47- 

54394 

01705 

3 

98295 

3 

58 

52  16 

7  44 

43946 

44 

56054 

45654 

47 

54.346 

01709 

3 

98291 

2 

59 

52  8 

7  52 

43990 

45 

56010 

45702 

48 

54298 

01712 

3 

98288 

1 

60 

52  0 

8  0 

440.34 

46 

55966 

45750 

49 

54250 

01716 

4 

98284 

0 

M. 

Hour  p.  M. 

Hour  A.  x. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

105° 

A 

A 

B 

B 

C 

C     74°  1 

.Seconds  of  time ;  1»    '2'    \     3' 

4»    5» 

6'    1' 

A    6 

Prop,  parts  of  cols.  B    6 

Ic   0 

11 

12 

1 

17 

18 
1 

23    28 

25    31 

2    2 

34    40 

37    43 

3    3 

Page  624] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

1S° 

A            A 

B 

B 

C 

C 

163° 

M. 

Hour  A.  M 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

9  52  0 

2  8  0 

9. 44034 

0 

10.  55966 

9. 45750 

0 

10.  542.50 

10.01716 

0 

9. 98284 

60 

1 

51  52 

8  8 

44078 

1 

55922 

45797 

1 

54203 

01719 

0 

98281 

59 

2 

51  44 

8  16 

44122   1 

55878 

45845 

2 

541.55 

01723 

0 

98277 

58 

8 

51  36 

8  24 

44166   2 

55834 

45892 

2 

54108 

01727 

0 

98273 

57 

4 

51  28 

8  ^2 

44210   3 
9. 44253   4 

557f;0 
10.  55747 

45940 
9. 45987' 

3 
4 

54060 
10.  54013 

01730 
10. 61734 

0    98270 
0  9.98266 

56 
55 

5 

9  51  20 

2  8  40 

6 

51  12 

8  48 

44297 

4 

55703 

46035 

5 

53965 

01738 

0    98262 

54 

7 

51  4 

8  56 

44341 

5 

55659 

46082 

5 

53918 

01741 

0  '   98259 

53 

8 

50  56 

9  4 

44385 

6 

55615 

46130 

6 

53870 

01745 

0    98255 

52 

9 
10 

50  48 

9  12 

44428 

6 

55572 
10. 5.5528 

46177 
9. 46224 

7 
8 

53823 
10. 53776 

01749 

1    98251 
1  9.98248 

51 
,50 

9  50  40 

2  9  20 

9. 44472 

7 

10.01752 

11 

50  32 

9  28 

44516   8 

55484 

46271 

9 

53729 

017.56 

98244 

49 

12 

50  24 

9  36 

44559   9 

55441 

46319 

9 

53681 

01760 

98240 

48 

13 

50  16 

9  44 

44602   9 

55398 

46366 

10 

53634 

01763 

98237 

47 

14 

15 

50  8 

9  50  0 

9  52 

44646  10 
9.44689  1  11 

553.54 
10.5.5311 

46413 
9. 46460 

11 
12 

5.3587 

01767 

98233 
9. 98229 

46 
45 

2  10  0 

10.  ,53540 

10.01771 

16 

4  )  52 

10  8 

447.33  1  11 

55267 

46507 

12 

53493 

01774 

98226 

44 

17 

49  44 

10  16 

44776  12 

55224 

46554 

13 

53446 

01778 

98222 

43 

18 

4  J  36 

10  24 

44819  13 

55181 

46601 

14 

53399 

01782 

98218 

42 

19 
20 

49  28 
9  49  20 

10  32 
2  10  40 

44862 

14 
14 

55138 
10.  55095 

46648 
9.46694 

15 
15 

53352 
10. 53306 

01785 
10.01'78'9 

98215 

41 

9.  44905 

9.98211 

40 

21 

49  12 

10  48 

44948  1  15 

5.5052 

46741 

16 

53259 

01793 

98207 

39 

22    49  4 

10  56 

44992  16 

55008 

46788 

17 

53212 

01796 

98204 

38 

23    48  56 

11  4 

45035   16 

54965 

46835 

18 

,53165 

01800 

1 

98200 

37 

24    48  48 

11  12 

46077  17 

54923 

46881 

19 

53119 

01804 

98196 

36 

25  9  48  40 

2  11  20 

9.45120  18 

10.  .54880 

9. 46928 

19 

10. 53072 

10.01808 

2 

9.98192 

35 

26    48  32 

11  28  ^ 

45163  18 

54837 

46975 

20 

53025 

01811 

2 

98189 

34 

27    48  24 

11  36  ' 

45206   19 

54794 

47021 

21 

52979 

01815 

2 

98185 

33 

28    48  16 

11  44 

45249  20 

54751 

47068 

22 

52932 

01819 

2 

98181 

32 

29 
30 

48  8 

11  52 
2  12  0 

45292  21 
9.453.34  21 

54708 

47114 

22 

52886 

01823 

2 

98177 

31 
30 

9  48  0 

10.54666 

9.  47160 

23 

10.  52840 

10.  01826 

2 

9.98174 

31 

47  52 

12  8 

45377  i  22 

54623 

47207 

24 

52793 

01830 

2 

98170 

29 

32 

47  44 

12  16  ' 

45419  23 

54581 

47253 

25 

52747 

01834 

2 

98166 

28 

33 

47  36 

12  24 

45462  :  23 

54538 

47299 

26 

52701 

01838 

2 

98162 

27 

34 

47  28 

12  32 
2  12  40 

45504  :  24 
9.4.5547  25 

54496 
10.  54453 

47346 
9. 47392 

26 

27 

52654 

10.  52608 

01841 

2 

98159 

26 
25 

35 

9  47  20 

10.01845 

2 

9.981.55 

36 

47  12 

12  48 

4.5589  26 

54411 

47438 

28 

52562 

01849 

2 

98151 

24 

37 

47  4 

12  56 

45632  26 

54368 

47484 

29 

52516 

018,53 

2 

98147 

23 

38    46  56 

13  4 

45674  27 

54326 

47.530 

29 

52470 

01856 

2 

98144 

22 

39  46  48 

40  9  46  40 

13  12 
2  13  20 

45716 

28 
28' 

54284 
10.  .54242 

47576 
9. 47622 

30 
31 

52424 

01860 
10.01864 

2 
2 

98140 
9»98136 

21 
20 

9. 45758 

10. 52378 

41    46  32 

13  28 

45801  29 

54199 

47668 

32 

52.332 

01868 

3 

98132 

19 

42    46  24 

13  36 

45843  30 

54157 

47714 

32 

52286 

01871 

3 

98129 

18 

43    46  16 

13  44 

45885  31 

54115 

47760 

33 

52240 

01875 

3 

98125 

17 

44  46  8 

45  9  46  0 

13  52 
2  14  0 

4,5927 

31 

54073 
10.  .54031 

47806 
9.  47852 

34 
35 

.52194 
10.  ,52148 

01879 
10. 01883 

3 
3 

98121 
9.98117 

16 
15 

9. 45969 

32 

46    45  52 

14  8 

46011 

33 

53989 

47897 

36 

52103 

01887 

3 

98113 

14 

47    45  44 

14  16 

46053 

33 

53947 

47943 

36 

52057 

01890 

3 

98110 

13 

48  ■  45  36 

14  24 

46095  i  34 

53905 

47989 

37 

52011 

01894 

3 

98106 

12 

49    45  28 

14  32 

461.36  1  35 

53864 

48035 

38 

51965 

01898 

3 

98102 

11 

50  i  9  45  20 

2  14  40 

9.46178  .36 

10. 53822 

9. 48080 

39 

10.51920 

10.01902 

3 

9. 98098 

10 

51    45  12 

14  48 

46220  i  36 

53780 

48126 

39 

51874 

01906 

3 

98094 

9 

52  j   45  4 

14  56 

46262  37 

53738 

48171 

40 

51829 

01910 

3 

98090 

8 

53  I   44  56 

15  4 

46303  38 

53697 

48217 

41 

51783 

01913 

3 

98087 

7 

54 

44  48 

15  12 

46.345  38 

53655 
10.53614 

48262 
9.  48.307 

42 
43 

51738 

01917 

3 
3 

98083 

6 
5 

55 

9  44  40 

2  15  20 

9.46386  39 

10. 51693 

10. 01921 

9. 98079 

56 

44  32 

15  28 

46428  40 

53572 

48353 

43 

5ia47 

01925 

3 

98075 

4 

57 

44  24 

15  36 

46469  41 

•   53531 

48398 

44 

51602 

01929 

4 

98071 

3 

58 

44  16 

15  44 

46511  !  41 

53489 

48443 

45 

51.5-57 

01933 

4 

98067 

2 

59 

44  8 

15  52 

46552  1  42 

5.3448 

48489 

46 

51511 

01937 

4 

98063 

1 

60 
M. 

44  0 

16  0 

46594 

43 

53406 
Secant. 

48534 

46 

51466 

01940 

4 
Diff 

98060 

0 
M. 

Hour  p.  M. 

Hour  A.  M. 

Casine. 

Diff. 

Cotangent 

Diff. 

Tangent. 

Cosecant. 

Sine. 

106° 

A            A 

B 

B 

C 

C 

73° 

Seconds  of  time 

1" 

«• 

3« 

4' 

&> 

6< 

7" 

Prop,  parts  of  cols. 

(1 

5 
6 
0 

11 

12 

1 

16 

17 

1 

21 
•23 

2 

27 

29 

2 

32 

35 

3 

37 
41 
3 

TABLE  44. 

[Page  625 

Log.  Sines,  Tangents,  and  Secants. 

17° 

A           A 

B            B 

C 

C    162° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Difl.  Cosine. 

M. 

0 

9  44  0 

2  16  0 

9. 46594 

0 

10.  53406 

9. 48584 

0 

10.  51466 

10.  01940 

0  9.98060 

60 

1 

48  52 

16  8 

46685 

1 

53365 

48579 

1 

51421 

01944 

0    98056 

59 

2 

48  44 

16  16 

46676 

1 

53324 

48624 

1 

51376 

01948 

0    98052 

58 

8 

48  86 

16  24 

46717 

2 

53283 

48669 

2 

51331 

019.52 

0   98048 

57 

4 
5 

43  28 

16  32 

46758 

3 

54242 

48714 

3 

51286 

01956 

0   98044 

56 
55 

9  43  20 

2  16  40 

9. 46800 

3 

10. 53200 

9.48759 

4 

10. 51241 

10.  01960 

0  9.98040 

6 

43  12 

16  48 

4()S41 

4 

53159 

48804 

4 

51196 

01964 

0 

98036 

54 

1 

43  4 

16  56 

4(i8S2 

5 

53118 

48849 

5 

51151 

01968 

0 

98032 

58 

8 

42  56 

17  4 

46923 

5 

53077 

48894 

6 

51106 

01971 

98029 

52 

9 
10 

42  48 

17  12 

46964 

6 

7 

53036 
10. 52995 

48939 

7 

51061 

01975 

98025 

51 

9  42  40 

2  17  20 

9.  47005 

9. 48984 

7 

10. 51016 

10.  01979 

9. 98021 

50 

11 

42  32 

17  28 

47045 

7 

52955 

49029 

8 

50971 

01983 

1  1   98017 

49 

12 

42  24 

17  36 

47086 

8 

52914 

49073 

9 

50927 

01987 

1  1  98013 

48 

13 

42  16 

17  44 

47127 

9 

52873 

49118  i  10 

50882 

01991 

1  1  98009 

47 

14 
15 

42  8 

17  52 
2  18  0 

47168 

9 

52832 
10. 52791 

49163 

10 

50837 

01995 

1  1  98005 
1  9.98001 

46 

45 

9  42  0 

9. 47209 

10 

9. 49207 

11  110.50793 

10. 01999 

16 

41  52 

18  8 

47249 

11 

52751 

49252 

12 

50748 

02008 

97997 

44 

17 

41  44 

18  16 

47290 

11 

52710 

49296 

12 

50704 

02007 

97998 

43 

18 

41  36 

18  24 

47830 

12 

52670 

49341 

13 

50659 

02011 

97989 

42 

19 

41  28 

18  32 

47371 

13 

52629 

49385 

14 

50615 

02014 

1  '  97986 

41 

20 

9  41  20 

2  18  40 

9.47411 

13 

10. 52589 

9. 49430 

15 

10. 50570 

10.02018 

1  9.97982 

40 

21 

41  12 

18  48 

47452 

14 

52548 

49474 

15 

50526 

02022 

1  I     979.78 

39 

22 

41  4 

18  56 

47492 

15 

52508 

49519 

16 

50481 

02026 

1   97974 

38 

28 

40  56 

19  4 

47533 

15 

52467 

49563 

17 

50487 

02080 

2   97970 

37 

24 

40  48 

19  12 

47573 

16 

52427 

49607 

18 

50393 

02084 
10.  02038 

2   97966 
2  9.97962 

36 
35 

25 

9  40  40 

2  19  20 

9.  47613 

17 

10. 52387 

9. 49652 

18 

10. 50848 

2(5 

40  32 

19  28 

47654 

17 

52346 

49696 

19 

50304 

02042 

2 

97958 

34 

27 

40  24 

19  36 

47694 

18 

52306 

49740 

20 

50260 

02046 

2 

97954 

33 

28 

40  16 

19  44 

47734 

19 

52266 

49784 

21 

50216 

02050 

2 

97950 

32 

29 

40  8 

19  52 

47774 

19 
20 

52226 

49828 

21 
22 

50172 

02054 

2 
2 

97946 

31 
30 

80 

9  40  0 

2  20  0 

9.47814 

10.52186 

9. 49872 

10. 50128 

10.  02058 

9. 97942 

81 

39  52 

20  8 

47854 

21 

52146 

49916 

23 

50084 

02062 

2 

97938 

29 

82 

39  44 

20  16 

47894 

21 

52106 

49960 

24 

50040 

02066 

2 

97934 

28 

88 

39  36 

20  24 

47934 

22 

52066 

50004 

24 

49996 

02070 

2 

97930 

27 

34 
85 

39  28 

20  32 

47974  j  23 

52026 

50048 
9. 50092 

25 
26 

49952 
10. 49908 

02074 

2 

97926 

26 
25 

9  39  20 

2  20  40 

9.  48014 

23 

10. 51986 

10.  02078 

2  9.97922 

36 

39  12 

20  48 

48054 

24 

51946 

50136 

26 

49864 

02082 

2 

97918 

24 

37 

39  4 

20  56 

48094 

25 

51906 

50180 

27 

49820 

02086 

2 

97914 

23 

38 

38  56 

21  4 

48133 

25 

51867 

50223 

28 

49777 

02090 

3 

97910 

22 

39 
40 

38  48 

21  12 
2  21  20 

48173 

26 

51827 

50267 

29 

49733 

02094 

3  i  97906 
3  9.97902 

21 
20 

9  38  40 

9. 48213 

27 

10.  51787 

9.50311 

29  ilO.  49689 

10.  02098 

41 

38  32 

21  28 

48252 

27 

51748 

50.355 

30  1   49645 

02102 

3  j  97898 

19 

42 

38  24 

21  86 

48292 

28 

51708 

50398 

31    49602 

02106 

3  ;  97894 

18 

43 

38  16 

21  44 

48332 

29 

51668 

50442 

32    49558 

02110 

3   97890 

17 

44 
45 

38  8 

21  52 
2  22  0 

48371 

29 
30 

51629 
10. 51589 

50485 

32    49515 

02114 

3 
3 

97886 
9. 97882 

16 
15 

9  38  0 

9.48411 

9. 50529 

33  10.49471 

10.02118 

46 

87  52 

22  8 

48450 

31 

51550 

50572 

34 

49428 

02122 

3 

97878 

14 

47 

37  44 

22  16 

48490 

31 

51510 

50616 

35 

49884 

02126 

3 

97874 

13 

48 

37  36 

22  24 

48529 

32 

51471 

50659 

35 

49341 

02130 

3 

97870 

12 

49 
50 

37  28 
9  37  20 

22  32 
2  22  40 

48568 

33 
33 

51432 
10. 51393 

50703 
9. 50746^ 

36 

49297 

02134 

3   97866 

11 
10 

9. 48607 

37 

10.  49254 

10. 02139 

3  9.97861 

51 

37  12 

22  48 

48647 

'34 

51353 

50789 

37 

49211 

02143 

3   97857 

9 

52 

37  4 

22  56 

48686 

35 

51314 

50833 

38 

49167 

02147 

3 

97853 

8 

58 

36  56 

23  4 

48725 

35 

51275 

50876 

39 

49124 

02151 

4 

97849 

t 

54 
55 

36  48 
9  36  40 

23  12 
2  23  20 

48764 

36 

51236 

50919 
9. 50962 

40 
40 

49081 

02155 

4 

97845 

6 
5 

9. 48803 

37 

10.51197 

10. 49038 

10. 02159 

4 

9.  97841 

56 

36  32 

23  28 

48842 

37 

51158 

51005  41 

48995 

02163 

4 

97887 

4 

57 

36  24 

23  36 

48881 

38 

51119 

51048 

42 

48952 

02167 

4 

97888 

3 

58 

36  16 

23  44 

48920 

39 

51080 

51092 

43 

48908 

02171 

4 

97829 

2 

59 

36  8 

23  52 

48959 

39 

51041 

511.35 

43 

48865 

02175 

4 

97825 

1 

60 

36  0 

24  0 

48998 

40 

51002 

51178 

44 

48822 

02179 

4 

97821 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent.]  Diflf. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

107° 

A           A 

B           B 

C 

C     72°  1 

Seconds  of  time 


Prop,  parts  of  cols.  -{B 
C 


10 
11' 

\ 


30 
33 
L3 


22489-03- 


40 


Page  626] 

TABLE  U. 

Log. 

Sines,  Tangents,  and  Secants. 

18° 

A 

A 

B            B 

C 

C     161° 

M. 
0 

Hour  A.M. 
9  36  0 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent.  Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine.  1 

M. 

2  24  0 

9. 48998 

0 

10.  51002 

9.51178 

0 

10.  48822 

10.  02179 

0  I  9.  97821  1 

60 

1 

35  52 

24  8 

49037 

1 

50963 

51221 

1 

48779 

02183 

0 

97817 

59 

2 

85  44 

24  16 

49076 

1 

50924 

51264 

1 

48736 

02188 

0 

97812 

58 

8 

35  36 

24  24 

49115 

2 

50885 

51806 

2 

48694 

02192 

0 

97808 

57 

4 
5 

35  28 

24«82 

49158 

3 

50847 

51349 

8 

48651 

02196 

0 
0 

97804 

56 
55 

9  35  20 

2  24  40 

9. 49192 

8 

10. 50808 

9. 51392 

3 

10. 48608 

10. 02200 

9. 97800 

6 

85  12 

24  48 

49281 

4 

50769 

51435 

4 

48565 

02204 

0 

97796 

54 

7 

35  4 

24  56 

49269 

4 

50731 

51478 

5 

48522 

02208 

0 

97792 

53 

8 

34  56 

25  4 

49308 

5 

50692 

51520 

6 

48480 

02212 

97788 

52 

9 

34  48 

25  12 

49347 

6 

50653 

51563 

6 

48437 

02216 

97784 

51 
50 

10 

9  34  40 

2  25  20 

9. 49385 

6 

10.  50615 

9.  51606 

7 

10. 48394 

10. 02221 

9. 97779 

11 

84  32 

25  28 

49424 

7 

50576 

51648 

8 

48352 

02225 

97775 

49 

12 

34  24 

25  86 

49462 

8 

50538 

51691 

8 

48309 

02229 

97771 

48 

18 

34  16 

25  44 

49500 

8 

50500 

51784 

9 

48266 

02233 

97767 

47 

14 

84  8 

25  52 

49539 

9 

50461 

51776 

10 

48224 

02237 

97763 

46 
45 

15 

9  34  0 

2  26  0 

9. 49577 

9 

10. 50428 

9. 51819 

10  10.48181 

10. 02241 

9. 97759 

1« 

38  52 

26  8 

49615 

10 

50385 

51861 

11 

48139 

02246 

97754 

44 

17 

83  44 

26  16 

49654 

11 

50346 

51903 

12 

48097 

02250 

97750 

43 

18 

33  36 

26  24 

49692 

11 

50308 

51946 

18 

48054 

02254 

97746 

42 

19 

33  28 

26  32 

49730 
9. 49768 

12 
13 

50270 
10.  50232 

51988 
9. 52031 

18 

48012 

02258 

97742 

41 
40 

20 

9  88  20 

2  26  40 

14 

10. 47969 

10. 02262 

9. 97738 

21 

.  33  12 

26  48 

49806 

13 

50194 

52073 

15 

47927 

02266 

97734 

39 

22 

83  4 

26  56 

49844 

14 

50156 

52115 

15 

47885 

02271 

2 

97729 

38 

23 

82  56 

27  4 

49882 

14 

50118 

52157 

16 

47843 

02275 

2 

97725 

37 

24 

32  48 

27  12 

49920 

15 

50080 

52200 

17 

17 

47800 

02279 

2 

97721 

36 

25 

9  32  40 

2  27  20 

9. 49958 

16 

10. 50042 

9. 52242 

10. 47758 

10. 02283 

2 

9. 97717 

85 

26 

32  82 

27  28 

49996 

16 

50004 

52284 

18 

47716 

02287 

2 

97713 

84 

27 

82  24 

27  86 

50084 

17 

49966 

52326 

19 

47674 

02292 

2 

97708 

33 

28 

32  16 

27  44 

50072 

18 

49928 

52368 

20 

47632 

02296 

2 

97704 

32 

29 

82  8 

27  52 

50110 

18 

49890 

52410 

20 

47590 

02300 

2 

97700 

81 

30 

9  82  0 

2  28  0 

9. 50148 

19 

10. 49852 

9. 52452 

21 

10. 47548 

10. 02304 

2 

9. 97696 

30 

31 

31  52 

28  8 

50185 

20 

49815 

52494 

22 

47506 

02309 

2 

97691 

29 

82 

31  44 

28  16 

50228 

20 

49777 

52536 

22 

47464 

02313 

2 

97687 

28 

83 

31  36 

28  24 

50261 

21 

49739 

52578 

28 

47422 

02317 

2 

>  97688 

27 

34 

81  28 

28  82 

50298 

21 

49702 

52620 

24 

47380 

02321 

2 

97679 

26 
25 

85 

9  81  20 

2  28  40 

9. 50336 

22 

10. 49664 

9. 52661 

24 

10. 47389 

10.  02326 

2 

9. 97674 

86 

31  12 

28  48 

50374 

23 

49626 

52708 

25 

47297 

02880 

3 

97670 

24 

37 

81  4 

28  56 

50411 

23 

49589 

52745 

26 

47255 

02334 

3 

97666 

23 

88 

30  56 

29  4 

50449 

24 

49551 

52787 

27 

47213 

02838 

3 

97662 

22 

39 
40 

30  48 

29  12 

50486 

25 

49514 

52829 

27 

47171 
10. 47130 

02848 

3 

97657 

21 
20 

9  30  40 

2  29  20 

9. 50523 

25 

10. 49477 

9. 52870 

28 

10. 02847 

3 

9. 97653 

41 

30  32 

29  28 

50561 

26 

49489 

52912 

29 

47088 

02351 

3 

97649 

19 

42 

30  24 

29  86 

50598 

26 

49402 

52953 

29 

47047 

02355 

3 

97645 

18 

43 

30  16 

29  44 

50635 

27 

49865 

52995 

80 

47005 

02360 

3 

97640 

17 

44 

30  8 

29  62 

50673 

28 

49327 

58087 

31 

46963 

02864 

3 

97636 

16 

45 

9  30  0 

2  30  0 

9.  50710 

28 

10. 49290 

9.  58078 

31 

10. 46922 

10. 02868 

8 

9. 97682 

15 

46 

29  52 

30  8 

50747 

29 

49253 

53120 

82 

46880 

02372 

8 

97628 

14 

47 

29  44 

30  16 

50784 

80 

49216 

53161 

83 

46889 

02377 

3 

97623 

18 

48 

29  36 

30  24 

50821 

30 

49179 

53202 

34 

46798 

02381 

3 

97619 

12 

49 

29  28 

30  32 

50858 

31 

49142 

58244 

84 

46756 

02385 

8 
4 

97615 
9. 97610 

11 
10 

50 

9  29  20 

2  30  40 

9. 50896 

31 

10. 49104 

9. 58285 

35 

10. 46715 

10.02390 

51 

29  12 

30  48 

50988 

82 

49067 

53327 

36 

46673 

02394 

4 

97606 

9 

52 

29  4 

30  56 

50970 

38 

49030 

53368 

36 

46632 

02398 

4 

97602 

8 

53 

28  56 

31  4 

r^007 

88 

48998 

53409 

37 

46591 

02408 

4 

97597 

/ 

54 
55 

28  48 
9  28  40 

31  12 
2  31  20 

51043 

84 
85 

48957 
10. 48920 

58450 
9. 53492 

38 
88 

46550 
10. 46508 

02407 
10. 02411 

4 
4 

97593 
9.  97589 

6 
5 

9.  51080 

56 

28  82 

31  28 

51117 

85 

48888 

53533 

89 

46467 

02416 

4 

97584 

4 

57 

28  24 

81  36 

51154 

36 

48846 

53574 

40 

46426 

02420 

4 

97580 

3 

58 

28  16 

31  44 

51191 

37 

48809 

53615 

41 

46385 

02424 

4 

97576 

2 

59 

28  8 

31  52 

51227 

87 

48773 

53656 

41 

46344 

02429 

4 

97571 

i 

60 

28  0 

82  0 

51264 

88 

48736 

53697 

42 

46303 

02488 

4 

97567 

0 
M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

108 

3 

A 

A 

B           B 

C 

C    71°| 

Seconds  of  time 

1» 

2« 

8» 

4' 

5> 

6» 

T 

Prop,  parts  of  cols.  <B 

5 
5 
1 

9 

10 

1 

14 
16 
2 

19 
21 

2 

24 

26 
3 

28 

31 

3 

38 

37 
4 

TABLE  U. 

[Page  627 

Log.  Sines,  Tangents,  and  Secants. 

10° 

A             A 

B 

B 

C 

C    106° 

M. 

Hour  A.  M. 

Hour  P.M. 

Sine. 

Dlff. 

Cosecant. 

Tangent. 

Diflf. 

Cotangent. 

Secant. 

Diflf. 

Cosine. 

M. 

0 

9  28  0 

2  32  0 

9. 51264 

0 

10.  48736 

9. 53697 

0 

10.  46303 

10.  02433 

0 

9. 97567 

60 

1 

27  52 

32  8 

51301 

1 

48699 

53738 

1  i   46262 

02437 

0 

97563 

59 

2 

27  44 

32  16 

51338 

1 

48662 

53779 

1  1   46221 

02442 

0 

97558 

58 

?, 

27  36 

32  24 

51374 

2 

48626 

53820 

2  I   46180 

02446 

0 

97554 

57 

4 
5 

27  28 
9  27  20 

32  32 
2  32  40' 

51411 

2 

48589 

53861 

3  !   46139 

02450 

0 
0 

97550 

56 
55 

9.  51447 

3  10.48553 

9. 53902 

3  i 10.  46098 

10. 02455 

9.97545 

(i 

27  12 

32  48 

51484 

4 

48516 

53943 

4  I   46057 

02459 

0 

97541 

54 

I 

27  4 

32  56 

51520 

4 

48480 

53984 

5  1   46016 

02464 

97536 

53 

8 

26  56 

33  4 

51557 

5 

48443 

54025 

5  'i   45975 

02468 

1   97532 

52 

9 

26  48 

33  12 

51593 

5  !   48407 

54065 
9. 54106 

6 

7 

45935 

02472 

97528 

51 
50 

10 

9  26  40 

2  33  20 

9. 51629 

6  10.48371 

10.  45894 

10. 02477 

9. 97523 

11 

26  32 

33  28 

51666 

7 

48334 

54147 

7  i   45853 

02481 

97519 

49 

12 

26  24 

33  36 

51702 

7 

48298 

54187 

8    4.5813 

02485 

97515 

48 

18 

26  16 

33  44 

51738 

8 

48262 

54228 

9    45772 

02490 

97510 

47 

14 

26  8 

33  52 

51774 

8 

48226 

54269 

9  !   45731 

02494 

97506 

46 
45 

15 

9  26  0 

2  34  0 

9.51811 

9 

10. 48189 

9. 54309 

10  10.45691 

10.  02499 

9. 97501 

16 

25  52 

34  8 

51847 

10 

48153 

54350 

11    45650 

02503 

97497 

44 

17 

25  44 

34  16 

51883 

10 

48117 

54390 

11    45610 

02508 

97492 

43 

18 

25  36 

34  24 

51919 

11 

48081 

54431 

12    45569 

02512 

97488 

42 

19 

25  28 

34  32 

51955 

11 

48045 

54471 

13    45529 

02516 

97484 

41 
40 

20 

9  25  20 

2  34  40 

9. 51991 

12 

10.  48009 

9.54512 

13  10.45488 

10. 02521 

9.  97479 

21 

25  12 

34  48 

52027  !  12 

47973 

54552 

14  ,   45448 

02525 

2 

97475 

39 

22 

25  4 

34  56 

52063 

13 

47937 

54593 

15    45407 

02530 

2 

97470 

38 

23 

24  56 

35  4 

52099 

14 

47901 

54633 

15    45367 

02534 

2 

97466 

37 

24 
25 

24  48 

35  12 

52135 

14 

47865 

54673 

16 

45327 
10.  45286 

02539 

2 

97461 

36 
35 

9  24  40 

2  35  20 

9.52171 

15 

10.  47829 

9. 54714 

17 

10.  02543 

2 

9. 97457 

26 

24  32 

35  28 

52207 

15 

47793 

54754 

17    45246 

02547 

2 

97453 

34 

27 

24  24 

35  36 

52242 

16 

47758 

54794 

18    45206 

02552 

2 

97448 

33 

28 

24  16 

35  44 

52278 

17 

47722 

54835 

19  ,   45165 

02556 

2 

97444 

32 

29 

24  8 

35  52 

52314 

17 

47686 

54875 

19  !   45125 

02561 

2 

97439 

31 
30 

30 

9  24  0 

2  36  0 

9.52350 

18 

10.  47650 

9.  54915 

20  10.45085 

10. 02565 

2 

9. 97435 

31 

23  52 

36  8 

52385 

18 

47615 

54955 

21  i   45045 

02570 

2 

97430 

29 

32 

23  44 

36  16 

52421 

19 

47579 

54995 

21 

45005 

02574 

2 

97426 

28 

33 

23  36 

36  24 

52456 

20 

47544 

55035 

22 

44965 

02579 

2 

97421 

27 

34 

23  28 

36  32 

52492 

20 

47508 

55075 

23 

44925 

02583 

3 

97417 

26 

35 

9  23  20 

2  36  40 

9. 52527 

21 

10.47473 

9.55115 

23 

10. 44885 

10.  02588 

3 

9. 97412 

25 

36 

23  12 

36  48 

52563 

21 

47437 

55155 

24 

44845 

02592 

3 

97408 

24 

37 

23  4 

36  56 

52598 

22 

47402 

55195 

25 

44805 

02597 

3 

97403 

23 

38 

22  56 

37  4 

52634 

23 

47366 

55235 

25 

44765 

02601 

3 

97399 

22 

39 

22  48 

37  12 

52669 

23 

47331 

55275 

26 

27 

44725 

02606 

3 

97394 
9. 97390 

21 
20 

40 

9  22  40 

2  37  20 

9. 52705 

24 

10. 47295 

9.  55315 

10.  44685 

10. 02610 

3 

41 

22  32 

37  28 

52740 

24 

47260 

55355 

27 

44645 

02615 

3 

97385 

19 

42 

22  24 

37  36 

52775 

25 

47225 

55395 

28 

44605 

02619 

3 

97381 

18 

43 

22  16 

37  44 

52811 

26 

47189 

55434 

29 

44566 

02624 

3 

97376 

17 

44 

45 

22  8 
9  22  0 

37  52 

52846 
9. 52881 

26 

27 

47154 

55474 

29 

44526 

02628 

3 

97372 

16 
15 

2  38  0 

10.47119 

9. 55514 

30  ;  10. 44486 

10. 02633 

3 

9. 97367 

46 

21  52 

38  8 

52916 

27 

47084 

55554 

31 

44446 

02637 

3 

97363 

14 

47 

21  44 

38  16 

52951 

28 

47049 

55593 

31 

44407- 

02642 

3 

97358 

13 

48 

21  36 

38  24 

52986 

29 

47014 

55633 

32 

44367 

02647 

4 

97353 

12 

49 
50 

21  28 

38  32 

53021 

29 

46979 

55673 

33 

44327 

02651 

4 

97349 

11 

9  21  20 

2  38  40 

9. 53056 

30 

10.  46944 

9.55712 

33 

10. 44288 

10. 02656 

4 

9. 97344 

10 

51 

21  12 

38  48 

53092 

30 

46908 

55752 

34 

44248 

02660 

4 

97340 

9 

52 

21  4 

38  56 

53126 

31 

46874 

55791 

35 

44209 

02665 

4 

97335 

8 

53 

20  56 

39  4 

53161 

32 

46839 

55831 

35 

44169 

02669 

4 

97331 

t 

54 
55 

20  48 

39  12 

53196 

32 

46804 

55870 

36 

441.30 

02674 

4 

97326 

6 
5 

9  20  40 

2  39  20 

9. 53231 

33 

10.  46769 

9. 55910 

37  !10.  44090 

10.  02678 

4 

9. 97322 

56 

20  32 

39  28 

53266 

33 

46734 

55949 

37 

44051 

02683 

4 

97317 

4 

n{ 

20  24 

39  36 

53301 

34 

46699 

55989 

38 

44011 

02(588 

4 

97312 

3 

58 

20  16 

39  44 

53336 

34 

46664 

56028 

39, 

4.3972 

02692 

4 

97308 

2 

59 

20  8 

39  52 

53370 

35 

46630 

56067 

39 

43933 

02697 

4 

97303 

1 

60 

20  0 

40  0 

53406 

36 

46595 

56107 

40 

43893 

02701 

4 

97299 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant.  * 

Cotangent. 

Difif. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

109= 

A            A 

B 

B 

C 

C     70°  1 

Seconds  of  time. 


Prop,  parts 


of  cols.! 

I' 


Page  628] 

TABLE  U, 

Log.  Sines,  Tangents,  and  Secants. 

20° 

A            A 

B 

B 

C 

C 

159° 

M. 

0 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Difl. 

Co.sine. 

M. 

60 

9  20  0 

2  40  0 

9. 58405 

0 

10.  46595 

9. 56107 

0 

10.  43898 

10. 02701 

0 

9.  97299 

1 

19  52 

40  8 

53440 

1 

46560 

56146 

1 

48854 

0270(5 

0 

97294 

59 

•) 

19  44 

40  16 

58475 

1 

46525 

56185 

1 

43815 

02711 

0 

97289 

58 

8 

19  36 

40  24 

5:^09 

2 

46491 

56224 

2 

43776 

02715 

0 

97285 

57 

4 
5 

19  28 

40  3t 
2  40  40 

53544 
9. 53578 

2 
3 

46456 
10.  46422 

56264 

3 
3 

43736 
10. 43697 

02720 
10.02724 

0 
0 

97280 

56 

9  19  20 

9. 56303 

9. 97276 

55 

6 

19  12 

40  48 

53613 

3 

46387 

56342 

4 

43658 

02729 

0 

97271 

54 

7 

19  4 

40  56 

53647   4 

46353 

56381 

4 

43619 

02734 

9726() 

53 

8 

18  56 

41  4 

58682 

5 

46318 

56420 

5 

43580 

02738 

972()2 

52 

9 
10 

18  48 

41  12 

53716 

5 
6 

46284 

56459 

6 

43541 
10. 43502 

.  02743 
10. 02748 

97257 
9. 97252 

51 
50 

9  18  40 

2  41  20 

9. 53751 

10.  46249 

9. 56498 

6 

11 

18  32 

41  28 

53785 . 

6 

46215 

5a537 

/ 

43463 

02752 

97248 

49 

12 

18  24 

41  36 

58819 

7 

46181 

56576 

8 

43424 

02757 

97243 

48 

13 

18  16 

41  44 

53854 

7 

46146 

56615 

8 

43385 

02762 

97238 

47 

14 

18  8 

41  52 

53888   8 

46112 

56654 

9    43846 

02766 

97234 

46 

15 

9  18  0 

2  42  0 

9. 58922   8 

10. 46078 

9. 56693 

10  110.43307 

10.02771 

J 

9. 97229 

45 

16 

17  52 

42  8 

53957   9 

46043 

56732 

10 

43268 

02776 

97224 

44 

17 

17  44 

42  16 

53991 

10 

46009 

56771 

11 

43229 

02780 

97220 

43 

18 

17  36 

42  24 

54025 

10 

45975 

56810 

12    43190 

02785 

97215 

42 

19 
20" 

17  28 

42  32 

54059 
9. 54093  ' 

11 
11 

45941 
10. 45907 

56849 
9.56887 

12  1   43151 

13  10.43113 

02790 

2 

97210 
9. 97206 

41 
40 

9  17  20 

2  42  40 

10. 02794 

21 

17  12 

42  48 

54127 

12 

45878 

56926 

13    43074 

02799 

2 

97201 

39 

22 

17  4 

42  56 

54161 

12 

45839 

56965 

14  !   43085 

02804 

2 

97196 

88 

28 

16  56 

43  4 

54195 

13 

45805 

57004 

15  !   42996 

02808 

2 

97192 

37 

24 

16  48 

43  12 

54229 

14 
14 

45771 
10.  45737 

57042 

15 

42958 
10.  42919 

02813 

2 

97187 

36 

25 

9  16  40 

2  43  20 

9. 54263 

9. 57081 

16 

10.  02818 

2 

9.  97182 

35 

26 

16  32 

43  28 

54297 

15 

45703 

57120 

17    42880 

02822 

2 

97178 

34 

27 

16  24 

43  36 

54831 

15 

45669 

57158 

17  i   42842 

02827. 

2 

97173 

88 

28 

16  16 

43  44 

54365 

16 

45635 

57197 

18  i   42803 

02832 

2 

97168 

82 

29 

16  8 

43  52 

54399 

16 

45601 

57235 

19    42765 
19  10.42726 

02837 

2 

97163 

31 
80 

30 

9  16  0 

2  44  0 

9. 54488 

17 

10. 45567 

9.  57274 

10. 02841 

2 

9. 97159 

81 

15  52 

44  8 

54466 

17 

45534 

57312 

20  i   42688 

02846 

2 

97154 

29 

82 

15  44 

44  16 

54500 

18 

'  45500 

57351 

21    42649 

02851 

3 

97149 

28 

88 

15  36 

44  24 

54534 

19 

45466 

57389 

21    42611 

02855 

3 

97145 

27 

84 
85 

15  28 

44  32 

•54567 

19 

45433 

57428 

22    42572 

02860 

3 

97140 

26 

9  15  20 

2  44  40 

9.54601  i  20  '10.45399 

9. 57466 

22  10.42534 

10.  02865 

8 

9.97135 

25 

86 

15  12 

44  48 

54635  20  1   45365 

57504 

23    42496 

02870 

3 

97180 

24 

87 

15  4 

44  56 

54668  1  21  i   45332 

57543 

24    42457 

02874 

3 

97126 

23 

88 

14  56 

45  4 

54702  1  21  1   45298 

57581 

24  i   42419 

02879 

3 

97121 

22 

39 
40 

14  48 
9  14  40 

45  12 
2  45  20 

54735 

22  1   45265 

23  10.45231 

57619 
9. 57658 

25 
26 

42381 

02884 

3 

97116 
9.97111 

21 
201 

9. 54769 

10.  42342 

10. 02889 

3 

41 

14  32 

45  28 

54802  '  23  i   45198 

57696 

26    42304 

02898 

3 

97107 

19' 

42 

14  24 

45  36 

54886  1  24 

45164 

57734 

27    42266 

02898 

3 

.  97102 

18 

48 

14  16 

45  44 

54869  1  24 

45131 

57772 

28  :   42228 

02903 

3 

97097 

17 

44 

14  8 

45  52 

54908  1  25 

45097 

57810 

28    42190 

02908 

3 

97092 

16 
15 

45 

9  14  0 

2  46  0 

9.54986  i  25 

10.  45064 

9. 57849 

29  10.42151 

10. 02913 

4 

9. 97087 

46 

13  52 

46  8 

54969  '  26 

45031 

57887 

30    42113 

02917 

4 

97083 

14 

47 

13  44 

46  16 

55003  26 

44997 

57925 

30    42075 

02922 

4 

97078 

13 

48 

13  36 

46  24 

55036 

27 

44964 

57963 

t  31    42037 

02927 

4 

97073 

12 

49 
50 

13  28 

46  32 

55069 

28 

44931 

58001 

,   31  i   41999 

02932 

4 
4 

97068 
9. 97068 

11 
10 

9  13  20 

2  46  40 

9. 55102 

28 

10. 44898 

9. 58039 

32  10.41961 

10.  02937 

51 

13  12 

46  48 

55136 

29 

44864 

58077 

33    41923 

02941 

4 

97059 

9 

52 

13  4 

46  56 

55169 

29 

44831 

58115 

33  1   41885 

02946 

4 

97054 

8 

58 

12  56 

47  4 

55202 

30 

44798 

58153 

34 

41847 

02951 

4 

97049 

•  7 

54 

12  48 

47  12 
2  47  20 

55235 

30 

44765 
10. 44732 

58191 

35 

41809 

02956 
10. 02961 

4 
4 

97044 
9. 97039 

6 

5 

55 

9  12  40 

9.55268  31 

9. 58229 

1  35 

10. 41771 

56 

12  32 

47  28 

55301  i  32 

44699 

58267 

i  36 

41733 

02965 

4 

97085 

4 

57 

12  24 

47  36 

55334  I  32 

44666 

58304 

1  37 

41696 

02970 

4 

97030 

8 

58 

12  16 

47  44 

55367  33 

44633 

58342 

!  37 

41658 

02975 

5 

97025 

2 

59 

12  8 

47  52 

55400  33 

44600 

58380 

1  38  1   41620 

02980 

5 

97020 

1 

60 

12  0 

48  0 

55433  34 

44567 

58418 

39  !   41582 

02985 

5 

97015 

0 

M. 
(5»° 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine.  |  Difl. 

Secant. 

Cotangent. 

Diff.  Tangent. 

Cosecant. 

Diff. 

Sine. 

110° 

A            A 

B 

1? 

c 

r 

Seconds  of  time 

!• 

2» 

8- 

4» 

b' 

6* 

J» 

Prop,  parts  of  cols.  •;  B 

4 

5 
1 

8 

10 
1 

13 
14 

2 

17 

19 

2 

21 

24 

3 

25 
29 
4  . 

30 
84 

4 

TABLE  44. 

[Page  629 

Log.  Sines,  Tangents,  and  Secants. 

21° 

A             A 

B 

B 

C 

C    158° 

M. 

Hour  A.M. 

Hour  P.M. 

Sine. 

Did. 

Cosecant. 

Tangent. 

Difif. 

Cotangent. 

Secant. 

Difif. 

Cosine. 

M. 

0 

9  12  0 

2  48  0 

9.55433 

0 

10.  44567 

9.  58418 

0 

10.  41582 

10.  02985 

0 

9.  97015 

60 

1 

11  52 

48  8 

55466 

1 

44534 

58455 

1 

41545 

02990 

0 

97010 

59 

2 

11  44 

48  16 

55499 

1 

44501 

58493 

1 

41507 

02995 

0 

97005 

58 

3 

11  36 

48  24 

55532 

2 

44468 

58531 

2 

41469 

02999 

0 

97001 

57 

4 

11  28 

48  32 

55564 

2 

44436 

58569 

2 

41431 

03004 

0 
0 

96996 

56 
"55 

5 

9  11  20 

2  48  40 

9. 55597 

3 

10. 44403 

9. 58606 

3 

10.  41394 

10. 03009 

9. 96991 

6 

11  12    48  48 

55630 

3 

^4370 

58644 

4 

41356 

03014 

0 

96986 

54 

7 

11  4  !   48  56 

55663 

4 

44337 

58681 

4 

41319 

03019 

1 

96981 

53 

8 

10  56    49  4 

55695 

4 

44305 

58719 

5 

41281 

03024 

1 

96976 

52 

9 
10 

10  48    49  12 
9  10  40  2  49  20 

55728 
9. 55764 

5 

44272 

58757 
9. 58794 

6 
6 

41243 

03029 

1 

96971 

51 
50 

5 

10. 44239 

10.41206 

10. 03034 

1 

9. 96966 

11 

10  32    49  28 

55793 

6 

44207 

58832 

7 

41168 

03038 

1 

96962 

49 

12 

10  24    49  36 

55826 

6 

44174 

58869 

7 

41131 

03043 

1 

96957 

48 

13 

10  16  i   49  44 

55858 

7 

44142 

58907 

8 

41093 

03048 

1 

96952 

47 

14 

10  8 

49  52 

55891 

7 

44109 

58944 

9 

41056 

03053 

1 

96947 

46 

15  ;  9  10  0 

2  50  0 

9. 55923 

8  ilO.  44077 

9. 58981 

9 

10. 41019 

10. 03058 

1 

9. 96942 

45 

16  1    9  52  !   50  8 

55956 

9 

44044 

59019 

10 

40981 

03063 

1 

96937 

44 

17 

9  44 

50  16 

55988 

9 

44012 

59056 

10 

40944 

03068 

1 

96932 

43 

18 

9  36 

50  24 

56021 

10 

43979 

59094 

11 

40906 

03073 

1 

96927 

42 

19 

9  28 

50  32 

56053 
9.56085 

10 
11 

43947 
10.  43915 

59131 

12 

40869 
10.  40832 

03078 
10. 03083 

2 
2 

96922 

41 
40 

20 

9  9  20  i  2  50  40 

9. 59168 

12 

9.96917 

21 

9  12  1   50  48 

56118 

11 

43882 

59205 

13 

40795 

03088 

2 

96912 

39 

22 

9  4    50  56 

56150 

12  1   43850 

59243 

14 

40757 

03093 

2 

96907 

38 

23 

8  56  1   51  4 

56182 

12  1   43818 

59280 

14 

40720 

03097 

2 

96903 

37 

24 
25 

8  48  1   51  12 

56215 
9. 56247 

13 
13 

43785 

59317 
9.59354 

15 

15 

40683 
10.  40646 

03102 
10.03107 

2 
2 

96898 

36 
35 

9  8  40  I  2  51  20 

10. 43753 

9.96893 

26 

8  32  1   51  28 

56279  1  14    43721 

59391  i  16 

40609 

03112 

2 

96888 

U 

27 

8  24    b\  36 

56311 

14    43689 

59429 

17 

40571 

03117 

2 

96883 

33 

28 

8  16    51  44 

56343 

15    43657 

59466 

17 

40534 

03122 

2 

96878 

32 

29 

8  8 

51  52 
2  52  0 

56375 

16    43625 

59503 

18 
19 

40497 
10.  40460 

03127 
10.  03132 

2 
2 

96873 

31 

30 

9  8  0 

9. 56408 

16  10.43592 

9. 59540 

9. 96868 

30 

31 

7  52  i   52  8 

56440 

17    43560 

59577 

19 

40423 

03137 

3 

96863 

29 

32 

7  44  1   52  16 

56472 

17    43528 

59614 

20 

40386 

03142 

3 

96858 

28 

33 

7  36  '   52  24 

56504  :  18    43496 

59651 

20 

40349 

03147 

3 

96853 

27 

34 

7  28    52  32 

56536  18    43464 
9.56568  1  19  10.43432 

59688 
9. 59725 

21 
22 

40312 
10. 40275 

03152 
10.03157 

3 

96848 

26 
25 

35 

9  7  20  2  52  40 

3 

9. 96843 

36  1    7  12    52  48 

•  56599  19    43401 

59762 

22 

40238 

03162 

3  i   96838 

24 

37  !    7  4    52  50 

56631   20    43369 

59799  23 

40201 

03167 

3 

96833 

23 

38  !    6  56    53  4 

56663  20    43337 

59835  i  23 

40165 

03172 

3 

96828 

22 

39  1    6  48    53  12 

56695  i  21 

43305 
10.  43273 

59872 

24 
25 

40128 
10. 40091 

03177 

3 

96823 

21 
20 

40 

9  6  40  2  53  20 

9.56727  21 

9. 59909 

10. 03182 

3  19.96818 

41 

6  32    53  28 

56759  22    43241 

59946 

25 

40054 

03187 

3   96813 

19 

42 

6  24    53  36 

56790  22    43210 

59983 

26 

40017 

03192 

3  j   96808 

18 

43 

6  16    53  44 

56822  23    43178 

60019  27 

39981 

03197 

4    96803 

17 

44 

6  8 

53  52 
2 '54  0 

56854  24  ']      43146 
9.56886  24  10.43114 

60056  1  27 
9.60093  1  28 

39944 

03202 

4  1   96798 

16 

45 

9  6  0 

10.  39907 

10.  03207 

4  19.96793 

15 

46     5  52    54  8 

56917  25    43083 

60130  1  28 

39870 

03212 

4  1   96788 

14 

47 

5  44    54  16 

56949  25    43051 

60166  29 

39834 

03217 

4    96783 

13 

48 

5  36    54  24 

56980  26    43020 

60203  30 

39797 

03222 

4  1   96778 

12 

49 
50 

5  28    54  32 
9  5  20  2  54  40 

57012 
'9. 57044 

26  1   42988 

60240  1  30 
9. 60276  31 

39760 
10.  39724 

03228 
10.  03233 

4    96772 
4  9.96767 

11 
10 

27  10.42956 

51  i    5  12  :   54  48 

57075  27 

42925 

60313  31 

39687 

03238 

4    96762 

9 

52 

5  4:   54  56 

57107  28 

42893 

60349  32 

39651 

03243 

4  1   96757 

8 

53 

4  56  1   55  4 

57138  28 

42862 

60386  33 

39614 

03248 

4  i   96752 

7 

54 
55" 

4  48 
9  4  40 

55  12 

57169 

29 

42831 

60422 

33 
34 

39578 
10. 39541 

03253 
10.03258 

4 
5 

96747 

6 
5 

2  55  20 

9. 57201 

29 

10.  42799 

9.  60459 

9. 96742 

56 

4  32 

55  28 

57232 

30 

42768 

60495  35 

39505 

03263 

5    96737 

4 

57 

4  24 

55  36 

57264 

30 

42736 

60532  35 

39468 

03268 

5    96732 

3 

58 

4  16    55  44 

57295 

31 

42705 

60568  36 

39432 

03273 

5  I   96727 

•> 

59 

4  8  1   55  52 

57326 

32  ;   42674 

60605  ;  36 

39395 

03278 

5  I   96722 

1 

60 

4  0 

56  0 

57358 

32 

42642 

60641  1  37 

39359 

03283 

5  1  96717 

i 

0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent.  Biff. 

Tangent. 

Cosecant. 

Difif.  1   Sine. 

M. 

111° 

A           A 

B 

B 

C 

C     68°  1 

Second  of  time 

1' 

2' 

3» 

4« 

5» 

6» 

7» 

Prop,  parts  of  cols. 

t 

4 
5 
1 

8 
9 

1 

12 
14 

16 
19 

2  ■ 

20 
23 

3 

24 

28 

4 

28 
32 
4 

1  Page  630] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

22° 

A 

A 

B 

B 

C 

c 

157° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

0 

9  4  0 

2  56  0 

9. 57358 

0 

10.  42642 

9.  60&41 

0 

10.  39359 

10. 03283 

0 

9.  96717 

1 

3  52 

56  8 

57389 

1    42611 

60677 

1 

39323 

03289 

0 

96711 

59 

2 

3  44 

56  16 

57420 

1  i   42580 

60714 

1 

39286 

03294 

0 

96706 

58 

3 

3  36 

56  24 

57451 

2  !   42549 

60750 

2 

39250 

03299 

0 

96701 

57 

4 

3  28 

56  32* 

57482 

2  '   42518 

60786 

2 
.3 

39214 
10.39177 

03304 
10.  03309 

0 
0' 

96696 
9. 96691 

56 
55 

5 

9  3  20 

2  56  40 

9. 57514 

3  |lO.  42486 

9. 60823 

6 

3  12 

56  48 

57545 

3  1   42455 

60859 

4 

39141 

03314 

96686 

54 

t 

3  4 

56  56 

57576 

4  !   42424 

60895 

4 

39105 

03319 

96681 

53 

8 

2  56 

57  4 

57607 

4    42393 

60931 

5 

39069 

03324 

96676 

52 

9 

2  48 

57  12 

57638 

5    42362 

60967 

5 

39033 

03330 
10.03335 

96670 

51 
50 

10 

9  2  40 

2  57  20 

9. 57669 

5  ilO.  42331 

9.  61004 

6 

10. 38996 

9. 96665 

11 

2  32 

57  28 

57700 

6    42300 

61040 

1 

38960 

03340 

96660 

49 

12 

2  24 

57  36 

57731 

6    42269 

61076 

/ 

38924 

03345 

96655 

48 

13 

2  16 

57  44 

57762 

7    42238 

61112 

8 

38888 

03350 

96650 

47 

14 
15 

2  8 

57  52 

57793 

7  i   42207 

61148 

8 
9 

38852 

03355 

96645 
9.  96640 

46 
45 

9  2  0 

2  58  0 

9. 57824 

8  110.42176 

9.61184 

10. 38816 

10. 03360 

16 

1  52 

58  8 

57855 

8  i   42145 

61220 

10 

•  38780 

03366 

96634 

44 

17 

1  44 

58  16 

57885 

9    42115 

61256 

10 

38744 

03371 

96629 

43 

18 

1  36 

58  24 

57916 

9    42084 

61292 

11 

38708 

03376 

2 

96624 

42 

19 

1  28 

58  32 

57947 

10    42053 

61328 

11 

38672 

03381 

2 

96619 
9.96614 

41 
40 

20 

9  1  20 

2  58  40 

9. 57978 

10  ilO.  42022 

9.  61364 

12 

10.  38636 

10. 03386 

2 

21 

1  12 

58  48 

58008 

11  !   41992 

61400 

13 

38600 

03392 

2 

96608 

39 

22 

1  4 

58  56 

58039 

11 

41961 

61436 

13 

38564 

03397 

2 

96603 

38 

23 

0  56 

59  4 

58070 

12 

41930 

61472 

14 

38528 

03402 

2 

96598 

37 

24 

0  48 

59  12 

58101 

12 

41899 

61508 

14 

38492 
10. 38456 

03407 

2 
2 

96593 
9. 96588 

36 
35 

25 

9  0  40 

2  59  20 

9. 58131 

13  10.41869 

9.  61544 

15 

10.  03412 

2(j 

0  32 

59  28 

58162 

13    41838 

61579 

15 

38421 

o:^i8 

2 

96582 

34 

27 

0  24 

59  36 

58192 

14  !   41808 

61615 

16 

38385 

03423* 

2 

96577 

33 

28 

0  16 

59  44 

58223 

14 

41777 

61651 

17 

38349 

03428 

2 

96572 

32 

29 

0  8 

59  52 

58253 

15 

41747 

61687 

17 

38313 
10.  38278 

03433 

3 

96567 

31 
30 

80 

9  0  0 

3  0  0 

9. 58284 

15 

10.41716 

9.  61722 

18 

10. 03438 

3 

9. 96562 

31 

8  59  52 

0  8 

58314 

16 

41686 

61758 

18 

38242 

03444 

3 

96556 

29 

32 

59  44 

0  16 

58345 

16 

41655 

61794 

19 

38206 

03449 

3 

96551 

28 

33 

59  36 

0  24 

58375 

17 

41625 

61830 

20 

38170 

03454 

3 

96546 

27 

34 

59  28 

0  32 

58406 

17  1   41594 

61865 

20 

21 

38135 

03459 
10. 03465 

3 
3 

96541 
9. 96535 

26 
25 

35 

8  59  20 

3  0  40 

9. 58436 

18  jlO.  41564 

9. 61901 

10. 38099 

36 

59  12 

0  48 

58467 

18  1   41533 

61936 

21 

38064 

03470 

3 

96530 

24 

37 

59  4 

0  56 

58497 

19 

41503 

61972 

22 

38028 

03475 

3 

96525 

23 

38 

58  56 

1  4 

58527 

19 

41473 

62008 

23 

37992 

03480 

3 

96520 

22 

39 
40 

58  48 

1  12 

58557 

20  !   41443 

62043 

23 

37957 

03486 

3 

96514 

21 
20 

8  58  40 

3  1  20 

9. 58588 

20  ilO.  41412 

9. 62079 

24 

10. 37921 

10. 03491 

3 

9. 96509 

41 

58  32 

1  28 

58618 

21  i   41382 

62114 

24 

37886 

03496 

4 

96504 

19 

42 

58  24 

1  36 

58648 

21  1   41352 

62150 

25 

37850 

03502 

4 

96498 

18 

43 

58  16 

1  44 

58678 

22 

41322 

62185 

26 

37815 

03507 

4 

96493 

17 

44 

58  8 

1  52 

58709 

22 

41291 

62221 

26 

27 

37779 

03512 

4 
4 

96488 

16 
15 

4o 

8  58  0 

3  2  0 

9. 58739 

23 

10.  41261 

9. 62256 

10.  37744 

10.03517 

9. 96483 

46 

57  52 

2  8 

58769 

23 

41231 

62292 

27 

37708 

03523 

4 

96477 

14 

47 

57  44 

2  16 

58799 

24 

41201 

62327 

28 

37673 

03528 

4 

96472 

13 

48 

57  36 

2  24 

58829 

24 

41171 

62362 

29 

37638 

03533 

4 

96467 

12 

49 

57  28 

2  32 

58859 

25 

41141 

62398 

29 

37602 

03539 

4 

96461 
9. 96456 

11 
10' 

50 

8  57  20 

3  2  40 

9. 58889 

25 

10.41111 

9. 62433 

30 

10. 37567 

10.  03544 

4 

51 

57  12 

2  48 

58919 

26 

41081 

62468 

30 

37532 

03549 

4 

96451 

9 

52 

57  4 

2  56 

58949 

26 

41051 

62504 

31 

37496 

03555 

5 

96445 

8 

53 

56  56 

3  4 

58979 

27 

41021 

62539 

32 

37461 

03560 

5 

96440 

7 

54 

56  48 

3  12 

59009 

27 

40991 

62574 

32 
33 

37426 

03565 

5 

96435 

6 
5 

55 

8  56  40 

3  3  20 

9. 59039 

28 

10. 40961 

9.  62609 

10.  37391 

10. 03571 

5 

9. 96429 

56 

56  32 

3  28 

59069 

28 

40931 

62645 

33 

37355 

03576 

5 

96424 

4 

57 

56  24 

3  36 

59098 

29 

40902 

62680 

34 

37320 

03581 

5 

96419 

3 

58 

56  16 

3  44 

59128 

29  !   40872 

62715 

35 

37285 

03587 

5 

96413 

2 

59 

56  8 

3  52 

59158 

30 

40842 

62750 

35 

37250 

03592 

5 

96408 

1 

60 

56  0 

4  0 

59188 

31 

4081.2 

62785 

36 

37215 

03597 

5 

96403 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

11 2° 

A 

A 

B 

B 

C 

C 

67° 

Seconds  of  time 

1» 

2» 

3* 

4' 

5- 

6- 

?• 

fA 
Prop,  parts  of  cols,  i  B 

Ic 

4 
4 
1 

8 
9 
1 

11 
13 
2 

15 

18 
3 

19 

22 

8 

23 

27 

4 

27 
81 

5 

TABLE  44. 

[Page  631 

Log.  Sines,  Tangents,  and  Secants. 

•23° 

A 

A 

B            B        C 

C    156° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

.  Tangent. 

Diff. 

Cotangent:   Secant. 

Difl. 

Cosine. 

M. 

0 

8  56  0 

3  4  0 

9. 59188 

0 

10.  40812 

9. 62785 

0 

10. 87215 

10. 08597 

0 

9. 96403 

60 

1 

55  52 

4  8 

59218 

0 

40782 

62820 

1 

37180 

03608 

0 

96.397 

59 

2 

55  44 

4  16 

59247 

1 

40758 

62855 

1 

37145 

03608 

0 

96392 

58 

S 

55  86 

4  24 

59277 

1 

40723 

62890 

2 

37110 

03613 

0 

96387 

57 

4 
5 

55  28 
"8  55  20 

4  32 

59307 
9. 59836 

2 
2 

40698 
10.  40664 

62926 
9. 62961 

2 

37074 

03619 

0 
0 

96381 
9. 96376 

56 
55 

3  4  40 

3 

10. 37039 

10. 03624 

« 

55  12 

4  48 

59866 

3 

40634 

62996 

3 

37004 

03680 

96370 

54 

7 

55  4 

4  56 

59896 

3 

40604 

63081 

4' 

36969 

03635 

96365 

58 

8 

54  56 

5  4 

59425 

4 

40575 

68066 

5 

36934 

03640 

96360 

52 

9 

54  48 

5  12 

59455 

4 

40545 

63101 

5 

.36899 

03646 

96854 
9. 96849 

51 
50 

10 

8  54  40 

8  5  20 

9.  59484 

5 

10. 40516 

9.  63135 

6 

10.  36865 

10. 08651 

11 

54  82 

5  28 

59514 

5 

40486 

68170 

6 

36880 

08657 

96843 

49 

1^ 

54  24 

5  36 

59543 

6 

40457 

68205 

7 

36795 

03662 

96388 

48 

1H 

54  16 

5  44 

59573 

6 

40427 

63240 

7 

36760 

03667 

96833 

47 

14 
15 

54  8 

5  52 

59602 

7 
7 

40398 
10.  40368 

68275 

8 

86725 

03673 

96327 

46 
45 

8  54  0 

3  6  0 

9. 59632 

9.  68310 

9 

10.  36690 

10.  03678 

9.  96822 

16 

53  52 

6  8 

59661 

8 

40389 

63345 

9 

86655 

03684 

96316 

44 

17 

58  44 

6  16 

59690 

8 

40810 

63879 

10 

36621 

03689 

2 

96.311 

48 

18 

58  36 

6  24 

59720 

9 

40280 

63414 

10 

36586 

03695 

2 

96805 

42 

19 
20 

53  28 

6  32 

59749 

9 

40251 

63449 

11  I   36551 

03700 

2 

96300 

41 

8  53  20 

3  6  40 

9. 59778 

10 

10. 40222 

9.  63484 

12  10.36.516 

10. 03706 

2 

9. 96294 

40 

21 

53  12 

6  48 

59808 

10 

40192 

63519 

12  1   86481 

03711 

2 

96289 

39 

22 

53  4 

6  56 

59837 

11 

40163 

63.553 

13    36447 

03716 

2 

96284 

38 

2S 

52  56 

7  4 

59866 

11 

40134 

6;i588 

13    36412 

03722 

2 

96278 

37 

24 
25 

52  48 
8  52  40 

7  12 

59895 

12 

40105 

63623 

14 

.36377 

03727 
10. 087.33 

2 
2 

.  96273 

36 
35 

3  7  20 

9. 59924 

12 

10.  40076 

9. 63657 

14 

10,  36843 

9. 96267 

26 

52  32 

7  28 

59954 

13 

40046 

63692 

15 

36308 

087.38 

2 

96262 

84 

27 

52  24 

7  86 

59983 

13 

40017 

63726 

16 

36274 

03744 

2 

96256 

83 

28 

52  16 

7  44 

60012 

14 

89988 

63761 

16 

86239 

03749 

3 

96251 

32 

29 

52  8 

7  52 

60041 

14 

39959 
10.  39930 

68796 

17 

36204 

03755 

3 

96245 

31 
30 

80 

8  52  0 

3  8  0 

9.  60070 

15 

9. 63880 

17 

10.36170 

10. 03760 

3 

9. 96240 

81 

51  52 

8  8 

60099 

15 

39901 

63865 

18  i   361.35 

03766 

3 

96234 

29 

82 

51  44 

8  16 

60128 

15 

89872 

6.3899  1  18    86101 

03771 

3 

■  96229 

28 

88 

51  36 

8  24 

60157 

16 

89848 

68934  19    36066 

03777 

3 

96228 

27 

34 
85 

51  28 

8  32 

60186 
9. 60215 

16 
17 

39814 

63968 

20    36032 

03782 
10. 03788 

3 
3 

96218 

26 

8  51  20 

3  8  40 

10.  39785 

9.64003 

20  |10.  3.5997 

9. 96212 

25 

86 

51  12 

8  48 

60244 

17 

39756 

64037 

21  1   35968 

03798 

3 

96207 

24 

87 

51  4 

8  56 

60273 

18 

89727 

64072  !  21  i   .35928 

03799 

3 

96201 

23 

88 

50  56 

9  4 

60302 

18 

89698 

64106 

22    .85894 

03804 

3 

96196 

22 

39 
40 

50  48 

9  12 

60331 

19  !   39669 

64140 

22    35860 

0.3810 

4 
4 

96190 
9. 96185 

21 
20 

8  50  40 

3  9  20 

9. 60359 

19  [10.39641 

9.  64175 

23  10.35825 

10. 03815 

41 

50  32 

9  28 

60888 

20 

89612 

64209 

24  j   a5791 

03821 

4 

96179 

19 

42 

50  24 

9  36 

60417 

20 

89583 

64243 

24    .35757 

03826 

4 

96174 

18 

48 

50  16 

9  44 

60446 

21 

39554 

64278 

25    35722 

03832 

4 

96168 

17 

44 
"45 

50  8 

9  52 

60474 

21    39526 

64812 

25    35688 

03838 

4 

96162 

16 

8  50  0 

3  10  0 

9. 60503 

22  10.89497 

9.64346  1  26  10.3.56.54 

10. 08843 

4 

9.961.57 

15 

46 

49  52 

10  8 

60582 

22 

89468 

64381 

26 

3.5619 

03849 

4 

96151 

14 

47 

49  44 

10  16 

60561 

28 

89489 

64415 

27 

.35585 

08854 

4 

96146 

18 

48 

49  86 

10  24 

60589 

28 

89411 

64449 

28 

85.551 

08860 

4 

96140 

12 

49 
50 

49  28 
8  49  20 

10  32 
3  10  40 

60618 

24 

39882 

64483 

28 

3.5517 

08865 
10.  03871 

4 

5 

96135 
9.96129 

11 
10 

9. 60646 

!  24 

10.  39:^4 

9.64517 

29 

10.  35483 

51 

49  12 

10  48 

60675 

i  25 

89325 

64552 

29  1   35448 

03877 

5 

96128 

9 

52 

49  4 

10  56 

60704 

i  25 

39296 

(M586 

30 

35414 

03882 

5 

96118 

8 

58 

48  56 

11  4 

60782 

26 

39268 

64620 

81 

35380 

03888 

5 

96112 

/ 

54 

55" 

48  48 
8  48  40 

11  12 

60761 
9. 60789 

26 
27 

39239 
10.39211 

64654 
9. 64688 

31 
32 

.35.346 
10.  .8.5812 

08893 
10.03899 

5 

5 

/96107 
9.96101 

6 
5 

8  11  20 

56 

48  32 

11  28 

60818 

27 

39182 

64722 

32 

35278 

08905 

5 

96095 

4 

57 

48  24 

11  36 

60846 

28 

89154 

64756 

38 

.35244 

03910 

5 

96090 

8 

58 

48  16 

11  44 

60875 

28 

89125 

64790 

38 

.35210 

03916 

5 

96084 

2 

59 

48  8 

11  52 

60903 

29 

39097 

64824 

.34 

.35176 

03921 

5 

96079 

1 

60 
M. 

48  0 

12  0 

60981 

29 

39069 

64858 

35 

35142 

03927 

6 

96073 

0 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff 

Tangent. 

.;Cosecant. 

Diff. 

Sine. 

M. 

113^ 

A 

A 

B            B        C 

C     66°  1 

Seconds  of  time 


Prop,  parts 


of  cols.  -<  B 


p 

age  632j 

TABLE  41. 
Log.  Sines,  Tangents,  and  Secants. 

24° 

A            A 

B            B 

C 

C 

165° 

M. 

60 

M. 

Hour  A.  M. 

Hour  p.  3C. 

Sine.   1  Diff.  j  Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

0 

8  48  0 

3  12  0 

9.60931  i  0  10.39069 

9.64858 

0 

10.  35142 

10. 03927 

0 

9. 96073 

1 

47  52 

12  8 

60960 

0    39040 

64892 

1 

35108 

03933 

0 

96067 

59 

2 

47  44 

12  16 

60988 

1  1   39012 

64926 

1 

35074 

03938 

0 

96062 

58 

3 

47  36 

12  24 

61016 

1  i   38984 

64960 

2 

35040 

03944 

0 

96056 

57 

4 
5 

47  28 

12  3g 

61045 
9.  61073 

2 
2 

38955 

64994 

2 

35006 

03950 

0 
0 

96050 

56 
55 

8  47  20 

3  12  40 

10. 38927 

9. 65028 

3  10.34972 

10. 03955 

9. 96045 

6 

47  12 

12  48 

61101 

3  !   38899 

65062 

3 

34938 

03961 

96039 

54 

7 

47  4 

12  56 

61129 

3    38871 

65096 

4 

34904 

03966 

96034 

53 

8 

46  56 

13  4 

61158 

4    38842 

65130 

4 

34870 

03972 

96028 

52 

9 
10 

46  48 

13  12 

61186 

4    38814 

65164 

5 

34836 

03978 

96022 

51 
50 

8  46  40 

3  13  20 

9.  61214 

5  10.38786 

9. 65197 

6 

10. 34803 

10. 03983 

9.96017 

11 

46  32 

13  28 

61242- 

5  ,   38758 

65231 

6 

34769 

03989 

96011 

49 

12 

46  24 

13  36 

61270 

6 

38730 

'  65265 

7 

34735 

03995 

96005 

48 

13 

46  16 

13  44 

61298 

6 

38702 

65299 

7 

34701 

04000 

96000 

47 

14 

46  8 

13  52 

61326 

6 

38674 

65333 

8 

34667 

04006 

95994 

46 
45 

15 

8  46  0 

3  14  0 

9. 6i;i54 

/ 

10. 38646 

9. 65366 

8 

10.  34634 

10. 04012 

9. 95988 

16 

45  52 

14  8 

61382 

7 

38618 

65400 

9 

34600 

04018 

2 

95982 

44 

17 

45  44 

14  16 

61411 

8 

38589 

65434 

9 

34566 

04023 

2 

95977 

43 

18 

45  36 

14  24 

61438 

8 

38562 

65467 

10 

34533 

04029 

2 

95971 

42 

19 
20 

45  28 
8  45  20 

14  32 
3  14  40 

61466 

9    38534 
9  10.38506 

65501  1  11 
9.65535  i  11 

34499 

04035 

2 
2 

95965 

41 
40 

9. 61494 

10.  34465 

10. 04040 

9. 95960 

21 

45  12 

14  48 

61522 

10  i   38478 

65568  12  i   34432 

04046 

2 

95954 

39 

22 

45  4 

14  56 

61550 

10 

38450 

65602  1  12 

34398 

04052 

2 

95948 

38 

23 

44  56 

15  4 

61578 

11 

38422 

65636 

13 

34364 

04058 

2 

95942 

37 

24 

44  48 

15  12 

61606 

11 

38394 

65669 

13  i   34331 

04063 

2 

95937 

36 
35 

25 

8  44  40 

3  15  20 

9. 61634 

12 

10. 38366 

9. 65703 

14  ilO.  34297 

10. 04069 

2 

9. 95931 

26 

44  32 

15  28 

61662 

12 

38338 

65736 

15 

34264 

04075 

2 

95925 

34 

27 

44  24 

15  36 

61689 

12 

38311 

65770 

15 

34230 

04080 

3 

95920 

33 

28 

44  16 

15  44 

61717 

13 

38283 

65803 

16 

34197 

04086 

3 

95914 

32 

29 
30 

44  8 

15  52 

61745 

13 

38255 

65837  16 

34163 

04092 

3 

95908 

31 

8  44  0 

3  16  0 

9.  61773 

14 

10. 38227 

9.65870  17  ,10.34130 

10. 04098 

3 

9. 95902 

30 

31 

43  52 

16  8 

61800 

14 

38200 

65904  17 

34096 

04103 

3 

95897 

29 

32 

43  44 

16  16 

61828 

15 

38172 

65937  18 

34063 

04109 

3 

95891 

28 

33 

43  36 

16  24 

61856  :  15 

38144 

65971  18 

34029 

04115 

3 

95885 

27 

34 
35 

43  28 

16  32 

61883  \   16  !   38117 

66004 

19  !   33996 

04121 

3 

95879 

26 
25" 

8  43  20 

3  16  40 

9.  61911 

16  ilO.  38089 

9. 66038 

20 

10.  33962 

10.  04127 

3 

9. 95873 

36 

43  12 

16  48 

61939 

17 

38061 

66071 

20 

33929 

04132 

3 

95868 

24 

37 

43  4 

16  56 

61966 

17 

38034 

66104 

21 

33896 

04138 

4 

95862 

23 

38 

42  56 

17  4 

61994 

18 

38006 

66138 

21 

33862 

04144 

4 

95856 

22 

39 

42  48 

17  12 

62021 

18 

37979 

66171 

22 

33829 

04150 

4 

95850 

21 
20 

40 

8  42  40 

3  17  20 

9.62049  1  18  10.37951 

9.66204  22  10.33796 

10. 04156 

4 

9. 95844 

41 

42  32 

17  28 

62076  i  19 

37924 

66238  1  23 

33762 

04161 

4 

95839 

19 

42 

42  24 

17  36 

62104 

19 

37896 

66271  23 

33729 

04167 

4 

95833 

18 

43 

42  16 

17  44 

62131 

20 

37869 

66304  1  24 

33696 

04173 

4 

95827 

17 

44 

42  8 

17  52 

62159 

20 

37841 

66337 

25 

33663 

04179 

4 

95821 
9.  95815 

16 
15 

45 

8  42  0 

3  18  0 

9. 62186 

21 

10.  37814 

9. 66371 

25 

10.  33629 

10.  04185 

4 

46 

41  52 

18  8 

62214 

21 

37786 

66404 

26 

33596 

04190 

4 

95810 

14 

47 

41  44 

18  16 

62241 

22 

37759 

66437 

26 

33563 

04196 

5 

95804 

13 

48 

41  36 

18  24 

62268 

22 

37732 

66470 

27 

33530 

04202 

5 

95798 

12 

49 
50 

41  28 
8  41  20 

18  32 

62296 

23 

37704 

66503 
9. 66537 

27 

28 

33497 

04208 

5 

95792 

11 
10 

3  18  40 

9.  62323  1  23  10.  37677 

10.  33463 

10. 04214 

5 

9.  95786 

51 

41  12 

18  48 

62350  ;  24 

37650 

66570 

28 

33430 

04220 

5 

95780 

9 

52 

41  4 

18  56 

62377  24 

37623 

66603 

29 

33397 

04225 

5 

95775 

8 

53 

40  56 

19  4 

62405  !  24 

37595 

66636 

30 

33364 

04231 

5 

95769 

7 

54 

55 

40  48 
8  40  40 

19  12 
3  19  20 

62432  25    37568 
9.62459  1  25  10.37541 

66669 
9. 66702 

30 
31 

33331 

04237 

5 
5 

95763 

6 
5 

10.  33298 

10. 04243 

9. 95757 

56 

40  32 

19  28 

62486  ■   26    37514 

66735 

31 

33265 

04249 

5 

95751 

4 

57 

40  24 

19  36 

62513  ;  26 

37487 

66768 

32 

33232 

04255 

5 

95745 

3 

58 

40  16 

19  44 

62541   27 

37459 

66801 

32 

33199 

04261 

6 

95739 

9 

59 

40  8 

19  52 

62568 

27 

37432 

66834 

33 

33166 

04267 

6 

95733 

1 

60 

40  0 

20  0 

'62595 

28 

37405 

66867 

33 
Diff. 

33133 

04272 

6 

95728 

0 
M. 

M. 

Hour  p.  M. 

Hour  A.M 

Cosine.   Diff. 

Secant. 

Cotangent. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

114° 

A            A 

B           B 

C 

C 

65° 

.Seconds  of  time 

1» 

i' 

){• 

4' 

5* 

17 

21 

4 

C 

21 

2.'i 
4 

7« 

24 

29 

Prop,  parts  of  colp.-fE 

5 

1 

7 

8 
1 

10 

13 
2 

14 
17 
3 

TABLE  44. 

Page  633 

Log.  Sines,  Tangents,  and  Secants. 

25° 

A 

A 

B 

B 

C 

C    154° 

M. 

Hour  A.  M. 

Hour  P.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

8  40  0 

3  20  0 

9. 62595 

0 

10. 87405 

9. 66867 

0 

10.  33133 

10. 04272 

0 

9. 95728 

60 

1 

39  52 

20  8 

62622 

0 

87378 

66900 

1 

38100 

04278 

0 

95722 

59 

9, 

39  44 

20  16 

62649 

1 

37351 

66933 

1 

38067 

04284 

0 

95716 

58 

8 

39  36 

20  24 

62676 

1 

37824 

66966 

2 

33034 

04290 

0 

95710 

57 

4 
5 

39  28 

20  32 

62703 

2 

87297 

66999 

2 

33001 

04296 

0 

95704 

56 
55 

8  39  20 

3  20  40 

9.  62730 

2 

10.  37270 

9. 67032 

3 

10. 32968 

10.04302 

9. 95698 

6 

39  12 

20  48 

62757 

3 

37243 

67065 

3 

32935 

04308 

95692 

54 

7 

39  4 

20  56 

62784 

3 

37216 

67098 

4 

32902 

04314 

95686 

53 

H 

38  56 

21  4 

62811 

4 

87189 

67131 

4 

32869 

04320 

95680 

52 

9 
10 

38  48 

21  12 

62838 

4 

87162 

67163 

5 
5 

32837 

04326 

95674 

51 

8  38  40 

3  21  20 

9.  62865 

4  10.37135 

9. 67196 

10. 32804 

10. 04332 

9. 95668 

50 

11 

38  32 

21  28 

62892 

5    37108 

67229 

6 

32771 

04337 

95663 

49 

12 

38  24 

21  36 

62918 

5    87082 

67262 

7 

32738 

04343 

95657 

48 

18 

38  16 

21  44 

62945 

6    87055 

67295 

7 

32705 

04349 

95651 

47 

14 

38  8 

21  52 

62972 

6    37028 

67327 

8 

.32673 

04355 

95645 

46 

15 

8  38  0 

3  22  0 

9. 62999 

7  10.37001 

9. 67860 

8 

10. 32640 

10. 64361 

2 

9. 95639 

45 

16 

37  52 

22  8 

63026 

7 

36974 

67393 

9 

32607 

04367 

2 

95683 

44 

17 

37  44 

22  16 

63052 

8 

36948 

67426 

9 

32574 

04373 

2 

95627 

43 

18 

37  36 

22  24 

63079 

8 

36921 

67458 

10 

32542 

04379 

2 

95621 

42 

19 

37  28 

22  32 

63106 

8 

36894 

67491 

10 

32509 

04385 

2 

95615 

41 
40 

20 

8  37  20 

3  22  40 

9. 63133 

9  10.36867 

9. 67524 

11 

10.  32476 

10. 04391 

2 

9. 95609 

21 

37  12 

22  48 

63159 

9  i   36841 

67556 

11 

32444 

04397 

2   95603 

39 

22 

37  4 

22  56 

63186 

10  !   36814 

67589 

12 

32411 

04403 

2   95597 

38 

28 

36  56 

23  4 

63213 

10    36787 

67622 

12 

32378 

04409 

2   95591 

37 

24 

36  48 

23  12 

63239 

11    36761 

67654 

13 

32346 

04415 

2   955a5 

36 

25 

8  36  40 

3  23  20 

9. 63266 

11  10.36734 

9. 67687 

14  10.32813 

10. 04421 

3 

9. 95579 

35 

26 

36  32 

23  28 

63292 

11 

36708 

67719 

14    32281 

04427 

3 

95.573 

34 

27 

36  24 

23  36 

63319 

12 

36681 

67752 

15    32248 

04433 

3 

95567 

83 

28 

36  16 

23  44 

63345 

12 

36655 

67785 

15    32215 

04439 

3 

95561 

32 

29 
80 

36  8 

23  52 

63372 
9. 63398 

13 

36628 

67817 

16    32183 

04445 

3 

95555 

31 
30 

8  36  0 

3  24  0 

13 

10.  36602 

9. 67850 

16  :10. 32150 

10. 04451 

3  19.95549 

81 

35  52 

24  8 

63425 

14    36575 

67882 

17 

32118 

04457 

3 

95543 

29 

82 

35  44 

24  16 

63451 

14    36549 

67915 

17 

32085 

04463 

3 

95537 

28 

88 

35  36 

24  24 

63478 

15    86522 

67947 

18 

32053 

04469 

3 

95531 

27 

34 

35  28 

24  32 

63504 

15    36496 

67980 

18 

32020 

04475 

3 

95525 

26 
25 

85 

8  35  20 

3  24  40 

9. 63531 

15  10.36469 

9.  68012 

19 

10. 31988 

10. 04481 

4 

9. 95519 

86 

35  12 

24  48 

63557 

16    .36443 

68044 

20 

31956 

04487 

4 

95513 

24 

87 

35  4 

24  56 

68583 

16    86417 

68077 

20 

31928 

04493 

4 

95507 

23 

88 

34  56 

25  4 

63610 

17  1   36390 

68109 

21 

31891 

04500 

4 

95500 

22 

39 

34  48 

25  12 

63636 

17  1   36364 

68142 

21 

31858 

04506 

4 

95494 

21 
20 

40 

8  34  40 

3  25  20 

9. 63662 

18  ;iO.  36338 

9.  68174 

22 

10. 31826 

10. 04512 

4 

9. 95488 

41 

34  32 

25  28 

63689 

18 

36311 

68206 

22 

31794 

04518 

4 

95482 

19 

42 

34  24 

25  36 

63715 

19 

36285 

68239 

23 

31761 

04524 

4 

95476 

18 

43 

34  16 

25  44 

63741 

19 

36259 

68271 

23 

31729 

04530 

4 

95470 

17 

44 

34  8 

25  52 

63767 

19 

36233 

68303 

24 

31697 

04536 

4 

95464 

16 

45 

8  34  0 

3  26  0 

9.  68794 

.20  10.36206 

9. 68336 

24  10.31664 

10. 04542 

5 

9. 95458 

15 

46 

33  52 

26  8 

68820 

20 

36180 

68368 

25 

31632 

04548 

5 

95452 

14 

47 

33  44 

26  16 

63846 

21 

36154 

68400 

25 

31600 

04554 

5 

95446 

13 

48 

33  36 

26  24 

63872 

21 

86128 

68432 

26 

31568 

04560 

0 

95440 

12 

49 

33  28 

26  32 

68898 

22 

36102 

68465 

27 

31535 

04566 

5 

95434 

11 
10 

50 

8  33  20 

3  26  40 

9.  63924 

22  10.36076 

9. 68497 

27  ilO.  31503 

10.  04573 

5 

9. 95427 

51 

33  12 

26  48 

63950 

23 

36050 

68529 

28 

31471 

04579 

5 

95461 

9 

52 

33  4 

26  56 

63976 

23 

36024 

68.561 

28 

31489 

04585 

5 

95415 

8 

53 

32  56 

27  4 

64002 

23 

35998 

68593 

29 

31407 

04591 

5 

95409 

7 

54 

32  48 

27  12 

64028 

24 

35972 

68626 

29 
30 

31374 
10. 31342 

04597 

5 

95403 

6 
5 

55 

8  32  40 

3  27  20 

9. 64054 

24 

10.  35946 

9. 68658 

10.  04603 

6 

9. 95397 

56 

32  32 

27  28 

64080 

25 

35920 

68690 

30 

31310 

04609 

6 

95391 

4 

57 

32  24 

27  36 

64106 

25 

85894 

68722 

31 

31278 

04616 

6 

95384 

3 

58 

32  16 

27  44 

64132 

26  1   85868 

68754 

31  1   31246 

04622 

6 

95378 

2 

59 

32  8 

27  52 

64158 

26 

85842 

68786 

32 

31214 

04628 

6 

95372 

1 

60 

32  0 

28  0 

64184 

26 

85816 

68818 

33 

31182 

04634 

6 

95366 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diflf. 

Sine. 

M. 

115° 

A 

A 

B 

B 

C 

C     64°  1 

Seconds  of  time !  1» 

2.  1  3. 

4" 

5«  1  6» 

7« 

f  A  1   3 

Prop,  parts  of  cols,  -j  B  ]   4 

vC    1 

7 
8 
2 

10 

12 
2 

13 

16 

3 

17    20 

20    24 

4    5 

23 
28 
5 

Page  634] 

TABLE  U. 

Log. 

Sines,  Tangents,  and  Secants. 

26° 

M. 

A 

A 

B 

B 

C 

c 

153° 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff.  Cosine. 

M. 

0 

8  32  0 

3  28  0 

9.64184 

0 

10.  35816 

9. 68818 

0 

10.31182 

10. 04634 

0  9.95366 

60 

1 

31  52  !   28  8 

64210 

0 

35790 

68850 

1 

31150 

04640 

0   95360 

59 

2 

31  44 

28  16 

64236 

1 

35764 

68882 

1 

31118 

04646 

0    95354 

58 

8 

31  36 

28  24 

64262 

1 

35738 

68914 

2 

31086 

04652 

0    95348 

57 

4 
5 

31  28 

28  32< 

64288 
9.64313 

2 
~2' 

35712 
10735687 

68946 
9.  68978 

2 
3 

31054 
10.31022 

04659 
10. 04665 

0  .   95341 

1  9.95335 

56 
55 

8  31  20 

3  28  40 

6 

31  12  '   28  48 

64;«9 

3 

:i5661 

69010 

3 

30990 

04671 

1  i  95329 

54 

7 

31  4  i   28  56 

64365 

3 

35635 

69042 

4 

30958 

04677 

1  !  95323 

53 

8 

30  56    29  4 

64391 

3 

35609 

69074 

4 

3092f) 

04683 

1  1  95317 

52 

9 
10 

30  48 

29  12 
3  29  20 

64417 

4 
4 

35583 
10. 35558 

69106 

5 
5 

30894 
10. 30862 

04690 
10. 04696 

1   95310 
1  9.95304 

51 
50 

8  30  40 

9.64442 

9. 69138 

11 

30  32  1   29  28 

64468 

5 

35532 

69170 

6 

30830 

04702 

1  I  95298 

49 

12 

30  24    29  36 

64494 

5 

35506 

69202 

6 

30798 

04708 

1    95292 

48 

13 

30  16    29  44 

64519 

5 

35481 

69234 

7  ' 

30766 

04714 

1  1  95286 

47 

14 

30  8    29  52 

64545 

6 

35455 

69266 

8 

30734 
10.  30702 

04721 

1  1  95279 

46 
45" 

15 

8  30  0  !  3  30  0 

9.  64571 

6 

10. 35429 

9.  69298 

10. 04727 

2  i  9. 95273 

16 

29  52    30  8 

64596 

7 

35404 

69329 

8 

30671 

04733 

2  1  95267 

44 

17 

29  44  1   30  16 

64622 

7 

35378 

69361 

9 

30639 

04739 

2  '  95261 

43 

18 

29  36 

30  24 

64647 

8 

35353 

69393 

9 

30607 

04746 

2  ;  95254 

42 

19 
20 

29  28 

30  32 

64673 
9.64698 

8 

35327 

69425 

10 

30575 

04752 
10. 04758 

2 
2 

95248 

41 
40 

8  29  20 

3  30  40 

8 

10. 35302 

9. 69457 

11 

10. 30543 

9. 95242 

21 

29  12    30  48 

64724 

9 

35276 

69488 

11 

30512 

04764 

2   95236 

39 

22 

29  4  1   30  56 

64749 

9 

35251 

69520 

12 

30480 

04771 

2   95229 

38 

23 

28  56 

31  4 

64775 

10 

35225 

69552 

12 

30448 

04777 

2  1  95223 

37 

24 

28  48 

31  12 

64800 

10 
11 

35200 
10.  35174 

69584 

13 
13 

30416 
10. 30385 

04783 
10.04789 

3  1  95217 

36 
35 

25 

8  28  40 

3  31  20 

9. 64826 

9. 69615 

3 

9.95211 

26 

28  32 

31  28 

64851 

11 

35149 

69647 

14 

30353 

04796 

3 

95204 

34 

27 

28  24 

31  36 

64877 

11 

35123 

69679 

•14 

30321 

04802 

3 

95198 

33 

28 

28  16 

31  44 

64902 

12 

35098 

69710 

15 

30290 

04808 

3 

95192 

32 

29 
30 

28  8    31  52 

64927 

12 

35073 
10.  35047 

69742 

15 
16 

30258 
10.  30226 

04815 

3  '  95185 

31 
30 

8  28  0  i  3  32  0 

9. 64953 

13 

9. 69774 

10. 04821 

3  9.95179 

31 

27  52    32  8 

64978 

13 

35022 

69805 

16 

30195 

04827 

3   95173 

29 

32 

27  44    32  16 

65003 

14 

34997 

69837 

17 

30163 

04833 

3 

95167 

28 

33 

27  36  i   32  24 

65029 

14 

34971 

69868 

17 

30132 

04840 

3 

95160 

27 

34 
"35" 

27  28    32  32 

65054 

14 
15 

•34946 
10. 34921 

69900 

18 

30100 
10. 30068 

04846 

4 

95154 

26 
25 

8  27  20 

3  32  40 

9.  65079 

9. 69932 

18 

10.04852 

4 

9.95148 

36 

27  12 

32  48 

65104 

15 

34896 

69963 

19 

30037 

04859 

4    95141 

24 

37 

27  4  !   32  56 

65130 

16 

34870 

69995 

20 

30005 

04865 

4    95135 

23 

38 

26  56    33  4 

65155 

16 

34845 

70026 

20 

29974 

04871 

4    95129 

22 

39 

26  48    33  12 

65180 

16 

34820 

70058 

21 

29942 

04878 

4  1   95122 

21 

40 

8  26  40  !  3  33  20 

9. 65205 

17 

10.  34795 

9.70089  !  21 

10.29911 

10. 04884 

4  9.95116 

20 

41 

26  32    33  28 

65230 

17 

34770 

70121 

22 

29879 

04890 

4    95110 

19 

42 

26  24 

33  36 

65255 

18 

34745 

70152 

22 

29848 

04897 

4    95103 

18 

43 

26  16 

33  44 

65281 

18 

34719 

70184 

23 

29816 

04903 

5    95097 

17 

44 

26  8 

33  52 

65306 

19 

34694 

70215 

23 

29785 

04910 

5   95090 

16 

45 

8  26  0 

3  34  0 

9. 65331 

19 

10.  34669 

9. 70247 

24 

10. 29753 

10. 04916 

5  9.95084 

15 

46 

25  52  :   34  8 

65356 

19 

34644 

70278 

24 

29722 

04922 

5   95078 

14 

47 

25  44    34  16 

65381 

20 

34619 

70309 

25 

29691 

04929 

5   95071 

13 

48 

25  36    34  24 

65406 

20 

34594 

70341 

25 

29659 

04935 

5   9.5065 

12 

49 

50' 

25  28    34  32 
8  25  20  3  M  40 

65431 
"9.65456 

21 
"21 

34569 
10. 34544 

70372 

26 
26 

29628 
10. 29596 

04941 
10.04948 

5   95059 
5  9.95052 

11 
10 

9.  70404 

51 

25  12  i  M  48 

65481 

22 

34519 

70435 

27 

29565 

04954 

5   95046 

9 

52 

25  4  I  M  56 

65506 

22 

34494 

70466 

27 

29534 

04961 

5   95039 

8 

53 

24  56  :   35  4 

65531 

22 

34469 

70498 

28 

29502 

04967 

6   95033- 

7 

54 

24  48  1   35  12 

65556 

23 

34444 

70529 

28 

29471 

04973 

6  !   95027 

6 

00 

8  24  40  i  3  35  20 

9. 65580 

23 

10.  34420 

9. 70560 

29 

10. 29440 

10. 04980 

6  9.95020 

5 

56 

24  32    35  28 

65605 

24 

34395 

70592 

30 

29408 

04986 

6    95014 

4 

57 

24  24    35  36 

65630 

24 

34370 

70623 

30 

29377 

04993 

6    95007 

3 

58 

24  16    35  44 

65655 

25 

34345 

70654 

31 

29346 

04999 

6   95001 

2 

59 

24  8    35  52 

65680 

25 

34320 

70685 

31 

29315 

05005 

6  i  94995 

1 

60 
M. 

24  0    36  0 

65705 

25 
Difl. 

34295 

70717 

32 

29283 

05012 

6   94988 

0 

Hour  p.  M.  1  Hour  a.  m. 

Cosine. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Difl.  j   Sine. 

M. 

116° 

A 

A 

B 

B 

C 

C 

68° 

Seconds  of  time 

!••   2« 

8* 

4« 

&•   6> 

7« 

(A 

Prop,  parts  of  cols.  <  B 

(C 

8    6 
4    8 
1    2 

10 
12 
2 

13 
16 
3 

16   19 

20   24 

4    6 

22 

28 
6 

TABLE  44. 

[Page  635 

Log. 

Sines,  Tangents,  and  Secants. 

27° 

A 

A 

B 

B 

C 

C    152° 

M. 

•Hour  A.M. 

Hour  P.  M. 

Sine.   i  Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff.  Cosine. 

M. 
60 

0 

8  24  0 

3  36  0 

9.65705  i  0 

10.  34295 

9.  70717i 

0 

10.  29283 

10. 05012 

0 

9. 94988 

1 

23  52 

36  8 

65729   0 

34271 

70748 

1 

29252 

05018 

0   94982 

59 

?, 

23  44 

36  16 

65754 

1 

34246 

70779 

1 

29221 

05025 

0  1   94975 

58 

n 

23  36 

36  24 

65779 

1 

34221 

70810 

2 

29190 

05081 

0 

94969 

57 

4 

23  28 

36  32 

65804 

2 

34196 

70841 
9. 70873 

2 
3 

29159 
10.  29127 

05088 

0 

94962 

56 
55 

5 

8  23  20 

3  36  40 

9.65828  i  2 

10. 34172 

10.05044 

9. 94956 

H 

23  12 

36  48 

65853  i  2 

34147 

70904 

3 

29096 

05051 

94949 

54 

7 

23  4 

36  56 

65878   3 

34122 

70935 

4 

29065 

05057 

94948 

58 

8 

22  56 

37  4 

65902  i  3 

34098 

70966 

4 

29034 

05064 

94986 

52 

9 

To 

22  48 

37  12 
3  37  2b 

65927 
9.65952 

4 

34073 

70997 

5 

29008 

05070 

94980 
9. 94928 

51 
50 

8  22  40 

4 

10. 34048 

9.  71028 

5 

10.  28972 

10.  05077 

n 

22  32 

37  28 

65976   4 

34024 

71059 

6 

28941 

05083 

94917 

49 

1!^ 

22  24 

37  36 

66001  ,  5 

33999 

71090 

6 

28910 

05089 

1    94911 

48 

18 

22  16 

37  44 

66025   5 

33975 

71121 

/ 

28879 

05096 

1  •      94904 

47 

u 

22  8 

37  52 

66050   6 

33950 

71153 

/ 

28847 
10.  28816 

05102 
10. 05109 

2 
2 

94898 

46 
45 

15 

8  22  0 

3  38  0 

9.66075  1  6 

10.  33925 

9.  71184 

8 

9. 94891 

IH 

21  52 

38  8 

66099   6 

33901 

71215 

8 

28785 

05115 

2 

94885 

44 

17 

21  44 

38  16 

66124  !  7 

38876 

71246 

9 

28754 

05122 

2 

94878 

43 

18 

21  36 

38  24 

66148   7 

33852 

71277 

9 

28723 

05129 

2 

94871 

42 

19 

21  28 

38  32 

66173   8 

33827 

71308 

10 
10 

28692 

05135 
10. 05142 

2 
2 

94865 
9. 94858 

41 
40 

20 

8  21  20 

3  38  40 

9. 66197   8 

10. 33803 

9. 71339 

10.28661 

21 

21  12 

38  48 

66221   8 

33779 

71370 

11 

28630 

05148 

2 

94852 

39 

9.2 

21  4 

38  56 

66246   9 

33754 

71401 

11 

28599 

05155 

2 

94845 

88 

23 

20  56 

39  4 

66270   9 

33730 

71431 

12 

28569 

05161 

3 

94839 

87 

24 
2o 

20  48 
8  20  40 

39  12 
3  39  20 

66295  I  10 
9.66319  10 

33705 
10.  33681 

71462 

12 
13 

28538 
10.  28507 

05168 

3 

94832 

36 

9. 71493 

10. 05174 

3 

9. 94826 

.35 

2<5 

20  32 

39  28 

66348  11 

33657 

71524 

13 

28476 

05181 

3 

94819 

.84 

27 

20  24 

39  36 

66368  11 

33632 

71555 

14 

28445 

05187 

3   94813 

33 

28 

20  16 

39  44 

66392  11 

33608 

71586 

14 

28414 

05194 

3    94806 

32 

29 

20  8 

89  52 

66416  12 

33584 

71617 

15 

28883 

05201 

3 

94799 

31 

80 

8  20  0 

3  40  0 

9. 66441   12 

10. 83559 

9.  71648 

15 

10.  28852 

10.  05207 

3 

9. 94793 

30 

81 

19  52 

40  8 

66465   13 

33535 

71679 

16 

28321 

05214 

3 

94786 

29 

82 

19  44 

40  16 

66489   13 

33511 

71709 

16 

28291 

05220 

4 

94780 

28 

88 

19  36 

'40  24 

66513  13 

83487 

71740 

17 

28260 

05227 

4 

94773 

27 

34 
85 

19  28 
8  19  20 

40  32 
3  40  40 

66537  14 
9. 66562  14 

33463 

71771 

17 

28229 
10.  28198 

05233 
10. 05240 

4 

4 

94767 
9.  94760 

26 
25 

10.  33438 

9.  71802 

18 

86 

19  12 

40  48 

66586  15 

33414 

71833 

19 

28167 

05247 

4 

94753 

24 

87 

19  4 

40  56 

66610  15 

83390 

71863 

19 

28137 

05253 

JL 

94747 

23 

88 

18  56 

41  4 

66634  15 

83366 

71894 

20 

28106 

05260 

4 

94740 

22 

89 

40" 

18  48 
8  18  40 

41  12 

66658 

16 
16 

33342 
10.  83318 

71925 
9.  71955 

20 
21 

28075 

05266 

4 
4 

947.34 

21 
20 

3  41  ao 

41  f8 

9. 66682 

10.  28045 

10.  05273 

9. 94727 

41 

18  32 

66706  17 

33294 

71986 

21 

28014 

05280 

4 

94720 

19 

42 

18  24 

41  36 

66731  17 

88269 

72017 

22 

27988 

05286 

5 

94714 

18 

48 

18  16 

41  44 

66755  17 

33245 

72048 

22 

27952 

05293 

5 

94707 

17 

44 

18  8 

41  52 

66779  18 

83221 

72078 

23 

27922 

05300 

5 

94700 
9. 94694 

16 
15 

45 

8  18  0 

8  42  0 

9.66803  ;  18 

10.  88197 

9.  72109 

23 

10. 27891 

10. 05306 

5 

4H 

17  52 

42  8 

66827  19 

33173 

72140 

24 

27860 

05313 

5  :  94687 

14 

47 

17  44 

42  16 

66851  19 

83149 

72170 

24 

27830 

05320 

5 

94680 

13 

48 

17  36 

42  24 

66875  19 

33125 

72201 

25 

27799 

05326 

5 

94674 

12 

49 
50 

17  28 

42  32 

66899 

20 
20 

33101 
10. 33078 

72231 
9. 72262 

25 
26 

27769 
10727738 

05333 
10. 05;340 

5 

5 

94667 

11 

8  17  20 

3  42  40 

9. 66922 

9. 94660 

10 

51 

17  12 

42  48 

66946  '  21 

33054 

72293 

26 

27707 

05346 

6 

94654 

9 

52 

17  4 

42  56 

66970  21 

33030 

72323 

27 

27677 

05353 

6 

94647 

8 

58 

16  56 

43  4 

66994  21 

33006 

72354 

27 

27646 

05360 

6 

94640 

7 

54 
55 

16  48 
8  16  40 

43  12 

67018  22 
9. 67042  22 

32982 
10.  32958 

72384 
9.  72415 

28 
28 

27616 
10. 27585 

05366 

6    94634 

6 

5 

3  48  20 

10.  05373 

6  9.94627 

5(> 

16  32 

43  28 

67066  23 

329:^ 

72445 

29 

27555 

05380 

6    94620 

4 

57 

16  24 

43  36 

67090  i  23 

32910 

72476 

29 

27524 

05386 

6 

94614 

8 

58 

16  16 

43  44 

67118  i  23 

32887 

72506 

30 

27494 

05393 

6 

94607 

2 

59 

16  8 

43  52 

67137  I  24 

32863 

72537 

30 

27463 

05400 

6 

94600 

1 

60 
M. 

16  0 

44  0 

67161  24 

32839 

72567 

31 

27433 

05407 

/ 

94593 

0 

Hour  p.  M. 

Hour  A.M. 

Cosine.  '  Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff.   Sine. 

M. 

117° 

A 

A 

B 

B 

C 

C     62°  j 

Seconds  of  time 

1»    2« 

3« 

4» 

5' 

6' 

7' 

Prop,  parts  of  cols.  -(B 

Ic 

3  6 

4  8 
1     2 

9 

12 
2 

12 

15 

3 

15 
19 
4 

18 

23 

5 

21 

27 
6 

Page  636] 

TABLE  44. 

Log. 

Sines,  Tangents,  and  Secants. 

28° 

A 

A 

B            B 

C 

C    151° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DiS. 

Cosecant. 

Tangent.  Diflf. !  Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

0 

8  16  0 

3  44  0 

9.  67161 

0 

10.  32839 

9.72567  1  0  10.27438 

10.  05407 

0 

9. 94593 

1 

15  52 

44  8 

67185 

0 

32815 

72598  1  1    27402 

05413 

0 

94587 

59 

2 

15  44 

44  16 

67208 

1 

32792 

72628 

1    27372  1 

05420 

0 

94580 

58 

8 

15  36 

44  24 

67232 

1 

32768 

72659 

2 

27341 

05427 

0 

94573 

57 

4 
5^ 

15  28 
8  15  20 

44  32^ 
3  44  40 

67256 
9.67280 

2 
2 

32744 

72689 

2 
3 

27311 

05433 

0 

94567 

56 
55 

10. 32720 

9. 72720 

10.  27280 

10.  05440 

9. 94560 

H 

15  12 

44  48 

67303 

2 

32697 

72750 

3 

27250 

05447 

94553 

54 

7 

15  4 

44  56 

67327 

3 

32678 

72780 

4 

27220 

05454 

94546 

58 

S 

14  56 

45  4 

67350 

3 

32650 

72811 

4 

27189 

05460 

94540 

52 

9 
10 

14  48 

45  12 

67374 
9.  67398 

3 
4 

32626 
10.  32602 

72841 

5 

27159 

05467 

94533 

51 
50 

8  14  40 

3  45  20 

9.72872 

5 

10.  27128 

10. 05474 

9. 94526 

11 

14  32 

45  28 

67421 

4 

32579 

72902 

6 

27098 

05481 

94519 

49 

12 

14  24 

45  36 

67445 

5 

32555 

72932 

6 

27068 

05487 

94513 

48 

18 

14  16 

45  44 

67468 

5 

32532 

72963 

7 

27037 

05494 

94506 

47 

14 

14  8 

45  52 

67492 

5 

32508 

72993 

7 

27007 

05501 

2 

94499 

46 
45 

15 

8  14  0 

3  46  0 

9. 67515 

6 

10. 32485 

9. 73023 

8 

10.  26977 

10. 05508 

2 

9. 94492 

16 

13  52 

46  8 

67539 

6 

32461 

73054 

8 

26946 

05515 

2 

94485 

44 

17 

13  44 

46  16 

67562 

7 

32438 

78084 

9 

26916 

05521 

2 

94479 

43 

18 

13  36 

46  24 

67586 

7 

32414 

73114 

9 

26886 

05528 

2 

94472 

42 

19 

13  28 

46  32 

67609 

7 

32391 

73144 

10 

26856 

05535 

2 

94465 

41 
40 

20 

8  13  20 

3  46  40 

9.  67633 

8 

10.  32367 

9. 73175 

10 

10. 26825 

10. 05542 

2 

9. 94458 

21 

13  12 

46  48 

67656 

8 

32344 

73205 

11 

26795 

05549 

2 

94451 

39 

22 

13  4 

46  56 

67680 

9 

32320 

73235 

11 

26765 

05555 

3 

94445 

38 

28 

12  56 

47  4 

67703 

9 

32297 

73265 

12 

26735 

05562 

3 

94438 

37 

24 

12  48 

47  12 

67726 

9 

32274 

73295 

12 

26705 

05569 

8 

94431 

36 
35 

25 

8  12  40 

3  47  20 

9. 67750 

10 

10. 32250 

9. 73326 

18 

10. 26674 

10. 05576 

8 

9.94^4 

26 

12  32 

47  28 

67773 

10 

32227 

73356 

18 

26644 

05583 

3 

94417 

34 

27 

12  24 

47  36 

67796 

10 

32204 

73386 

14 

26614 

05590 

8 

94410 

88 

28 

12  16 

47  44 

67820 

11 

32180 

73416 

14 

26584 

05596 

3 

94404 

32 

29 

12  8 

47  52 

67848 

11 

32157 

78446 
9.  73476 

15 

26554 

05603 

3 

94397 

81 
30 

80 

8  12  0 

3  48  0 

9. 67866 

12 

10.  32134 

15 

10. 26524 

10. 05610 

3 

9. 94390 

81 

11  52 

48  8 

67890 

12 

32110 

73507 

16 

26493 

05617 

4 

94383 

29 

82 

11  44 

48  16 

67913 

12 

32087 

73537 

16 

26463 

05624 

4 

94376 

28 

88 

11  36 

48  24 

67936 

13 

32064 

73567 

17 

26438 

05631 

.4 

94369 

27 

34 

11  28 

48  32 

67959 

13 

32041 

73597 

17 

26403 

05638 
10. 05645 

4 
4 

94362 

26 

;i5 

8  11  20 

3  48  40 

9.  67982 

14 

10.  32018 

9. 73627 

18 

10.  26873 

9. 94355 

25 

86 

11  12 

48  48 

68006 

14 

31994 

73657 

18 

26343 

05651 

4 

94349 

24 

87 

11  4 

48  56 

68029 

14 

31971 

78687 

19 

26318 

05658 

4 

94342 

23 

88 

10  56 

49  4 

68052 

15 

31948 

73717 

19 

26283 

05665 

4 

94335 

22 

39 

10  48 

49  12 

68075 

15 

81925 

73747 

20 

26253 

05672 

4 

94828 

21 
20 

40 

8  10  40 

3  49  20 

9. 68098 

16 

10.  31902 

9. 73777 

20 

10. 26223 

10. 05679 

5 

9. 94321 

41 

10  32 

49  28 

68121 

16 

31879 

73807 

21 

26193 

05686 

5 

94314 

19 

42 

10  24 

49  36 

68144 

16 

31856 

73837 

21 

26163 

05693 

0 

94307 

18 

48 

10  16 

49  44 

68167 

17 

31833 

78867 

22 

26133 

05700 

5 

94300 

17 

44 

10  8 

49  52 

68190 

17 

31810 

73897 
9. 73927 

22 
23 

26103 
10. 26073 

05707 

5 

94293 
9. 94286 

16 

15 

45 

8  10  0 

3  50  0 

9. 68213 

17 

10. 31787 

10. 05714 

5 

46 

9  52 

50  8 

68237 

18 

31763 

78957 

23 

26043 

05721 

5 

94279 

14 

47 

9  44 

50  16 

68260 

18 

31740 

78987 

24 

26013 

05727 

5 

94278 

13 

48 

9  36 

50  24 

68283 

19 

31717 

74017 

24 

25983 

05734 

5 

94266 

12 

49 
50 

9  28 

50  32 

68305 

19 

31695 

74047 

25 

25953 

05741 

6 

94259 

11 

8  9  20 

3  50  40 

9. 68328 

19 

10.31672 

9. 74077 

25 

10.  25923 

10. 05748 

6 

9. 94252 

10 

51 

9  12 

50  48 

68351 

20 

31649 

74107 

26 

25893 

05755 

6 

94245 

9 

52 

9  4 

50  56 

68374 

20 

31626 

74137 

26 

25863 

05762 

6 

94238 

8 

58 

8  56 

51  4 

68397 

21 

31603 

74166 

27 

25834 

05769 

6 

94231 

7 

54 

8  48 

51  12 

68420 

21 

31580 

74196 

27 

25804 

05776 

6 

94224 

6 
5 

55 

8  8  40 

3  51  20 

9. 68443 

21 

10.  31557 

9.  74226 

28 

10.  25774 

10.  05783 

6  9.94217 

56 

8  32 

51  28 

68466 

22 

31534 

74256 

28 

25744 

05790 

6 

94210 

4 

57 

8  24 

51  36 

68489 

22 

31511 

74286 

29 

25714 

05797 

7 

94203 

8 

58 

8  16 

51  44 

68512 

22 

31488 

74316 

29 

25684 

05804 

/ 

94196 

2 

59 

8  8 

51  52 

68534 

23 

31466 

74345 

30 

25655 

05811 

/ 

94189 

1 

60 

8  0 

52  0 

68557 

23 

31443 

74375 

30 

25625 

05818 

7 

94182 

0 
M 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

DIfl. 

Secant. 

Cotangent,  j  Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

118° 

A 

A 

B            B 

c 

C     61°  1 

Seconds  of  time 

1" 

2« 

8-  1  4» 

5' 

6» 

7- 

fA 
Prop,  parts  of  cols,  i  B 

Ic 

8 

4 

1 

6 

8 
2 

9    12 

11    15 

3    3 

15 
19 
4 

17 

23 

5 

20 

26 

6 

TABLE  44. 

[Page  637 

Log.  Sines,  Tangents,  and  Secants. 

29° 

A 

A 

B            B 

C 

C    160° 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

DifF.  Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

8  8  0 

3  52  0 

9. 68557 

0 

10.  31443 

9. 74375 

0 

10.  25625 

10. 05818 

0 

9. 94182 

60 

1 

7  52 

52  8 

68580 

0 

31420 

74405 

0 

25595 

05825 

0 

94175 

59 

?. 

7  44 

52  16 

68603 

1 

31397 

74435 

1 

25565 

05832 

0 

94168 

58 

8 

7  36 

52  24 

68625 

1 

31375 

74465 

1 

25535 

05839 

0 

94161 

57 

4 

7  28 

52  32 

68648 

1 

31352 

74494 
9. 74524 

2 
2 

25506 

05846 

0 

94154 

56 
55 

5 

8  7  20 

3  52  40 

9. 68671 

2 

10. 31329 

10.  25476 

10. 05853 

9. 94147 

fi 

7  12 

52  48 

68694 

2 

31306 

74554 

3 

25446 

05860 

94140 

54 

7  4 

52  56 

68716 

3 

31284 

74583 

3 

25417 

05867 

94133 

53 

8 

6  56 

53  4 

68739 

3 

31261 

74613 

4 

25387 

05874 

94126 

52 

9 

6  48 

53  12 

68762 

3 

31238 

74643 

4 

25357 

05881 

94119 

51 

10 

8  6  40 

3  53  20 

9.  68784 

4 

10. 31216 

9. 74673 

5 

10. 25327 

10. 05888 

9.94112 

50 

n 

6  32 

53  28 

68807 

4 

31193 

74702 

5 

25298 

05895 

94105 

49 

ii> 

6  24 

53  36 

68829 

4 

31171 

74732 

6 

25268 

05902 

94098 

48 

18 

6  16 

53  44 

68852 

5 

31148 

74762 

6 

252.38 

05910 

2 

94090 

47 

14 
15 

6  8 

53  52 

68875 

5 

31125 

74791 
9. 74821 

7 

25209 

0.5917 
10. 0.5924 

2 
2 

94083 

46 
45 

8  6  0 

3  54  0 

9.  68897 

6 

10.  31103 

7 

10. 25179 

9. 94076 

16 

5  52 

54  8 

68920 

6 

31080 

74851 

8 

25149 

05931 

2 

94069 

44 

17 

5  44 

54  16 

68942 

6 

31058 

74880 

8 

25120 

05938 

2 

94062 

43 

1« 

5  36 

54  24 

68965 

7 

31035 

74910 

9 

25090 

05945 

2 

94055 

42 

19 

5  28 

54  32 

68987 

7 

31013 

74939 

9 

25061 

05952 

2 

94048 

41 

90 

8  5  20 

3  54  40 

9. 69010 

7 

10.  80990 

9. 74969 

10 

10.  25031 

10.  05959 

2 

9. 94041 

40 

9^ 

5  12 

54  48 

69032 

8 

30968 

74998 

10 

25002 

05966 

3 

94034 

39 

99 

5  4 

54  56 

69055 

8 

30945 

75028 

11 

24972 

05973 

3 

94027 

38 

9'^ 

4  56 

55  4 

69077 

9 

30923 

75058 

11 

24942 

05980 

3 

94020 

37 

24 

4  48 

55  12 

69100 

9 
9 

30900 

75087 

12 

24913 

0.5988 

3 

94012 

36 

9h 

8  4  40 

3  55  20 

9. 69122 

10.  30878 

9. 75117 

12 

10.  24883 

10. 05995 

3 

9. 94005 

3b 

9f\ 

4  32 

55  28 

69144 

10 

.   30856 

75146 

13 

24854 

06002 

3 

93998 

34 

91 

4  24 

55  36 

69167 

10 

30833 

75176 

13 

24824 

06009 

3 

93991 

33 

?8 

4  16 

55  44 

69189 

10 

30811 

75205 

14 

24795 

06016 

3 

93984 

32 

29 

4  8 

55' 52 

69212 

11 

30788 

75235 

14 

24765 

06023 

3 

93977 

31 

80 

8  4  0 

3  56  0 

9. 69234 

11 

10. 30766 

9. 75264 

15 

10.  24736 

10. 06030 

4 

9. 93970 

30 

81 

3  52 

56  8 

69256 

12 

30744 

75294 

15 

24706 

06037 

4 

93963 

29 

82 

3  44 

56  16 

69279 

12 

30721 

75323 

16 

24677 

06045 

4 

93955 

28 

88 

3  36 

56  24 

69301 

12 

30699 

75353 

16 

24647 

06052 

4 

93948 

27 

34 

3  28 

56  32 

69323 

13 

30677 

75382 

17 

24618 

06059 
10. 06066 

4 
4 

9.3941 

26 

85 

8  3  20 

3  56  40 

9. 69345 

13 

10.  30655 

9.75411 

17 

10.  24-589 

9. 93934 

25 

86 

3  12 

56  48 

69368 

13 

30632 

75441 

18 

24559 

06073 

4 

93927 

24 

87 

3  4 

56  56 

69390 

14 

30610 

75470 

18 

24530 

06080 

4 

93920 

23 

88 

2  56 

57  4 

69412 

14 

30588 

75500 

19 

24500 

06088 

5 

93912 

22 

39 
40 

2  48 

57  12 

69434 

15 

30566 

75529 

19 

24471 

06095 

5 

93905 

21 
20 

8  2  40 

3  57  20 

9. 69456 

15 

10. 30544 

9. 75558 

20 

10. 24442 

10. 06102 

6 

9. 93898 

41 

2  32 

57  28 

69479 

15 

30521 

75588 

20 

24412 

06109 

5 

93891 

19 

42 

2  24 

57  36 

69501 

16 

30499 

75617 

21 

24383 

06116 

5 

93884 

18 

48 

2  16 

57  44 

69523 

16 

30477 

75647 

21 

24353 

06124 

5 

93876 

17 

44 
45 

2  8 

57  52 

69.545 

16 
17 

30455 

75676 

22 

24324 

06131 

5 

93869 

.16 
15 

8  2  0 

3  58  0 

9. 69567 

10.  30433 

9. 75705 

22 

10.  24295 

10.  06138 

5 

9. 93862 

46 

1  52 

58  8 

69589 

17 

30411 

75735 

23 

24265 

06145 

5 

93855 

14 

47 

1  44 

58  16 

69611 

17 

30889 

75764 

23 

24236 

06153 

6 

93847 

13 

48 

1  36 

58  24 

69633 

18 

30867 

75793 

24 

24207 

06160 

6 

93840 

12 

49 

1  28 

58  32 

69655 

18 
19 

30845 

75822 

24 

24178 

06167 

6 

938.33 

11 
10 

50 

8  1  20 

3  58  40 

9.  69677 

10.  30323 

9. 75852 

25 

10.  24148 

10.  06174 

6 

9. 93826 

51 

.1  12 

58  48 

69699 

19 

30801 

75881 

25 

24119 

06181 

6 

93819 

9 

52 

1  4 

58  56 

69721 

19 

30279 

75910 

26 

24090 

06189 

6 

9.3811 

8 

53 

0  56 

59  4 

69743 

20 

30257 

75939 

26 

24061 

06196 

6 

93804 

7 

54 
55 

0  48 

59  12 

69765 

20 

30235 

75969 

27 

24031 

06203 

6 

93797 



6 

8  0  40 

3  59  20 

9. 69787 

20 

10.  30213 

9. 75998 

27 

10.  24002 

10.  06211 

7 

9. 93789 

5 

56 

0  32 

59  28 

69809 

21 

30191 

76027 

28 

23973 

06218 

7 

93782 

4 

57 

0  24 

59  36 

69831 

21 

30169 

76056 

28 

28944 

06225 

7 

98775 

3 

58 

0  16 

59  44 

69853 

22 

30147 

76086 

29 

23914 

06232 

7 

93768 

2 

59 

0  8 

59  52 

69875 

22 

30125 

76115 

29 

23885 

06240 

7 

93760 

1 

60 
M. 

0  0 

4  0  0 

69897 

22 

30103 

76144 

29 

23856 

06247 

7 

93753 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

119° 

A 

A 

B           B 

C 

C     60°  1 

Seconds  of  time 


Prop,  parts  of  cols.-jB 
C 


Page  638j 

TABLE  44. 

Log. 

Sines,  Tangents,  and  Secants. 

80° 

A 

A 

B 

B 

C 

C    1490 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diflf. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

8  0  0 

4  0  0 

9. 69897 

0 

10. 30103 

9.  76144 

0 

10.  23856 

10. 06247 

0 

9. 93753 

60 

1 

7  59  52 

0  8 

69919 

0 

30081 

76173 

0 

23827 

06254 

^i 

93746 

59 

2 

59  44 

0  16 

69941 

1 

30059 

76202 

1 

23798 

06262 

0  ' 

93738 

58 

3 

59  36 

0  24 

69963 

1 

30037 

76231 

1 

23769 

06269 

0 

93731 

57 

4 
5 

59  28 
7  59  20 

0  m 

4  0  40 

69984 
9. 70006 

1 
2 

30016 
10. 29994 

76261 

2 

23739 

06276 
10. 06283 

0  ' 

93724 
9. 93717 

56 
55 

9. 76290 

2 

10. 23710 

6 

59  12 

0  48 

70028 

2 

29972 

76319 

3 

23681 

06291 

93709 

54 

7 

59  4 

0  56 

70050 

3 

29950 

76348 

3 

23652 

06298 

1 

93702 

53 

8 

58  56 

1  4 

70072 

3 

29928 

76377 

4 

23623 

06305 

93695 

52 

9 

58  48 

1  12 

70093 

3 

29907 

76406 

4 

23594 

06313 



93087 

51 

10 

7  58  40 

4  1  20 

9. 70115' 

4 

10.  29885 

9.  76435 

5 

10.  23565 

10.  06320 

9.  93680 

50 

11 

58  32 

1  28 

70137 

4 

29863 

76464 

5 

23536 

06327 

93673 

49 

12 

58  24 

1  36 

70159 

4 

29841 

76493 

6 

23507 

06335 

936()5 

48 

18 

58  16 

1  44 

70180 

5 

29820 

76522 

6 

23478 

06342 

2 

93658 

47 

14 

58  8 

1  52 

70202 

5 
5 

29798 
10. 29776 

76551 

7 

23449 
10.  23420 

06350 

2 

93650 
9. 93643 

46 
45 

15 

7  58  0 

4  2  0 

9. 70224 

9. 76580 

7 

10. 06357 

2 

16 

57  52 

2  8 

70245 

6 

29755 

76609 

8 

23391 

063(>4 

2 

93636 

44 

17 

57  44 

2  16 

70267 

6 

29733 

76639 

8 

23361 

06372 

2 

93628 

43 

18 

57  36 

2  24 

70288 

6 

29712 

76668 

9 

23332 

06379 

2 

93621 

42 

19 

57  28 

2  32 
4  2  40 

70310 

7 

29690 

76697 

9 

23303 

06386 

2 

93614 
9. 93606 

41 
40 

20 

7  57  20 

9.  70332 

7 

10.  29668 

9. 76725 

10 

10.  23275 

10.  06394 

2 

21 

57  12 

2  48 

70353 

8 

29647 

76754 

10 

23246 

06401 

3 

93599 

39 

22 

57  4 

2  56 

70375 

8 

29625 

76783 

11 

23217 

06409 

3 

93591 

38 

23 

56  56 

3  4 

70396 

8 

29604 

76812 

11 

23188 

06416, 

3 

93584 

37 

24 

56  48 

3  12 

70418 

9 

29582 

76841 

12 

23159 
10.  23130 

06423 

3 

93577 

36 

25 

7  56  40 

4  3  20 

9. 70439 

9 

10. 29561 

9. 76870 

12 

10. 06431 

3 

9. 93569 

35 

26' 

56  32 

3  28 

70461 

9 

29539 

76899 

13 

23101 

06438 

3 

93562 

34 

27 

56  24 

3  36 

70482 

10 

29518 

76928 

13 

23072 

06446 

3 

93554 

33 

28 

56  16 

3  44 

70504 

10 

29496 

76957 

13 

23043 

06453 

3 

93547 

32 

29 

56  8 

3  52 

70525 

10 

29475 

76986 

14 

23014 

06461 

4 

93539 
9. 93532 

31 
30 

30 

7  56  0 

4  4  0 

9. 70547 

11 

10.  29453 

9.  77015 

14 

10.  22985 

10.  06468 

4 

31 

55  52 

4  8 

70568 

11 

29432 

77044 

15 

22956 

06475 

4 

93525 

29 

32 

55  44 

4  16 

70590 

11 

29410 

77073 

15 

22927 

06483 

4 

93517 

28 

33 

55  36 

4  24 

70611 

12 

29389 

77101 

16 

22899 

06490 

4 

93510 

27 

34 

55  28 

4  32 

70633 
9.70654 

12 

29367 

77130 

16 

22870 

06498 

4 

93502 

26 

35 

7  55  20 

4  4  40 

13 

10.  29346 

9. 77159 

17 

10.  22841 

10. 06505 

4 

9.  93495 

25 

36 

55  12 

4  48 

70675 

13 

29325 

77188 

17 

22812 

06513 

4 

93487 

24 

37 

55  4 

4  56 

70697 

13 

29303 

77217 

18 

22783 

06520 

5 

93480 

23 

38 

54  56 

5  4 

70718 

14 

29282 

77246 

18 

22754 

06528 

5 

93472 

22 

39 

54  48 

5  12 

70739 

14 

29261 

77274 

19 

22726 

06535 

5 

93465 

21 
20 

40 

7  54  40 

4  5  20 

9. 70761 

14 

10. 29239 

9. 77303 

19 

10.  22697 

10.  0a543 

5 

9.  93457 

41 

54  32 

5  28 

70782 

15 

29218 

77332 

20 

22668 

06550 

5 

93450 

19 

42 

54  24 

5  36 

70803 

15 

29197 

77361 

20 

22639 

06558 

5 

93442 

18 

43 

54  16 

5  44 

70824 

15 

29176 

77390 

21 

22610 

06565 

5 

93435 

17 

44 

54  8 

5  52 

70846 

16 
16 

29154 
10.29133 

77418 

21 

22582 
10.  22553 

06573 

5 

93427 
9. 93420 

16 
15 

45 

7  54  0 

4  6  0 

9. 70867 

9.  77447 

22 

10. 06580 

6 

46 

53  52 

6  8 

70888 

16 

29112 

77476 

22 

22524 

06588 

6 

93412 

14 

47 

53  44 

6  16 

70909 

17 

29091 

77505 

23 

22495 

06595 

6 

93405 

13 

48 

53  36 

6  24 

70931 

17 

29069 

77533 

23 

22467 

06603 

6 

93397 

12 

49 
50 

53  28 
7  53  20 

6  32 

70952 
9.70973 

18 
18 

29048 
10.  29027 

77562 
9. 77591 

24 

22438 

06610 

6 
"  6 

93390 
9. 93382 

11 
10 

4  6  40 

24 

10.  22409 

10.06618 

51 

53  12 

6  48 

70994 

18 

29006 

77619 

25 

22.381 

06625 

6 

93375 

9 

52 

53  4 

6  56 

71015 

19 

28985 

77648 

25 

22352 

06633 

6 

93367 

8 

53 

52  56 

7  4 

71036 

19 

28964 

77677 

26 

22323 

06640 

7 

93360 

7 

54 

55 

52  48 

7  12 

71058 

19 

28942 

77706 

26 
26 

22294 
10.  22266 

06648 

7 

93352 

6 
5 

7  52  40 

4  7  20 

9.  71079 

20 

10.  28921 

9.  77734 

10. 06656 

7 

9. 93344 

56 

52  32 

7  28 

71100 

20 

28900 

77763 

27 

22237 

06663 

7 

93337 

4 

57 

52  24 

7  36 

71121 

20 

28879 

77791 

27 

22209 

06671 

7 

93329 

3 

58 

52  16 

7  44 

71142 

21 

28858 

77820 

28 

22180 

06678 

7 

93322 

2 

59 

52  8 

7  52 

71163 

21 

'28837 

77849 

28 

22151 

06686 

7 

93314 

1 

60 

52  0 

8  0 

71184 

21 

28816 

77877 

29 

22123 

06693 

7 

93307 

0 

M. 

Hour  p.  M 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

jDiff. 

Sine. 

M. 

120^ 

A 

A 

B 

B 

C 

C    69°  1 

Seconds  of  time 

1« 

2- 

8* 

4« 

&• 

6« 

J' 

A 

Prop,  parts  of  cols.^B 

Ic 

3 
4 
1 

5 
7 
2 

8 
11 
3 

11 
14 
4 

13 

18 
5 

16 
22 
6 

19 
25 

7 

TABLE  44. 

[Page  639 

Log.  Sines,  Tangents,  and  Secants. 

31° 

A            A 

B 

B 

C 

C   148° 

M., 

Hour  A.  M. 

Hour  P.M. 

Sine. 

Diflf. 

Cosecant. 

Tangent.  Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  52  0 

4  8  0 

9.71184 

0 

10. 28816 

9. 77877 

0 

10. 22123 

10. 06693 

0 

9. 93307 

60 

1 

51  52 

8  8 

71205 

0 

28795 

77906 

0 

22094 

06701 

0 

98299 

59 

9, 

51  44 

8  16 

71226 

1 

28774 

77935 

1 

22065 

06709 

0 

93291 

58 

8 

51  36 

8  24 

71247 

1 

28753 

77963 

1 

22087 

06716 

0 

93284 

57 

4 

51  28 

8  32 

71268 

1 

28732 

77992 

2 

22008 

06724 

93276 

56 
55 

5 

7  51  20 

4  8  40 

9. 71289 

2  jlO.  28711 

9. 78020 

2 

10.  21980 

10.  06731 

1  i  9. 93269  1 

fi 

51  12 

8  48 

71310 

2  1   28690 

78049 

3 

21951 

06739 

93261 

54 

7 

51  4 

8  56 

71331 

2  !   28669 

78077 

3 

21923 

06747 

93253 

58 

S 

50  56 

9  4 

71352 

3    28648 

78106 

4 

21894 

06754 

93246 

52 

9 
10 

50  48 

9  12 
4  9  20 

71378 

3    28627 
•3  110.28607 

78135  1  4 

21865 

06762 

93238 

51 
50 

7  50  40 

9. 71393 

9.  78168 

5 

10.  21887 

10. 06770 

1  9.93280 

11 

50  32 

9  28 

71414 

4  '       28586 

78192 

5 

21808 

06777 

1  ;   93223 

49 

12 

50  24 

9  36 

71435 

4    28565 

78220 

6 

21780 

06785 

2    93215 

48 

IS 

50  16 

9  44 

71456  i  4  !   28544 

78249 

6 

21751 

06793 

2    93207 

47 

14 

50  8 

9  52 

71477 

5 

5 

28523 

78277 
9. 78306 

7 

21723 

06800 
10. 06808 

2    93200 
2    9.93192" 

46 
45 

15 

7  50  0 

4  10  0 

9. 71498 

10. 28502 

t 

10. 21694 

16 

49  52 

10  8 

71519   5    28481 

78334 

8 

21666 

06816 

2    93184 

44 

17 

49  44 

10  16 

71539 

6  ;   28461 

78863 

8 

21637 

06823 

2  ,   93177 

43 

18 

49  36 

10  24 

71560 

6  1   28440 

78391 

9 

21609 

06831 

2    93169 

42 

19 
20 

49  28 

10  32 

71581 
9. 71602 

7 
7 

28419 

78419 

9 
9 

21581 

06839 

2   93161 

41 
40 

7  49  20 

4  10  40 

10. 28398 

9. 78448 

10. 21552 

10. 06846 

3  9.93154 

?.\ 

49  12 

10  48 

71622 

7 

28378 

78476 

10 

21524 

06854 

3   93146 

39 

22 

49  4 

10  56 

71643   8 

28357 

78505 

10 

21495 

06862 

3   93138 

38 

28 

48  56 

11  4 

71664  !  8 

28336 

78533 

11 

21467 

06869 

3   93131 

37 

24 

48  48 

11  12 

71685 

8 

28315 

78562  11 

21438 

06877 

3   93123 

36 
35 

25 

7  48  40 

4  11  20 

9.  71705 

9 

10.  28295 

9. 78590  12 

10. 21410 

10.  06885 

3  9.93115 

26 

48  32 

11  28 

71726 

9  [   28274 

78618  12 

21382 

06892 

3   93108 

34 

27 

48  24 

11  36 

71747 

9    28253 

78647  13 

21358 

06900 

3   93100 

33 

28 

48  16 

11  44 

71767 

10    28233 

78675  !  13 

21325 

06908 

4   93092 

32 

29 

48  8 

11  52. 

71788 

10 

28212 
10.  28191 

78704 

14 
14 

21296 

06916 

4 
4 

93084 

31 
30 

80 

7  48  0 

4  12  0 

9.  71809 

10 

9.  78732 

10.  21268 

10. 06923 

9. 93077 

81 

47  52 

12  8 

71829 

11  1   28171 

78760  15 

21240 

06931 

4    93069 

29 

82 

47  44 

12  16 

71850 

11  1   28150 

78789  ;  15 

21211 

06939 

4    93061 

28 

88 

47  36 

12  24 

71870 

11  1   28130 

78817  16 

21188 

06947 

4    98053 

27 

34 

47  28 

12  32 

71891 

12  I   28109 

78845  i  16 

21155 

06954 

4 
5 

93046 

26 
25 

85 

7  47  20 

4  12  40 

9. 71911 

12  110.28089 

9.78874  !  17 

10.  21126 

10. 06962 

9. 98038 

86 

47  12 

12  48 

71932 

12  1   28068 

78902  17 

21098 

06970 

5   93030 

24 

87 

47  4 

12  56 

71952 

13    28048 

78930  17 

21070 

06978 

5   93022 

23 

88 

46  56 

13  4 

71973 

13    28027 

78959  18 

21041 

06986 

5   93014 

22 

39 

46  48 

13  12 

71994 

13  1   28006 

78987  t  18 

21013 
10. 20985 

06993 
10. 07001 

5 
5 

93007 

21 

40 

7  46  40 

4  13  20 

9.72014  1  14  10.27986 

9.79015  19 

9. 92999 

20 

41 

46  32 

13  28 

72034  !  14    27966 

79043  19 

20957 

07009 

5    92991 

19 

42 

46  24 

13  36 

72055 

14    27945 

79072  20 

20928 

07017 

5    92983 

18 

48 

46  16 

13  44 

72075 

15    27925 

79100  20 

20900 

07024 

6  ;  92976 

17 

44 

46  8 

13  52 

72096 

15  i   27904 

79128  21 
9. 79156  21 

20872 

07032 

6  !  92968 

16 
15 

45 

7  46  0 

4  14  0 

9.  72116 

15 

10. 27884 

10.  20844 

10. 07040 

6  9. 92960 

46 

45  52 

14  8 

72137 

16 

27863 

79185  22 

20815 

07048 

6  1   92952 

14 

47 

45  44 

14  16 

72157 

16 

27848 

79213  22 

20787 

07056 

6  1   92944 

13 

48 

45  36 

14  24 

72177 

16 

27823 

79241  23 

20759 

07064 

6  1  92936 

12 

49 
50 

45  28 
7  45  20 

14  82 
4  14  40 

72198 

17    27802 

79269  1  23 

20731 

07071 

6   92929 

11 
10 

9.72218  i  17  10.27782 

9.79297  1  24 

10.  20703 

10. 07079 

6  9.92921 

51 

45  12 

14  48 

72238  1  18  1   27762 

79326  1  24 

20674 

07087 

7  1  92913 

9 

52 

45  4 

14  56 

72259  18    27741 

79354  25 

20646 

07095 

7  !  92905 

8 

58 

44  56 

15  4 

72279  1  18    27721 

79382  25 

20618 

07103 

7    92897 

1 

54 
55 

44  48 

15  12 
4  15  20 

72299 

19    27701 
19  10.27680 

79410  26 

20590 
10.  20562 

07111 
10.07119 

7  I   92889 
7  19.92881 

6 
5 

7  44  40 

9.  72320 

9.  79438 

26 

56 

44  32 

15  28 

72340  i  19 

27660 

79466 

26 

205;w 

07126 

7    92874 

4 

57 

44  24 

15  36 

72360  ;  20 

27640 

79495 

27 

20505 

07134 

7    92866 

3 

58 

44  16 

15  44 

72381  20 

27619 

79523 

27 

20477 

07142 

7    92858 

2 

59 

44  8 

15  52 

72401  1  20 

27599 

79551 

28 

20449 

07150 

8 

92850 

1 

60 

44  0 

16  0 

72421 

21 

27579 

79579 

28 

20421 

07158 

8 

92842 

0 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

DiflF. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

121° 

A           A 

B 

B 

C 

C     58°  1 

Seconds  of  time 

1»    2" 

3« 

4» 

5« 

6'    7" 

Prop,  parts  of  cols.  B 
1  c 

3  5    8 

4  i   7    11 
1     2    3 

10    13 
14    18 
4    h 

15  j  18 

21  1  25 

6  '   7 

Page  640] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

82° 

A 

A 

B 

B 

C 

C 

147° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine.   1  Diff. 

Cosecant. 

Tangent.  Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

0 

7  44  0 

4  16  0 

9. 72421 

0 

10.  27579 

9.79579   0 

10. 20421 

10. 07158 

0 

9. 92842 

1 

48  52 

16  8 

72441 

0 

27559 

79607   0 

20398 

07166 

0 

92834 

59 

9 

48  44 

16  16 

72461 

1 

27539 

79635   1 

20365 

07174 

0 

92826 

58 

8 

43  86 

16  24 

72482 

1 

27518 

79663   1 

20337 

07182 

0    92818 

57 

4 
5 

43  28 

16  3» 

72502 

1 

27498 

79691 

2 

20309 

07190 

1 

92810 

56 
55 

7  43  20 

4  16  40 

9. 72522   2 

10. 27478 

9.  79719 

2 

10.  20281 

10. 07197 

1 

9. 92803 

H 

43  12 

16  48 

72542   2 

27458 

79747 

8 

20258 

07205 

1 

92795 

54 

7 

48  4 

16  56 

72562   2 

27438 

79776 

3 

20224 

07213 

1 

92787 

53 

8 

42  56 

17  4 

72582   3 

27418 

79804   4 

20196 

07221 

1 

92779 

52 

9 
10 

42  48 

17  12 

72602   3 

27398 

79832  i  4 

20168 

07229 

1 

92771 
9. 92768 

51 
50 

7  42  40 

4  17  20 

9. 72622   3 

10.  27878 

9. 79860   5 

10.  20140 

10. 07237 

1 

11 

42  32 

17  28 

72643   4 

27857 

79888   5 

20112 

07245 

1 

92755 

49 

12 

42  24 

17  36 

72668  ;  4 

27887 

79916   6 

20084 

07258 

2 

92747 

48 

18 

42  16 

17  44 

72688   4 

27317 

79944  ;  6 

20056 

07261 

2 

92739 

47 

14 
15 

42  8 

17  52 

72708 

5 
5 

27297 

79972 
'9.  80000 

7 
7 

20028 

07269 
10. 07277 

2 
2 

92731 
9. 92728 

46 
45 

7  42  0 

4  18  0 

9. 72723 

10. 27277 

10.20000 

U) 

41  52 

18  8 

72743   5 

27257 

80028 

7 

19972 

07285 

2 

92715 

44 

17 

41  44 

18  16 

72768   6 

27237 

80056 

8 

19944 

07293 

2 

92707 

48 

18 

41  36 

18  24 

72788   6 

27217 

80084 

8 

19916 

07301 

2 

92699 

42 

19 
20 

41  28 
7  41  20 

18  32 

72808   6 

27197 

80112 

9 

19888 

07309 

3 

92691 

41 
40 

4  18  40 

9.72828   7 

10.  27177 

9.80140  1  9 

10. 19860 

10. 07817 

3  i 9. 92683 

21 

41  12 

18  48 

72848   7 

27157 

80168  1  10 

19832 

07325 

3  !  92675 

39 

22 

41  4 

18  56 

72863   7 

27137 

80195  10 

19805 

07338 

3  '  92667 

38 

28 

40  56 

19  4 

72883  ,  8 

27117 

80223  11 

19777 

07:341 

8  ;   92659 

87 

24 

40  48 

19  12 

72902   8 

27098 

80251   11 

19749 

07349 

8  i   92651 

36 

25 

7  40  40 

4  19  20 

9.72922   8 

10.  27078 

9.80279  12 

10. 19721 

10. 07857 

8  i  9. 92648 

35 

26 

40  82 

19  28 

72942   9 

27058 

80307  12 

19693 

07365 

8  !  926:35 

34 

27 

40  24 

19  36 

72962   9 

27038 

80335  13 

19665 

07873 

4 

92627 

33 

28 

40  16 

19  44 

72982  i  9 

27018 

80868  13 

19687 

07381 

4 

92619 

32 

29 
80 

40  8 

19  52 

78002 

10 
10 

26998 
10. 26978 

80391   18 
9.80419  14 

19609 

07389 

4 

92611 
9. 92603 

31 
80 

7  40  0 

4  20  0 

9.  73022 

10. 19581 

10. 07397 

4 

81 

39  52 

20  8 

73041  :  10 

26959 

80447  14 

19553 

07405 

4 

92595 

29 

82 

39  44 

20  16 

78061  ;  11 

26989 

80474  15 

19526 

07413 

4 

92587 

28 

88 

89  36 

20  24 

78081  11 

26919 

80502  ,   15 

19498 

07421 

4 

92579 

27 

34 

39  28 

20  82 

78101  11 

26899 

80580  :  16 

19470 

07429 

5  !  92571 

26 

85 

7  39  20 

4  20  40 

9.78121  12 

10.  26879 

9.80558  1  16 

10. 19442 

10.  07487 

5  (9.92568 

25 

86 

39  12 

20  48 

78140  12 

26860 

80586  17 

19414 

07445 

5  !  92555 

24 

87 

89  4 

20  56 

73160  12 

26840 

80614  17 

19886 

07454 

5  1  92546 

23 

88 

38  56 

21  4 

73180  1  13 

26820 

80642  1  18 

19358 

07462 

5  !  92538 

22 

89 
40 

38  48 

21  12 

73200  i  13 

26800 

80669  18 
9.80697  j  19 

19831 

07470 

5 
5~ 

92580 

21 

7  38  40 

4  21  20 

9. 78219  13 

10.  26781 

10. 19808 

10. 07478 

9. 92522 

20 

41 

88  82 

21  28 

73239  14 

26761 

80725  1  19 

19275 

07486 

6  1  92514 

19 

42 

88  24 

21  86 

73259  !  14 

26741 

80753  1  20 

19247 

07494 

6   92506 

18 

48 

88  16 

21  44 

78278  :  14 

26722 

80781  :  20 

19219 

07502 

6   92498 

17 

44 
45 

38  8 
"7'38  0 

21  52 
4  22  0 

73298  15 

26702 

80808  20 

19192 

07510 

6   92490 

16 

9.73818  15 

10.  26682 

9.80886  1  21 

10. 19164 

10. 07518 

6 

9.  92482 

15 

46 

37  52 

22  8 

78387  15 

26663 

80864  i  21 

19136 

07527 

6 

92478 

14 

47 

37  44 

22  16 

78857  1  16 

26643 

80892  i  22 

19108 

07535 

6 

92465 

13 

48 

87  36 

22  24 

78377  '  16 

26628 

80919  !  22 

19081 

07543 

6 

92457 

12 

49 

37  28 

22  32 

73396  16 

26604 

80947  j  28 

19058 

07551 

7 
"^7" 

92449 

11 
10 

50 

7  37  20 

4  22  40 

9.73416  17 

10.  26584 

9.80975  1  28 

10. 19025 

10. 07559 

9. 92441 

51 

87  12 

22  48 

73435  1  17 

26565 

81003 

24 

18997 

07567 

/ 

92483 

9 

52 

37  4 

22  56 

7:3455  i  17 

26545 

81030 

24 

18970 

07575 

7 

92425 

8 

58 

36  56 

23  4 

73474  18 

26526 

81058 

25 

18942 

07584 

7 

92416 

7 

54 

36  48 

23  12 

73494  i  18 

26506 

81086 

25 

18914 

07592 

7 

92408 

6 
5 

55 

7  36  40 

4  28  20 

9.73518  ;  18 

10.  26487 

9.81113 

26 

10. 18887 

10. 07600 

7 

9. 92400 

56 

36  32 

28  28 

78533  19 

26467 

81141 

26 

18859 

07608 

8 

92392 

4 

57 

86  24 

23  36 

78552  i  19 

26448 

81169 

26 

18831 

07616 

8 

92884 

8 

58 

36  16 

23  44 

78572  19 

26428 

81196 

27 

18804 

07624 

8  1   92376 

2 

59 

36  8 

23  52 

73591  20 

26409 

81224  27 

18776 

07638 

8   92367 

1 

60 

M. 

36  0 

24  0 

73611  20 

26389 

81252  !  28 

18748 

07641 

8 

92359 

0 

Hour  p.  M. 

Hour  A.  M. 

Cosine.   Dili. 

Secant. 

Cotangent.  Diff. 

Tangent. 

Ccsecant. 

Diff. 

Sine. 

M. 

1-220 

A 

A 

B 

B 

C 

C 

57° 

Seconds  of  time 

1» 

2» 

8> 

4» 

6< 

6> 

7' 

fA 

Prop,  parts  of  cols.  iB 

Ic 

2 
3 
1 

6 

7 
2 

7 

10 

3 

10 
14 
4 

12 
17 
5 

15 

21 

6 

17 
24 

7 

TABLE  U. 

[Page  641 

Log.  Sines,  Tangents,  and  Secants. 

83° 

A 

A 

B 

B 

C 

C    146° 

M. 
0 

Hour  A.  M. 

Hour  P.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

7  36  0 

4  24  0 

9. 73611 

0 

10. 26389 

9.  81252 

0 

10. 18748 

10. 07641 

0 

9. 92359 

60 

1 

35  52 

24  8 

73630 

0 

26370 

81279 

0 

18721 

07649 

0 

92351 

59 

'? 

35  44 

24  16 

73650 

1 

26350 

81307 

1 

18693 

07657 

0 

92343 

58 

8 

35  36 

24  24 

73669 

1 

26331 

81335 

1 

18665 

07665 

0 

92335 

57 

4 

35  28 

24  32 

73689 

1 

26311 

81362 

2 

18638 

07674 

1 

92326 

56 

5 

7  35  20 

4  24  40 

9. 73708 

2 

10.  26292 

9. 81390 

2 

10. 18610 

10. 07682 

1 

9. 92318 

55 

6 

35  12 

24  48 

73727 

2 

26273 

81418 

3 

18582 

07690 

1 

92310 

54 

7 

35  4 

24  56 

73747 

2 

26253 

81445 

3 

18555 

07698 

1 

92302 

53 

8 

34  56 

25  4 

73766 

3 

26234 

81473 

4 

18527 

07707 

1 

92293 

52 

9 
10 

34  48 

25  12 

73785 

3 

26215 

81500 

4 

18500 

07715 

1 

92285 

51 
50 

7  34  40 

4  25  20 

9. 73805 

3 

10. 26195 

9. 81528 

5 

10. 18472 

10. 07723 

1 

9. 92277 

n 

34  32 

25  28 

73824 

3 

26176 

81556 

5 

18444 

07731 

2 

92269 

49 

12 

34  24 

25  36 

73843 

4 

26157 

81583 

5 

18417 

07740 

2    92260 

48 

18 

34  16 

25  44 

73863 

4 

26137 

81611 

6 

18389 

07748 

2 

92252 

47 

14 
15 

34  8 

25  52 

73882 

4 

26118 

81638 

6 

18362 

07756 

2 

92244 

46 

7  34  0 

4  26  0 

9. 73901 

5 

10. 26099 

9. 81666 

7 

10. 18334 

10. 07765 

2 

9. 92235 

45 

Ifi 

33  52 

26  8 

73921 

•  5 

26079 

81693 

7 

18307 

07773 

2 

92227 

44 

17 

33  44 

26  16 

73940 

5 

26060 

81721 

8 

18279 

07781 

2 

92219 

43 

18 

33  36 

26  24 

73959 

6 

26041 

81748   8 

18252 

07789 

3 

92211 

42 

19 
20 

33  28 

26  32 

73978 

6 

26022 

81776 

9 

18224 

07798 

3 

92202 

41 

7  33  20 

4  26  40 

9.73997 

6 

10. 26003 

9. 81803 

9 

10. 18197 

10. 07806 

3 

9. 92194 

40 

21 

33  12 

26  48 

74017 

7 

25983 

81831 

10 

18169 

07814 

3 

92186 

39 

22 

33  4 

26  56 

74036 

7 

25964 

81858 

10 

18142 

07823 

3 

92177 

38 

28 

32  56 

27  4 

74055 

7 

25945 

81886 

11 

18114 

07831 

3 

92169 

37 

24 

32  48 

27  12 

74074 

8 

25926 

81913 

11 

18087 

07339 

3 

92161 

36 

25 

7  32  40 

4  27  20 

9.74093 

8 

10.  25907 

9. 81941 

11 

10. 18059 

10. 07848 

3 

9. 92152 

35 

26 

32  32 

27  28 

74113 

8 

25887 

81968 

12 

18032 

07856 

4 

92144 

34 

27 

32  24 

27  36 

74132 

9 

25868 

81996 

12 

18004 

07864 

4 

92186 

33 

28 

32  16 

27  44 

74151 

9 

25849 

82023 

13 

17977 

07873 

4 

92127 

32 

29 

32  8 

27  52 

74170 

9 

25830 

82051 

13 

17949 

07881 

4 

92119 

31 

80 

7  32  0 

4  28  0 

9. 74189 

10 

10.  25811 

9.  82078 

14 

10. 17922 

10.  07889 

4 

9.92111 

30 

81 

31  52 

28  8 

74208 

10 

25792 

82106 

14 

17894 

07898 

4 

92102 

29 

82 

31  44 

28  16 

74227 

10 

25773 

82133 

15 

17867 

07906 

4 

92094 

28 

88 

31  36 

28  24 

74246 

10 

25754 

82161 

15 

17839 

07914 

5 

92086 

27 

34 

31  28 

28  32 

74265 

11 

25735 

82188 

16 

17812 

07923 

5 

92077 

26 

85 

7  31  20 

4  28  40 

9.  74284 

11  10.25716 

9.  82215 

16 

10. 17785 

10. 07931 

5 

9. 92069 

25 

8H 

31  12 

28  48 

74303 

11    25697 

82243 

16 

17757 

07940 

5 

92060 

24 

87 

31  4 

28  56 

74322 

12    25678 

82270 

17 

17730 

07948 

5 

92052 

23 

88 

30  56 

29  4 

74341 

12    25659 

82298 

17 

17702 

07956 

5 

92044 

22 

39 

30  48 

29  12 

74360 

12    25640 

82325 

18 

17675 

07965 

6 

92035 
9. 92027 

21 
20 

40 

7  30  40 

4  29  20 

9.  74379 

13 

10. 25621 

9. 82352 

18 

10. 17648 

10. 07973 

6 

41 

30  32 

29  28 

74398 

13 

25602 

82380 

19 

17620 

07982 

6 

92018 

19 

42 

30  24 

29  36 

74417 

13 

25583 

82407 

19 

17593 

07990 

6 

92010 

18 

48 

30  16 

29  44 

74436 

14 

25564 

82435 

20 

17565 

07998 

6 

92002 

17 

44 
45 

30  8 

29  52 

74455 

14 

25545 

82462  I  20 

17538 
10. 17511 

08007 

6 

91993 

16 

7  30  0 

4  30  0 

9. 74474 

14 

10.  25526 

9.  82489 

21 

10. 08015 

6 

9. 91985 

15 

46 

29  52 

30  8 

74493 

15 

25507 

82517 

21 

17483 

08024 

6 

91976 

14 

47 

29  44 

30  16 

74512 

15 

25488 

82544 

22 

17456 

08032 

/ 

91968 

13 

48 

29  36 

30  24 

74531 

15 

25469 

82571 

22 

17429 

08041 

7 

91959 

12 

49 

29  28 

30  32 

74549 

16 

25451 

82599 

22 

17401 

08049 

/ 

91951 

11 

50 

7  29  20 

4  30  40 

9. 74568 

16 

10.  25432 

9.  82626 

23 

10. 17374 

10.  08058 

7 

9.  91942 

10 

51 

29  12 

30  48 

74587 

16 

25413 

82653 

23 

17347 

08066 

/ 

91934 

9 

52 

29  4 

30  56 

74606 

17 

25394 

82681 

24 

17319 

08075 

7 

91925 

8 

53 

28  56 

31  4 

74625 

17 

25375 

82708 

24 

17292 

08083 

/ 

91917 

/ 

54 
55 

28  48 

31  12 

74644 

17 

25356 

82735 

25 

17265 

08092 

8 

91908 
9. 91900 

6 

0 

7  28  40 

4  31  20 

9.  74662 

17 

10.  25338 

9. 82762 

25 

10. 17238 

10. 08100 

8 

56 

28  32 

31  28 

74681 

18 

25319 

82790 

26 

17210 

08109 

8 

91891 

4 

57 

28  24 

31  36 

74700 

18 

25300 

82817 

26 

17183 

08117 

8 

91888 

3 

58 

28  16 

31  44 

74719 

18 

25281 

82844 

27 

17156 

08126 

8 

91874 

'  2 

59 

28  8 

31  52 

74737 

19 

25263 

82871  i  27 

17129 

08134 

8 

91866 

1 

60 

28  0 

32  0 

74756 

19 

25244 

82899  27 

17101 

08143 

8 

91857 

0 

M. 

Hour  P.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent.  Difl. 

Tangent. 

Cosecant. 

Difl. 

Sine.    M.  1 

123= 

A 

A 

B 

B 

c 

C     66°  1 

Seconds  of  time 

1' 

2» 

3» 

4" 

5» 

6« 

7« 

fA 

Prop,  parts  of  cols.  <B 

[c 

2 
3 

1 

6 

7 
2 

7 

10 

3 

10 
14 

4 

12 
17 

5 

14 

21 

6 

17 

24 

7 

22489—03- 


-41 


Page  642] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

84° 

A 

A 

B 

B 

C 

C 

145° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

7  28  0 

4  32  0 

9.  74756 

0 

10.  25244 

9. 82899 

0 

10. 17101 

10.  08143 

0 

9. 91857 

60 

1 

27  52 

32  8 

74775 

0 

25225 

82926 

0 

17074 

08151 

0 

91849 

59 

2 

27  44 

32  16 

74794 

1 

25206 

82953 

1 

17047 

08160 

0 

91840 

58 

3 

27  36 

32  24 

74812 

1 

25188 

82980 

1 

17020 

08168 

0 

91832 

57 

4 
5 

27  28 

32  'S» 

74831 

1 

25169 

83008 

2 

16992 

08177 

91823 

56 
55 

7  27  20 

4  32  40 

9.  74850 

2 

10. 25150 

9. 83035 

2 

10. 16965 

10. 08185 

9.  91815 

6 

27  12 

32  48 

74868 

2 

25132 

83062 

3 

16938 

08194 

91806 

54 

7 

27  4 

32  56 

74887 

2 

25113 

83089 

3 

16911 

08202 

91798 

53 

8 

26  56 

33  4 

74906 

2 

25094 

83117 

4 

16883 

08211 

91789 

52 

9 

26  48 

33  12 

74924 

3 

25076 

83144 

4 

16856 

08219 

91781 

51 
50 

10 

7  26  40 

4  33  20 

9.  74943 

3 

10.  25057 

9. 83171 

5 

10. 16829 

10.  08228 

9.91772 

11 

26  32 

33  28 

74961 

3 

25039 

83198 

5 

16802 

08237 

2    91763 

49 

12 

26  24 

33  36 

74980 

4 

25020 

83225 

5 

16775 

08245 

2   91755 

48 

13 

26  16 

33  44 

74999 

4 

25001 

83252 

6 

16748 

08254 

2   91746 

47 

14 
15 

26  8 

33  52 
4  34  0 

75017 

4 

24983 

83280 

6 

7 

16720 
10. 16693 

08262 
10. 08271 

2   91738 
2  9.91729 

46 
45 

7  26  0 

9.  75036 

5 

10. 24964 

9. 83307 

16 

25  52 

34  8 

75054 

5 

24946 

83334 

7 

16666 

08280 

2   91720 

44 

17 

25  44 

34  16 

75073 

5 

24927 

83361 

8 

16639 

08288 

2   91712 

43 

18 

25  36 

34  24 

75091 

6 

24909 

83388 

8 

16612 

08297 

3  1  91703 

42 

19 

25  28 

34  32 

75110 

6 

24890 

83415 

9 

16585 
10. 16558 

08305 

3 
3 

91695 

41 
40 

20 

7  25  20 

4  34  40 

9.  75128 

6 

10.  24872 

9.83442 

9 

10. 08314 

9. 91686 

21 

25  12 

34  48 

75147 

6 

24853 

83470 

9 

16530 

08323 

3   91677 

.39 

22 

25  4 

34  56 

75165 

7 

24835 

83497 

10 

16503 

08331 

3   91669 

38 

23 

24  56 

35  4 

75184 

7 

24816 

83524 

10 

16476 

08340 

3  '     91660 

37 

24 

24  48 

35  12 

75202 

7 

24798 

83551 

11 

16449 

08349 

3 

91651 
9. 91643 

36 
35 

25 

7  24  40 

4  35  20 

9. 75221 

8 

10. 24779 

9.  83578 

11 

10. 16422 

10.08357 

4 

26 

24  32 

35  28 

752.39 

8 

24761 

83605 

12 

16395 

08366 

4   91634 

.34 

27 

24  24 

35  36 

75258 

8 

24742 

83632 

12 

16368 

08375 

4  j  91625 

33 

28 

24  16 

35  44 

75276 

9 

24724 

83659 

13 

16341 

08383 

4  1  91617 

32 

29 
30 

24  8 

35  52 

75294 

9 

24706 

83686 

13 



14 

16314 

08392 

4  !  91608 

31 
30 

7  24  0 

4  36  0 

9. 75313 

9  10.24687 

9. 83713 

10. 16287 

10. 08401 

4  9.91599 

31 
32 

23  52 

36  8 

75331 

9 

24669 

83740 

14 

16260 

08409 

4 

91591 

29 

23  44 

36  16 

75350 

10 

24650 

83768 

14 

16232 

08418 

5 

91582 

28 

33 

23  36 

36  24 

75368 

10 

24632 

83/795 

15 

16205 

08427 

5 

91573 

27 

34 

23  28 

36  32 

75386 

10 

24614 

83822 

15 

16178 

08435 

5 

91565 

26 

25 

35 

7  23  20 

4  36  40 

9. 75405 

11 

10. 24595 

9. 83849 

16 

10. 16151 

10. 08444 

5 

9. 91556 

36 

23  12 

36  48 

75423 

11 

24577 

83876 

16 

16124 

08453 

5 

91547 

24 

37 

23  4 

36  56 

75441 

11 

24559 

83903 

17 

16097 

08462 

5 

91538 

23 

38 

22  56 

37  4 

75459 

12  1   24541 

83930 

17 

16070 

08470 

5 

91530 

22 

39 
40 

22  48 
7  22  40 

37  12 
4  37  20 

75478 

12 

24522 
10.  24504 

83957 

18 

16043 

08479 

6 

91521 

21 
20 

9. 75496 

12 

9. 83984 

18 

10. 16016 

10. 08488 

6 

9.91512 

41 

22  32 

37  28 

75514 

13  i   24486 

84011 

18 

15989 

08496 

6 

91504 

19 

42 

22  24 

37  36 

75533 

13    24467 

84038 

19 

15962 

08505 

6 

91495 

18 

43 

22  16 

37  44 

75551 

13    24449 

84065 

19 

15935 

08514 

6 

91486 

17 

44 
45 

22  8 
7  22  0 

37  52 

4  38  0 

75569 
9.  75587 

13 
14 

24431 

84092 

20 

15908 

08523 

6  :  91477 

16 

10.24413 

9.84119 

20 

10. 15881 

10.  08531 

7  9.91469 

15 

46 

21  52 

38  8 

75605 

14    24395 

84146 

21 

15854 

08540 

7   91460 

14 

47 

21  44 

38  16 

75624 

14  2.^76 

15  24358 

84173 

21 

15827 

0a549 

7   91451 

13 

48 

21  36 

38  24 

75642 

84200 

22 

15800 

08558 

7  ;  91442 

12 

49 

21  28 

38  32 

75660 

15 
15 

24340 

84227 

22 

15773 

08567 

7 

91433 
9. 91425 

11 
10 

50 

7  21  20 

4  38  40 

9. 75678 

10. 24322 

9. 84254 

23 

10. 15746 

10.  08575 

7 

51 

21  12 

38  48 

75696 

16    24304 

84280 

23 

15720 

08584 

7  \     91416 

9 

52 

21  4 

38  56 

75714 

16    24286 

84307 

23 

15693 

08593 

8   91407 

8 

53 

20  56 

39  4 

75733 

16    24267 

84334 

24 

15666 

08602 

8   91398 

7 

54 

20  48 

39  12 

75751 

17    24249 
17  10.24231 

84361 

24 
25 

15639 
10715612 

08611 

8 

91389 
9. 91381 

6 
5 

55 

7  20  40 

4  39  20 

9.  75769 

9. 84388 

10. 08619 

8 

56 

20  32 

39  28 

75787 

17  i   24213 

84415 

25 

15585 

08628 

8   91.372 

4 

57 

20  24 

39  36 

75805 

17 

24195 

84442 

26 

15558 

08637 

8   91363 

3 

58 

20  16 

39  44 

75823 

18 

24177 

84469 

26 

15531 

08646 

8  i   91354 

2 

59 

20  8 

39  52 

75841 

18 

24159 

84496 

27 

15504 

08655 

9 

91.345 

1 

60 
M. 

20  0 

40  0 

75859 

18 

24141 

84523 

27 

15477 

08664 

9 

91336 

0 
M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

124= 

A 

A 

B 

B 

C 

C 

56 

Seconds  of  time 

1'    » 

g.    4. 

S- 

e* 

7« 

(A 

Prop,  parts  of  cols.  <B 

Ic 

2  5 

3  7 
1    2 

7    9 
10    14 
3  ,   4 

11 

17 

6 

14 
20 

7 

16 
24 

8 

TABLE  4A. 

[Page  643 

] 

Log. 

Sines,  Tangents,  and  Secante. 

86° 

A 

A 

B 

B 

C 

C    144° 

M. 
0 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff.  Cotangent. 

Secant. 

Diff.   Cosine. 

M. 

7  20  0 

4  40  0 

9. 75859 

0 

10. 24141 

9. 84523 

0  10. 15477 

10.  08664 

0  9.91886 

60 

1 

19  52 

40  8 

75877 

0 

24128 

84550 

0    15450 

08672 

0 

91328 

59 

^ 

19  44 

40  16 

75895 

1 

24105 

84576 

1  1   15424 

08681 

0 

91319 

58 

8 

19  36 

40  24 

75913 

1 

24087 

84608 

1 

15397 

08690 

0 

91810 

57 

4 
5 

19  28 

40  32 

75981 
9. 75949 

1 

24069 

84630 

2 
2 

15870 
10. 15348 

08699 
10. 08708 

91801 

56 
55 

7  19  20 

4  40  40 

1 

10.  24051 

9. 84657 

9. 91292 

6 

19  12 

40  48 

75967 

2 

24088 

84684 

8 

15316 

08717 

91288 

54 

7 

19  4 

40  56 

75985 

2 

24015 

84711 

8 

15289 

08726 

91274 

53 

8 

18  56 

41  4 

76008 

2 

28997 

84788 

4 

15262 

08784 

91266 

52 

9 

18  48 

41  12 

76021 

3 

28979 

84764 

4 

15236 

08743 

91257 

51 
50 

10 

7  18  40 

4  41  20 

9. 76089 

3 

10. 28961 

9. 84791 

4 

10. 15209 

10. 08752 

2 

9. 91248 

n 

18  32 

41  28 

76057 

3 

28943 

84818 

5 

15182 

08761 

2 

91239 

49 

12 

18  24 

41  86 

76075 

4 

28925 

84845 

5 

15155 

08770 

2 

91280 

48 

18 

18  16 

41  44 

76093 

4 

28907 

84872 

6 

15128 

08779 

2 

91221 

47 

14 

18  8 

41  52 

76111 

4 

28889 

84899 

6 

15101 

08788 

2 
2 

91212 

46 
45 

15 

7  18  0 

4  42  0 

9.  76129 

4 

10. 28871 

9. 84925 

7 

10. 15075 

10. 08797 

9. 91203 

16 

17  52 

42  8 

76146 

5 

23854 

84952 

7 

15048 

08806 

2 

91194 

44 

17 

17  44 

42  16 

76164 

5 

28886 

84979 

8 

15021 

08815 

3 

91185 

48 

18 

17  36 

42  24 

76182 

5 

28818 

85006 

8 

14994 

08824 

3 

91176 

42 

19 
20 

17  28 

42  32 

76200 
9. 76218 

6 
6 

23800 
10.  28782 

85033 
9. 85059 

8 
9 

14967 
10.  14941 

08838 
10. 08842 

3 
3 

91167 
9.91L58 

41 
40 

7  17  20 

4  42  40 

21 

17  12 

42  48 

76236 

6 

28764 

85086 

9 

14914 

08851 

3 

91149 

89 

22 

17  4 

42  56 

76253 

6 

23747 

85113 

10 

14887 

08859 

8 

91141 

88 

28 

16  56 

48  4 

76271 

7 

23729 

85140 

10 

14860 

08868 

3 

91182 

37 

24 
25 

16  48 
7  16  40 

48  12 

76289 

7 

23711 

85166 

11 

14884 

08877 

4 

91128 

36 

4  48  20 

9. 76307 

7 

10. 28698 

9.  85193 

11 

10. 14807 

10.  08886 

4 

9.91114 

85 

26 

16  82 

48  28 

76324 

8 

28676 

85220 

12 

14780 

08895 

4 

91105 

34 

27 

16  24 

43  86 

76342 

8 

28658 

85247 

12 

14753 

08904 

4 

91096 

33 

28 

16  16 

48  44 

76360 

8 

2.3640 

85273 

12 

14727 

08918 

4 

91087 

32 

29 
80 

16  8 

48  52 

76378 

9 

23622 

85300 
9. 85327 

13 
13 

14700 

08922 
10. 08981 

4 
5 

91078 

31 
30 

7  16  0 

4  44  0 

9.  76895 

9 

10.  28605 

10. 14678 

9. 91069 

31 

15  52 

44  8 

76418 

9 

28587 

85354 

14 

14646 

08940 

5 

91060 

29 

82 

15  44 

44  16 

76431 

9 

28569 

85380 

14 

14620 

08949 

5 

91051 

28 

88 

15  86 

44  24 

76448 

10 

23552 

85407 

15 

14593 

08958 

5 

91042 

27 

84 
85 

15  28 
7  15  20 

44  32 

76466 
9. 76484 

10 
10 

2:3534 

85434 

15 
16 

14566 

08967 

5 

91033 

-26 

4  44  40 

10.  23516 

9.85460 

10.  14540 

10. 08977 

5 

9. 91023 

25 

86 

15  12 

44  48 

76501 

11 

23499 

85487 

16 

14513 

08986 

5 

91014 

24 

37 

15  4 

44  56 

76519 

11 

2;W81 

85514 

16 

14486 

08995 

6 

91005 

28 

38 

14  56 

45  4 

76587 

11 

2;W68 

85540 

17 

14460 

09004 

6 

90996 

22 

89 
40 

14  48 
.7" 14  40" 

45  12 

76554 

12 
12 

28446 

85567 
9.85594 

17 
18 

14438 

09018 

6 

90987 

21 
20 

4  45  20 

9.  76572 

10.  28428 

10. 14406 

10.  09022 

6 

9. 90978 

41 

14  32 

45  28 

76590 

12 

28410 

85620 

18 

14880 

09031 

6 

90969 

19 

42 

14  24 

45  86 

76607 

12 

28893 

85647 

19 

14853 

09040 

6 

90960 

18 

43 

14  16 

45  44 

76625 

18 

23375 

85674 

19 

14826 

09049 

6 

90951 

17 

44 
45 

14  8 
7  14  0 

45  52 
4  46  0 

76642 
9. 76660 

13 
13 

28858 
10.28840 

85700 
9. 85727 

20 
20" 

14800 
10.  14273 

09058 

7 

90942 

16 

15 

10. 09067 

7 

9. 90938 

46 

13  52 

46  8 

76677 

14 

28328 

85754 

20 

14246 

09076 

7 

90924 

14 

47 

13  44 

46  16 

76695 

14 

28305 

85780 

21 

14220 

09085 

7 

90915 

13 

48 

13  36 

46  24 

76712 

14 

23288 

85807 

21 

14193 

09094 

7 

90906 

12 

49 

13  28 

46  32 

76730 

14 
15 

23270 
10.28253 

85884 
9:85860 

22 
22 

14166 
10. 14140 

09104 
10. 09113 

7 
8 

90896 

11 
10 

50 

7  13  20 

4  46  40 

1  9.  76747 

9. 90887 

51 

13  12 

46  48 

76765 

15 

23285 

85887 

28 

14113 

09122 

8 

90878 

9 

52 

13  4 

46  56 

76782 

15 

2.3218 

85918 

23 

14087 

09181 

8  :  90869 

8 

53 

12  56 

47  4 

76800 

16 

23200 

85940 

24 

14060 

09140 

8    90860 

7 

54 
55 

12  48 
7  12  40 

47  12 
4  47  20 

76817 

16 
16 

23188 
10.23165 

85967 
9.85998 

24 

14088 

09149 
10.09158 

8 
8 

90851 

6 

1  9. 76835 

24  10.14007 

9. 90842 

5 

56 

12  32 

47  28 

1   76852 

17 

23148 

86020 

25    13980 

09168 

8 

90882 

4 

57 

12  24 

47  36 

76870 

17 

23180 

86046 

25    13954 

09177 

9 

90828 

3 

58 

12  16 

47  44 

76887 

17 

23113 

86078 

26    13927 

09186 

9 

90814 

2 

59 

12  8 

47  52 

76904 

17 

28096 

86100 

26    13900 

09195 

9 

90805 

1 

60 

12  0 

48  0 

76922 

18 

23078 

86126 

27    18874 

09204 

9 

90796 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff.  Tangent. 

Cosecant. 

Diff. 

Sine. 

126° 

A 

A 

B 

B 

C 

'       "M 

Seconds  of  time 1' 

L'»    3'    4' 

o» 

6^ 

7' 

Prop,  parts  of  cols.'jB 
[0 

2 
3 

1 

4 

7 
2 

7 
10 

3 

9 
13 
5 

11 
17 
6 

13 
20 

7 

16 
23 

8 

Page  644] 

TABLE  U. 

Log.  Sines,  Tangents,  and  Secants. 

86° 

A 

A 

B 

B 

C 

C   148°  1 

M. 
0 

Hour  A.  M.  Hour  p.  m. 

Sine. 

Diff. 

Closecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

7  12  0  4  48  0 

9. 76922 

0 

10. 23078 

9. 86126 

0 

10. 13874 

10.  09204 

0 

9. 90796 

60 

1 

11  52    48  8 

76939 

0 

23061 

86153 

0 

13847 

09213 

0  '  90787 

59 

2 

11  44    48  16 

76957 

1 

23043 

86179 

1 

13821 

09223 

0  1  90777 

58 

3 

11  36  1   48  24 

76974 

1 

23026 

86206 

1 

13794 

09232 

0 

90768 

57 

4 

5 

11  28 
7  11  20 

48  3^ 

76991 

1 

23009 

86232 

2 

13768 

09241 

1 

90759 

56 
55 

4  48  40 

9.77009 

1 

10. 22991 

9.  86259 

2 

10. 13741 

10. 09250 

1 

9.  90750 

6 

11  12    48  48 

77026 

2 

22974 

86285 

3 

13715 

09259 

1 

90741 

54 

1 

11  4  1   48  56 

77043 

2 

22957 

86312 

3 

13688 

09269 

1 

90731 

53 

8 

10  56  1   49  4 

77061 

2 

22939 

86338 

4 

13662 

09278 

1 

90722 

52 

9 
10 

10  48 

49  12 

77078 
9.  77095 

3 
3 

22922 
10.  22905 

86365 

4 

13635 

09287 

1 

90713 

51 
50 

7  10  40 

4  49  20 

9. 86392 

4 

10. 13608 

10. 09296 

2 

9.90704 

11 

10  32 

49  28 

77112 

3 

22888 

86418 

5 

13582 

09306 

2 

90694 

49 

12 

10  24 

49  36 

77130 

3 

22870 

86445 

5 

13555 

09315 

2 

90685 

49 

13 

10  16 

49  44 

77147 

4 

22853 

86471 

6 

13529 

09324 

2 

90676 

47 

14 

10  8 

49  52 

77164 

4 

22836 

86498 

6 

7 

13502 
10. 13476 

09333 

2 
2 

90667 
9. 90657 

46 
45 

15 

7  10  0 

4  50  0 

9.  77181 

4 

10.  22819 

9.  86524 

10. 09343 

16 

9  52 

50  8 

77199 

5 

22801 

86551 

/ 

13449 

09352 

2 

90648 

44 

17 

9  44 

50  16 

77216 

5 

22784 

86577 

7 

13423 

09361 

3 

90639 

43 

18 

9  36 

50  24 

77233 

5 

22767 

86603 

8 

13397 

09370 

3 

90630 

42 

19 
20 

9  28 

50  32 
4  50  40 

77250 

5 

22750 

86630 
9. 86656 

8 

13370 

09380 

3 

90620 

41 

7  9  20 

9. 77268 

6 

10. 22732 

9 

10. 13344 

10. 09389 

3 

9. 90611 

40 

21 

9  12 

50  48 

77285 

6 

22715 

86683 

9 

13317 

09398 

3 

90602 

39 

22 

9  4 

50  56 

77302 

6 

22698 

86709 

10 

13291 

09408 

3 

90592 

38 

23 

8  56 

51  4 

77319 

7 

22681 

86736 

10 

13264 

09417 

4 

90583 

37 

24 
25 

8  48 

51  12 
4  51  20 

77336 

7 

22664 

86762 

11 

13238 

09426 

4 

90574 

36 
35 

7  8  40 

9.  77353 

/ 

10.  22647 

9. 86789 

11 

10.13211 

10. 09435 

4 

9.90565 

26 

8  32 

51  28 

77370 

7 

22630 

86815 

11 

13185 

09445 

4 

90555 

34 

27 

8  24 

51  36 

77387 

8 

22613 

86842 

12 

13158 

09454 

4 

90546 

33 

28 

8  16 

51  44 

77405 

8 

22595 

86868 

12 

13132 

09463 

4 

90537 

32 

29 
3b 

8  8 

51  52 

77422 

8 

22578 

86894 

13 
13 

13106 

09473 

5 

90527 
4.  90518 

31 
30 

7  8  0 

4  52  0 

9.  77439 

9 

10. 22561 

9. 86921 

10. 13079 

10. 09482 

5 

31 

7  52 

52  8 

77456 

9 

22544 

86947 

14 

13053 

09491 

5 

90509 

29 

32 

7  44 

52  16 

77473 

9 

22527 

86974 

14 

13026 

09501 

5 

90499 

28 

33 

7  36 

52  24 

77490 

9 

22510 

87000 

15 

13000 

09510 

5 

90490 

27 

34 
35^ 

7  28  1   52  32 

77507 

10 

22493 

87027 

15 

12973 

09520 

5 

90480 

26 

7  7  20 

4  52  40 

9.  77524 

10 

10.  22476 

9. 87053 

15 

10. 12947 

10. 09529 

5 

9. 90471 

25 

36 

7  12 

52  48 

77541 

10 

22459 

87079 

16 

12921 

09538 

6 

90462 

24 

37 

7  4 

52  56 

77558 

11 

22442 

87106 

16 

12894 

09548 

6 

90452 

23 

38 

6  56 

53  4 

77575 

11 

22425 

87132 

17 

12868 

09557 

6 

90443 

22 

39 
40 

6  48 

53  12 

77592 

11 

22408 

87158 

17 

12842 

09566 

6 

90434 

21 
20 

7  6  40 

4  53  20 

9. 77609 

11 

10.  22391 

9. 87185 

18 

10. 12815 

10.  09576 

6 

9. 90424 

41 

6  32 

53  28 

77626 

12 

22374 

87211 

18 

12789 

09585 

6 

90415 

19 

42 

6  24 

53  36 

77643 

12 

22357 

87238 

18 

12762 

09595 

7 

90405 

18 

43 

6  16 

53  44 

77660 

12 

22340 

87264 

19 

12736 

09604 

7 

90396 

17 

44 
45 

6  8 

53  52 

77677 

13  i   22323 

87290 

19 
20 

12710 
10. 12683 

09614 

7 

90386 

16 
15 

7  6  0 

4  54  0 

9. 77694 

13  10.22306 

9.  87317 

10. 09623 

9. 90377 

46 

5  52 

,54  8 

77711 

13    22289 

87^3 

20 

12657 

09632 

7 

90368 

14 

47 

5  44 

54  16 

77728 

13    22272 

87369 

21 

12631 

09642 

7 

90358 

13 

48 

5  36 

54  24 

77744 

14    22256 

87396 

21 

12604 

09651 

7 

90349 

12 

49 
50 

5  28 

54  32 

77761 

14 
14 

22239 

87422 

22 
22 

12578 
10. 12552 

09661 

8 
8 

90339 

11 
10^ 

7  5  20 

4  54  40 

9. 77778 

10.  22222 

9.  87448 

10. 09670 

9. 90330 

51 

5  12 

54  48 

77795 

15 

22205 

87475 

22 

12525 

09680 

8 

90320 

9 

52 

5  4 

54  56 

77812 

15 

22188 

87501 

23 

12499 

09689 

8 

90311 

8 

53 

4  56 

55  4 

77829 

15 

22171 

87527 

23 

12473 

09699 

8 

90301 

7 

54 

4  48 

55  12 
4  55  20 

77846 

15 
16 

22154 

87554 

24 
24 

12446 
10. 12420 

09708 

8 
9 

90292 
9. 90282 

6 
5 

55 

7  4  40 

9. 77862 

10.  22138 

9. 87580 

10.09718 

56 

4  32 

55  28 

'  77879 

16 

22121 

87606 

25 

12394 

09727 

9 

90273 

4 

57 

4  24 

55  36 

77896 

16 

22104 

87633 

25 

12367 

09737 

9 

90263 

3 

58 

4  16 

55  44 

77913 

16 

22087 

87659 

26 

12341 

09746 

9 

90254 

2 

59 

4  8 

55  52 

77930 

17 

22070 

87685 

26 

12315 

09756 

9 

90244 

1 

60 

4  0 

56  0 

77946 

17 

22054 

87711 

26 

12289 

09765 

9 

90235 

0 

M.  Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

126° 

A 

A 

B 

B 

C 

C 

58° 

Seconds  of  time 1" 

2« 

8' 

4" 

o" 

6* 

'1 

fA    2 

Prop,  parts  of  cols.  -{B    3 

Ic   1 

4 

7 
2 

6 
10 

4 

9 
13 

5 

11    13    15 

17    20  '■    23 

6     7     8 

TABLE  U. 

iPage  645 

Log. 

Sines,  Tangents,  and  Secants. 

87° 

A 

A         B 

B 

C 

C    142° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

0 

7  4  0 

4  56  0 

9. 77946 

0 

10. 22054 

9. 87711 

0 

10. 12289 

10.  09765 

0 

9. 90235 

60 

1 

3  52 

56  8 

77963 

0 

22037 

87738 

0 

12262 

09775 

0 

90225 

59 

2 

3  44 

56  16 

77980 

1 

22020 

87764 

1 

12286 

09784 

0 

90216 

58 

8 

8  36 

56  24 

77997 

1 

22003 

87790 

1 

12210 

09794 

0 

90206 

57 

4 

3  28 

56  82 

78013 

1 

21987 

87817 

2 

12188 

09803 

2^ 

90197 

56 

5 

7  3  20 

4  56  40 

9.  78030 

1 

10.  21970 

9.  87843 

2 

10. 12157 

10.09813 

9. 90187 

oo 

6 

3  12 

56  48 

78047 

2 

21953 

87869 

3 

12131 

09822 

90178 

54 

7 

3  4 

56  56 

78063 

2 

21937 

87895 

3 

12105 

09832 

90168 

53 

8 

2  56 

57  4 

78080 

2 

21920 

87922 

3 

12078 

09841 

90159 

52 

9 

2  48 

57  12 

78097 

2 

21903 

87948 

4 

12052 
10.  12026 

09851 

90149 
9. 90139 

51 
50 

10 

7  2  40 

4  57  20 

9. 78113 

3 

10. 21887 

9.  87974 

4 

iO.  09861 

2 

n 

2  32 

57  28 

78130 

3 

21870 

88000 

o 

12000 

09870 

2 

90130 

49 

12 

2  24 

57  36 

78147 

3 

218.58 

88027 

5 

11978 

09880 

2 

90120 

48 

18 

2  16 

57  44 

78163 

4 

21837 

88053 

6 

11947 

09889 

2 

90111 

47 

14 

2  8 

57  52 

78180 

4 

21820 

88079 

6 

11921 

09899 

2 

90101 

46 

15 

7  2  0 

4  58  0 

9. 78197 

4 

10. 21803 

9. 88105 

7 

10.  11895 

10. 09909 

2 

9. 90091 

45 

16 

1  52 

58  8 

78213 

4 

21787 

88131 

7 

11869 

09918 

3 

90082 

44 

17 

1  44 

58  16 

78230 

5 

21770 

88158 

1 

11842 

09928 

3 

90072 

43 

18 

1  36 

58  24 

78246 

5 

21754 

88184 

8 

11816 

09937 

3 

90063 

42 

19 

1  28 

58  32 

78263 

5 

21737 

88210 

8 

11790 

09947 

3 

90053 

41 
40 

20 

7  1  20 

4  58  40 

9.  78280 

5 

10.21720 

9. 88236 

9 

10. 11764 

10. 09957 

3 

9. 90043 

21 

1  12 

58  48 

78296 

6 

21704 

88262 

9 

11738 

09966 

3 

90084 

39 

22 

1  4 

58  56 

78313 

6 

21687 

88289 

10 

11711 

09976 

4 

90024 

38 

23 

0  56 

59  4 

78329 

6 

21671 

88315 

10 

11685 

09986 

4 

90014 

37 

24 

0  48 

59  12 

78346 

t 

21654 

88341 

10 

11659 

09995 
10.  10005 

4 
4 

90005 

36 
35 

25 

7  0  40 

4  59  20 

9. 78362 

7 

10.  21638 

9. 88367 

11 

10. 11638 

9.  89995 

26 

0  32 

59  28 

78379 

7 

21621 

88393 

11 

11607 

10015 

4 

89985 

34 

27 

0  24 

59  36 

78395 

7 

21605 

88420 

12 

11580 

10024 

4 

89976 

33 

28 

0  16 

59  44 

78412 

8 

21588 

88446 

12 

11554 

10034 

5 

89966 

32 

29 

0  8 

59  52 

78428 

8 

21572 

88472 

13 

11528 

10044 

5 

89956 

31 
30 

80 

7  0  0 

5  0  0 

9.78445 

8 

10.  21555 

9. 88498 

13 

10. 11502 

10. 10053 

5 

9. 89947 

81 

6  59  52 

0  8 

78461 

9 

21539 

88524 

14 

11476 

10063 

5 

89937 

29 

82 

59  44 

0  16 

78478 

9 

21522 

88550 

14 

11450 

10073 

5 

89927 

28 

88 

59  86 

0  24 

78494 

9 

21506 

88577 

14 

11428 

10082 

5 

89918 

27 

34 

59  28 

0  32 

78510 

9 
10 

21490 

88603 

15 
15 

11397 
iO.  11371 

10092 
10. 10102 

5 
6 

89908 
9. 89898 

26 
25 

85 

6  59  20 

5  0  40 

9.  78527 

10.  21473 

9.  88629 

36 

59  12 

0  48 

78543 

10 

21457 

88655 

16 

11845 

10112 

6 

89888 

24 

87 

59  4 

0  56 

78560 

10 

21440 

88681 

16 

11819 

10121 

6 

89879 

23 

88 

58  56 

1  4 

78576 

10 

21424 

88707 

17 

11293 

10131 

6 

89869 

22 

39 

58  48 

1  12 

78592 

11 

21408 

88733 

17 

11267 

10141 

6 

89859 

21 
20 

40 

6  58  40 

5  1  20 

9. 78609 

11 

10. 21391 

9. 88759 

17 

10. 11241 

10. 10151 

6 

9. 89849 

41 

58  32 

1  28 

78625 

11 

21375 

88786 

18 

11214 

10160 

7 

89840 

19 

42 

58  24 

1  36 

78642 

12 

21358 

88812 

18 

11188 

10170 

7 

89880 

18 

48 

58  16 

1  44 

78658 

12 

21342 

88838 

19 

11162 

10180 

7 

89820 

17 

44 
45 

58  8 
6  58  0 

1  52 

78674 
9.  78691 

12 

21326 

88864 
9. 88890 

19 
20 

11136 
10. 11110' 

10190 
10. 10199 

~7~ 

89810 

16 
15 

5  2  0 

12 

10.  21809 

9. 89801 

46 

57  52 

2  8 

78707 

13 

21293 

88916 

20 

11084 

10209 

7 

89791 

14 

47 

57  44 

2  16 

78723 

13 

21277 

88942 

20 

11058 

10219 

8 

89781 

13 

48 

57  36 

2  24 

78739 

13 

21261 

88968 

21 

11032 

10229 

8 

89771 

12 

49 
50 

57  28 
6  57  20 

2  32 
5  2  40 

78756 
9.  78772 

13 
14 

21244 

88994 
9. 89020 

21 
22 

11006 
10. 10980 

10239 
10. 10248 

8 
8 

89761 

11 
10 

10.  21228 

9. 89752 

51 

57  12 

2  48 

78788 

14 

21212 

89046 

22 

10954 

10258 

8 

89742 

9 

52 

57  4 

2  56 

78805 

14 

21195 

89073 

23 

10927 

10268 

8 

89732 

8 

53 

56  56 

8  4 

78821 

15 

21179 

89099 

23 

10901 

10278 

9 

89722 

7 

54 
55 

56  48 

3  12 
5  3  20 

78837 

15 

21163 
10.  21147 

89125 

24 
24 

10875 
10. 10849" 

10288 
10.10298 

9 
9 

89712 
9. 89702 

6 
5 

6  56  40 

9. 78853 

15 

9. 89151 

56 

56  32 

3  28 

78869 

15 

21181 

89177 

24 

10823 

10307 

9 

89693 

4 

57 

56  24 

8  86 

78886 

16 

21114 

89203 

25 

10797 

10317 

9 

89683 

8 

58 

56  16 

3  44 

78902 

16 

21098 

89229 

25 

10771 

10327 

9 

89678 

2 

59 

56  8 

3  52 

78918 

16 

21082 

89255 

26 

10745 

10337 

10 

89668 

1 

60 

56  0 

4  0 

78934 

16 

21066 

89281 

26 

10719 

10347 

10 

89658 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

127° 

A 

A        B 

B 

C 

C     52°  1 

Seconds  of  time 

1» 

23 

33    48 

5' 

«' 

7' 

Prop,  parts  of  col8.<B 

•> 
3 

1 

•1 

7 

6    8 

10    13 

4    5 

10 

16 

6 

12 
20 

7 

14 
23 

8 

Page  646] 

TABLE  44. 

Log.  Sines,  Tangents,  and  Secants. 

88° 

A 

A 

B 

B        C 

C    141° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Difl. 

Cosine. 

M. 

0 

6  56  0 

5  4  0 

9.  78934 

0 

10.  21066 

9. 89281 

0 

10. 10719 

10. 10347 

0 

9. 89653 

60 

1 

55  52 

4  8 

78950 

0 

21050 

89307 

0 

10693 

10357 

0 

89643 

59 

o 

55  44    4  16  1 

78967 

1 

21033 

89333 

1 

10667 

10367 

0 

89633 

58 

3 

55  36 

4  24 

78983 

1 

21017 

89359 

1 

10641 

10376 

1 

89624 

57 

4 

55  28 

4  32 1 

78999 

1 
1 

21001 
10.  20985 

89385 

2 

10615 
10. 10589 

10386 
10. 10396 

1 
1 

89614 
9.89604 

56 

55' 

5 

6  55  20 

5  4  40 

9.  79015 

9. 89411 

2 

6 

55  12 

4  48 

79031 

2 

20969 

89437 

3 

10563 

10406 

1 

89594 

54 

7 

55  4 

4  56 

79047 

2 

20953 

89463 

3 

10537 

10416 

1 

89584 

53 

8 

54  56 

5  4 

79063 

2 

20937 

89489 

3 

10511 

10426 

1 

89574 

52 

9 

54  48 

5  12 

79079 

2 

20921 

89515 

■  4 

10485 

10436 

2 

89564 

51 
50 

10 

6  54  40 

5  5  20 

9.79095 

3 

10. 20905 

9.  89541 

4 

10. 10459 

10. 10446 

2 

9. 89554 

11 

54  32 

5  28 

79111 

3  !   20889 

89567 

5 

10433 

10456 

2 

89544 

49 

12 

54  24 

5  36 

79128 

3    20872 

89593 

5 

10407 

10466 

2 

89534 

48 

13 

54  16 

5  44 

79144 

3  ,   20856 

89619 

6 

10381 

10476 

2 

89524 

47 

14 
15 

54  8 

5  52 

79160 

4 
4" 

20840 

89645 

6 
6 

10355 

10486 
10. 10496 

2 
3 

89514 

46 
>45 

6  54  0 

5  6  0 

9.  79176 

10. 20824 

9. 89671 

10. 10329 

9. 89504 

16 

53  52 

6  8 

79192 

4 

20808 

89697 

7 

10303 

10505 

3 

89495 

44 

17 

53  44 

6  16 

79208 

0 

20792 

89723 

/ 

10277 

10515 

3 

89485 

43 

18 

53  36 

6  24 

79224 

0 

20776 

89749 

8 

10251 

10525 

3 

89475 

42 

19 

53  28 

6  32 

79240 

5 

20760 

89775 

8 

10225 

10535 

3 
3 

89465 

41 

20 

6  53  20 

5  6  40 

9. 79256 

5 

10. 20744 

9. 89801 

9 

10.  10199 

10.  10545 

9. 89455 

40 

21 

53  12 

6  48 

79272 

6 

20728 

89827 

9 

10173 

10555 

4 

89445 

39 

22 

53  4 

6  56 

79288 

6 

20712 

89853 

10 

10147 

10565 

4 

89435 

38 

23 

52  56 

7  4 

79304 

6  '   20696  1 

89879 

10 

10121 

10575 

4 

89425 

37 

24 

52  48 

7  12 

79319 

6 

20681 

89905 

10 

10095 

10585 

4 

89415 

36 
35 

25 

6  52  40 

5  7  20 

9. 79335 

7 

10.  20665 

9. 89931 

11 

10. 10069 

10. 10595 

4 

9. 89405 

26 

52  32 

7  28 

79351 

7 

20649 

89957 

11 

10043 

10605 

4 

89395 

34 

27 

52  24 

7  36 

79367 

7    20633 

89983 

12 

10017 

10615 

5 

89385 

33 

28 

52  16 

7  44 

79383 

/ 

20617 

90009 

12 

09991 

10625 

5 

89375 

32 

29 
30 

52  8 

7  52 

79399 

8 

20601 
10. 20585 

90035 

13 

09965 

10636 

5 

89364 

31 
30 

6  52  0 

5  8  0 

9.  79415 

8 

9. 90061 

13 

10. 09939 

10. 10646 

5 

9. 89354 

31 

51  52 

8  8 

79431 

8 

20569 

90086 

13 

09914 

10656 

5 

89344 

29 

32 

51  44 

8  16 

79447 

8 

20553 

90112 

14 

09888 

10666 

5 

89334 

28 

33 

51  36 

8  24 

79463 

9 

20537 

90138 

14 

09862 

10676 

6 

89324 

27 

34 

51  28 

8  32 

79478 

9  ;   20522 

90164 

15 

09836 

10686 

6 

89314 

26 

35 

6  51  20 

5  8  40 

9.  79494 

9  10.20506 

9. 90190 

15 

10.  09810 

10. 10696 

6 

9. 89304 

25 

36 

61  12 

8  48 

79510 

10    20490 

90216 

16 

09784 

10706 

6 

89294 

24 

37 

51  4 

8  56 

79526 

10    20474 

90242 

16 

09758 

10716 

6 

89284 

23 

38 

50  56 

•  9  4 

79542 

10  '       20458 

90268 

16 

09732 

10726 

6 

89274 

22 

39 
40 

50  48 
6  50  40 

9  12 
5  9  20 

79558 

10 

20442 

90294 

17 

09706 

10736 

7 

89264 
9. 89254 

21 
20 

9. 79573 

11 

10.  20427 

9. 90320 

17 

10. 09680 

10. 10746 

7 

41 

50  32 

9  28 

79589 

11 

20411 

90346 

18 

09654 

10756 

7 

89244 

19 

42 

50  24 

9  36 

79605 

11    20395 

90371 

18 

09629 

10767 

7 

89233 

18 

43 

50  16 

9  44 

79621 

11  !   20379 

90397 

19 

09603 

10777 

7 

89223 

17 

44 

50  8 

9  52 

79636 

12  \      20364 

90423 

19 

09577 

10787 

7 

89213 

16 
15 

45 

6  50  0 

5  10  0 

9.  79652 

12  10.20348 

9. 90449 

19 

10. 09551 

10. 10797 

8 

9. 89203 

46 

49  52 

10  8 

79668 

12 

20332 

90475 

20 

09525 

10807 

8 

89193 

14 

47 

49  44 

10  16 

79684 

12 

20316 

90501 

20 

09499 

10817 

8 

89183 

13 

48 

49  36 

10  24 

79699 

13 

20301 

90527 

21 

09473 

10827 

8 

89173 

12 

49 

49  28 

10  32 

79715 

.13 

20285 

90553 

21 

09447 

10838 

8 

89162 

11 
10 

50 

6  49  20 

5  10  40 

9.  79731 

13 

10. 20269 

9. 90578 

22 

10.  09422 

10. 10848 

8 

9.  89152 

51 

49  12 

10  48 

79746 

14 

20254 

90604 

22 

09396 

10858 

9 

89142 

9 

52 

49  4 

10  56 

79762 

14 

20238 

90630 

22 

09370 

10868 

9 

89132 

8 

53 

48  56 

11  4 

79778 

14 

20222 

90656 

23 

09344 

10878 

9 

89122 

7 

54 

48  48 

11  12 

79793 

14 

20207 

90682 

23 

09318 

10888 

9 

89112 

6 
5 

55 

6  48  40 

5  11  20 

9. 79809 

15 

10.  20191 

9. 90708 

24 

10.  09292 

10. 10899 

9 

9. 89101 

56 

48  32 

11  28 

79825 

15 

20175 

90734 

24 

09266 

10909 

9 

89091 

4 

57 

48  24 

11  36 

79840 

15 

20160 

90759 

25 

09241 

10919 

10 

89081 

3 

58 

48  16 

11  44 

79856 

15 

20144 

90785 

25 

09215 

10929 

10 

89071 

2 

59 

48  8 

11  52 

79872 

16 

20128 

90811 

26 

09189 

10940 

10 

89060 

1 

60 

48  0 

12  0 

79887 

16 

20113 

90837 

26 

09163 

10950 

10 

89050 

0 
M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant, 

Difl. 

Sine. 

128' 

A 

A 

B 

B        C 

C 

51° 

Seconds  of  time 

1« 

2' 

8< 

4» 

&> 

6» 

7' 

Prop,  parts  of  cols.-jB 

Ic 

2 
3 

1 

4 
6 
3 

6 
10 
4 

8 
13 
5 

10 

16 

6 

12 

19 

8 

14 

23 

9 

TABLE  44. 

[Page  647 

Log. 

Sines,  Tangents,  and  Secants. 

89° 

M. 

A 

A 

B           B 

C 

C    140° 

Hour  A.  M. 

Hour  P.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent.  ,  Difl. ,  Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  48  0 

5  12  0 

9. 79887 

0 

10.  20113 

9. 90837 

0  10.09163 

10. 10950 

0 

9.  89050 

60 

1 

47  o2 

12  8 

79903 

0 

20097 

90863 

0    09137 

10960 

0 

89040 

59 

2 

47  44 

12  16 

79918 

1 

20082 

90889 

1    09111 

10970 

0 

89030 

58 

3 

47  36 

12  24 

79934 

1 

20066 

90914 

1    09086 

10980 

1 

89020 

57 

4 
5 

47  28 
6  47  20 

12  32 
5  12  40 

79950 
9.799(55 

1 
1 

20050 
10.20035" 

90940   2    09060 
9.90966   2  10.09034 

10991 
10. 11001 

1 

89009 

56 
55 

1 

9. 88999 

6 

47  12 

12  48 

79981 

2 

20019 

90992   3  '   09008 

11011 

1 

88989 

54 

7 

47  4 

12  56 

79996 

2 

20004 

91018   3  1   08982 

11022 

1 

88978 

53 

8 

46  56" 

13  4 

80012 

2 

19988 

91043   3    08957 

11032 

1 

88968 

52 

9 

46  48 

13  12 

80027 

2 

19973 

91069 

4    08931 

11042 

2 

88958 

51 
50 

10 

6  46  40- 

5  13  20 

9. 80043 

3 

10. 19957 

9. 91095 

4  10.08905 

10. 11052 

2 

9. 88948 

11 

46  32 

13  28 

80058 

3 

19942 

91121 

5    08879 

11063 

2 

88937 

49 

12 

46  24 

13  36 

80074 

3 

19926 

91147 

5    08853 

11073 

2 

88927 

48 

13 

46  16. 

13  44 

80089 

3 

19911 

91172 

6    08828 

11083 

2 

88917 

47 

14 
15 

46  8 

13  52 

80105 
9. 80120 

4 
4 

19895 
10. 19880 

91198  1  6 

08802 

11094 

2 
3 

88906 
9. 88896 

46 
45 

6  46  0 

5  14  0 

9.91224  1  6 

10. 08776 

10. 11104 

16 

45  52 

14  8 

80136 

4 

19864 

91250  ;  7 

08750 

11114 

3 

88886 

44 

17 

45  44 

14  16 

80151 

4 

19849 

91276  1  7 

08724 

11125 

,  3 

88875 

43 

18 

45  36 

14  24 

80166 

5 

19834 

91301  1  8 

08699 

11135 

3 

88865 

42 

19 
20 

45  28 
6  45  20 

14  32 
5  14  40 

80182 
9.80197 

5 
5 

19818 
10. 19803 

91327  i  8 
9.91353  i  9 

•  08673 

11145 

3 
3 

88855 
9. 88844 

41 
40 

10.  08647 

10.11156 

21 

45  12 

14  48 

80213 

5 

19787 

91379  ;  9    08621 

11166 

4 

88834 

39. 

22 

45  4 

14  56 

80228 

6 

19772 

91404 

9    08596 

11176 

4 

88824 

38 

23 

44  56 

15  4 

80244 

6 

19756 

91430 

10  1   08570 

11187 

4 

88813 

37 

24 
25 

44  48 
6  44  40 

15  12 
5  15  20 

80259 

6 
6 

19741 

91456 
9.  91482 

10    08544 

11197 
10. 11207 

4 
4 

88803 
9788793 

36 
35 

9. 80274 

10. 19726 

11 

10. 08518 

26 

44  32 

15  28 

80290 

7 

19710 

91507 

11 

08493 

11218 

5 

88782 

34 

27 

44  24 

15  36 

80305 

7 

19695 

91533  12 

08467 

11228 

5 

88772 

33 

28 

44  16 

15  44 

80320 

7 

19680 

91559  12 

08441 

11239 

5 

88761 

32 

29 

44  8 

15  52 

80336 

7 

19664 

91585  12 

08415 

11249 

5 

88751 

31 

30 

6  44  0 

5  16  0 

9. 80351 

8 

10. 19649 

9. 91610  13 

10.  08390 

10. 11259 

5 

9. 88741 

30 

31 

43  52 

16  8 

80366 

8 

19634 

91636  13 

08364 

11270 

5 

88730 

29 

32 

43  44 

16  16 

80382 

8 

19618 

91662  14 

08338 

11280 

6 

88720 

28 

33 

43  36 

16  24 

80397 

8 

19603 

91688  14 

08312 

11291 

6 

88709 

27 

34 
35 

43  28 
6  43  20 

16  32 
5  16  40 

80412 

9. 80428 

9 
9 

19588 
10. 19572 

91713  15 

08287 

11301 

6 

6 

88699 
9. 88688 

26 
25" 

9.91739  15 

10.  08261 

10. 11312 

36 

43  12 

16  48 

80443 

9 

19557 

91765  15  :   08235 

11322 

6 

88678 

24 

37 

43  4 

16  56 

80458 

9 

19542 

91791  16  1   08209 

11332 

6 

88668 

23 

38 

42  56 

17  4 

80473 

10 

19527 

91816 

16  i   08184 

11343 

7 

88657 

22 

39 
40 

42  48 

17  12 

80489 
9. 80504 

10 
10 

19511 
10. 19496 

91842 
9. 91868 

17  !   08158 
17  10.08132 

11353 

/ 

88647 

21 
20 

6  42  40 

5  17  20 

10. 11364 

7 

9. 88636 

41 

42  32 

17  28 

80519 

10 

19481 

91893 

18  !   08107 

11374 

/ 

88626 

19 

42 

42  24 

17  36 

80534 

11 

19466 

91919 

18 

08081 

11385 

7 

88615 

18 

43 

42  16 

.  17  44 

80550 

11 

19450 

91945 

18 

08055 

11395 

7 

88605 

17 

44 
45 

42  8 
6  42  0 

17  52 
5  18  0 

80565 
9. 80580 

11 

19435 

91971 

19 

08029 

11406 

8 

88594 

16 

12 

10. 19420 

9. 91996 

19  10.08004 

10. 11416 

8 

9. 88584 

15 

46 

41  52 

18  8 

80595 

12 

19405 

92022 

20 

07978 

11427 

8 

88573 

14 

47 

41  44 

18  16 

80610 

12 

19390 

92018 

20 

07952 

11437 

8 

88563 

13 

48 

41  36 

18  24 

80625 

12 

19375 

92073 

21 

07927 

11448 

8 

88552 

12 

49 
50 

41  28 
6  41  20 

18  32 
5  18  40 

80641 
9. 80656 

13 
13 

19359 
10. 19344 

92099 

21 

07901 

11458 
10.11469 

9 
9 

88542 

11 
10 

9. 92125  21 

10. 07875 

9. 88531 

51 

41  12 

18  48 

80671 

13 

19329 

92150  22  i   07850 

11479 

9 

88521 

9 

52 

41  4 

18  56 

80686 

13 

19314 

92176  22 

07824 

11490 

9 

88510 

8 

53 

40  56 

19  4 

80701 

14 

19299 

92202 

23 

07798 

11501 

9 

88499 

7 

54 
55 

40  48 
6  40  40 

19  12 
5  19  20 

80716 

14 
14 

19284 

92227 

23 

07773 

11511 

9 

88489 

6 
5 

9. 80731 

10. 19269 

9. 92253 

24  :10. 07747 

10. 11522 

10 

9. 88478 

56 

40  32 

19  28 

89746 

14 

19254 

92279 

24 

07721 

11532 

10 

88468 

4 

57 

40  24 

19  36 

80762 

15 

19238 

92304 

24 

07696 

11543 

10 

88457 

3 

58 

40  16 

19  44 

80777 

15 

19223 

92330 

25 

07670 

11553 

10 

88447 

2 

59 

40  8 

19  52 

80792 

15 

19208 

92356 

25 

07644 

11564 

10 

88436 

1 

60 

40  0 

20  0 

80807 

15 

19193 

92381 

26 

07619 

11575 

10 

88425 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

129° 

A 

A 

B           B 

C 

C     50°  j 

Seconds  of  time 

1» 

2» 

3' 

4» 

5» 

6» 

7« 

Prop,  parts  of  cols.^B 

2 
3 
1 

4 
6 
3 

6 
10 
4 

8 
13 
6 

10 
16 

7 

12 
19 
8 

13 

23 

9 

Page  648J 

TABLE  44. 

Log. 

Sines,  Tangents,  and  Secants. 

40° 

A 

A 

B            B 

C 

C 

189° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine.   DIff. 

j  Cosecant. 

Tangent. 

Diff.  1  Cotangent. 

decant. 

Diff. 

Cosine. 

M. 

0 

6  40  0, 

6  20  0 

9. 80807  1  0 

10. 19193 

9. 92381 

0  10.07619 

10. 11575 

0 

9. 88425 

60 

1 

39  52 

20  8 

S0822   0 

19178 

92407 

0    07593 

11585 

0 

88415 

59 

2 

39  44 

20  16 

80837   0 

19163 

92433 

1    07567 

11596 

0 

88404 

58 

3 

39  36 

20  24 

S0852   1 

19148 

92458 

1    07542 

11606 

1 

88394 

57 

4 

39  28 

20  32^ 

80867  1  1 

i   19133 

92484 

2 

07516 
10.07490 

11617 
10.11628 

1 
1 

88383 
9. 88372 

56 
55 

5 

6  39  20 

5  20  40 

9.80882  i  1 

10. 19118 

9. 92510 

2 

6 

39  12 

20  48 

80897 

1 

1   19103 

92535 

3 

07465 

11638 

1 

88362 

54 

7 

39  4 

20  56 

80912 

2 

I   19088 

92561 

3 

07439 

11649 

1 

88351 

53 

8 

38  56 

21  4 

80927 

2 

1   19073 

92587 

3 

07413 

11660 

1 

88340 

52 

9 

38  48 

21  12 

80942  ;  2 

19058 

92612 

4 

07388 

11670 

2 

88330 

51 

10 

6  38  40 

5  21  20 

9. 80957 

2 

10. 19043 

9. 92638 

4  ilO.  07362 

10. 11681 

2 

9. 88319 

50 

11 

38  32 

21  28 

80972 

3 

'       19028 

92663 

o 

07337 

11692 

2 

88308 

49 

12 

38  24 

21  36 

80987  ''.    3 

19013 

92689 

5 

07311 

11702 

2 

88298 

48 

13 

38  16 

21  44 

81002  '    3 

18998 

92715 

6 

07285 

11713 

2 

88287 

47 

14 

38  8 

21  52 

81017  i  3 

18983 

92740 

6 

07260 

11724 
10.  li7:S4 

3 
3 

88276 
9. 88266 

46 
45 

15 

6  38  0 

5  22  0 

9.81032  i  4 

10. 18968 

9. 92766 

6  10.07234 

16 

37  52 

22  8 

81047  '  4 

18953 

92792 

7 

07208 

11745 

3 

88255 

44 

17 

37  44 

'22  16 

81061   4 

18939 

92817 

t 

07183 

11756 

3 

88244 

43 

18 

37  36 

22  24 

81076 

4 

18924 

92843 

8 

07157 

11766 

3 

88234 

42 

19 

37  28 

22  32 

81091 

5 

18909 

92868 

8 

07132 

11777 

3 

88223 

41 

20 

6  37  20 

5  22  40 

9.  81106 

0 

10. 18894 

9. 92894 

9  10.07106 

10. 11788 

4 

9. 88212 

40 

21 

37  12 

22  48 

81121 

5 

18879 

92920 

9 

07080 

11799 

4 

88201 

39 

22 

37  4 

22  56 

81136 

5 

18864 

92945 

9 

07055 

11809 

4 

88191 

38 

23 

36  56 

23  4 

81151 

6 

18849 

92971 

10 

07029 

11820 

4 

88180 

37 

24 

36  48 

23  12 

81166 

6 

18834 

92996 

10 

07004 

11831 

4 

88169 

36 
35 

25 

6  36  40 

5  23  20 

9.81180 

6 

10. 18820 

9. 93022 

11 

10. 06978 

10. 11842 

4 

9. 88158 

26 

36  32 

23  28 

81195 

6 

18805 

93048 

11    06952 

11852 

5 

88148 

34 

27 

36  24 

23  36 

81210 

i 

18790 

93073 

12 

06927 

11863 

5 

88137 

33 

28 

36  16 

23  44 

81225 

i 

18775 

93099 

12 

06901 

11874 

5 

88126 

32 

29 
"30 

36  8 

23  52 

81240 

7 

18760 
10. 18746 

93124 

12 
13 

06876 

11885 
10.11895 

5 
5 

88115 

31 
30 

6  36  0 

5  24  0 

9.  81254 

7 

9. 93150 

10. 06850 

9. 88105 

31 

35  52 

24  8 

81269 

8 

18731 

93175 

13 

06825 

11906 

6 

88094 

29 

32 

35  44 

24  16 

81284 

8 

18716 

93201 

14 

06799 

11917 

6 

88083 

28 

33 

35  36 

24  24 

81299 

8 

18701 

93227 

14 

06773 

11928 

6 

88072 

27 

34 

35  28 

24  32 

81314 

8 

18686 

93252 

14 
15 

06748 

11939 

6 

88061 

26 
25 

35 

6  35  20 

5  24  40 

9. 81328 

9 

10. 18672 

9. 93278 

10.  06722 

10. 11949 

6 

9,88051 

36 

35  12 

24  48 

81343 

9 

18657 

93303 

15 

06697 

11960 

6 

88040 

24 

37 

35  4 

24  56 

81358 

9 

18642 

93329 

16 

06671 

11971 

7 

88029 

23 

38 

34  56 

25  4 

81372 

9 

18628 

93354 

16 

06646 

11982 

7 

88018 

22 

39 

34  48 

25  12 

81387 

10 

18613 

93380 

17 

06620 
10.  06594 

11993 

7 

88007 

21 
20 

40 

6  34  40 

5  25  20 

9. 81402 

10 

10. 18598 

9. 93406 

17 

10. 12004 

7 

9. 87996 

41 

34  32 

25  28 

81417 

10 

18583 

93431 

17 

06569 

12015 

7 

87985 

19 

42 

34  24 

25  36 

81431 

10 

18569 

93457 

18 

06543 

12025 

8 

87975 

18 

43 

34  16 

25  44 

81446 

11 

18554 

93482 

18 

06518 

12036 

.8 

87964 

17 

44 
45 

34  8 

25  52 

81461 
9.  81475 

11 
11 

18539 
10.18525 

93508  1  19 

06492 

12047 

8 

87953 
9. 87942 

16 
15" 

6  34  0 

5  26  0 

9.  93533  19  10.  06467  | 

10. 12058 

8 

46 

33  52 

26  8 

81490 

11 

18510 

93559  ■  20 

06441 

12069 

8 

87931 

14 

47 

33  44 

26  16 

81505 

12 

18495 

93584  20 

06416 

12080 

8 

87920 

13 

48 

33  36 

26  24 

81519 

12 

18481 

93610  20 

06390 

12091 

9 

87909 

12 

49 

33  28 

26  32 
5  26  40 

81534 
9.  81549 

12 

18466 

93636  21 

06364 

12102 
10.12113 

9 
9 

87898 

11 
10 

50 

6  33  20 

12 

10. 18451 

9.  93661   21  10.  06339  | 

9. 87887 

51 

33  12 

26  48 

81563 

13 

18437 

93687  22 

06313 

12123 

9 

87877 

9 

52 

33  4 

26  56 

81578 

13 

18422 

93712 

22 

06288 

12134 

9 

87866 

8 

53 

32  56 

27  4 

81592 

13 

18408 

93738 

23 

0<J262 

12145 

10 

87855 

7 

54 

32  48 

27  12 
5  27  20 

81607 
9.81622 

13 
14 

18393 
10. 18378 

93763 
9.93789 

23 

06237 

12156 

10. 12167 

10 
10 

87844 
9.  87833 

6 
5 

55 

6  32  40 

23  10.06211  1 

56 

32  32 

27  28 

81636 

14 

18364 

93814 

24 

06186 

12178 

10 

87822 

4 

57 

32  24 

27  36 

81651 

14 

18349 

93840 

24 

06160 

12189 

10 

87811 

3 

58 

32  16 

27  44 

81665 

14 

18335 

93865 

25 

06135 

12200 

10 

87800 

2 

59 

32  8 

27  52 

81680 

15 

18320 

93891 

25 

06109 

12211 

11 

87789 

1 

60 

32  0 

28  0 

81694 

15 

18306 

93916 

26 

06084 

12222 

11 

87778 

0 

M. 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difl. 

Secant. 

Cotangent.  Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

180' 

) 

A 

A 

B            B 

C 

C 

49° 

Seconds  of  time 1  ■ 


Prop,  parts  of  cols.-jB 
C 


TABLE  44. 

[Page  649 

Log. 

Sines,  Tangents,  and  Secants. 

41° 

A 

A 

B             B 

C 

C    138° 

M. 

Hour  A.  M. 

;  Hour  p.  m. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff.  Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

6  32  0 

5  28  0 

9.  81694 

0 

10. 18306 

9. 93916 

0 

10. 06084 

10. 12222 

0 

9. 87778 

60 

1 

31  52 

28  8 

81709 

0 

18291 

93942 

0 

06058 

12233 

0 

87767 

59 

9 

31  44 

28  16 

81723 

:  0 

18277 

93967 

1 

06033 

12244 

0 

87756 

58 

8 

31  36 

:   28  24 

81738 

1 

18262 

93993 

1 

06007 

12255 

87745 

57 

4 

31  28 

I   28  32 

81752 

1 

18248 

94018 

2 

05982 

12266 

87734 

56 

5 

6  31  20 

5  28  40 

9. 81767 

!  1 

10. 18233 

9. 94044 

2 

10.  05956 

10. 12277 

9. 87723 

55 

6 

31  12 

28  48 

81781 

1 

18219 

94069 

3 

05931 

12288 

87712 

54 

/ 

31  4 

28  56 

81796 

2 

18204 

94095 

3 

05905 

12299 

87701 

53 

8 

30  56 

29  4 

81810 

2 

18190 

94120 

3 

05880 

12310 

87690 

52 

9 
To 

30  48 

29  12 

81825 

2 

18175 
10. 18161 

94146 

4 

05854 

12321 

2 

87679 
9. 87668 

51 
50 

6  30  40 

5  29  20 

9. 81839 

2 

9. 94171 

4 

10.  05829 

10. 12332 

2 

11 

30  32 

29  28 

81854 

3 

18146 

94197 

5 

05803 

12343 

2 

87657 

49 

12 

30  24 

29  36 

81868 

3 

18132 

94222 

5 

05778 

12354 

2 

87646 

48 

13 

^30  16 

29  44 

81882 

3 

18118 

94248 

6 

05752 

12365 

2 

87635 

47 

14 
15 

30  8 

29  52 

81897 

3 

18103 

94273 

6 
6 

05727 
10. 05701 

12376 
10. 12387 

3 
3 

87624 
9.87613 

46 
45 

6  30  0 

5  30  0 

9. 81911 

4 

10. 18089 

9. 94299 

16 

29  52 

30  8 

81926 

4 

18074 

94324 

7 

05676 

12399 

3 

87601 

44 

17 

29  44 

30  16 

81940 

4 

18060 

94350 

7 

05650 

12410 

3 

87590 

43 

18 

29  36 

30  24 

81955 

4 

18045 

94375 

8 

05625 

12421 

3 

87579 

42 

19 
20 

29  28 

30  32 

81969 

5 

18031 

94401  {  8 

05599 

12432 

4 

87568 

41 

6  29  20 

5  30  40 

9. 81983 

5 

10. 18017 

9. 94426 

8 

10.  05574 

10. 12443 

4 

9. 87557 

40 

21 

29  12 

30  48 

81998 

5 

18002 

94452 

9 

05548 

12454 

4 

87546 

39 

22 

29  4 

30  56 

82012 

5 

17988 

94477 

9 

05523 

12465 

4 

87535 

38 

23 

28  56 

31  4 

82026 

5 

17974 

94503 

10 

05497 

12476 

4 

87524 

37 

24 

28  48' 

31  12 

82041 

6 

17959 

94528 
9. 94554 

10 

05472 

12487 

4 

87513 

36 
35 

25 

6  28  40 

5  31  20 

9.  82055 

6 

10. 17945 

11  ilO.  05446 

10. 12499 

5 

9. 87501 

26 

28  32 

31  28 

82069 

6 

17931 

94579 

11 

05421 

12510 

5 

87490 

34 

27 

28  24 

31  36 

82084 

6 

17916 

94604 

11 

05396 

12521 

5 

87479 

33 

28 

28  16 

31  44 

82098 

7 

17902 

94630 

12 

05370 

12532 

5 

87468 

32 

29 
30 

28  8 
6  28  0 

31  52 
5  32  0 

82112 

7 
7 

17888 
10. 17874 

94655 
9.94681 

12 

05345 

12543 

5 

87457 

31 
30 

9. 82126 

13 

10.  05319 

10. 12554 

6 

9.  87446 

31 

27  52 

32  8 

82141 

t 

17859 

94706 

13 

05294 

12566 

6 

87434 

29 

32 

27  44 

32  16 

82155 

8 

17845 

94732 

14 

05268 

12577 

6 

87423 

28 

33 

27  36 

32  24 

82169 

8 

17831 

94757 

14 

05243 

12588 

6 

87412 

27 

34 
35 

27  28 

32  32 

82184 

8 

17816 

94783 

14 

05217 

12599 

6 

87401 

26 
25 

6  27  20 

5  32  40 

9. 82198 

8 

10. 17802 

9. 94808 

15  110.05192 

10. 12610 

7 

9. 87390 

36 

27  12 

32  48 

82212 

9 

17788 

94834 

15 

05166 

12622 

7 

87378 

24 

37 

27  4 

32  56 

82226 

9 

17774 

94859 

16 

05141 

12633 

7 

87367 

23 

38 

26  56 

33  4 

82240 

9 

17760 

94884 

16 

05116 

12644 

7 

87356 

22 

39 
40 

26  48 

33  12 

82255 

9 

17745 

94910 

17 

05090 

12655 
10. 12666 

7 

87345 

21 
20 

6  26  40 

5  33  20 

9. 82269 

10 

10. 17731 

9. 94935 

17 

10. 05065 

7 

9. 87334 

41 

26  32 

33  28 

82283 

10 

17717 

94961 

17 

05039 

12678 

8 

87322 

19 

42 

26  24 

33  36 

82297 

10 

17703 

94986 

18 

05014 

12689 

8 

87311 

18 

43 

26  16 

33  44 

82311 

10 

17689 

95012 

18 

04988 

12700 

8 

87300 

17 

44 
45" 

26  8 

33  52 

82326 

10 

17674 

95037 

19 

04963 

12712 

8 

87288 

16 
15 

6  26  0 

5  34  0 

9. 82340 

11 

10. 17660 

9. 95062 

19 

10. 04938 

10. 12723 

8 

9.87277 

46 

25  52 

34  8 

82354 

11 

17646 

95088 

20    04912 

12734 

9 

87266 

14 

47 

25  44 

34  16 

82368 

11 

17632 

95113 

20    04887 

12745 

9 

87255 

13 

48 

25  36 

34  24 

82382 

11 

17618 

95139  20  1   04861 

12757 

9 

87243 

12 

49 
50 

25  28 

34  32 

82396 
9. 82410 

12 
12 

17604 
10. 17590 

95164 

21 
21 

04836 

12768 
10. 12779 

9 

87232 

11 
10 

6  25  20 

5  34  40 

9. 95190 

10. 04810 

9 

9. 87221 

51 

25  12 

34  48 

82424 

12 

17576 

95215 

22 

04785 

12791 

10 

87209 

9 

52 

25  4 

34  56 

82439 

12 

17561 

95240 

22 

04760 

12802 

10 

87198 

8 

53 

24  56 

35  4 

82453 

13 

17547 

95266 

22 

04734 

12813 

10 

87187 

7 

54 

24  48 

35  12 

82467 

13 
13 

17533 

95291 

23 

04709 
10. 04683 

12825 
10.  12836 

10 
10 

87175 

6 

5 

55 

6  24  40 

5  35  20 

9. 82481 

10. 17519 

9.95317 

23 

9.  87164 

56 

24  32 

35  28 

82495 

13 

17505 

95342 

24 

04658 

12847 

10 

87153 

4 

57 

24  24 

35  36 

82509 

14 

17491 

95368 

24 

04632 

12859 

11 

87141 

3 

58 

24  16 

35  44 

82523 

14 

17477 

95393 

25 

04607 

12870 

11 

87130 

2 

59 

24  8 

35  52 

82537 

14 

17463 

95418 

25 

04582 

12881 

11 

87119 

1 

60 

M. 
131- 

24  0 

36  0 

82551 

14 

17449 

95444 

25 

04556 

12893 

11 

87107 

0 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

A 

A 

B           B 

C 

C     48°  1 

Seconds  of  time 

U 

2' 

3> 

4»  1  5"    6» 

7» 

Prop,  parts  of  cols.  ■{  B 

2 
3 

1 

4 
6 
3 

6 
10 
4 

7 
13 
6 

9 
16 

11 
19 

8 

12 
22 
10 

Page  650] 

TABLE  44. 

Log. 

Sines,  Tangents,  and  Secants. 

42° 

A 

A 

B 

B 

C 

C 

187° 

M. 

Hour  A.  H. 

Hour  p.  M. 

Sine. 

Difif. 

Cosecant. 

Tangent. 

Difl. 

Cotangent. 

Secant. 

Diff.  1  Cosine. 

M. 

0 

6  24  0 

5  36  0 

9.  82551 

0 

10. 17449 

9. 95444 

0 

10.  04556 

10. 12893 

0 

9.  87107 

60 

1 

23  52 

36  8 

82565 

0 

17435 

95469 

0 

04531 

12904 

0 

87096 

59 

2 

23  44 

36  16 

82579 

0 

17421 

95495 

1 

04505 

12915 

0 

87085 

58 

3 

23  36 

36  24 

82593 

17407 

95520 

1 

04480 

12927 

87073 

57 

4 
5' 

23  28 

36  ^ 

82607 

17393 

95545 

2 
2 

04455 

12938 
10.12950 

"r 

87062. 

56 
55 

6  23  20 

5  36  40 

9. 82621 

10. 17379 

9. 95571 

10.  04429 

9. 87050 

6 

23  12 

36  48 

82635 

17365 

95596 

3 

04404 

12961 

1  \      87039 

54 

7 

23  4 

36  56 

82649 

2 

17351 

95622 

3 

04378 

12972 

1  ;   87028 

53 

8 

22  56 

37  4 

82(563 

2 

17337 

95647 

3  i   04353 

12984 

2    87016 

52 

9 
10 

22  48 

37  12 

82677 

2 

17323 

95672 

4  i   04328 

12995 

2   87005 

51 

6  22  40 

5  37  20 

9.  82691 

2 

10. 17309 

9. 95698 

4 

10.  04302 

10. 13007 

2 

9.  86993 

50 

11 

22  32 

37  28 

82705 

3 

17295 

95723 

5 

04277 

13018 

2 

86982 

49 

12 

22  24 

37  36 

82719 

3 

17281 

95748 

5 

04252 

13030 

2 

86970 

48 

13 

22  16 

37  44 

82733 

3 

17267 

95774 

5 

04226 

1.3041 

3 

86959 

47 

14 
15 

22  8 

37  52 
5  38  0 

82747 

3 

17253 

95799 
9. 95825 

6 

04201 

13053 

3 
3" 

86947 

46 
45 

6  22  0 

9. 82761 

3 

10. 17239 

6 

10.04175 

10.13064 

9. 86936 

16 

21  52 

38  8 

82775 

4 

17225 

95850 

7  i   04150 

13076 

3 

86924 

44 

17 

21  44 

38  16 

82788 

4 

17212 

95875 

7    04125 

13087 

3 

86913 

43 

18 

21  36 

38  24 

82802 

4 

17198 

95901 

8  1   04099 

13098 

3 

86902 

42 

19 
20 

21  28 
6  21  20 

38  32 

82816 

4 

17184 

95926 

8  j   04074 

13110 

4 

86890 

41 
40 

5  38  40 

9. 82830 

5 

10. 17170 

9. 95952 

8  10.04048 

10. 13121 

4 

9. 86879 

21 

21  12 

38  48 

82844 

5 

17156 

95977 

9  1   04023 

13133 

4 

86867 

39 

22 

21  4 

38  56 

82858 

5 

17142 

96002 

9 

03998 

13145 

4 

86855 

38 

23 

20  56 

39  4 

82872 

5 

17128 

96028 

10 

03972 

13156 

4 

86844 

37 

24 

20  48 

39  12 

82885 

6 

17115 

96053 

10 
11 

03947 
10.  03922 

13168 

5- 

5 

86832 
9. 86821 

36 
35 

25 

6  20  40 

5  39  20 

9.  82899 

6 

10. 17101 

9. 96078 

10.13179 

26 

20  32 

39  28 

82913 

6 

17087 

96104 

11 

03896 

13191 

5 

86809 

34 

27 

20  24 

39  36 

82927 

6 

17073 

96129 

11 

03871 

13202 

5 

86798 

33 

28 

20  16 

39 '44 

82941 

6 

17059 

96155 

12 

03845 

13214 

5 

86786 

32 

29 
30 

20  8 

39  52 

82955 

7 

17045 

96180 

12 

03820 

13225 

6 

86775 

31 
30^ 

6  20  0 

5  40  0 

9. 82968 

7 

10. 17032 

9. 96205 

13 

10. 03795 

10. 13237 

6  ! 9. 86763 

31 

19  52 

40  8 

82982 

t 

17018 

96231 

13 

03769 

13248 

6 

86752 

29 

32 

19  44 

40  16 

82996 

7 

17004 

96256 

14 

03744 

1.3260 

6 

86740 

28 

33 

19  36 

40  24 

83010 

8 

16990 

96281 

14 

03719 

13272 

6 

86728 

27 

34 
35 

19  28 

40  32 
5  40  40 

83023 

8 
8 

16977 

96307 

14 

03693 

13283 

7 

86717 

26 

6  19  20 

9. 83037 

10. 16963 

9. 96332 

15  110.03668 

10. 13295 

7 

9. 86705 

25 

36 

19  12 

40  48 

83051 

8 

16949 

96357 

15 

03643 

13306 

1 

86694 

24 

37 

19  4 

40  56 

83065 

8 

16935 

96383 

16 

03617 

13318 

1 

86682 

23 

38 

18  56 

41  4 

83078 

9 

16922 

96408 

16 

03592 

13330 

7 

86670 

22 

39 

40 

18  48 
6  18  40 

41  12 

83092 

9 

16908 

96433 

16 

03567 

13341 
10. 13353 

8 
8 

86659 

21 
20 

5  41  20 

9. 83106 

9 

10. 16894 

9. 96459 

17 

10. 03541 

9. 86647 

41 

18  32 

41  28 

83120 

9 

16880 

96484 

17 

03516 

13365 

8 

86635 

19 

42 

18  24 

41  36 

83133 

10 

16867 

96510 

18 

03490 

13376 

8 

86624 

18 

43 

18  16 

41  44 

83147 

10 

16853 

965.35 

18 

03465 

1,3388 

8 

86612 

17 

44 
45 

18  8 
6  18  0^ 

41  52 

83161 
9.  83174 

10 
10 

16839 

96560 

19 

03440 

13400 
10.13411 

8 
9 

86600 
9. 86589 

16 
15 

5  42  0 

10. 16826 

9. 96586 

19  10.03414 

46 

17  52 

42  8 

83188 

11 

16812 

96611 

19  I   03389 

13423 

9 

86577 

14 

47 

17  44 

42  16 

83202 

11 

16798 

96636 

20 

03364 

13435 

9 

86565 

13 

48 

17  36 

42  24 

83215 

11 

16785 

96662 

20 

03338 

1.3446 

9 

86554 

12 

49 

17  28 

42  32 

83229 

11 
11 

16771 

96687 

21 
21 

03313 
10. 03288 

1.3458 
10. 13470 

9 
To 

86542 

11 
10 

50 

6  17  20 

5  42  40 

9. 83242 

10. 16758 

9. 96712 

9. 86530 

51 

17  12 

42  48 

83256 

12 

16744 

96738 

22 

03262 

13482 

10 

86518 

9 

52 

17  4 

42  56 

83270 

12 

16730 

96763 

22 

03237 

13493 

10 

86507 

8 

53 

16  56 

43  4 

83283 

12 

16717 

96788 

22 

03212 

13505 

10  !  86495 

7 

54 
55 

16  48 
6  16  40 

43  12 

83297 

12 
13 

16703 
10. 16690 

96814 

23 

03186 

13517 

10 
fl 

86483 

6 

5  43  20 

9.  8.3310 

9.  96839 

23 

10.  03161 

10. 1.3528 

9. 86472 

5 

56 

16  32 

43  28 

83324 

13 

16676 

96864 

24 

03136 

13540 

11  1   86460 

4 

57 

16  24 

43  36 

83338 

13 

16662 

96890 

24 

03110 

13552 

11    86448 

3 

58 

16  16 

43  44 

83351 

13 

16649 

96915 

25 

03085 

13564 

11 

86436 

9 

59 

16  8 

43  52 

83365 

14 

16635 

96940 

25 

03060 

13575 

11 

86425 

1 

60 
M. 

16  0 

44  0 

83378 

14 

16622 

96966 

25 

03034 

13587 

12 

86413 

0 
M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Difl. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

182 

0 

A 

A 

B 

B 

C 

C 

47° 

Seconds  of  time 

1> 

2> 

3« 

4' 

5'    6' 

7' 

Prop,  parts  of  cols.  <  B 

Ic 

2 
3 
1 

3 
6 
3 

6 
10 
4 

7 

13 

6 

9 
16 

10 
19 

9 

12 
•22 
10 

TABLE  U. 

[Page  651 

Log. 

Sines,  Tangents,  and  Secants. 

43° 

A 

A 

B 

B 

C 

C     136° 

M. 
0 

Hour  A.  M. 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 
60 

6  16  0 

5  44  0 

9. 88378 

0 

10. 16622 

9. 96966 

0 

10. 03034 

10. 13587 

0 

9. 86413 

1 

15  52 

44  8 

88392 

0 

16608 

96991 

0 

08009 

13599 

0 

86401 

59 

2 

15  44 

44  16 

88405 

0 

16595 

97016 

1 

02984 

13611 

0 

86889 

58 

8 

15  36 

44  24 

88419 

1 

16581 

97042 

1 

02958 

13623 

86877 

57 

4 

15  28 

44  82 

88432 

1 

16568 

97067 

2 

02933 

13634 

86366 
9. 86354 

56 
55 

5 

6  15  20 

5  44  40 

9. 88446 

1 

10. 16554 

9. 97092 

2 

10. 02908 

10. 13646 

6 

15  12 

44  48 

88459 

1 

16541 

97118 

3 

02882 

13658 

86342 

54 

7 

15  4 

44  56 

88473 

2 

16527 

97143 

3 

02857 

13670 

86330 

58 

H 

14  56 

45  4 

83486 

2 

16514 

97168 

3 

02832 

13682 

2 

86818 

52 

9 

14  48 

45  12 

83500 

2 

16500 

97193 

4 
4 

02807 

18694 

2 

86806 

51 
50 

10 

6  14  40 

5  45  20 

9. 83513 

2 

10. 16487 

9.  97219 

10.  02781 

10. 13705 

2 

9. 86295 

11 

14  32 

45  28 

83527 

2 

16478 

97244 

5 

02756 

13717 

2 

86288 

49 

12 

14  24 

45  86 

83540 

8 

16460 

97269 

5 

02731 

18729 

2 

86271 

48 

18 

14  16 

45  44 

83554 

3 

16446 

97295 

5 

02705 

18741 

3 

86259 

47 

14 
15 

14  8 

45  52 

88567 
9. 83581 

3 
3 

16488 

97320 

6 

02680 
10. 02655 

18753 
10.13765 

3 

86247 

46 
45 

6  14  0 

5  46  0 

10. 16419 

9. 97345 

6 

3 

9. 86235 

16 

13  52 

46  8 

83594 

4 

16406 

97871 

7 

02629 

13777 

3 

86223 

44 

17 

13  44 

46  16 

83608 

4 

16892 

97896 

7- 

02604 

13789 

3 

86211 

48 

18 

13  36 

46  24 

83621 

4 

16379 

97421 

8 

02579 

13800 

4 

86200 

42 

19 

20 

13  28 
6  18  20 

46  82 

83634 

4 

16366 
10.16352 

97447 
"9. 97472 

8 

02553 

13812 

4 

86188 

41 
40 

5  46  40 

9. 83648 

4 

8 

10.  02528 

10. 13824 

4 

9. 86176 

21 

18  12 

46  48 

88661 

5 

16839 

97497 

9 

02503 

13836 

4 

86164 

39 

22 

13  4 

46  56 

83674 

5 

16326 

97528 

9 

02477 

13848 

4 

86152 

38 

23 

12  56 

47  4 

83688 

5 

16312 

97548 

10 

02452 

13860 

5 

86140 

37 

24 

12  48 

47  12 

83701 

5 

16299 

97573 
9. 97598 

10 

02427 

13872 
10. 13884 

5 

86128 

36 

25 

6  12  40 

5  47  20 

9. 88715 

6 

10. 16285 

11 

10.  02402 

5 

9.86116 

35 

26 

12  32 

47  28 

83728 

6 

16272 

97624 

11 

02376 

13896 

5 

86104 

84 

27 

12  24 

47  36 

88741 

6 

16259 

97649 

11 

02351 

13908 

5 

86092 

88 

28 

12  16 

47  44 

88755 

6 

16245 

97674 

12 

02326 

13920 

6 

86080 

82 

29 

12  8 

47  52 

83768 

6 

7 

16282 

97700 

12 

02300 

13982 

6 

86068 
9. 86056 

31 
80 

80 

6  12  0 

5  48  0 

9. 83781 

10. 16219 

9. 97725 

13 

10.  02275 

10. 18944 

6 

81 

11  52 

48  8 

83795 

7 

16205 

97750 

18 

02250 

13956 

6 

86044 

29 

82 

11  44 

48  16 

83808 

7 

16192 

97776 

13 

02224 

13968 

6 

86082 

28 

33 

11  36 

48  24 

83821 

/ 

16179 

97801 

14 

02199 

18980 

7 

86020 

27 

34 
85 

11  28 
6  11  20 

48  32 

83834 

8 
8 

16166 

97826 

14 

02174 
10.  02149 

18992 

7 

86008 
9. 85996 

26 
25 

5  48  40 

9. 83848 

10. 16152 

9. 97851 

15 

10. 14004 

7 

m 

11  12 

48  48 

83861 

8 

16139 

97877 

15 

02123 

14016 

7 

85984 

24 

37 

11  4 

48  56 

83874 

8 

16126 

97902 

16 

02098 

14028 

7 

85972 

23 

38 

10  56 

49  .  4 

88887 

8 

16118 

97927 

16 

02073 

14040 

8 

85960 

22 

39 
40 

10  48 
6  10  40 

49  12 

83901 

9 
9 

16099 
10. 16086 

97953 
9.97978 

16 
17 

02047 

14052 
10. 14064 

8 

85948 

21 

5  49  20 

9. 83914 

10. 02022 

8 

9.  85986 

20 

41 

10  32 

49  28 

83927 

9 

16073 

98003 

17 

01997 

14076 

8 

85924 

19 

42 

10  24 

49  86 

83940 

9 

16060 

98029 

18 

01971 

14088 

8 

85912 

18 

48 

10  16 

49  44 

83954 

10 

16046 

98054 

18 

01946 

14100 

9 

85900 

17 

44 
45 

10  8 

49  52 

88967 

10 
10 

16088 

98079 

19 

01921 
10. 01896 

14112 

9 

85888 
9. 85876 

16 
15 

6  10  0 

5  50  0 

9. 88980 

10. 16020 

9. 98104 

19 

10. 14124 

9 

46 

9  52 

50  8 

88993 

10 

16007 

98180 

19 

01870 

14136 

9 

85864 

14 

47 

9  44 

50  16 

84006 

10 

15994 

98155 

20 

01845 

14149 

9 

85851 

18 

48 

9  36 

50  24 

84020 

11 

15980 

98180 

20 

01820 

14161 

10 

85839 

12 

49 
50 

9  28 

50  32 

84033 

11 

15967 

98206 

21 
21 

01794 

14173 

10 

85827 
9. 85815 

11 
10 

6  9  20 

5  50  40 

9. 84046 

11 

10. 15954 

9. 98281 

10.  01769 

10.  14185 

10 

51 

9  12 

50  48 

84059 

11 

15941 

98256 

22 

01744 

14197 

10 

85803 

9 

52 

9  4 

50  56 

84072 

12 

15928 

98281 

22 

01719 

14209 

10 

85791 

8 

58 

8  56 

51  4 

84085 

12 

15915 

98307 

22 

01693 

14221 

11 

85779 

7 

54 

8  48 

51  12 

84098 

12 

15902 

98382 

23 

01668 

14234 

11 

85766 

6 

55 

6  8  40 

5  51  20 

9.  84112 

12 

10. 15888 

9. 98357 

23 

10. 01648 

10. 14246 

11 

9.  85754 

5 

56 

8  32 

51  28 

84125 

12 

15875 

98383 

24 

01617 

14258 

11 

85742 

4 

57 

8  24 

51  36 

84188 

18 

15862 

98408 

24 

01592 

14270 

11 

85780 

8 

58 

8  16 

51  44 

84151 

13 

15849 

98438 

24 

01567 

14282 

12 

85718 

2 

59 

8  8 

51  52 

84164 

13 

15886 

98458 

25 

01542 

14294 

12 

85706 

1 

60 

8  0 

52  0 

84177 

IS 

15823 

98484 

25 

01516 

14307 

12 

85693 

0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diflf. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

133° 

A 

A 

B 

B 

C 

C     46°n 

Seconds  of  time 

1» 

2s 

3» 

4» 

6»    6' 

T 

Prop,  parts  of  cols.<B 

2 
3 
2 

3 
6 
3 

5 
9 
5 

7 

13 

6 

8    10 
16    19 

8    9 

12 
22 
11 

Page  652] 

TABLE  44. 

Log. 

Sines,  Tangents,  and  Secants. 

44° 

A 

A 

B 

B 

C 

C 

185° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent.  Diff. 

Cotangent. 

Secant. 

iDiff. 

Cosine. 

M. 
60 

0 

6  8  0 

5  52  0 

9.  84177 

0 

10. 15823 

9. 98484   0 

10.  01516 

10. 14807 

1  0 

9. 85693 

1 

7  52 

52  8 

84190 

0 

15810 

98509   0 

01491 

14319 

0 

85681 

59 

2 

7  44 

52  16 

84203 

0 

15797 

98534 

1 

01466 

14331 

0 

85669 

58 

3 

7  36 

52  24 

84216 

1 

15784 

98560 

1 

01440 

14343 

i   85657 

57 

4 
5 

7  28 
6  7  20 

52  34 

84229 
9.84242 

1 

15771 

98585 

2 

01415 

14355 

1  85645 

56 

5  52  40 

1 

10. 15758 

9. 98610 

2 

10. 01390 

10. 14368 

9.  85682 

55 

(3 

7  12 

52  48 

84255 

1 

15745 

98635 

8 

01865 

14380 

85620 

54 

t 

7  4 

52  56 

84269 

2 

15731 

98661   3 

01839 

14892 

85608 

53 

8 

6  56 

53  4 

84282 

2 

15718 

98686   3 

01314 

14404 

2 

85596 

52 

9 

6  48 

53  12 

84295 

2 

15705 

98711   4 

01289 

14417 

2 

85583 
9.  85571 

51 
50 

6  6  40 

5  53  20 

9. 84308 

2 

10. 15692 

9. 98787   4 

10. 01263 

10. 14429 

2 

11 

6  32 

53  28 

84321 

2 

15679 

98762   5 

01238 

14441 

2 

85559 

49 

12 

6  24 

53  36 

84334 

3 

15666 

98787 

5 

01213 

14458 

2 

85547 

48 

18 

6  16 

53  44 

84347 

3 

15653 

98812 

5 

01188 

14466 

3 

85534 

47 

14 

6  8 

53  52 

84360 

3 

15640 

98888 

6 

01162 

14478 

3 

85522 

46 

15 

6  6  0 

5  54  0 

9. 84373 

3 

10. 15627 

9. 98868 

6 

10. 01137 

10. 14490 

3 

9. 85510 

45 

16 

5  52 

54  8 

84385 

3 

15615 

98888 

7 

01112 

14503 

3 

85497 

44 

17 

5  44 

54  16 

84398 

4 

15602 

98913 

7 

01087 

14515 

4 

85485 

43 

18 

5  36 

54  24 

84411 

4 

15589 

98989 

8 

01061 

14527 

4 

85478 

42 

19 
20" 

5  28 

54  32 

84424 

4 

15576 

98964 

8 

01086 

14540 

4 

85460 

41 
40 

6  5  20 

5  54  40 

9. 84437 

4 

10. 15563 

9. 98989 

8 

10.  01011 

10. 14552 

4 

9. 85448 

21 

5  12 

54  48 

84450 

5 

15550 

99015  i  9 

00985 

14564 

4 

85436 

89 

22 

5  4 

54  56 

84463 

5 

15537 

99040  1  9 

00960 

14577 

5 

85423 

38 

23 

4  56 

55  4 

84476 

o 

15524 

99065  10 

00985 

14589 

5 

85411 

37 

24 

4  48 

55  12 

84489 

5 

15511 

99090  10 

00910 

14601 

5 

85399 

36 

25 

6  4  40 

5  55  20 

9. 84502 

5 

10. 15498 

9.99116  11 

10. 00884 

10. 14614 

5 

9. 85386 

35 

26 

4  32 

55  28 

84515 

6 

15485 

99141  11 

00859 

14626 

5 

85874 

34 

27 

4  24 

55  36 

84528 

6 

15472 

99166  11 

00834 

14689 

6 

85361 

33 

28 

4  16 

55  44 

84540 

6 

15460 

99191  12 

00809 

14651 

6 

85349 

32 

29 
30 

4  8 

55  52 

84553 

6 

15447 

99217  12 

00783 

14663 

6 

85887 

81 
30 

6  4  0 

5  56  0 

9.  84566 

6 

10. 15434 

9. 99242 

13 

10.  00758 

10. 14676 

6 

9. 85824 

31 

3  52 

56  8 

84579 

7 

15421 

99267 

13 

00733 

14688 

6 

85312 

29 

32 

3  44 

56  16 

84592 

7 

15408 

99298 

13 

00707 

14701 

7 

85299 

28 

33 

3  36 

56  24 

84605 

7 

15395 

99318 

14 

00682 

14713 

7 

85287 

27 

34 
35 

3  28 

56  32 

84618 

7 

15382 

99348 

14 

00657 

14726 

7 

85274 

26 
25 

6  3  20 

5  56  40 

9.  84630 

8 

10. 15370 

9. 99368 

15 

10. 00632 

10. 14738 

7 

9. 85262 

36 

3  12 

56  48 

84643 

8 

15857 

99394 

15 

00606 

14750 

7 

85250 

24 

37 

3  4 

56  56 

84656 

8 

15844 

99419 

16 

00581 

14763 

8 

85237 

23 

38 

2  56 

57  4 

84669 

8 

15331 

99444 

16 

00556 

14775 

8 

85225 

22 

39 
40 

2  48 

57  12 

84682 

8 

15318 

99469 

16 

00531 

14788 

8 

85212 

21 
20 

6  2  40 

5  57  20 

9.  84694 

9 

10. 15306 

9.99495  1  17 

10. 00505 

10. 14800 

8 

9. 85200 

41 

2  32 

57  28 

84707 

9 

15293 

99520  17 

00480 

14813 

8 

85187 

19 

42 

2  24 

57  36 

84720 

9 

15280 

99545  18 

00455 

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